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astro-ph0508611

c

we have presented a new interstellar deuterium abundance study of the sight line toward 9 , and the revision of a result for , both based on spectra . our new measurement of @xmath44@xmath45 toward shows that column density measurements based on saturated lines might be erroneous , even up to a factor of two , and that the error bars might be underestimated due to systematic effects . this sight line exhibits a low d / o ratio , in agreement with those obtained toward other distant targets . 9 is the farthest galactic target for which the deuterium abundance has been measured from ultraviolet absorption lines so far , both in terms of distance and column densities . the low deuterium abundance measured on this line of sight is in agreement with the trend reported by hbrard & moos ( @xcite ) and reinforced by wood et al . ( @xcite ) : on large scales , the deuterium abundance is lower than the one measured within the local bubble . the question however remains open to know if this low deuterium abundance is the value representative of the present epoch , or the signature that a significant amount of deuterium has been depleted onto dust grains . finally , we have shown that d / h presents more dispersion than d / o does . as oxygen is considered to be a good proxy for hydrogen , this discrepancy is puzzling . this might call into question the homogeneity of the o / h ratio , or some or column density measurements . the complete explanation is still to be found . this work is based on data obtained by the nasa - cnes - csa mission operated by the johns hopkins university . financial support has been provided by nasa contract nas5 - 32985 . we thank d. massa and a. w. fullerton for their help on the stellar profile of 9 , as well as c. m. oliveira and a. vidal - madjar for useful comments on this paper . most of this work was performed during the stay of g.h . at the johns hopkins university in 2004 . was also supported by cnes . t.m.t . was supported in part by nasa grant nng04gg73 g . this work used the profile fitting procedure owens.f developed by m. lemoine and the french team . abgrall , h. , roueff , e. , launay , f. , roncin , j. y. , & subtil , j. l. 1993 , , 101 , 323 abgrall , h. , roueff , e. , launay , f. , roncin , j. y. , & subtil , j. l. 1993 , , 101 , 273 andr , m. k. , oliveira , c. m. , howk , j. c. , et al . 2003 , , 591 , 1000 beideck , d. j. , schectman , r. m. , federman , s. r. , & ellis , d. g. 1994 , , 428 , 393 bianchi , l. , & garcia , m. 2002 , , 581 , 610 bowen , d. v. , jenkins , e. b. , tripp , t. m. , sembach , k. r. , & savage , b. d. 2004 , in `` astrophysics in the far ultraviolet : five years of discovery with fuse '' , eds . g. sonneborn , h. w. moos , & b .- andersson ( san francisco : asp ) , in press ( astro - ph/0410008 ) cartledge , s. i. b. , lauroesch , j. t. , meyer , d. m. , & sofia , u. j. 2004 , , 613 , 1037 diplas , a. & savage , b. d. 1994 , , 93 , 211 draine , b. t. 2004 , in _ origin and evolution of the elements _ , ed . a. mcwilliams & m. rauch ( cambridge : cambridge univ . press ) , p. 320 ferlet , r. , et al . 2000 , , 538 , l69 fitzpatrick , e.l . , & spitzer , l. , jr . 1994 , , 427 , 232 friedman , s. d. et al . 2002 , , 140 , 37 friedman , s. d. et al . 2005 , , submitted hbrard , g. , mallouris , c. , ferlet , r. , koester , d. , lemoine , m. , vidal - madjar , a. , & york , d. 1999 , , 350 , 643 hbrard , g. et al . 2002 , , 140 , 103 h ' ebrard , g. & moos , h. w. 2003 , , 599 , 297 hog , e. , kuzmin , a. , bastian , u. , fabricius , c. , kuimov , k. , lindegren , l. , makarov , v. v. , & roeser , s. 1998 , , 335 , l65 hoopes , c. g. , sembach , k. r. , h ' ebrard , g. , moos , h. w. , & knauth , d.c . 2003 , , 586 , 1094 howk , j. c. , sembach , k. r. , roth , k. c. , & kruk , j. w. 2000 , , 544 , 867 jenkins , e. b. , tripp , t. m. , woniak , p. a. , sofia , u. j. , & sonneborn , g. 1999 , , 520 , 182 jenkins , e. b. , & tripp , t. m. 2001 , , 137 , 297 jura , m. a. 1982 , in advances in ultraviolet astronomy , ed . y. knauth , d. c. , andersson , b .- g . , mccandliss , s. r. , & moos , h. w. 2003 , , 596 , l51 lacour , s. , andr , m. k. , sonnentrucker , p. , le petit , f. , dsert , j .- m . , ferlet , r. , roueff , e. , welty , d. e. , york , d. g. 2005 , , 430 , 967 laurent , c. , vidal - madjar , a. , & york , d. g. 1979 , , 229 , 923 lebouteiller , v. , kuassivi , & ferlet , r. 2005 , , in press ( astro - ph/0507404 ) lemoine , m. et al . 1999 , new astronomy , 4 , 231 lemoine , m. et al . 2002 , , 140 , 67 linsky , j. l. et al . 2005 , submitted to mathys , g. 1988 , , 76 , 427 meyer , d. m. , cardelli , j. a. , & sofia , u. j. 1997 , , 490 , l103 meyer , d. m. , jura , m. , & cardelli , j. a. 1998 , , 493 , 222 meyer , d. m. 2001 , xviith iap colloquium , paris , edited by r. ferlet et al . , p. 135 moos , h. w. et al . 2000 , , 538 , l1 moos , h. w. et al . 2002 , , 140 , 3 morton , d. c. 1991 , , 77 , 119 morton , d. c. 2003 , , 149 , 205 oliveira , c. m. , h ' ebrard , g. , howk , j. c. , kruk , j. w. , chayer , p. , moos , h. w. 2003 , , 587 , 235 oliveira , c. m. , dupuis , j. , chayer , p. , moos , h. m. 2005a , , 625 , 232 pellerin , a. , et al . 2002 , , 143 , 159 press , w. , teukolsky , s. , vetterling , w. , and flannery , b. 1995 . numerical recipes in c. cambridge university press , second edition prochaska , j. x. , tripp , t. m. , & howk , j. c. 2005 , , 620 , l39 sahnow , d. j. et al . 2000 , , 538 , l7 savage , b. d. , & sembach , k. r. 1996 , ara&a , 34 , 279 savage , b. d. , meade , m. r. , & sembach , k. r. 2001 , , 136 , 631 sfeir , d. m. , lallement , r. , crifo , f. , & welsh , b. y. 1999 , , 346 , 785 sofia , u. j. , fabian , d. , & howk , j. c. 2000 , , 531 , 384 sonneborn , g. , tripp , t. m. , ferlet , r. , jenkins , e. b. , sofia , u. j. , vidal - madjar , a. , & woniak , p. r. 2000 , , 545 , 277 sonnentrucker , p. , friedman , s. d. , welty , d. e. , york , d. g. , & snow , t. p. 2003 , , 596 , 350 timmes , f. x. , truran , j. w. , lauroesch , j. t. , & york , d. g. 1997 , , 476 , 464 tripp , t. m. , lu , l. , & savage , b. d. 1996 , , 102 , 239 verner , d. a. , barthel , p. d. , & tytler , d. 1994 , , 108 , 287 welsh , b. y. , sasseen , t. , craig , n. , jelinsky , s. , & albert , c. e. 1997 , , 112 , 507 williger , g. m. , oliveira , c. , brard , g. , dupuis , j. , dreizler , s. , moos 2005 , , 625 , 210 wood , b. e. , linsky , j. l. , hbrard , g. , williger , g. m. , moos , h. w. , blair , w. p. 2004 , , 609 , 838

we present a study of the deuterium abundance along the extended sight line toward 9 with the _ far ultraviolet spectroscopic explorer _ ( _ fuse _ ) . our new results confirm that the gas - phase deuterium abundance in the distant interstellar medium is significantly lower than the one measured within the local bubble . as oxygen is considered to be a good proxy for hydrogen within the interstellar medium , this discrepancy is puzzling .

we present a study of the deuterium abundance along the extended sight line toward 9 with the _ far ultraviolet spectroscopic explorer _ ( _ fuse _ ) . 9 is a o9.5iii star located in the galactic disk at a distance of kpc away from the sun . both in terms of distance and column densities , 9 has the longest and densest sight line observed in the galactic disk for which a deuterium abundance has been measured from ultraviolet absorption lines so far . because many interstellar clouds are probed along this sight line , possible variations in the properties of individual clouds should be averaged out . this would yield a deuterium abundance which is characteristic of the interstellar medium on scales larger than the local bubble . the spectra of 9 show numerous blended interstellar and stellar features . we have measured interstellar column densities of neutral atoms , ions , and molecules by simultaneously fitting the interstellar absorption lines detected in the different channels . as far as possible , saturated lines were excluded from the fits in order to minimize possible systematic errors . _ iue _ ( _ international ultraviolet explorer _ ) archival data are also used to measure neutral hydrogen . we report d / o and d / h ( s ) . our new results confirm that the gas - phase deuterium abundance in the distant interstellar medium is significantly lower than the one measured within the local bubble . we supplement our study with a revision of the oxygen abundance toward , a moderately distant ( pc ) sdob star , located pc below the galactic plane . excluding saturated lines from the fits of the spectra is critical ; this led us to derive an column density about two times larger than the one previously reported for . the corresponding updated d / o ratio on this sight line is d / o ( s ) , which is lower than the one measured within the local bubble . the dataset available now outside the local bubble , which is based primarily on measurements , shows a contrast between the constancy of d / o and the variability of d / h . as oxygen is considered to be a good proxy for hydrogen within the interstellar medium , this discrepancy is puzzling .

1505.04799

i

the large magellanic cloud ( lmc ) harbors the nearest giant extragalactic hii region @xcite , the tarantula nebula ( 30 doradus ) . the central region of the nebula is dominated by the cluster ngc 2070 , a collective of several dense sub - clusters ( @xcite ) whose light is dominated by massive ob stars . the most prominent of these sub - clusters is the very central super star cluster ( ssc ) r 136 . this region has a number of characteristics that make it extraordinary . first of all , it displays an extreme rate of star formation ( sf ) , with one quarter of the total massive recent ( @xmath4 myr ) star formation in the lmc contained within 15@xmath5 from 30 doradus @xcite . moreover , with a stellar mass of at least @xmath6 concentrated within a radius of 4.7 pc @xcite , this cluster can be classified as a relatively low - mass clone of more distant starburst clusters , likely building blocks of starburst galaxies . over the years , there have been debates over whether or not ngc 2070 is a young analog of old globular clusters . recent arguments seem to suggest a positive answer . using photometry @xcite found that ngc2070 s initial mass function ( imf ) is salpeter - like down to @xmath7 , giving the first direct evidence that solar - like stars are formed in a starburst cluster . using multi - epoch spectroscopy of o - type stars , @xcite measured a velocity dispersion between 4 and 5 kms@xmath8 , close to the expected value if it were in virial equilibrium . in this case the velocity dispersion would be low enough to allow the cluster to stay bound . due to the proximity of the lmc , 30 doradus can be imaged with the hubble space telescope ( hst ) on scales down to @xmath9 pc , resolving stars down to the sub - solar regime . by coupling hst imaging with ground - based spectroscopy diagnostics , we know that the region has undergone continuous sf activity or a superposition of multiple bursts of sf . indeed , over the whole region , there is evidence of at least three events : i ) an on - going off - center activity , as documented by the presence of embedded o - type stars and luminous infrared protostars along an arc of molecular gas and warm dust around 30 doradus @xcite ; ii ) a recent event , represented by the ssc r 136 itself , 2 myr old or less , as inferred from spectroscopy of the o stars ( @xcite ) , 3 - 4 myr old from hst imaging ( @xcite ) ; iii ) an `` old '' event , documented by the presence of hodge 301 , a 25 myr old cluster ( @xcite ) located only 3 arcmin northwest of r 136 . however , most of high resolution studies are limited to a few bands and cover only small patches of the 30 doradus complex . the hubble tarantula treasury project ( http ; sabbi et al . 2015 , in prep . ) , an hst survey covering a @xmath10 wide area around 30 doradus at high resolution , fills this gap . this unique data - set , which combines resolution and spatial coverage , can be exploited in varied ways , including studies of massive sf , low mass sf , the imf , the reddening distribution , etc .. in our current paper , we take the opportunity to explore the sf during the last 50 myr for the central 40 pc of 30 doradus , a.k.a . the starburst cluster ngc 2070 , by comparing the observational color - magnitude diagrams ( cmds ) with state - of - the - art synthetic cmds . these simulations incorporate the latest ( v.1.2s ) set of padova and trieste stellar evolution code ( parsec ) isochrones ( see @xcite and @xcite ) , the first theoretical library to include homogeneously all stellar phases from pre - main sequence ( pms ) to post - main sequence for all masses between @xmath11 and @xmath12 . for the first time , we derive the history of the region using low and intermediate mass stars , either in the pms or main sequence ( ms ) phases , _ simultaneously_. in particular , we exploit magnitudes and colors of the pms turn ons ( hereafter ton ; see section [ tons ] ) , i.e. the cmd loci where the pms phase joins to the ms . this `` hook '' has been demonstrated to be particularly sensitive to age ( see , e.g. , @xcite ) . we use both the optical f555w vs f555w@xmath3f775w and the near infrared ( nir ) f110w vs f110w@xmath3f160w cmds of the http sample , which offer complementary advantages in terms of higher spatial resolution ( the optical ) and lower reddening sensitivity ( the nir ) . to recover the sf rate of ngc 2070 since the beginning of its activity , there are three important factors that must be accounted for : differential reddening , lmc field contamination , and stellar crowding . the first causes the cmd features to appear redder and more scattered , mimicking older populations and lowering the age resolution . field contamination mostly adds low mass stars to the sample , mimicking much older populations and a steeper imf . finally , stellar confusion affects completeness and , therefore , the reachable look - back time . moreover , unaccounted incompleteness can also mimic mass segregation . the paper is structured as follows . in section 2 we briefly describe the observations . section 3 is dedicated to the physics of the ton clock . in section 4 we identify the general properties of the stellar populations in the http data - set , with special emphasis on ngc 2070 . in section 5 we perform artificial star tests , the only way to take crowding into account , and we recover the sfh of ngc 2070 using the synthetic cmd approach . field contamination is also carefully discussed . results are presented in section 6 and compared to the literature in section 7 . section 8 compares ngc 2070 with other starburst clusters . our conclusions ( section 9 ) close the paper . throughout the paper , for the sake of simplicity , we will refer to the entire http data - set as `` 30 doradus '' , the starburst cluster as ngc 2070 and its core as r 136 .

we focus on the stars within 20 pc of the center of the massive ionizing cluster of 30 doradus , ngc 2070 . we recovered the star formation history by comparing deep optical and nir color - magnitude diagrams ( cmds ) with state - of - the - art synthetic cmds generated with the latest parsec models , which include all stellar phases from pre - main sequence to post - main sequence . for the first time in this region we are able to measure the star formation using intermediate and low mass stars simultaneously .

we present a study of the recent star formation of 30 doradus in the large magellanic cloud ( lmc ) using the panchromatic imaging survey hubble tarantula treasury project ( http ) . in this paper we focus on the stars within 20 pc of the center of the massive ionizing cluster of 30 doradus , ngc 2070 . we recovered the star formation history by comparing deep optical and nir color - magnitude diagrams ( cmds ) with state - of - the - art synthetic cmds generated with the latest parsec models , which include all stellar phases from pre - main sequence to post - main sequence . for the first time in this region we are able to measure the star formation using intermediate and low mass stars simultaneously . our results suggest that ngc2070 experienced a prolonged activity . in particular , we find that the star formation in the region : i ) exceeded the average lmc rate myr ago ; ii ) accelerated dramatically myr ago ; and iii ) reached a peak value 1 - 3 myr ago . we did not find significant deviations from a kroupa initial mass function down to 0.5 m . the average internal reddening e(bv ) is found to be between 0.3 and 0.4 mag .

astro-ph0107510

i

much observational evidence suggests that strong obscuration absorbs the strong continuum source in active galactic nuclei over a significant fraction of the solid angle ( lawrence & elvis 1982 , antonucci & miller 1985 , maiolino et al . the effects of this absorption are clearly visible in the x - ray spectra of many agns , where a photoelectric cutoff at energies of a kev or so ( depending on the column density of the gas ) is observed , and in the mid - infrared , where we observe the thermal re - emission of the absorbed uv radiation from the dust associated with the absorbing gas.this circumnuclear material obscures the optical emission of the broad line region , but not that of the more distant narrow line region . as a consequence , objects observed along a line of sight covered by this material appear in the optical as type 2 agns . the simplest geometry for this cold gas surrounding the nucleus , is that of a torus covering @xmath5% of the solid angle ( antonucci & miller 1985 , krolik & begelman 1989 ) . axial symmetry in the material in the central @xmath4 100 pc of nearby agns is suggested by the biconical shapes ( pogge 1989 ) seen well in high resolution hst images ( tadhunter & tsvetanov 1989 , malkan et al . 1998 ) , and polarization requires a highly non - spherical shape ( antonucci & miller 1985 ) . one of the unsolved questions about the structure of this putative torus is its typical dimensions . detailed models of homogeneous circumnuclear tori , both on the 1 pc and 100 pc scale , reproduce the observed infrared sed ( pier & krolik 1992 , granato & danese 1994 ) . hard x - ray observations show that at least 50% of nearby seyfert 2s are obscured by a column density higher than 10@xmath6 @xmath2 ( risaliti et al . 1999 ) . in these cases it is unlikely that the typical dimensions of a homogeneous torus exceed a few parsecs , since otherwise the dynamical mass of the obscuring material would be too large ( risaliti et al . 1999 ) . however , detailed observations both in the x - rays and in the near ir / optical band suggest that the structure of the circumnuclear material is more complex than a simple homogeneous torus . large variations in the cold obscuring column density have been known in a few objects for many years ( ives et al . 1976 , warwick et al . 1988 ) . a more systematic study by malizia et al . ( 1997 ) , shows that variations of several 10@xmath7 @xmath2 are rather common in both type 1 and type 2 seyferts ( 17 out of 23 sources observed at least 3 times shows n@xmath0 variations ) . changes in months or less suggest much smaller sizes , whether the observed change is due to motions across the line of sight , or to a varying ionization state . the broad emission line region ( belr ) has been suggested as a site for this variable absorption in type 1 agns ( ives et al . 1976 ) . since the belr is either hidden or not present in type 2 agn this explanation appears implausible for type 2 objects , which comprise 80% of all agn ( maiolino & rieke 1995 ) . in this paper we investigate the variability of the x - ray absorbing column density in x - ray - defined seyfert 2s having column densities higher than @xmath8 @xmath2 , but less than 10@xmath6 @xmath2 , i.e. compton thin . this includes optically defined both types 1.8 and 1.9 objects ( which show broad lines only in long wavelength lines , e.g. h@xmath9 , pa@xmath9 , osterbrock 1989 ) as well as type 2 seyferts , and all show evidence for cool absorbing material . we collected all the data available in the literature for seyfert 2s and we complemented them with the analysis of unpublished data in the asca and bepposax public archives . we found that a sample of 25 sources were observed at least twice in the hard x - rays . 11 objects out of these 25 have 5 or more hard x - ray observations in a time interval of several years , and we can therefore obtain for them an `` n@xmath0 light curve '' . in the next section we show that variations in n@xmath0 are almost universally present . we analyze in greater detail the well - observed 11 sources , dividing them in two subsamples with n@xmath10 @xmath2 ( 6 objects ) and n@xmath3 @xmath2 ( 5 objects ) . previous x - ray studies show that sources with 10@xmath11 @xmath12n@xmath13 @xmath2 are mostly type 1.8 and 1.9 ( risaliti et al . 1999 ) while those with n@xmath14 @xmath2 are mostly pure seyfert 2s . this dichotomy is also present in our sources : 3 out of 5 objects in the low - n@xmath0 subsample are intermediate type , while 5 out of 6 in the high - n@xmath0 subsample are type 2s ( table 1 ) . in section three we analyze the n@xmath0 variability of the well studied subsample using a `` structure function '' similar to that used in studies of brightness variability of quasars ( fiore et al . 1998 , di clemente et al . 1996 ) . in section four we discuss our results and we compare them with current models of the circumnuclear medium of agns . our conclusions are summarized in section 5 .

these variations rule out the simplest version of the unified models , based on a homogeneous obscuring torus , and suggest the presence of clumpy circumnuclear material on a scale well below a parsec . for lightly obscured agn ( n ) the structure function shows an increase at a timescale of yr , indicating a second absorber , most probably on a 5 - 10 pc scale associated with the host galaxy .

we present a study of the variations in the absorbing column density of 25 x - ray defined seyfert 2 galaxies , as inferred from hard x - ray observations , on timescales from months to several years . we show that a significant variation of n ( from 20% to 80% ) is observed in almost all ( 22/25 ) the sources with multiple x - ray observations , although x - ray absorption never vanishes . for a subsample of 11 sources observed at least five times the typical variation time , as defined by a structure function , is less than one year for both heavily absorbed ( n ) and moderately absorbed ( n ) sources . these variations rule out the simplest version of the unified models , based on a homogeneous obscuring torus , and suggest the presence of clumpy circumnuclear material on a scale well below a parsec . we propose a modification of the torus model in which an overabundance of slightly dusty belr clouds obscures the belr . the belr needs , like the torus , to have an axisymmetric structure . this model is closely related to that of elvis ( 2000 ) for type 1 agn . for lightly obscured agn ( n ) the structure function shows an increase at a timescale of yr , indicating a second absorber , most probably on a 5 - 10 pc scale associated with the host galaxy .

astro-ph0107510

c

in the previous section we demonstrated that n@xmath0 variability in a timescale from months to years is present in the great majority , and possibly in all , seyfert 2 galaxies . the structure function described in the previous section is useful to quantify the general n@xmath0 variability properties of our sources . a physical interpretation of our results must explain both the shape of this function and the different properties of the individual sources . there are two physical reasons that can explain the variability of the absorbing column density : variations in the ionization state of the absorber , due to variations in the ionizing radiation , and variations in the amount of absorbing gas along the line of sight . in the first case , the absorber can be homogeneous , and the variation in n@xmath0 should be correlated with intrinsic flux variations . in the second case , the absorber must be clumpy , and the variation timescales will be correlated with the typical crossing time of an absorbing cloud along the line of sight . however we already showed that a change in ionization does not fit the data ( section 2 , fig . 2 ) we can therefore adopt the second scenario -motions in a clumpy medium- and use the information collected in the previous sections to estimate the distance from the center of the obscuring gas . we can idealize the situation by assuming the typical timescale of variation , _ t _ , to be the crossing time of a discrete cloud across the line of sight . assuming that the absorption is due to spherical clouds moving with keplerian velocities , the distance from the central black hole of mass _ m _ is given by : @xmath36 where @xmath37 is the density of the cloud . the black hole mass and the cloud density have been normalized to extreme values for a putative torus ( krolik & begelman 1989 ) in order to obtain the greatest distance . the black hole mass m@xmath38 m@xmath39 is obtained from mass measurements of central black holes in nearby galaxies ( kormendy & richstone 1998 ) . the typical average density @xmath40 in a standard torus can be evaluated as the ratio between the column density and the thickness of the torus . objects of subsample b have n@xmath41 several 10@xmath42 @xmath2 , then @xmath43 @xmath44 . given the clumpiness of the torus , the actual density of a cloud can be higher , however the value @xmath45 @xmath44 can be regarded as an upper limit . even though most of the physical parameters in the equation above are poorly constrained , several conclusions can nevertheless be drawn . first , the shorter timescale n@xmath0 variations ( @xmath4 2 month or less ) must be due to material that is nearer to the center than about 10@xmath46 cm , while the radius of the standard model torus is 1 - 3 pc ( krolik & begelman 1992 ) . the only physical parameter that can reasonably be larger , assuming different physical conditions , is the cloud density : for example , photoionization models suggest that belr clouds have @xmath47 @xmath44 ( netzer 1990 ) . even in this case though it is hard to imagine a reasonable geometry with distances larger than @xmath48 cm , since this would imply that the absorbing material is confined in a thin slab whose depth is less than 10@xmath49 of the distance from the center , but covering a large solid angle . these parameters are even better constrained for two of the objects in our sample for which a measurement of the black hole mass is available : centaurus a ( m@xmath50 m@xmath39 , marconi et al . 2001 ) and ngc 4258 ( m@xmath51 m@xmath39 , miyoshi et al . 1995 ) . using the fastest n@xmath0 variations observed ( which are only upper limits to the actual variation timescales ) we obtain : @xmath52 and @xmath53 these results pose severe problems to the standard torus model , according to which the x - ray absorption is due to cold gas distributed in a toroidal geometry on the parsec scale . an alternative possibility , within the standard agn model ( antonucci 1993 ) is that the x - ray absorber is located in the broad emission line region , much nearer to the central black hole than the `` standard '' torus . an indication for an absorber on the belr scale is also provided by recent high resolution soft x - ray spectra obtained with xmm - newton ( sako et al . if we assume that the broad line clouds are responsible for the absorption in the x - rays , we can find a consistent combination of the parameters in eq . 1 . for example , assuming @xmath54n@xmath1 @xmath2 , m=10@xmath55 m@xmath39 , @xmath56 @xmath44 , typical for seyfert galaxies ( netzer 1990 ) , and t=5 days we obtain r@xmath57 cm , @xmath4 3 light days , a distance typical for the belr based on reverberation mapping ( peterson et al . our point can be graphically illustrated as in fig . 6 , where we show that our observed variability is not compatible with a parsec - scale torus , while a variability of @xmath4 1 day could be in agreement with an absorber located in the belr . the typical column density of the obscuring clouds also lies in the regime of belr clouds . this variability consequently requires that the circumnuclear absorber is not homogeneous , but clumped into several clouds . assuming gaussian fluctuations , the average number of clouds along the line of sight , n@xmath58 , should be of the order @xmath59 . the right hand axis of fig . 1 shows this number to be of order a few for most of the sample . in no case though , even for n@xmath60 , did n@xmath0 drop below 5@xmath61 @xmath2 , well above the lowest detectable value for these observations therefore , despite the large variability in n@xmath0 , there are no changes from type 2 to type 1 . from fig . 1 we estimate that the average column density of the single clouds , n@xmath62 , range from a few 10@xmath7 @xmath2 in low - n@xmath0 objects , up to several 10@xmath42 @xmath2 in high n@xmath0 objects . we report the estimates of n@xmath63 in the last column of table 2 . the n@xmath63 distribution is plotted the histogram in fig . however , the standard model for agns fails to explain x - ray absorption through the broad line clouds because it would predict several unseen features . photoionization models require that in type 1 agns the covering factor of the broad line clouds ( assuming an isotropic distribution around the central black hole ) is typically 10% and certainly much lower than 100% . we would then expect that ( 1 ) 10% of type 1 agns would be x - ray absorbed , and ( 2 ) , repeated observations of the same object would reveal , in 10% of the cases , an x - ray absorbed spectrum . at present about 20 bright seyfert 1s have been extensively studied in the x - rays for several years , by means of several x - ray observatories ( turner & pounds 1989 , nandra & pounds 1989 , nandra et al . 1997 ) , and these effects have been observed only in one case ( ngc 3516 , costantini et al . 2000 ) . in the optical , where many more objects have been extensively observed , there are only few known cases of transition from type 1 to type 2 or vice versa ( ngc 7603 , tohline & osterbrock 1976 ; mkn 1018 , cohen et al . 1986 ; ngc 7582 , aretxaga et al . 1999 ; for other cases see references in aretxaga et al . we conclude that the standard agn model is not able to reproduce the observed variability of x - ray absorption in seyfert 2 galaxies . from the discussion above we conclude that the observed x - ray variability must be explained by an absorber with the following properties : ( 1 ) close to the central engine ( unless moving faster than keplerian ) , ( 2 ) clumped ( to explain the n@xmath0 variability , with n@xmath64 ) , ( 3 ) covers a significant fraction , @xmath65 , of the solid angle ( in order to reproduce the 4:1 ratio between seyfert 2s and seyfert 1s ) , and ( 4 ) since agn rarely change from type 2 to type 1 , the absorber can not be spherically symmetric so that the 80% of lines of sight covered must always remain the same . a straightforward extension of the standard unified model that can reproduce the right x - ray absorption properties is to suppose that in seyfert 2s the belcs are , somewhat paradoxically , _ much more numerous _ than in seyfert 1s , so that the covering factor is 100% and on average several clouds cover the line of sight . we can repeat the argument used above to rule out the parsec - scale torus , to constrain the variability timescales within this model : assuming that the absorber is made by belcs ( @xmath66 @xmath44 ) moving with keplerian velocity , we can obtain a consistent distance from the center only assuming variations on timescales of days . assuming a typical velocity of 5000 km s@xmath67 for the belcs , the crossing time of a cloud is @xmath68 days , and the distance from the center is r@xmath69 cm . rewriting equation 3 for a belr absorber , and using a typical n@xmath0 variation for the high - n@xmath0 subsample , we have : @xmath70 such a model is novel because would ascribe the differences between type 1 and type 2 agns to physical properties , rather than to orientation effects . orientation is reintroduced because the x - ray absorber can not be spherically distributed around the center ( because of the shortage of objects changing from type 1 to type 2 and vice versa , as outlined in the previous section ) . the simplest possible geometry for a non - spherically symmetric absorber is axisymmetric : a bi - cylinder or a bi - cone . this geometry is appealing because the same structure has been recently proposed by elvis ( 2000 ) in order to explain the absorption and scattering properties of type 1 agns . according to this model , some disk instability generates a two - phase wind from a narrow range of disk radii : the warm phase , with temperatures of the order of @xmath71 k , is responsible for most of the scattering phenomena observed in agns , and for both the uv narrow absorption lines and the x - ray warm absorbers seen in a significant fraction of type 1 agns by the hubble space telescope ( crenshaw et al . 1999 ) and asca ( reynolds 1998 ) . the cold phase of the wind is formed by the belcs ( figure 8) . a simple extension of this model could be that in type 2 agns the belcs confined the warm wind are far more common and completely cover all lines of sight , i.e. on average more than one cloud is present along each line of sight . the fraction of matter in the different phases of multi - phase media , e.g. the ism , is not predictable with current theory , and may be history dependent . some alteration in the seed medium produced by a change in the disk instability at least provides a plausible site for such a bi - modal state to originate . a variation of this is that a larger radial thickness of the wind might produce the dichotomy between type 1 and type 2 agn . in this case , the average distance of the center of the x - ray absorber could be significantly larger than the distance of the belr , since the belcs will be only those located close to the inner edge of the wind ( fig . indeed , indications of a large thickness of the belr come also from reverberation mapping studies , according to which low ionization lines , as mgii @xmath722800 , are emitted by a region several times farther from the center than that emitting high ionization lines like heii @xmath721640 and nv @xmath721240 ( peterson 1993 ) . an interesting prediction of this model is that the change from type 2 to type 1 could occasionally happen , when the line of sight is freed from clouds , because of random motions . in these cases , broad lines in the optical and soft x - rays outburst would be observable . the duration of these breaks in the clouds is of the same order of the crossing time of a cloud along the line of sight . assuming the parameters used in eq . 2 , and a column density for a single cloud of @xmath8 @xmath2 , we can estimate this time to be t@xmath4 1 day , too short to be caught with anything but the most intense monitoring . the probability @xmath73 that this happens depends on the average number of clouds n@xmath58 along the line of sight . assuming n@xmath58=4 and n@xmath58=10 ( two plausible values , see fig . 1 ) we have p@xmath41% and p@xmath4 0.01% , respectively . a detailed study of this case will be presented in nicastro et al . 2001 ( in preparation ) . a problem with this `` many clouds '' model comes from to the optical emission of seyfert 2s . agns that are obscured only by the broad line cloud gas should not be obscured in the optical continuum , but only in the resonant lines themselves . but seyfert 2s continua are weak ( koski 1978 ) . instead seyfert 2s clearly suffer extinction due to dust ( peterson 1997 ) . some dust must then be present in the belcs of type 2 agn . certainly the outer layers of clouds are heavily shielded from the ionizing continuum and could be the locus of dust formation , although the timescales required in our case are probably too short . another possibility is that the material inflowing from the host galaxy and feeding the agn is dusty , and part of the dust is transferred to the external part of the wind , that is much thicker and farther from the center than in the `` optically thin '' model of elvis 2000 . therefore , part of the dust could survive until it reaches the wind . the amount of inflowing material could be the physical quantity that tunes the thickness of the wind , thus determining the type 1 or type 2 classification . this possibility is interesting , given the growing evidence suggesting a low dust to gas ratio in the absorbing medium of many agns ( maiolino et al . 2000 , risaliti et al . a dust poor absorber , located close to the central black hole , has already been suggested by granato et al . these authors show that the infrared emission of seyfert 2s is best reproduced assuming a low dust - to - gas ratio , and suggest that most of the x - ray absorber is located inside the agn sublimation radius . our `` intrinsic '' model for the difference between type 1 and type 2 agn also explains the otherwise puzzling lack of strong infrared dust emission observed in most seyfert 1s . edelson et al . ( 1987 ) show that only about 1/3 of seyfert 1s show strong dust contribution to infrared emission in iras . this observational fact is hard to include in the standard unified models : seyfert 1s should have the same obscuring tori as seyfert 2s , and therefore their infrared emission should be of the same order of that of seyfert 1s , with respect to the bolometric intensity . the model we proposed predicts that orientation apply only to objects with `` many '' clouds , that are type 2 if seen through the wind and type 1 ( with high ir dust emission ) if seen pole - on . objects with `` few '' clouds are type 1 along every line of sight , and are not expected to be strong ir emitters . finally , this scenario is appealing because it predicts a link between the absorbing column density and the amount of material inflowing from the host galaxy , in agreement with the finding that heavily absorbed agns are preferentially hosted in strongly barred galaxies ( maiolino et al . 1999 ) . within this model we can estimate the fraction @xmath74 of objects with `` many '' clouds and the average opening angle , @xmath9 , of the wind ( fig . 8) . using the ratio 4:1 between type 2s and type 1s ( maiolino et al . 1995 ) and the fraction 1/3 for the dust emitting type 1s ( edelson et al . 1987 ) we obtain @xmath75 and @xmath76% . we note that the opening angle of the wind in the model of elvis 2000 is higher ( @xmath77 ) . however , the presence of a second absorber ( see next section ) can reduce this discrepancy . the increase in the n@xmath0 structure function for low n@xmath0 objects at t@xmath4 5 years is not explained by a `` many clouds '' , belr , origin for the cold x - ray absorber . instead an additional , second , absorber is needed , located much farther from the center . inhomogeneities in this absorber could be related to the long term variability on timescales of years revealed in our sample of objects with n@xmath3 @xmath2 . assuming a column density variation of 5@xmath78 @xmath2 ( typical for the long - timescale variations observed in the low - n@xmath0 subsample ) , we can parametrize the distance from the center of this second absorber as follows : @xmath79 this absorber can be compatible with the standard torus model ( r@xmath80 cm ) , in objects with a lower m@xmath81 or with a lower cloud density . the existence of a second absorber is needed by the belc - origin model , that , in the original version of elvis ( 2000 ) implies a covering factor of @xmath4 0.5 and so can not reproduce the high ratio between seyfert 2s and seyfert 1s , which is known to be @xmath82 for nearby objects ( maiolino & rieke 1995 ) . moreover , strong suggestions of the existence of two distinct absorbers come from the analysis of the x - ray spectra of several nearby agns ( malaguti et al . 1999 , turner et al . 2000 , vignali et al . 1998 ) the orientations of the two absorbers are likely unrelated , since neither radio jet axes nor emission line bi - cones ( pogge 1989 ) align with galaxy minor axes ( ulvestad & wilson 1984 ) . there will then be objects obscured only by one of the two absorbers . this obviously would increase the fraction of obscured lines of sight . objects obscured only by the more distant medium can not have column density variations in timescales of days . this is in agreement with the measurements described in the previous sections . a consequence of this second absorber is that the ratio between free and wind - covered lines of sight can be higher than predicted in the previous section , since some fraction of the objects are type 2 because they are covered by the farther absorber . this would reduce the opening angle discrepancy between our model and that of elvis ( 2000 ) . we can give a quantitative estimate of this effect if we assume that intermediate type objects ( @xmath4 sample a ) are those observed through the outer torus , but not through the wind . we therefore have a new , lower , ratio between type 1.8 - 2 and type 1 - 1.5 objects , and an estimate of the covering factor of the outer obscurer from the ratio between intermediate and type 1 seyferts . with these number we calculate an half - opening angle of 35@xmath83 and a fraction of objects with `` many clouds '' @xmath74=75% . the half - opening angle is still significantly lower that in the model by elvis ( 2000 ) . however , we note that in the elvis model the wind is turned by radiation pressure . we expect that the wind in our model , more massive that that of elvis ( 2000 ) , is harder to turn by radiation pressure .

11 sources observed at least five times the typical variation time , as defined by a structure function , is less than one year for both heavily absorbed ( n ) and moderately absorbed ( n ) sources . the belr needs , like the torus , to have an axisymmetric structure . this model is closely related to that of elvis ( 2000 ) for type 1 agn .

we present a study of the variations in the absorbing column density of 25 x - ray defined seyfert 2 galaxies , as inferred from hard x - ray observations , on timescales from months to several years . we show that a significant variation of n ( from 20% to 80% ) is observed in almost all ( 22/25 ) the sources with multiple x - ray observations , although x - ray absorption never vanishes . for a subsample of 11 sources observed at least five times the typical variation time , as defined by a structure function , is less than one year for both heavily absorbed ( n ) and moderately absorbed ( n ) sources . these variations rule out the simplest version of the unified models , based on a homogeneous obscuring torus , and suggest the presence of clumpy circumnuclear material on a scale well below a parsec . we propose a modification of the torus model in which an overabundance of slightly dusty belr clouds obscures the belr . the belr needs , like the torus , to have an axisymmetric structure . this model is closely related to that of elvis ( 2000 ) for type 1 agn . for lightly obscured agn ( n ) the structure function shows an increase at a timescale of yr , indicating a second absorber , most probably on a 5 - 10 pc scale associated with the host galaxy .

cond-mat9612251

i

in recent years , one - dimensional ( 1d ) semiconductor nanostructures have received increasing attention . the potential technological application of quantum wires ( qwrs ) , e.g. in laser devices , has fueled a search for new fabrication techniques and improved sample quality . @xcite in this area , recent investigations have focused on two classes of structures , the so - called v - shaped @xcite and t - shaped @xcite qwrs ( v - qwrs and t - qwrs ) . due to high control on growth conditions and strong confinement of the electron and hole wavefunctions on the scale of few nanometers , v - qwrs and t - qwrs share desirable optical properties for device applications , such as large exciton binding energy and small linewidth . v - qwrs are obtained from a gaas substrate grown along the [ 001 ] crystallographic direction , patterned with [ @xmath010]-oriented v - shaped grooves obtained by chemical etching . the active region consists of a gaas layer cladded between two al@xmath1ga@xmath2as regions @xcite or gaas / alas superlattices @xcite ( sls ) overgrown on the patterned substrate . the confining potential ( see fig . [ fig : geom ] ) has a crescent shape profile . t - qwrs are obtained by first growing a gaas / al@xmath1ga@xmath2as sl on a ( 001 ) substrate . after cleavage , a gaas quantum well ( qw ) is grown over the exposed ( 110 ) surface , resulting in a t - shaped active region . @xcite in both cases , the electron and hole wavefunctions are confined in the [ 001 ] and [ 110 ] crystallographic directions , while the qwr free axis is parallel to the [ @xmath010 ] direction . the optical spectroscopy of qwrs is more complex than for qws of similar lateral dimension , since in qwrs linewidths can be comparable to intersubband splittings . on the other hand , a remarkable peculiarity of qwrs with respect to qws is that the optical activity is strongly anisotropic when light is linearly polarized , with the electric field directed parallel or perpendicular to the wire axis . this has long been recognized to be a band structure effect due to the quasi-1d character of electronic state , combined with heavy- and light - hole ( hh and lh ) mixing . @xcite the anisotropic absorption is therefore used as a simple tool to reveal the 1d character of electronic states in nanostructured materials . in principle , the optical anisotropy can be exploited to single out detailed information on the electronic states , since , as we will show , it is very sensitive to specific details of the band structure . in practice , this approach has been sofar limited by the lack of realistic calculations for complex geometries , as the present v - qwrs and t - qwrs . indeed , common theoretical methods , even within semi - empirical schemes as the tight - binding or the envelope function approach , require a large scale computational effort . in order to keep calculations tractable , up to now the optical properties of qwrs have been investigated theoretically only for rather idealized structures @xcite , yielding results that can not be directly compared with experimental spectra . calculations have been performed for realistic qwr geometries @xcite , but they have sofar neglected hh - lh mixing . recently , we have demonstrated , by a combined theoretical - experimental study of v - qwrs , @xcite that accurate band structure calculations for realistic structures provide quantitative predictions of photoluminescence excitation ( ple ) spectra , and that detailed information on the valence band states can be singled out of the ple anisotropy , despite the dominant role of the light conduction electrons in the optical spectra . such calculations were based on a recently devised method which provides the band structure for qwrs of arbitrary geometry at a relatively small computational cost . the accuracy and the short computer times make such calculations a practical characterization tool in conjunction with experimental results , as well as a predictive tool for new devices . in this paper , we present a theoretical investigation of the electronic and optical properties of v - qwrs and t - qwrs . we focus on the relationship between optical anisotropy and band structure , and we show how the analysis of optical anisotropy permits a detailed spectroscopy of valence states , even when the large linewidth of the spectra does not allow an identification of the valence - to - conduction subband transitions . for t - qwrs we also predict a huge spin - splitting of the lowest valence subband , originating from the interaction between the lowest hh levels of the intersecting qws . for both classes of wires , calculations are performed by the numerical method introduced in ref . here described in detail , thereby demonstrating its accuracy and flexibility . the main approximation that is still present in our approach is the neglect of excitonic effects . indeed , recent calculations which fully include coulomb interaction in realistic qwr profiles @xcite ( but do not include hh - lh mixing ) demonstrate that electron - hole interaction , besides giving rise to bound excitonic states below the band edge , also modifies the excitonic continuum above the band edge . however , our previous investigation in v - qwrs @xcite has shown that quantitative agreement is obtained between the observed ple anisotropy , which probe the excitonic continuum , and the anisotropy in absorption spectra calculated neglecting excitonic effects . we interpret this result as an indication that the electron - hole coulomb interaction , by mixing isotropically the ( optically anisotropic ) electron and hole states , does not change the average anisotropy as obtained by single particle band structure calculations . this is of course compatible with the possibility that the relative intensity of the absorption peaks for a given polarization may be strongly affected . @xcite the above arguments suggest that the approximation of neglecting electron - hole coulomb coupling is a reasonable one for our purpose of studying optical anisotropies . of course , its accuracy for the present v- and t - qwrs must be established a posteriori by comparison with experiments , as we will do later on in this paper . the theoretical background and the numerical method used in our calculations are outlined in sec . [ sec : metodo ] . sections [ sec : v ] and [ sec : t ] report the results of our calculations , focusing on the band structure and optical anisotropy , for v - qwrs and t - qwrs , respectively .

we present a theoretical investigation of the electronic and optical properties of v- and t - shaped quantum wires . valence band mixing as well as realistic sample geometries are fully included through an accurate and efficient approach that is described here in detail . we investigate the resulting valence band structure , which shows some significant peculiarities , such as an anomalously large spin splitting in the lowest heavy hole subband of t - shaped wires . for both classes of wires

we present a theoretical investigation of the electronic and optical properties of v- and t - shaped quantum wires . valence band mixing as well as realistic sample geometries are fully included through an accurate and efficient approach that is described here in detail . we investigate the resulting valence band structure , which shows some significant peculiarities , such as an anomalously large spin splitting in the lowest heavy hole subband of t - shaped wires . for both classes of wires we obtain good agreement between calculated optical absorption and recent experimental spectra , and we demonstrate that the analysis of optical anisotropy can be used as an effective tool to extract information on valence states , usually very difficult to obtain otherwise .

astro-ph0605681

c

we have analyzed the emission - line and host properties of 85224 galaxies from the sloan digital sky survey . we show that seyferts and liners form two separate branches on the standard optical diagnostic diagrams . we present a new optical classification scheme that successfully separates purely star - forming galaxies , seyferts , liners , and composite agn@xmath37star - forming galaxies . we show that vs diagnostic diagram easily discriminates between seyferts , liners and galaxies dominated by star - formation ( including composites ) . we use our new classification scheme to investigate the host properties of agn galaxies as a function of distance from the star - forming sequence . we find that : * the ratio of seyferts to liners is invariant with distance from the star - forming sequence . this result implies that star formation and agn power are coupled . * the stellar populations of seyferts and liners age with distance from the star - forming sequence . liners have a substantially older stellar population than the other spectral types . the youngest stellar population in liners has d4000 and values consistent with the oldest stellar population in seyferts on average . * the stellar mass and mass - to - light ratios of seyferts and liners are not strongly correlated with distance from the star - forming sequence . however , liners have slightly higher stellar masses and mass - to - light ratios on average than seyferts or composite objects . we use as an indicator of the accretion rate in eddington units . we compare the host properties of seyfert and liner galaxies as a function of and . we show that : * the strongest difference between seyfert and liner galaxies is . * when the host properties of seyferts and liners are considered in terms of , the differences in host properties is resolved and the host properties of seyferts and liners form a smooth sequence with . * when the host properties of seyferts and liners are considered in terms of , the smooth sequence seen with disappears . these results indicate that most ( if not all ) liners contain agn , and that the major fundamental difference between seyferts and liners is accretion rate . we use theoretical agn photoionization models to show that the liner branch requires a lower ionization parameter ( up to an order of magnitude ) than the seyfert branch , and that strong liners ( log()@xmath106 ) require a harder ionizing radiation field than galaxies on the seyfert branch . these results suggest that the transition between seyferts and liners is analogous to the high - state and low - state transition in x - ray binaries .

we present an analysis of the host properties of 85224 emission - line galaxies selected from the sloan digital sky survey . we show that seyferts and liners form clearly separated branches on the standard optical diagnostic diagrams . we derive a new empirical classification scheme which cleanly separates star - forming galaxies , composite agn- galaxies , seyferts and liners and we study the host galaxy properties of these different classes of objects . we then consider the quantity l[oiii]/ , which is an indicator of the black hole accretion rate relative to the eddington rate . liners and seyferts form a continuous sequence , with liners dominant at low and seyferts dominant at high . these results suggest that the majority of liners are agn and that the seyfert / liner dichotomy is analogous to the high / low - state transition for x - ray binary systems . we apply theoretical photo - ionization models and show that pure liners require a harder ionizing radiation field with lower ionization parameter than seyfert galaxies , consistent with the low and high x - ray binary states .

we present an analysis of the host properties of 85224 emission - line galaxies selected from the sloan digital sky survey . we show that seyferts and liners form clearly separated branches on the standard optical diagnostic diagrams . we derive a new empirical classification scheme which cleanly separates star - forming galaxies , composite agn- galaxies , seyferts and liners and we study the host galaxy properties of these different classes of objects . liners are older , more massive , less dusty and more concentrated , and they and have higher velocity dispersions and lower [ oiii ] luminosities than seyfert galaxies . seyferts and liners are most strongly distinguished by their [ oiii ] luminosities . we then consider the quantity l[oiii]/ , which is an indicator of the black hole accretion rate relative to the eddington rate . remarkably , we find that at _ fixed _ l[oiii]/ , all differences between seyfert and liner host properties disappear . liners and seyferts form a continuous sequence , with liners dominant at low and seyferts dominant at high . these results suggest that the majority of liners are agn and that the seyfert / liner dichotomy is analogous to the high / low - state transition for x - ray binary systems . we apply theoretical photo - ionization models and show that pure liners require a harder ionizing radiation field with lower ionization parameter than seyfert galaxies , consistent with the low and high x - ray binary states .

1112.1697

i

the discovery of the unusual @xmath22-ray / x - ray transient swiftj164449.3 + 573451 ( hereafter , ) , which coincided with the nucleus of an inactive galaxy at @xmath23 , has opened a new window into high - energy transient phenomena , with potential implications to our understanding of relativistic outflows in systems such as gamma - ray bursts ( grbs ) and active galactic nuclei ( agn ) . the prevailing interpretation for this event is the tidal disruption of a star by a dormant supermassive black hole ( smbh ) with a mass of @xmath24 m@xmath9 ( @xcite ; but see @xcite for alternative explanations ) . the argument for a tidal disruption origin is based on : ( i ) a positional coincidence ( @xmath25 kpc ) with the host galaxy nucleus ; ( ii ) rapid time variability in @xmath22-rays and x - rays ( @xmath26 s ) , which requires a compact source of @xmath27 au , a few times the schwarzschild radius of a @xmath28 m@xmath9 black hole ; ( iii ) high @xmath22-ray and x - ray luminosity of @xmath29 erg s@xmath30 , which exceeds the eddington limit of a @xmath28 m@xmath9 black hole by @xmath31 orders of magnitude ; ( iv ) a lack of previous radio to @xmath22-ray activity from this source to much deeper limits than the observed outburst , pointing to a rapid onset ; and ( v ) long - term x - ray luminosity evolution following @xmath32 , as expected from the fallback of tidally disrupted material ( e.g. , @xcite ) . equally important , was accompanied by bright radio synchrotron emission , with an initial peak in the millimeter band ( @xmath33 mjy ) and a steep spectral slope at lower frequencies indicative of self - absorption ( @xcite ; hereafter , zbs11 ) . the properties of the radio emission established the existence of a relativistic outflow with a lorentz factor of @xmath34 ( zbs11 , @xcite ) . the spectral energy distribution also demonstrated that the lack of detected optical variability required significant rest - frame extinction ( @xmath35 mag ; zbs11 , @xcite ) , and that the x - rays were produced by a distinct emission component , rather than inverse compton scattering by the radio - emitting relativistic electrons ( zbs11 ) . finally , the evolution of the radio emission on a timescale of @xmath36 d pointed to an ambient density with a radial profile of roughly @xmath37 , as well as a mild increase in the energy of the outflow ( zbs11 ) . the formation of a relativistic jet with dominant x - ray and radio emission were not predicted in standard tidal disruption models ( e.g. , @xcite ) , which instead focused on the thermal optical / uv emission from the long - term accretion of the stellar debris . a signature of the latter process is a mass accretion rate that evolves as @xmath38 , presumably leading to emission with the same temporal dependence ( e.g. , @xcite ) . shortly before the discovery of , @xcite investigated the potential signature of a putative relativistic outflow , and concluded that the interaction of the outflow with the ambient medium will lead to radio emission on a timescale of @xmath39 yr ( for typical off - axis observers ) . while the mechanism for the radio emission from is interaction with an external medium , the actual light curves differ from the off - axis prediction . to address this issue , in a follow - up paper @xcite ( hereafter , mgm11 ) reconsidered the model for a relativistic jet interacting with an ambient medium . they draw on the inferences from the early radio emission described in zbs11 to infer the properties of the environment and the jet kinetic energy , and use this information to predict the future evolution of the radio emission . this long - term radio evolution is of great interest because it can provide several critical insights : * the integrated energy release in the relativistic outflow , including the anticipated injection from on - going accretion . * the density profile around a previously - dormant smbh on @xmath40 pc scales , which can not be otherwise probed in agn . * the potential to spatially resolve the outflow with very long baseline interferometry ( vlbi ) , and hence to measure the dynamical evolution ( expansion and potentially spreading ) of a relativistic jet . * predictions for the radio emission from tidal disruption jets as viewed by off - axis observers on timescales of months to years to decades . the energy scale and jet dynamics are of particular importance since the total energy input and the structure of the jet may also have implications for relativistic jets in grbs and agn . the ability to trace the environment on parsec scales provides a unique probe of gas inflow or outflow around an inactive smbh on scales that can not be probed outside of the milky way . finally , the long - term radio emission from will inform future radio searches for tidal disruption events ( tdes ) that can overcome the low detection rate in @xmath22-rays / x - rays ( due to beaming ) , and obscuration due to extinction in the optical / uv ( as in the case of ) . to extract these critical properties we are undertaking long - term monitoring of the radio emission from using a wide range of centimeter- and millimeter - band facilities . here we present radio observations of that extend to @xmath11 d , and use these observations to determine the evolution of the total energy and ambient density . we find that the evolution of both quantities deviates from the behavior at @xmath41 month ( presented in zbs11 ) , thereby providing crucial insight into the structure of the relativistic outflow and the ambient medium . this paper is the first in a series that will investigate the long - term radio evolution of and the implications for relativistic jets and parsec - scale environments around supermassive black holes , including efforts to resolve the source with vlbi and to measure polarization . the current paper is organized as follows . we describe the radio observations in [ sec : obs ] , and summarize the radio evolution at @xmath42 d in [ sec : prem ] . in [ sec : model ] we present our modeling of the radio emission , which utilizes the formulation of mgm11 . the implications for the energy scale and ambient density are discussed in [ sec : energy ] and [ sec : density ] , respectively , and we finally consider the implications for relativistic jets and the parsec - scale environments of smbhs in [ sec : implic ] .

we present continued radio observations of the tidal disruption event swiftj164449.3 + 573451 extending to days after discovery . the lorentz factor is , the ambient density is , and the projected angular size isas , below the resolution of the vlba+effelsberg . assuming no future changes in the observed evolution and a final integrated total energy of erg

we present continued radio observations of the tidal disruption event swiftj164449.3 + 573451 extending to days after discovery . the data were obtained with the evla , ami large array , carma , the sma , and the vlba+effelsberg as part of a long - term program to monitor the expansion and energy scale of the relativistic outflow , and to trace the parsec - scale environment around a previously - dormant supermassive black hole ( smbh ) . the new observations reveal a significant change in the radio evolution starting at month , with a brightening at all frequencies that requires an increase in the energy by about an order of magnitude , and an overall density profile around the smbh of ( pc ) with a significant flattening at pc . the increase in energy can not be explained with continuous injection from an tail , which is observed in the x - rays . instead , we conclude that the relativistic jet was launched with a wide range of lorentz factors , obeying . the similar ratio of duration to dynamical timescale for and grbs suggests that this result may be applicable to grb jets as well . the radial density profile may be indicative of bondi accretion , with the inferred flattening at pc in good agreement with the bondi radius for a m black hole . the density at pc is about a factor of 30 times lower than inferred for the milky way galactic center , potentially due to a smaller number of mass - shedding massive stars . from our latest observations ( d ) we find that the jet energy is erg ( erg for ) , the radius is pc , the lorentz factor is , the ambient density is , and the projected angular size isas , below the resolution of the vlba+effelsberg . assuming no future changes in the observed evolution and a final integrated total energy of erg , we predict that the radio emission from should be detectable with the evla for several decades , and will be resolvable with vlbi in a few years .

1112.1697

c

we presented radio observations of extending to @xmath0 d and spanning a wide range of frequencies . the evolution of the radio emission changes dramatically at @xmath257 month , requiring an increase in the total energy by about an order of magnitude , a density profile of @xmath2 ( @xmath3 pc ) , and a flattening at @xmath4 pc . a comparison of the model to optical limits and near - ir detections indicates a cooling break at @xmath233 hz and host galaxy extinction of @xmath258 mag . the increase in energy can not be explained by injection from an @xmath5 tail that is expected in tidal disruption events and which matches the evolution of the x - ray emission . we conclude that a natural explanation is a structured outflow with @xmath6 . the inferred density profile and the radial scale of the density enhancement are in rough agreement with the expectation for bondi accretion from a circumnuclear medium . the jet energetics and structure , as well as the detailed density profile on @xmath259 pc scale are a testament to the important insight that can be gained from continued radio observations of . in particular , the radial density profile is traced in greater detail than even the inner parsec of the milky way . continued radio observations will probe the environment to a scale of @xmath260 pc in the coming decade . using the results of our analysis we can predict the future evolution of the radio emission ( modulo any future unpredictable changes in energy and/or density as we have found here ) . we use the evolution of @xmath107 and @xmath119 as inferred from the data at @xmath261 d , and assume that the density will continue to evolve as @xmath218 and that the energy will increase to a maximum beaming - corrected value of @xmath262 $ ] with @xmath263 erg . the resulting light curves at 6 and 22 ghz are shown in figure [ fig : predlc ] . the long - term evolution is marked by a break when @xmath102 achieves its maximum value , corresponding to about @xmath264 , @xmath265 , and @xmath266 yr for our three choices of maximum energy . using the @xmath267 sensitivity of the evla in an observation of a few hours , we find that the emission at 22 and 6 ghz should be detectable for at least @xmath268 yr and @xmath269 yr , respectively . indeed , any significant upgrades to the evla or the construction of more sensitive radio facilities in the coming decades may extend the range of detectability to centuries . the same is true if the total energy scale is @xmath270 erg . an equally important question is whether the jet will be resolvable with vlbi in the future . the projected radius is @xmath271 , as long as the jet maintains its collimation . in figure [ fig : predrad ] we plot the predicted future evolution of @xmath156 using the prescription described above . we find that for @xmath14 and a best - case vlbi angular resolution of @xmath272 mas ( fwhm ) , the source should become resolvable at @xmath273 yr . on this timescale the 22 ghz flux density is expected to be only @xmath274 mjy ( figure [ fig : predlc ] ) , still accessible with vlbi . while the flux density at 6 ghz is expected to be larger by about a factor of @xmath275 , the angular resolution at this frequency is poorer by about a factor of 3.7 , making it less competitive than 22 ghz . thus , we conclude that the radio emission from may be marginally resolved in a few years . on the other hand , if the jet undergoes significant spreading on the timescale at which it becomes non - relativistic ( as expected for grb jets : e.g. , @xcite ) it is possible that it will become resolvable at @xmath276 yr when the expected 22 ghz flux density is still @xmath260 mjy . we are undertaking continued multi - frequency radio monitoring of to follow the long - term evolution of the relativistic outflow and the radial profile of the ambient medium . even in the absence of any future dramatic changes relative to the current evolution , we expect that in the next few years we may be able to determine the total energy of the relativistic outflow , measure the spreading of the jet , and study the radial density profile to a scale of @xmath260 pc . future papers in this series will detail these results . we thank ramesh narayan , ryan chornock , and nicholas stone for helpful discussions , and glen petitpas for assistance with the sma data reduction . acknowledges support from swift ao6 grant nnx10ai24 g and from the national science foundation through grant ast-1107973 . a.b . is supported by a marie curie outgoing international fellowship ( fp7 ) of the european union ( project number 275596 ) . this work is partially based on observations with the 100-m telescope of the mpifr ( max - planck - institut f@xmath277r radioastronomie ) at effelsberg . the submillimeter array is a joint project between the smithsonian astrophysical observatory and the academia sinica institute of astronomy and astrophysics , and is funded by the smithsonian institution and the academia sinica . support for carma construction was derived from the gordon and betty moore foundation , the kenneth t. and eileen l. norris foundation , the james s. mcdonnell foundation , the associates of the california institute of technology , the university of chicago , the states of california , illinois , and maryland , and the national science foundation . ongoing carma development and operations are supported by the national science foundation under a cooperative agreement , and by the carma partner universities . the ami arrays are supported by the university of cambridge and the stfc . this work made use of data supplied by the uk swift science data centre at the university of leicester . , m. , van langevelde , h. j. , reynolds , c. , & cotton , b. 2006 , in astronomical society of the pacific conference series , vol . 351 , astronomical data analysis software and systems xv , ed . c. gabriel , c. arviset , d. ponz , & s. enrique , 497 rccr 0.15 in 6.79 & evla & 1.4 & @xmath278 + 126.59 & evla & 1.4 & @xmath279 + 174.47 & evla & 1.4 & @xmath280 + 197.41 & evla & 1.4 & @xmath281 + 3.87 & evla & 4.9 & @xmath282 + 4.76 & evla & 4.9 & @xmath283 + 5.00 & evla & 4.9 & @xmath283 + 5.79 & evla & 4.9 & @xmath284 + 6.78 & evla & 4.9 & @xmath285 + 7.77 & evla & 4.9 & @xmath286 + 9.79 & evla & 4.9 & @xmath287 + 14.98 & evla & 4.9 & @xmath288 + 22.78 & evla & 4.9 & @xmath289 + 35.86 & evla & 4.9 & @xmath290 + 50.65 & evla & 4.9 & @xmath291 + 67.61 & evla & 4.9 & @xmath292 + 94.64 & evla & 4.9 & @xmath293 + 111.62 & evla & 4.9 & @xmath294 + 126.51 & evla & 4.9 & @xmath294 + 143.62 & evla & 4.9 & @xmath295 + 164.38 & evla & 4.9 & @xmath296 + 174.47 & evla & 4.9 & @xmath297 + 197.41 & evla & 4.9 & @xmath298 + 213.32 & evla & 4.9 & @xmath299 + 3.87 & evla & 6.7 & @xmath300 + 4.76 & evla & 6.7 & @xmath301 + 5.00 & evla & 6.7 & @xmath302 + 5.79 & evla & 6.7 & @xmath303 + 6.79 & evla & 6.7 & @xmath287 + 7.77 & evla & 6.7 & @xmath304 + 9.79 & evla & 6.7 & @xmath305 + 14.98 & evla & 6.7 & @xmath306 + 22.78 & evla & 6.7 & @xmath307 + 35.86 & evla & 6.7 & @xmath308 + 50.65 & evla & 6.7 & @xmath309 + 67.61 & evla & 6.7 & @xmath310 + 94.64 & evla & 6.7 & @xmath311 + 111.62 & evla & 6.7 & @xmath312 + 126.51 & evla & 6.7 & @xmath313 + 143.62 & evla & 6.7 & @xmath314 + 164.38 & evla & 6.7 & @xmath315 + 174.47 & evla & 6.7 & @xmath316 + 197.41 & evla & 6.7 & @xmath317 + 213.32 & evla & 6.7 & @xmath318 + 14.97 & evla & 8.4 & @xmath319 + 127.69 & evla & 8.4 & @xmath320 + 159.77 & evla & 8.4 & @xmath321 + 174.47 & evla & 8.4 & @xmath322 + 177.50 & evla & 8.4 & @xmath323 + 197.41 & evla & 8.4 & @xmath324 + 213.32 & evla & 8.4 & @xmath325 + 219.22 & evla & 8.4 & @xmath326 + 5.81 & ami - la & 15.4 & @xmath327 + 6.64 & ami - la & 15.4 & @xmath328 + 7.62 & ami - la & 15.4 & @xmath329 + 8.55 & ami - la & 15.4 & @xmath330 + 9.56 & ami - la & 15.4 & @xmath331 + 10.78 & ami - la & 15.4 & @xmath332 + 11.56 & ami - la & 15.4 & @xmath333 + 13.64 & ami - la & 15.4 & @xmath334 + 14.57 & ami - la & 15.4 & @xmath335 + 16.47 & ami - la & 15.4 & @xmath336 + 18.65 & ami - la & 15.4 & @xmath337 + 19.73 & ami - la & 15.4 & @xmath338 + 21.78 & ami - la & 15.4 & @xmath339 + 22.76 & ami - la & 15.4 & @xmath340 + 25.38 & ami - la & 15.4 & @xmath341 + 26.74 & ami - la & 15.4 & @xmath342 + 31.45 & ami - la & 15.4 & @xmath343 + 33.61 & ami - la & 15.4 & @xmath344 + 34.79 & ami - la & 15.4 & @xmath345 + 35.71 & ami - la & 15.4 & @xmath346 + 37.49 & ami - la & 15.4 & @xmath347 + 38.60 & ami - la & 15.4 & @xmath348 + 39.78 & ami - la & 15.4 & @xmath349 + 40.67 & ami - la & 15.4 & @xmath350 + 41.69 & ami - la & 15.4 & @xmath351 + 43.63 & ami - la & 15.4 & @xmath352 + 45.74 & ami - la & 15.4 & @xmath353 + 48.69 & ami - la & 15.4 & @xmath354 + 49.64 & ami - la & 15.4 & @xmath355 + 50.54 & ami - la & 15.4 & @xmath356 + 53.39 & ami - la & 15.4 & @xmath357 + 55.62 & ami - la & 15.4 & @xmath358 + 56.52 & ami - la & 15.4 & @xmath359 + 60.73 & ami - la & 15.4 & @xmath360 + 62.54 & ami - la & 15.4 & @xmath361 + 63.45 & ami - la & 15.4 & @xmath362 + 65.51 & ami - la & 15.4 & @xmath363 + 68.60 & ami - la & 15.4 & @xmath364 + 70.69 & ami - la & 15.4 & @xmath365 + 71.38 & ami - la & 15.4 & @xmath366 + 73.48 & ami - la & 15.4 & @xmath367 + 74.48 & ami - la & 15.4 & @xmath368 + 76.65 & ami - la & 15.4 & @xmath369 + 77.47 & ami - la & 15.4 & @xmath370 + 78.49 & ami - la & 15.4 & @xmath371 + 79.49 & ami - la & 15.4 & @xmath372 + 80.47 & ami - la & 15.4 & @xmath373 + 81.48 & ami - la & 15.4 & @xmath374 + 83.42 & ami - la & 15.4 & @xmath375 + 86.65 & ami - la & 15.4 & @xmath376 + 88.37 & ami - la & 15.4 & @xmath377 + 89.64 & ami - la & 15.4 & @xmath378 + 91.58 & ami - la & 15.4 & @xmath379 + 92.58 & ami - la & 15.4 & @xmath380 + 95.39 & ami - la & 15.4 & @xmath381 + 98.42 & ami - la & 15.4 & @xmath382 + 100.61 & ami - la & 15.4 & @xmath383 + 101.60 & ami - la & 15.4 & @xmath384 + 102.60 & ami - la & 15.4 & @xmath385 + 105.59 & ami - la & 15.4 & @xmath386 + 107.38 & ami - la & 15.4 & @xmath387 + 108.32 & ami - la & 15.4 & @xmath388 + 110.34 & ami - la & 15.4 & @xmath389 + 112.50 & ami - la & 15.4 & @xmath390 + 113.50 & ami - la & 15.4 & @xmath391 + 115.49 & ami - la & 15.4 & @xmath392 + 118.31 & ami - la & 15.4 & @xmath393 + 119.48 & ami - la & 15.4 & @xmath394 + 120.55 & ami - la & 15.4 & @xmath395 + 121.55 & ami - la & 15.4 & @xmath396 + 122.18 & ami - la & 15.4 & @xmath397 + 123.45 & ami - la & 15.4 & @xmath398 + 124.38 & ami - la & 15.4 & @xmath399 + 125.51 & ami - la & 15.4 & @xmath400 + 127.38 & ami - la & 15.4 & @xmath401 + 128.35 & ami - la & 15.4 & @xmath402 + 130.38 & ami - la & 15.4 & @xmath403 + 131.41 & ami - la & 15.4 & @xmath404 + 132.49 & ami - la & 15.4 & @xmath405 + 133.35 & ami - la & 15.4 & @xmath406 + 134.36 & ami - la & 15.4 & @xmath407 + 135.32 & ami - la & 15.4 & @xmath408 + 136.46 & ami - la & 15.4 & @xmath409 + 137.51 & ami - la & 15.4 & @xmath410 + 138.51 & ami - la & 15.4 & @xmath411 + 139.51 & ami - la & 15.4 & @xmath412 + 140.50 & ami - la & 15.4 & @xmath413 + 141.13 & ami - la & 15.4 & @xmath414 + 142.30 & ami - la & 15.4 & @xmath415 + 143.26 & ami - la & 15.4 & @xmath416 + 144.42 & ami - la & 15.4 & @xmath417 + 146.48 & ami - la & 15.4 & @xmath418 + 147.48 & ami - la & 15.4 & @xmath419 + 148.27 & ami - la & 15.4 & @xmath420 + 149.27 & ami - la & 15.4 & @xmath421 + 150.47 & ami - la & 15.4 & @xmath422 + 151.22 & ami - la & 15.4 & @xmath423 + 152.27 & ami - la & 15.4 & @xmath424 + 153.46 & ami - la & 15.4 & @xmath425 + 155.45 & ami - la & 15.4 & @xmath426 + 156.35 & ami - la & 15.4 & @xmath427 + 157.45 & ami - la & 15.4 & @xmath428 + 158.29 & ami - la & 15.4 & @xmath429 + 159.28 & ami - la & 15.4 & @xmath430 + 160.27 & ami - la & 15.4 & @xmath431 + 161.20 & ami - la & 15.4 & @xmath432 + 162.21 & ami - la & 15.4 & @xmath433 + 163.28 & ami - la & 15.4 & @xmath434 + 166.00 & ami - la & 15.4 & @xmath435 + 168.13 & ami - la & 15.4 & @xmath436 + 169.13 & ami - la & 15.4 & @xmath437 + 172.25 & ami - la & 15.4 & @xmath438 + 174.33 & ami - la & 15.4 & @xmath439 + 177.32 & ami - la & 15.4 & @xmath440 + 181.30 & ami - la & 15.4 & @xmath441 + 184.03 & ami - la & 15.4 & @xmath442 + 187.19 & ami - la & 15.4 & @xmath443 + 187.91 & ami - la & 15.4 & @xmath444 + 189.37 & ami - la & 15.4 & @xmath445 + 193.19 & ami - la & 15.4 & @xmath446 + 194.01 & ami - la & 15.4 & @xmath447 + 197.02 & ami - la & 15.4 & @xmath448 + 200.01 & ami - la & 15.4 & @xmath449 + 203.01 & ami - la & 15.4 & @xmath450 + 207.08 & ami - la & 15.4 & @xmath451 + 210.19 & ami - la & 15.4 & @xmath452 + 214.17 & ami - la & 15.4 & @xmath453 + 217.16 & ami - la & 15.4 & @xmath454 + 220.20 & ami - la & 15.4 & @xmath455 + 221.22 & ami - la & 15.4 & @xmath456 + 225.91 & ami - la & 15.4 & @xmath457 + 232.87 & ami - la & 15.4 & @xmath458 + 235.01 & ami - la & 15.4 & @xmath459 + 237.85 & ami - la & 15.4 & @xmath460 + 4.79 & evla & 19.1 & @xmath461 + 6.75 & evla & 19.1 & @xmath462 + 7.77 & evla & 19.1 & @xmath463 + 8.87 & evla & 19.1 & @xmath464 + 9.78 & evla & 19.1 & @xmath465 + 21.89 & evla & 19.1 & @xmath466 + 31.74 & evla & 19.1 & @xmath467 + 35.86 & evla & 19.1 & @xmath468 + 50.65 & evla & 19.1 & @xmath469 + 67.61 & evla & 19.1 & @xmath470 + 94.64 & evla & 19.1 & @xmath471 + 111.62 & evla & 19.1 & @xmath472 + 127.83 & evla & 19.1 & @xmath473 + 142.62 & evla & 19.1 & @xmath474 + 159.77 & evla & 19.1 & @xmath475 + 177.50 & evla & 19.1 & @xmath476 + 198.22 & evla & 19.1 & @xmath477 + 219.22 & evla & 19.1 & @xmath478 + 4.79 & evla & 24.4 & @xmath479 + 6.75 & evla & 24.4 & @xmath480 + 7.77 & evla & 24.4 & @xmath481 + 8.87 & evla & 24.4 & @xmath482 + 9.78 & evla & 24.4 & @xmath483 + 21.89 & evla & 24.4 & @xmath484 + 31.74 & evla & 24.4 & @xmath485 + 35.86 & evla & 24.4 & @xmath486 + 50.65 & evla & 24.4 & @xmath487 + 67.61 & evla & 24.4 & @xmath488 + 94.64 & evla & 24.4 & @xmath489 + 111.62 & evla & 24.4 & @xmath490 + 127.83 & evla & 24.4 & @xmath491 + 142.62 & evla & 24.4 & @xmath492 + 159.77 & evla & 24.4 & @xmath493 + 177.50 & evla & 24.4 & @xmath494 + 198.22 & evla & 24.4 & @xmath495 + 219.22 & evla & 24.4 & @xmath496 + 5.75 & evla & 43.6 & @xmath497 + 6.75 & evla & 43.6 & @xmath498 + 8.87 & evla & 43.6 & @xmath499 + 111.62 & evla & 43.6 & @xmath500 + 127.83 & evla & 43.6 & @xmath501 + 159.77 & evla & 43.6 & @xmath502 + 177.50 & evla & 43.6 & @xmath503 + 198.22 & evla & 43.6 & @xmath504 + 219.22 & evla & 43.6 & @xmath505 + 4.90 & carma & 87 & @xmath506 + 8.19 & carma & 87 & @xmath507 + 9.14 & carma & 87 & @xmath508 + 10.23 & carma & 87 & @xmath509 + 12.14 & carma & 87 & @xmath510 + 17.66 & carma & 87 & @xmath511 + 22.11 & carma & 87 & @xmath512 + 25.12 & carma & 87 & @xmath513 + 99.75 & carma & 87 & @xmath514 + 131.52 & carma & 87 & @xmath515 + 148.66 & carma & 87 & @xmath516 + 175.56 & carma & 87 & @xmath517 + 19.25 & sma & 200 & @xmath518 + 24.32 & sma & 200 & @xmath519 + 10.30 & sma & 230 & @xmath520 + 11.13 & sma & 230 & @xmath521 + 17.23 & sma & 230 & @xmath522 + 18.25 & sma & 230 & @xmath523 + 20.24 & sma & 230 & @xmath524 + 21.25 & sma & 230 & @xmath525 + 125.05 & sma & 230 & @xmath526 + 5.13 & sma & 345 & @xmath527 ccccccccccc 0.1 in @xmath528 & @xmath529 & @xmath530 & @xmath531 & @xmath532 & @xmath533 & @xmath534 & @xmath535 & @xmath536 & @xmath537 & @xmath538 + @xmath539 & @xmath540 & @xmath541 & @xmath542 & @xmath543 & @xmath544 & @xmath545 & @xmath546 & @xmath547 & @xmath548 & @xmath549 + @xmath550 & @xmath551 & @xmath552 & @xmath553 & @xmath554 & @xmath555 & @xmath533 & @xmath535 & @xmath556 & @xmath557 & @xmath558 + @xmath559 & @xmath560 & @xmath561 & @xmath562 & @xmath563 & @xmath564 & @xmath565 & @xmath566 & @xmath567 & @xmath568 & @xmath569 + @xmath570 & @xmath571 & @xmath572 & @xmath573 & @xmath574 & @xmath575 & @xmath576 & @xmath577 & @xmath578 & @xmath579 & @xmath580 + @xmath581 & @xmath560 & @xmath582 & @xmath583 & @xmath584 & @xmath585 & @xmath586 & @xmath587 & @xmath588 & @xmath589 & @xmath590 + @xmath591 & @xmath592 & @xmath593 & @xmath594 & @xmath595 & @xmath596 & @xmath575 & @xmath597 & @xmath536 & @xmath598 & @xmath599 + @xmath600 & @xmath571 & @xmath601 & @xmath602 & @xmath603 & @xmath604 & @xmath605 & @xmath606 & @xmath607 & @xmath608 & @xmath609 + @xmath610 & @xmath611 & @xmath612 & @xmath613 & @xmath614 & @xmath615 & @xmath596 & @xmath616 & @xmath617 & @xmath618 & @xmath619 + @xmath620 & @xmath621 & @xmath622 & @xmath623 & @xmath624 & @xmath615 & @xmath604 & @xmath625 & @xmath626 & @xmath627 & @xmath628 + @xmath629 & @xmath630 & @xmath631 & @xmath632 & @xmath633 & @xmath634 & @xmath635 & @xmath636 & @xmath624 & @xmath627 & @xmath637 + @xmath638 & @xmath639 & @xmath592 & @xmath640 & @xmath641 & @xmath642 & @xmath643 & @xmath644 & @xmath645 & @xmath646 & @xmath647

the new observations reveal a significant change in the radio evolution starting at month , with a brightening at all frequencies that requires an increase in the energy by about an order of magnitude , and an overall density profile around the smbh of ( pc ) with a significant flattening at pc . the increase in energy can not be explained with continuous injection from an tail , which is observed in the x - rays . . the radial density profile may be indicative of bondi accretion , with the inferred flattening at pc in good agreement with the bondi radius for a m black hole . , we predict that the radio emission from should be detectable with the evla for several decades , and will be resolvable with vlbi in a few years .

we present continued radio observations of the tidal disruption event swiftj164449.3 + 573451 extending to days after discovery . the data were obtained with the evla , ami large array , carma , the sma , and the vlba+effelsberg as part of a long - term program to monitor the expansion and energy scale of the relativistic outflow , and to trace the parsec - scale environment around a previously - dormant supermassive black hole ( smbh ) . the new observations reveal a significant change in the radio evolution starting at month , with a brightening at all frequencies that requires an increase in the energy by about an order of magnitude , and an overall density profile around the smbh of ( pc ) with a significant flattening at pc . the increase in energy can not be explained with continuous injection from an tail , which is observed in the x - rays . instead , we conclude that the relativistic jet was launched with a wide range of lorentz factors , obeying . the similar ratio of duration to dynamical timescale for and grbs suggests that this result may be applicable to grb jets as well . the radial density profile may be indicative of bondi accretion , with the inferred flattening at pc in good agreement with the bondi radius for a m black hole . the density at pc is about a factor of 30 times lower than inferred for the milky way galactic center , potentially due to a smaller number of mass - shedding massive stars . from our latest observations ( d ) we find that the jet energy is erg ( erg for ) , the radius is pc , the lorentz factor is , the ambient density is , and the projected angular size isas , below the resolution of the vlba+effelsberg . assuming no future changes in the observed evolution and a final integrated total energy of erg , we predict that the radio emission from should be detectable with the evla for several decades , and will be resolvable with vlbi in a few years .

cond-mat0507131

i

magnetic neutron scattering ( mns ) in high temperature superconducting cuprates usually detects about @xmath1 of the spectral weight dictated by a naive application of sum rules . for example the total weight in a wide range of energy and momentum in a recent experiment@xcite in la@xmath2ba@xmath3cuo@xmath4 , with @xmath5 , is @xmath6 whereas in the insulating phase the naive expectation from sum rules is that one should find @xmath7 . it is usually argued that this value should be corrected for the hole destruction of moments by a @xmath8 factor which still leaves a large fraction of spectral weight undetected . this rises various problems in the interpretation of mns . for example it has been argued that the average of the dynamical susceptibility weighted by the fourier transform of the magnetic interaction can be used to estimate the energy involved in magnetic pairing and its temperature dependence.@xcite clearly to obtain an absolute estimate the spectral weight problem needs to be sorted out first . furthermore modeling the dynamical structure factor probed by mns becomes rather problematic since sensible theoretical models do satisfy sum rules . indeed any theoretical claim of intensity agreement with the measured dynamical structure factor in absolute units needs to explain how the sum rule is satisfied or why it is violated . this is even more stringent in spin only models for which neither @xmath8 factors nor shielding corrections apply . the purpose of this work is to explain this apparent discrepancy . we provide theoretical estimates of the various factors which correct the sum rule and estimate what fraction of the spectral weight is accessible to present day experimental conditions . theoretical estimates are performed in the antiferromagnetic ( afm ) phase using the heisenberg and the hubbard model combining spin - wave theory , numerical results and the time dependent gutzwiller approximation ( tdga)@xcite and in the doped phase in the hubbard model within the tdga . apart from the mentioned @xmath8 factor we discuss the so called `` shielding factors '' due to an incomplete formation of magnetic moments . we estimate the spectral weight loss to electronic transitions at energies too high to be detectable by present day inelastic magnetic neutron scattering experiments and also the weight in multimagnon processes which is either at too high energies or is so broad in energy and momentum that it is not detectable in unpolarized neutron scattering experiments . after consideration of all these factors we arrive to the conclusion that within the experimental uncertainties the sum rule is not violated ( which is reassuring ) on the other hand a major fraction of the spectral weight is very hard to detect with present experimental conditions . the outline of the paper is at follows . in sec . [ mns ] we shortly review the theory of magnetic neutron scattering and the relevant sum rules to fix notations . this section has also a pedagogical character . apart from the well known total moment sum rule we discuss sum rules for each component of the dynamical structure factor tensor which , to the best of our knowledge , have not been applied in the present context . we also highlight some simple experimental facts that are usually assumed as granted in experimental works , like domain averages ( sec . [ da ] ) , but often overlooked in theoretical works . in sec . [ hf ] we discuss the spectral weight distribution in the undoped case and in sec . [ ahf ] we discuss the doped case . we conclude in sec .

we present estimates in the hubbard and heisenberg models for the spectral weight in magnetic neutron scattering experiments on the cuprates . with the aid of spin - wave theory and the time dependent gutzwiller approximation in addition to the well known total moment sum rule we discuss sum rules for each component of the dynamical structure factor tensor which are peculiar for spin 1/2 systems . the various factors that reduce the spectral weight at the relevant energies are singled out and analyzed like : shielding factors , weight at electronic energies , multimagnon process etc . although about 10% 15% of the naively expected weight is detected in experiments after consideration of these factors the missing weight is within the experimental uncertainties . a large fraction of the spectral weight is hard to detect with present experimental conditions .

we present estimates in the hubbard and heisenberg models for the spectral weight in magnetic neutron scattering experiments on the cuprates . with the aid of spin - wave theory and the time dependent gutzwiller approximation we discuss how the spectral weight is distributed among the different channels and between high and low energies . in addition to the well known total moment sum rule we discuss sum rules for each component of the dynamical structure factor tensor which are peculiar for spin 1/2 systems . the various factors that reduce the spectral weight at the relevant energies are singled out and analyzed like : shielding factors , weight at electronic energies , multimagnon process etc . although about 10% 15% of the naively expected weight is detected in experiments after consideration of these factors the missing weight is within the experimental uncertainties . a large fraction of the spectral weight is hard to detect with present experimental conditions .

1202.1829

i

bright submillimeter - selected galaxies ( smgs * ? ? ? * ) provide a powerful probe into the distant universe . thanks to the negative @xmath5-correction in the rayleigh - jeans tail of the dust thermal emission , flux limited submillimeter surveys with 850 @xmath2 m flux density @xmath18 mjy reach an almost uniform integrated infrared ( ir ) luminosity limit across a wide redshift range ( @xmath19 ) and yield a galaxy population mostly at redshifts between @xmath20 @xcite . with star formation rates ( sfrs ) of @xmath21 @xmath22 yr@xmath13 , the smgs are the most intense star - forming galaxies , despite their inevitably short - lived nature ( lifetime @xmath23 0.1 gyr ) . although such intense starburst systems are extremely rare in the local universe , smgs and the lyman break galaxies may contribute equally to the comoving sfr density at @xmath24 @xcite . in addition to their unique energetics , they also represent an important stage in massive galaxy formation . multiple lines of evidence suggest that smgs are likely the progenitors of massive elliptical galaxies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , which apparently have formed bulk of their stars rapidly at an early epoch ( e.g. , * ? ? ? our understanding of this important high - redshift galaxy population are limited by the sensitivity and spatial resolution of current facilities . gravitational lensing offers an elegant solution by effectively lifting both limiting factors . also thanks to the negative @xmath5-correction , it is relatively straightforward to identify strongly lensed smgs in large area submillimeter surveys . @xcite and @xcite predict that extragalactic sources with 500 @xmath2 m flux density @xmath25 mjy are mostly strongly lensed or blended smgs , nearby late - type galaxies , and radio active galactic nuclei ( agns ) . as demonstrated by @xcite , objects in the last two categories can be easily removed using data at other wavelengths , leading to an extremely high success rate in identifying strongly lensed smgs with this technique ( see also @xcite ) . this simple flux selection has produced a few well - studied strongly lensed smgs ( lockman01 @xmath26 : @xcite ; id141 @xmath27 : @xcite ; hls j091828.6@xmath28514223 @xmath29 : @xcite ; and hatlas12@xmath100 @xmath30 , the subject of this paper ) , all of which were discovered by the _ space observatory @xcite . more complex selection processes have been proposed ( e.g. , * ? ? ? * ) , which would allow selecting hundreds of fainter lensed galaxies with _ the brightest of the lensed smgs might also be detected by the _ planck _ mission @xcite . with @xmath34 resolutions , such sources are probably blended with fainter sources even in the highest frequency / resolution channels of _ planck _ ( 545 and 857 ghz , or 550 and 350 @xmath2 m ) . the phase - i 130 deg@xmath4 of the _ herschel_-astrophysical terahertz large area survey ( h - atlas ; * ? ? ? * ) covers 28 _ planck _ sources in the _ planck _ early release compact source catalog ( ercsc ; * ? ? ? @xcite find that sixteen of them are high galactic latitude cirrus , ten are low - redshift galaxies , and one is resolved into two similarly bright nearby spirals ( ngc 3719 and 3720 ) . only one _ planck _ source is dominated by high - redshift galaxies : plckerc857 g270.59 + 58.52 ( @xmath31 jy , @xmath32 jy ) . with 18 , 25 , and 36 angular resolutions at 250 , 350 and 500 @xmath2 m , respectively , _ herschel _ detect 16 objects within a 4.23 radius of the _ planck _ position ( _ planck _ has a full - width - half - maximum [ fwhm ] resolution of 4.23 at 857ghz ) . there are 15 faint ( @xmath33 mjy ) sources surrounding an unusually bright source ( hatlas j114637.9@xmath1001132 , hereafter hatlas12@xmath100 ; @xmath34 mjy ) . taking into account the differences in the beam size and the filter transmission , the _ herschel _ sources account for only @xmath328% and @xmath324% of the _ planck _ flux densities at 545 and 857 ghz , respectively , suggesting that the _ planck _ measurements are boosted because of either positive noise spikes ( i.e. , eddington bias ; * ? ? ? * ) or blending with an over - density of sources that are below the confusion limit of _ herschel _ @xcite . the reader is referred to @xcite for a detailed _ planck_-_herschel _ comparison . hatlas12@xmath100 peaks at 350 @xmath2 m in flux density ( `` 350 @xmath2 m peaker '' ) , implying a high photometric redshift given typical dust temperatures . subsequent detections of multiple carbon - monoxide ( co ) lines from this unusually bright object determined a redshift of @xmath35 ( zspectrometer , carma , z - spec ; * ? ? ? * van der werf et al . in prep ; riechers et al . in prep ) . the high 500 @xmath2 m flux density ( @xmath36 mjy ) , in combination with the confirmed high redshift , makes hatlas12@xmath100 an excellent strong lens candidate . it is also the only strongly lensed smg candidate associated with a _ detection in the entire 130 deg@xmath4 h - atlas phase - i region . although the _ planck _ detection is partly due to spurious factors ( i.e. , eddington bias and/or blending ) , the confirmation of the lensed nature of the dominating source demonstrates that _ planck _ can efficiently identify the brightest lensed smgs once galactic cirrus and low - redshift galaxies are removed . in this paper we present a detailed multi - wavelength analysis of this _ planck_-associated smg . we describe our high - resolution keck adaptive optics imaging , submillimeter array ( sma ) and jansky very large array ( jvla ) interferometric observations , and the panchromatic photometry in [ sec : obs ] . we then perform a joint strong lens modeling at rest - frame 0.5 @xmath2 m , 200 @xmath2 m , and co(1@xmath60 ) in [ sec : model ] . in [ sec : sed ] we derive the intrinsic physical properties of the smg from its spectral energy distribution ( sed ) . we conclude by discussing the physical properties of hatlas12@xmath100 in the context of unlensed @xmath17 smgs ( [ sec : summary ] ) . throughout we adopt a @xmath37cdm cosmology with @xmath38 , @xmath39 and @xmath40 = 70 km s@xmath13 mpc@xmath13 .

hatlas j114637.9 is selected from the _ herschel_-astrophysical terahertz large area survey ( h - atlas ) as a strong lens candidate mainly based on its unusually high 500 m flux density ( mjy ) . it is the only high - redshift _ planck _ detection in the 130 deg h - atlas phase - i area . keck adaptive optics images reveal a quadruply imaged galaxy in the-band while the submillimeter array and the jansky very large array show doubly imaged 880 m and co(1 ) sources , indicating differentiated distributions of the various components in the galaxy . in the source plane ,

we present high - resolution maps of stars , dust , and molecular gas in a strongly lensed submillimeter galaxy ( smg ) at . hatlas j114637.9 is selected from the _ herschel_-astrophysical terahertz large area survey ( h - atlas ) as a strong lens candidate mainly based on its unusually high 500 m flux density ( mjy ) . it is the only high - redshift _ planck _ detection in the 130 deg h - atlas phase - i area . keck adaptive optics images reveal a quadruply imaged galaxy in the-band while the submillimeter array and the jansky very large array show doubly imaged 880 m and co(1 ) sources , indicating differentiated distributions of the various components in the galaxy . in the source plane , the stars reside in three major kpc - scale clumps extended over.6 kpc , the dust in a compact ( kpc ) region kpc north of the stars , and the cold molecular gas in an extended ( kpc ) disk kpc northeast of the stars . the emission from the stars , dust , and gas are magnified by , , and times , respectively , by four lensing galaxies at . intrinsically , the lensed galaxy is a warm ( k ) , hyper - luminous ( ; sfr yr ) , gas - rich ( ) , young ( myr ) , and short - lived ( myr ) starburst . with physical properties similar to unlensed smgs , hatlas j114637.9 offers a detailed view of a typical smg through a powerful cosmic microscope .

1202.1829

c

we have presented high - resolution @xmath5-band , 880 @xmath2 m , and co(1@xmath60 ) observations and the near - ir - to - centimeter sed of a _ herschel_-selected strongly lensed smg at @xmath279 ( hatlas12@xmath100 ) . the smg shows distinctly different morphologies in the three images , suggesting differential magnification due to stratified morphologies . a joint strong lens modeling shows that the smg is lensed by four galaxies at @xmath7 and the luminosity - weighted magnification factors are @xmath168 in @xmath5 , @xmath170 at 880 @xmath2 m , and @xmath172 at co(1@xmath60 ) . in the source plane , the smg consists of several stellar clumps extended over @xmath31.6 kpc with @xmath236\times10^{10}$ ] @xmath12 of stars , a compact ( @xmath31 kpc ) starburst enshrouded by @xmath244\times10 ^ 8 $ ] of dust at @xmath360k , and an extended ( @xmath36 kpc ) cold molecular gas reservoir with @xmath263\times10^{10}$ ] @xmath12 of gas . the starburst and its gas reservoir are located @xmath34 kpc from the stars . similar separations between optical and submillimeter / radio emission have been observed in unlensed high - redshift dusty starbursts ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? . however , these previous results could also be attributed to astrometry offsets across different facilities ; @xcite might be the only exception , whose tied the astrometry of the images to larger radio and optical fields . in hatlas12@xmath100 , the physical separations amongst stars , dust , and gas are less ambiguous because of the clear wavelength - dependent morphologies in the image plane : fortuitously , the stars and dust / gas straddle across the caustic , so the less obscured @xmath5-band region is quadruply imaged while the heavily obscured starburst and its gas reservoir are doubly imaged . because of the @xmath34 kpc separation between the stars and the gas - rich starburst and their similar masses , it is tempting to suggest that the smg is in the process of a major merger , which presumably is driving the starburst activity in @xmath17 smgs ( e.g. , * ? ? ? * ; * ? ? ? however , spatial separation of this scale can also be explained by differential dust obscuration in a single galaxy , as has been proposed for other high - redshift smgs where spatial offsets have been observed between rest - frame uv and submillimeter ( e.g. , gn20 and aztec 3 ; * ? ? ? * ; * ? ? ? differential magnification may affect the observed far - ir sed as well as the co ladder , as hotter dust and higher-@xmath42 co lines may have more compact morphologies @xcite . however , because the magnification map is smooth in the area , the six times difference in the sizes of the co(1@xmath60 ) and the dust emitting region only lead to a @xmath310% difference in magnification , which is smaller than the 1@xmath46 errors of our estimates of the magnification factors . therefore , differential magnification is unlikely to be significant enough to affect the far - ir sed and future co ladder measurements in hatlas12@xmath100 . how does the massive gaseous disk compare with the disks in other smgs ? we estimate an dynamical mass of @xmath265\times10^{11}$]@xmath12 and a gas fraction of @xmath308% for the co(1@xmath60 ) disk using the `` isotropic virial estimator '' ( e.g. , * ? ? ? * ) : @xmath309 where @xmath310 is the co line fwhm in km s@xmath13 and @xmath311 is half of the fwhm size of the disk in kpc . combined with the fwhm disk radius , we further estimate a gas surface density of @xmath312 @xmath12 pc@xmath313 . both @xmath314 and @xmath315 are similar to those of the extended co(1@xmath60 ) disks in the two @xmath316 smgs in @xcite . but both values are significantly smaller than those of the kinematically resolved co(6@xmath65 ) disk of the `` cosmic eyelash '' ( @xmath317 , @xmath318@xmath12pc@xmath313 ; * ? ? ? * ) . the discrepancies illustrate the limitations of these widely used but crude estimators _ and/or _ that high excitation co lines probe more compact and denser regions in a disk . higher resolution observations are clearly needed to resolve this issue . without spatially resolved gas kinematics , we refrain from estimating the disk stability parameter of @xcite . hatlas12@xmath100 is a gas - rich , initial starburst system similar to unlensed smgs and local ulirgs . its intrinsic ir luminosity well exceeds @xmath319 @xmath10 ( i.e. , hy - lirg ) , implying an enormous rate of star formation ( @xmath251 @xmath12 yr@xmath13 ) . although the molecular gas reservoir is massive and it constitutes @xmath267% of the _ visible _ baryonic mass ( @xmath320 ) and @xmath269% of the dynamical mass , it will exhaust in just @xmath321 myr at the current sfr ( assuming no gas accretion ) . the star formation timescale , @xmath322/sfr = @xmath323 myr , is only @xmath31% of the cosmic age at @xmath279 ( @xmath324 gyr ) , suggesting that hatlas12@xmath100 is an initial starburst system with maturity @xmath325 @xcite . the specific sfr , ssfr = sfr/@xmath225 = @xmath326 gyr@xmath13 , is consistent with the average @xmath17 smgs , but it is an order of magnitude higher than the median value of the star - forming main sequence of lyman break galaxies at the same epoch @xcite . we can also estimate the star formation efficiency : @xmath327 , where @xmath328 is the dynamical or free - fall timescale . for @xmath329 = 3 kpc and @xmath330 , we obtain @xmath331 , or [ 11@xmath3324]% per dynamical timescale , which is comparable to unlensed smgs but is an order of magnitude higher than normal starforming galaxies @xcite . the dust mass of @xmath244\times10^{8}$ ] @xmath12 is similar to the average dust mass of unlensed smgs ( e.g. , * ? ? ? * ) , and the gas - to - dust ratio , @xmath333/0.07 m@xmath4 kg@xmath334/0.8 ) , is comparable to that of the milky way . assuming that the dust emission is indicative of the size of the starburst and a starburst disk radius of @xmath335 kpc , the star formation surface density of @xmath336 @xmath234 kpc@xmath313 approaches the eddington limit of radiation pressure supported starburst disks ( @xmath337 @xmath234 kpc@xmath313 ; * * ; * ? ? ? * ) , similar to local ulirgs such as arp 220 and the host galaxy of the @xmath338 quasar sdss j114816.64 + 525150.3 @xcite . in conclusion , hatlas12@xmath100 is a _ bona fide _ smg with an intrinsic submillimeter flux density of @xmath339 mjy . the starburst disk , where most of the molecular gas and dust reside , is spatially separated from the less obscured stellar population by @xmath34 kpc , suggesting either a major merger or differentiated dust obscuration . the @xmath31 kpc radius starburst disk is presumably supported in large by radiation pressure on the dust grains . its physical properties , such as molecular gas mass , stellar mass , gas - to - dust ratio , gas fraction , sfr , star formation efficiency , and radio - to - far - ir luminosity ratio , are all very similar to unlensed @xmath17 smgs @xcite . the lensing boost of the effective angular resolution and sensitivity has allowed us to examine in unprecedented details the properties of a typical starburst galaxy when the universe is only 1/7 of its current age . hatlas12@xmath100 provides a prelude to a golden age of smg research , as _ herschel _ is unveiling hundreds of strongly lensed smgs before the mission completes ( e.g. , * ? ? ? * wardlow et al . in prep ) . we thank the anonymous referee for comments that helped improve the paper . hf , ac , jlw and sk acknowledge support from nsf career ast-0645427 . ipf is supported by the spanish grants esp2007 - 65812-c02 - 02 and aya2010 - 21697-c05 - 04 . sgd acknowledges a partial support from the nsf grant ast-0909182 . gdz and mn acknowledge support from asi / inaf agreement i/072/09/0 ( `` _ _ planck _ _ lfi activity of phase e2 '' ) and from miur through the prin 2009 . some of the data presented herein were obtained at the w.m . keck observatory , which is operated as a scientific partnership among the california institute of technology , the university of california and the national aeronautics and space administration . the observatory was made possible by the generous financial support of the w.m . keck foundation . the authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of mauna kea has always had within the indigenous hawaiian community . we are most fortunate to have the opportunity to conduct observations from this mountain . herschel_-atlas is a project with _ herschel _ , which is an esa space observatory with science instruments provided by european - led principal investigator consortia and with important participation from nasa . the h - atlas website is http://www.h - atlas.org/. the us participants acknowledge support from the nasa _ herschel_science center / jpl . partly based on observations obtained with _ planck _ ( http://www.esa.int/planck ) , an esa science mission with instruments and contributions directly funded by esa member states , nasa , and canada . support for carma construction was derived from the gordon and betty moore foundation , the kenneth t. and eileen l. norris foundation , the james s. mcdonnell foundation , the associates of the california institute of technology , the university of chicago , the states of california , illinois , and maryland , and the national science foundation . ongoing carma development and operations are supported by the national science foundation under a cooperative agreement , and by the carma partner universities .

the emission from the stars , dust , and gas are magnified by , , and times , respectively , by four lensing galaxies at . intrinsically , the lensed galaxy is a warm ( k ) , hyper - luminous ( ; sfr yr ) , gas - rich ( ) , young ( myr ) , and short - lived ( myr ) starburst . with physical properties similar to unlensed smgs , hatlas j114637.9 offers a detailed view of a typical smg through a powerful cosmic microscope .

we present high - resolution maps of stars , dust , and molecular gas in a strongly lensed submillimeter galaxy ( smg ) at . hatlas j114637.9 is selected from the _ herschel_-astrophysical terahertz large area survey ( h - atlas ) as a strong lens candidate mainly based on its unusually high 500 m flux density ( mjy ) . it is the only high - redshift _ planck _ detection in the 130 deg h - atlas phase - i area . keck adaptive optics images reveal a quadruply imaged galaxy in the-band while the submillimeter array and the jansky very large array show doubly imaged 880 m and co(1 ) sources , indicating differentiated distributions of the various components in the galaxy . in the source plane , the stars reside in three major kpc - scale clumps extended over.6 kpc , the dust in a compact ( kpc ) region kpc north of the stars , and the cold molecular gas in an extended ( kpc ) disk kpc northeast of the stars . the emission from the stars , dust , and gas are magnified by , , and times , respectively , by four lensing galaxies at . intrinsically , the lensed galaxy is a warm ( k ) , hyper - luminous ( ; sfr yr ) , gas - rich ( ) , young ( myr ) , and short - lived ( myr ) starburst . with physical properties similar to unlensed smgs , hatlas j114637.9 offers a detailed view of a typical smg through a powerful cosmic microscope .

astro-ph0603044

i

mapping the cosmic microwave background ( cmb ) polarization is one of the major challenges of future missions of observational cosmology . cmb polarization is linear and therefore can be described by the first three stokes parameters i , q and u which are generally combined to produce three fields ( modes ) , @xmath0 , @xmath1 and @xmath2 @xcite . the polarization of the cmb photons carries extra physical informations that are not accessible by the study of the temperature anisotropies . therefore its measurement helps breaking down the degeneracies on cosmological parameters as encounter with temperature anisotropies measurements only @xcite . furthermore , the study of the cmb polarization is also a fundamental tool to estimate the energy scale of inflation which has been proposed to solve the problems of flatness , of isotropy and of the seed perturbations for the formation of the structures in the universe . inflationary models predict the presence of tensor perturbations of the metric which will lead to an unique signature in the cmb polarization @xmath2 modes . the detection of the latter would be a strong proof of such an epoch and also a way to constrain the energy scale at which inflation occurs by measuring the tensor to scalar ratio , @xmath9 @xcite . since the beginning of the cmb anisotropies observations with the cosmic background explorer ( cobe ) @xcite , a great amount of experiments have been designed to determine the cmb temperature angular power spectrum @xcite . by contrast , the polarization anisotropies , which are between 2 and 5 orders of magnitude weaker than temperature ones are not accurately measured yet . a first detection of the cmb @xmath1 modes has been performed by dasi @xcite , capmap @xcite , cbi @xcite and more recently by boomerang @xcite and wmap @xcite . the @xmath6 temperature - polarization cross correlation has been measured by wmap @xcite and boomerang @xcite . no detection of the cmb @xmath2 modes has been reported yet . nevertheless , constraints on the tensor to scalar ratio , @xmath9 , have been set by the wmap team . they set an upper limit of @xmath10 ( 95% cl ) @xcite for the temperature and polarization analysis and of @xmath11 ( 95@xmath12 cl ) @xcite for a polarization - only analysis . the detection of such low signals is possible by improving the instrumental sensitivity , but this is not the only issue in the determination of the cmb polarization power spectra . other astrophysical emissions as for example the diffuse galactic emission including free - free , dust and synchrotron and the extragalactic - sources emissions also contribute to the sky brightness at the frequencies of interest for cmb studies , and therefore must be efficiently subtracted . these _ foregrounds _ are particularly important for the study of the cmb polarization . excluding the free - free emission which is not polarized , the other contributions are expected to be significantly polarized with similar power on the @xmath1 and @xmath2 modes . recent measurements of the galactic synchrotron polarization emission at 1.41 ghz @xcite and at 23 ghz by wmap @xcite show this emission is significantly polarized at large angular scales . further , archeops measurements at 353 ghz show that the galactic dust diffuse emission is polarized up to a level of 5 to 10 % both in the galactic center @xcite and at high galactic latitudes @xcite . finally , for the polarization of extragalactic point sources the sparsity of the data available makes reliable predictions difficult @xcite . a direct subtraction of these foreground contributions on the cmb data will require an accurate knowledge of their spatial distributions and of the electromagnetic spectra of their anisotropies . for the synchrotron emission a full sky map at 408 mhz in temperature is available @xcite and more recently the wmap team provided a map at 30 ghz from the mem decomposition of the first year observations @xcite . a fake polarized synchrotron emission template was constructed by @xcite based on the parkes 2400 mhz @xcite and haslam 408 mhz @xcite surveys . furthermore , the electromagnetic spectrum of synchrotron anisotropies and its spatial distribution are neither accurately known in temperature nor polarization although a first estimate was produced by @xcite . recently , the 23 ghz polarized wmap data is used as a tracer of the synchrotron polarization @xcite . for the thermal dust emission a full sky map at 100 @xmath13 m as well as templates for cmb use were extracted from the iras and firas data @xcite . no realistic template exists for the dust polarized emission , although a fake one , based on the polarization angles measured at 23 ghz has been constructed by the planck collaborationbernard / psm/ ] . the dust emission in temperature can be approximated by a grey body spectrum of mean temperature 17 k and emissivity between 1.7 and 2.2 @xcite . currently no measurement on the electromagnetic spectrum of the dust polarized emission is available although it is expected to be the same that for temperature @xcite . to try to overcome the above limitations , a great amount of work has been dedicated to design and implement algorithms for component separation which can discriminate between cmb and foregrounds . these methods can also extract , directly from the cmb data , the emission properties of foregrounds . wiener filtering has been successfully tested assuming known gaussian priors for each component and with the electromagnetic spectrum of the anisotropies as an input @xcite . maximum entropy based methods ( mem ) , assuming entropic priors for the spatial distribution of each of the component , have been intensively used for small sky patches @xcite and extended to full sky analysis @xcite . they were adapted to account for spatial anisotropies in the electromagnetic spectra @xcite . more recently , @xcite has developed a new method to perform cmb component separation by parameter estimation and applied it to temperature simulations of the planck satellite experiments . independent component analysis ( ica ) techniques have also been applied to planck simulations in temperature @xcite and extended to polarization @xcite using the fastica algorithm . these methods require no prior on the spectral or spatial distribution of the components but can not make use of the available physical knowledge on the foreground and cmb emissions . in addition , the spectral matching independent component analysis ( smica ) @xcite has been developed to consider both the fully blind analysis for which no prior is assumed and the semi - blind analysis incorporating previous physical knowledge on the astrophysical components . this algorithm , based on the expectation - maximization algorithm ( em ) @xcite , uses the spectral diversity of the components and was developed for temperature only . we present in this paper , polemica ( polarized expectation - maximization independent component analysis ) , an extension of this method to polarization including both the blind and semi - blind analysis . this paper is organized as follows . a simple model of the microwave sky emission in temperature and polarization is described in section [ simus ] . section [ mdmc ] presents the polemica multi - detectors multi - components ( md - mc ) blind component separation algorithm . section [ simus_list ] describe the simulations of the planck satellite experiment used for testing the algorithm . we present in section [ testing ] the application of polemica to the planck simulations with a _ simplified _ model to test the algorithm s performances . finally , in section [ realistic_model ] , we apply our algorithm to more _ realistic _ planck simulations and discuss the separability problem in this case . we summarize and conclude in section [ conclusions ] .

gaussian _ dust emission . finally , we have applied our algorithm to more _ realistic _ planck full sky simulations , including synchrotron , _ realistic _ dust and free - free emissions . cosmic microwave background cosmology : observations methods : data analysis

we present in this paper the polemica ( polarized expectation - maximization independent component analysis ) algorithm which is an extension to polarization of the smica ( spectral matching independent component analysis ) temperature multi - detectors multi - components ( md - mc ) component separation method . this algorithm allows us to estimate blindly in harmonic space multiple physical components from multi - detectors polarized sky maps . assuming a linear noisy mixture of components we are able to reconstruct jointly the anisotropies electromagnetic spectra of the components for each mode , and , as well as the temperature and polarization spatial power spectra , , , , , and for each of the physical components and for the noise on each of the detectors . polemica is specially developed to estimate the cmb temperature and polarization power spectra from sky observations including both cmb and foreground emissions . this has been tested intensively using as a first approach full sky simulations of the planck satellite polarized channels for a 14-months nominal mission assuming a _ simplified _ linear sky model including cmb , and optionally galactic synchrotron emission and a _ gaussian _ dust emission . finally , we have applied our algorithm to more _ realistic _ planck full sky simulations , including synchrotron , _ realistic _ dust and free - free emissions . cosmic microwave background cosmology : observations methods : data analysis

astro-ph0603044

i

we present in this paper the polemica algorithm which is an extension to polarization of the smica temperature md - mc blind component separation method developed by @xcite . both algorithms work in harmonic space and are based on the spectral matching of the data to a noisy linear mixture of uncorrelated physical components using the em algorithm to maximize the likelihood function . by contrast to the temperature data which are described by a single scalar quantity @xmath0 , the combined temperature and polarization data are described in harmonic space by three correlated scalar quantities @xmath0 , @xmath1 and @xmath2 corresponding to the @xmath17 , @xmath18 and @xmath19 stokes parameters in real space . we have developed a new formalism to jointly deal with the 6 resulting auto and cross angular power spectra , @xmath3 , @xmath4 , @xmath5 , @xmath6 , @xmath7 and @xmath8 . using this formalism we have constructed the likelihood function and proved that the em algorithm can be also applied to polarization data . under the assumption of uncorrelated gaussian distributed components and noise , the free parameters in the fit are the mixing matrix describing the electromagnetic spectrum of the physical components for @xmath0 , @xmath1 and @xmath2 , the temperature and polarization angular power spectra of the physical components and the temperature and polarization noise power spectra for each of the detectors . + we have , as a first approach , intensively and successfully tested the polemica method on simulations of the planck satellite experiment considering a 14-months nominal mission and no systematic effects . for these tests , we suppose a _ simplified _ linear model for the sky emission including cmb , synchrotron with constant spectral index and _ simplified_-dust ( gaussian realization ) emissions . we construct full sky maps for all the polarized channels from 30 to 353 ghz including at least one of the above physical components and considering white noise and infinite resolution . the method permits blind separation on these simulations allowing us to reconstruct the noise and physical component s temperature and polarization power spectra as well as the mixing matrix when we consider equal electromagnetic spectrum in @xmath0 , @xmath1 and @xmath2 . when we relax this hypothesis the reconstruction of the electromagnetic spectrum for the cmb @xmath2 modes is significantly degraded as could be expected because of the low signal to noise ratio . these results indicate that the polemica method allows us to both constrain the electromagnetic spectrum of the physical components and also to inter - calibrate the data based on the reconstructed cmb electromagnetic spectrum . + after setting the general performances of the algorithm , we have performed the separation on a more _ realistic _ model that includes _ realistic_-dust , synchrotron and free - free components in section [ realistic_model ] . we have encountered in this case a separability problem , that mixes up components and prevents the algorithm to converge , when performing _ blind _ separations . we have shown that this is due to spatial correlations between galactic components in temperature . thus , when working on sets of @xmath18 and @xmath19 maps and maximizing the likelihood for @xmath4 , @xmath5 and @xmath8 modes only , this separability problem does not occur and _ cmb semi - blind _ and _ blind _ separations are possible . for this _ polarization - only _ case , we have shown that considering our _ realistic _ sky model and our algorithm , in the planck case , we have no need to put priors on the galactic components electromagnetic spectra to reconstruct the cmb polarized power spectra . nevertheless , adding priors on the cmb electromagnetic spectrum helps to perform a more accurate separation . finally , real experiments present finite resolution , partial effective sky coverage , systematic effects and , often , correlated noise . all these issues must be dealt with by the component separation algorithms and will with no doubt significantly limit the precision to which the cmb signal may be reconstructed . polemica , as it was already the case for smica , can account for beam and filtering smoothing . systematic effects and correlated noise can be modeled as extra components in the data for which the spectral dependence can be estimated in a _ blind _ analysis . moreover , the strong spatial correlation in temperature between galactic physical emissions : dust , synchrotron and free - free , is a major problem for blind component separation algorithms which generally assumed uncorrelated components . although not observed yet , we can also imagine spatial correlation of the galactic emissions in polarization . work is in progress to adapt the polemica algorithm to the case of correlated components . in addition , foreground emissions have in general spatially varying electromagnetic spectra far beyond the simple linear model presented here . work is also in progress to adapt polemica to the case of foregrounds with spatially varying electromagnetic spectrum .

we present in this paper the polemica ( polarized expectation - maximization independent component analysis ) algorithm which is an extension to polarization of the smica ( spectral matching independent component analysis ) temperature multi - detectors multi - components ( md - mc ) component separation method . this algorithm allows us to estimate blindly in harmonic space multiple physical components from multi - detectors polarized sky maps . assuming a linear noisy mixture of components we are able to reconstruct jointly the anisotropies electromagnetic spectra of the components for each mode , and , as well as the temperature and polarization spatial power spectra , , , , , and for each of the physical components and for the noise on each of the detectors . this has been tested intensively using as a first approach full sky simulations of the planck satellite polarized channels for a 14-months nominal mission assuming a _ simplified _ linear sky model including cmb , and optionally galactic synchrotron emission and a _

we present in this paper the polemica ( polarized expectation - maximization independent component analysis ) algorithm which is an extension to polarization of the smica ( spectral matching independent component analysis ) temperature multi - detectors multi - components ( md - mc ) component separation method . this algorithm allows us to estimate blindly in harmonic space multiple physical components from multi - detectors polarized sky maps . assuming a linear noisy mixture of components we are able to reconstruct jointly the anisotropies electromagnetic spectra of the components for each mode , and , as well as the temperature and polarization spatial power spectra , , , , , and for each of the physical components and for the noise on each of the detectors . polemica is specially developed to estimate the cmb temperature and polarization power spectra from sky observations including both cmb and foreground emissions . this has been tested intensively using as a first approach full sky simulations of the planck satellite polarized channels for a 14-months nominal mission assuming a _ simplified _ linear sky model including cmb , and optionally galactic synchrotron emission and a _ gaussian _ dust emission . finally , we have applied our algorithm to more _ realistic _ planck full sky simulations , including synchrotron , _ realistic _ dust and free - free emissions . cosmic microwave background cosmology : observations methods : data analysis

astro-ph0409053

i

this paper presents the 8th catalog of gamma - ray burst ( grb ) localizations obtained by arrival time analysis , or `` triangulation '' between the missions in the 3rd interplanetary network ( ipn ) , which began operations in 1990 and continues to operate today . two of these catalogs ( hurley et al . 1999a , b ) were supplements to the batse 3b and 4br burst catalogs ( meegan et al . 1996 ; paciesas et al . 1999 ) . the others involved bursts observed by numerous other spacecraft ( laros et al . 1997 , 1998 ; hurley et al . , 2000a , b , c ) . in this paper , we present ipn data on 211 _ untriggered bursts which occurred throughout the entire _ compton gamma - ray observatory ( cgro ) mission ( 1991 april through 2000 may ) . the batse data on these events , such as durations , fluxes , fluences , and coarse location information , appear in two catalogs , kommers et al . ( 2001 ) and stern et al . a final ipn supplement catalog , to the batse 5b catalog , is in preparation ( hurley et al . 2004 , briggs et al . , 2004 ) . _ _ the purpose of searching the batse data for untriggered events was mainly to extend the number - intensity ( log n - log s ) distribution to weaker bursts than those that could trigger the detector , and thus to gain more information on the burst distribution , particularly at the weak end . other objectives included the detection of bursts from known and unknown soft gamma repeaters , and very soft transients which could constitute a previously unknown phenomenon . ( one significant outcome of this effort was the detection of the bursting pulsar ) . the purpose of searching the ipn data for these events was to confirm as many of them as possible , reduce the sizes of their error circles , and validate the procedures used to identify these untriggered events .

( 2001 ) and stern et al . ( 2001 ) . ipn confirmations have been obtained by analyzing the data from 11 experiments . for any given burst observed by batse and one other distant spacecraft , arrival time analysis ( or `` triangulation '' ) results in an annulus of possible arrival directions we have been able to identify the probable origin of bursts as soft gamma repeaters . the vast majority of the ipn - detected events , however , are grbs , and the confirmation of them validates many of the procedures utilized to detect batse untriggered bursts .

we present interplanetary network ( ipn ) detection and localization information for 211 gamma - ray bursts ( grbs ) observed as untriggered events by the burst and transient source experiment ( batse ) , and published in catalogs by kommers et al . ( 2001 ) and stern et al . ( 2001 ) . ipn confirmations have been obtained by analyzing the data from 11 experiments . for any given burst observed by batse and one other distant spacecraft , arrival time analysis ( or `` triangulation '' ) results in an annulus of possible arrival directions whose half - width varies between 14 arcseconds and 5.6 degrees , depending on the intensity , time history , and arrival direction of the burst , as well as the distance between the spacecraft . this annulus generally intersects the batse error circle , resulting in a reduction of the area of up to a factor of 650 . when three widely separated spacecraft observed a burst , the result is an error box whose area is as much as 30000 times smaller than that of the batse error circle . because the ipn instruments are considerably less sensitive than batse , they generally did not detect the weakest untriggered bursts , but did detect the more intense ones which failed to trigger batse when the trigger was disabled . in a few cases , we have been able to identify the probable origin of bursts as soft gamma repeaters . the vast majority of the ipn - detected events , however , are grbs , and the confirmation of them validates many of the procedures utilized to detect batse untriggered bursts .

astro-ph0210132

r

in this subsection , we present the results of the numerical simulations for the angular images of uhecrs in a variety of conditions concerning strength and correlation length of the egmf and the limiting magnitudes of galaxies . we show the angular images for two energy range @xmath104 ev and above @xmath10 ev , about at which the gzk cutoff of the energy spectrum is predicted . for comparison , we also show the agasa events with the angular images . it is noted that the current agasa data set contains 49 events with energies of @xmath104 ev and 8 events above @xmath10 ev . the calculated angular images of uhecrs originating the galaxies more luminous than @xmath105 ( upper ) , @xmath106 ( middle ) , @xmath107 ( bottom ) for number ( left ) and luminosity ( right ) weighted sources in the case of @xmath108 are shown in figure [ fig5 ] for energy range @xmath104 ev . the agasa 49 events in this energy range are also shown as circles of radius proportional to their energies . spatial structure of the lsc is reflected by prominent high intensity region running north and south at @xmath109 for @xmath105 and @xmath106 . since the luminous galaxies which distribute outward than the faint ones make a substantial contribution in the case of luminosity weighted sources , the region of high intensity becomes to be less obvious in the case of @xmath105 . in other cases , there is no significant difference simply due to small variance of absolute magnitudes of the individual galaxy . we can see that the angular image becomes to be isotropic and show good correlation with agasa events as restricting sources to more luminous galaxies . such correlation of the agasa events with angular image of uhecrs is also pointed out in the case of galaxies with huge infrared luminosity @xcite . even for @xmath110 , there are high intensity regions around @xmath111 which do not correlate with the agasa events . however , if we select sources , which contribute to the currently observed cosmic ray flux , from our ors sample , these high intensity regions can be eliminated . an example in the case of @xmath112 is shown in figure [ fig21 ] as we explain later . figure [ fig6 ] shows the predicted angular image of uhecrs for @xmath113(1,1 ) ( upper ) , ( 1,10 ) ( middle ) , ( 10,1 ) ( bottom ) and @xmath105 ( left ) , @xmath107 ( right ) with energies of @xmath104 ev . the angular image is distorted for @xmath113(1,10 ) , ( 10,1 ) , and dependence on the correlation length is relatively weak because the deflection angle of uhecrs is proportional to @xmath114 . as we will show later , this distortion of the angular image is crucial for the small scale clustering . in figure [ fig7 ] , we show the angular image for @xmath108 ( upper ) , @xmath115 ( middle ) , @xmath116 ( bottom ) and @xmath105 ( left ) , @xmath107 ( right ) with the energy range @xmath117 ev . ( highest energy of the events observed by the agasa is @xmath118 ev . ) because protons with energies above @xmath10 ev must originate within about 50 mpc from us due to photopion production , only nearby galaxies are able to make a substantial contribution to the angular image so that the spatial structure of the lsc is clearly visible . there is no correlation for @xmath105 between the agasa events and the angular image of uhecrs . for @xmath110 , arrival distribution is relatively isotropic , but still has no correlation with the agasa events . as we conclude later , the agasa events above @xmath10 ev might be of different origin , if they are confirmed . we present in this subsection the results of the numerical simulations for the energy spectra of uhecrs . figure [ fig8 ] shows the energy spectrum in the case of @xmath119 ( upper ) , @xmath120 ( middle ) , @xmath121 ( bottom ) ng and @xmath110 for number weighted sources . they are normalized arbitrary , but with the same factors for all the values of the correlation length . the substantial deflection in the egmf results in a significant increase of the path length , then leading to a time delay exceeding the age of the universe or a decrease of energy below @xmath122 ev due to pair production for protons injected at sufficiently large distance , as easily seen in figure [ fig4 ] . thus , the stronger egmf make the gzk cutoff around @xmath10 ev less sharp or eliminate it in figure [ fig8 ] . when the correlation length of the egmf is small , protons can not be deflected effectively and thus its path length and equivalently energy loss is smaller than that for longer correlation length . this can also be seen in figure [ fig4 ] and figure [ fig8 ] . especially , effects of changing the correlation length are large at @xmath123 ev for @xmath124 ng and at @xmath125 ev for @xmath126 ng , where gyroradii of uhecrs are about @xmath72 mpc and thus deflection is strong enough for the diffusion approximation to become applicable in the case of @xmath127 and @xmath128 mpc . in order to determine normalization of the energy spectrum and quantify statistical significance of mean deviation between the fitted energy spectrum and the observed one , we introduce @xmath129 in the similar way as the two point correlation function explained in the previous section . this is defined by @xmath130 where @xmath131 is the energy spectrum observed by the agasa at @xmath132 , and @xmath99 is @xmath133 error at this energy bin . the origin of cosmic rays with energies below @xmath21 ev is also one of the major open questions in astro - particle physics . berezinsky et al.(2002 ) showed that predicted uhecrs flux from grbs fall short of the observed flux below @xmath21 ev assuming an injection spectrum @xmath20 , which is advocated in vietri ( 1995 ) and waxman ( 1995 ) , and also used in this study . however , there are another possible extra - galactic and galactic uhecr production sites , such as agns and young neutron stars @xcite . maximum energy of cosmic ray achieved by them may be lower than @xmath21 ev . in this case , these galactic and/or extra - galactic components may substantially contribute to the cosmic ray flux below @xmath21 ev . throughout the paper , we assume that these components bridge the gap between the observed flux and the predicted one of berezinsky et al.(2002 ) , and restrict ourselves to the energy spectrum only above @xmath21 ev . figure [ fig9 ] shows the energy spectrum normalized so as to minimize @xmath129 in the case of @xmath119 ( upper ) , @xmath120 ( middle ) , @xmath121 ( bottom ) ng and @xmath105 ( left ) , @xmath107 ( right ) for number weighted sources . we also show the significance values @xmath129 in this figure . the predicted energy spectrum for @xmath134 provide good fit to the agasa data , including the extension above @xmath10 ev . however , arrival distribution is significantly anisotropic and inconsistent with the agasa ( see the next subsection ) . in the case of @xmath135 , the energy spectrum can be well fitted with the agasa data below @xmath136 ev , but the gzk cutoff is predicted above @xmath136 ev due to the energy loss by photopion production in contrast to the agasa data . this is because luminous galaxies near the earth are less than dwarf galaxies ( see figure [ fig2 ] ) . although the energy spectrum extends beyond @xmath10 ev for the stronger egmf , it does not provide good fit with the agasa data at @xmath137 ev , where the current data have adequate statistics . consequently , @xmath129 for the stronger egmf is larger than that for @xmath119 ng as easily seen in figure [ fig9 ] . in the same way as figure [ fig9 ] , we show the energy spectra for luminosity weighted sources in figure [ fig10 ] . since contributions from the dwarf galaxies are suppressed in this case , the cutoff of the energy spectra for @xmath105 is predicted . for @xmath110 , the results are almost the same as number weighted ones . in this subsection , we show the results of statistics on the arrival directions of uhecrs . figure [ fig11 ] shows the predicted first harmonics for number weighted sources as a function of limiting magnitude . the error bars represent the statistical error due to the finite number of simulated events , whose number is set to be that observed by the agasa in the energy range of @xmath74 ev . arrival directions of uhecrs are restricted in the range @xmath103 in order to compare our results with the agasa data . the solid lines indicate the harmonic amplitude obtained by the agasa data . the shaded region is expected from the statistical fluctuation of isotropic source distribution with the chance probability larger than @xmath138 . clearly visible in figure [ fig11 ] is that the anisotropy is least for @xmath139 , which is caused by broadened distribution of luminous galaxies in the lsc . the amplitude at @xmath3 is consistent with isotropic source distribution within 1 @xmath16 level for all the @xmath140 . compared with the agasa data , a significant anisotropy can be seen for @xmath141 , although the energy spectra in these cases extend above @xmath10 ev as shown in the previous subsection . increase of the amplitude around @xmath142 is mainly due to two giant galaxies existing in the almost same direction @xmath143 in the vicinity of our galaxy ( at @xmath144 30 mpc ) . comparing the results of different strength of the egmf , we find that the anisotropy in the cases of 10 , 100 ng is larger than that of 1 ng below @xmath145 contrary to expectation . we note again that stronger egmf results in shorter cosmic ray horizon because of time delay and energy loss due to the substantial deflection in the egmf ( see figure [ fig4 ] ) . that is , spatial structure of nearby galaxies is strongly reflected in the large scale anisotropy for the strong egmf . above @xmath145 , since luminous galaxies distribute outward , the anisotropy in the cases of the strong egmf is smaller as expected . also , increase of correlation length results in more effective deflections , and then leads to smaller anisotropy in the case of 1 , 10 ng . however , this dependence is opposite for 100 ng , which is caused by a reason somewhat similar to that of slightly large anisotropy for the strong egmf below @xmath145 explained above . gyroradius of proton with energy @xmath9 ev in the egmf of 100 ng is 1 mpc , which is smaller than @xmath146 mpc . in this case , uhecr deflection is strong enough for the diffusion approximation to become applicable . thus , the cosmic ray horizon is extremely shorter than that for @xmath147 mpc , so that the anisotropy arise from nearby galaxies in the lsc . figure [ fig12 ] shows the predicted second harmonics for number weighted sources in the same manner as the first harmonics . dependence on the limiting magnitude is weaker than that of the first harmonics . there is no parameter set @xmath148 which is consistent with isotropic source distribution . we also calculated the first and second harmonics for luminosity weighted sources , and found that the anisotropy is slightly less than that of number weighted sources for @xmath149 because of small contributions from the dwarf galaxies , which concentrate in the lsc . for @xmath150 , the results are almost the same as number weighted sources . the two point correlation functions are shown for number weighted sources in the case of @xmath151 ( left panels ) and @xmath152 ( right panels ) in figure [ fig13 ] . the histograms represent the agasa data , which show the statistically significant correlation at the smallest angle scale @xmath153 . @xmath154 defined in the previous section is also shown . at larger angles @xmath155 , there are relatively strong correlation for @xmath151 , which is not consistent with the observed isotropic distribution , whereas arrival distributions for @xmath152 are sufficiently isotropic . among the cases of @xmath152 , noticeable feature is coexistence of a strong correlation at small angles and sufficiently isotropic distribution at larger scale for @xmath108 . this is a consequence of the sharp peak of the uhecr angular image in the case of @xmath108 ( see figure [ fig5 ] ) . this strong correlation at small angles is reduced or eliminated for longer correlation length or stronger egmf . due to small number of observed events , the statistics of the two point correlation function is limited . for this reason , @xmath154 for @xmath108 is equal to that for @xmath156 . however , if the future experiments like the pierre auger array @xcite confirm the small scale clustering of uhecr arrival directions with more event number , the case of @xmath108 will be favored with better significance . let us summarize the results of the three quantities ( energy spectrum , harmonic amplitude , two point correlation function ) . first , the energy spectrum for @xmath119 ng provide better fit to the agasa data than that for strong egmf in terms of @xmath129 . among this case , the extension of the energy spectrum is also reproduced for @xmath157 , although there is significant large scale anisotropy contrary to the agasa data in this case . in the case of @xmath158 , the gzk cutoff is predicted . second , the amplitude of the first harmonics is consistent with the agasa data at @xmath159 irrespective of @xmath140 . the amplitude of the second harmonics is not consistent with the agasa for any @xmath160 . finally , the two point correlation function for @xmath161 indicate coexistence of a strong correlation at small angles @xmath153 and sufficiently isotropic distribution at larger scale . in sum , the source model of @xmath161 seems to reproduce the observation better than another parameter sets . the amplitude of the second harmonics and the extension of the energy spectrum can not be explained in this source model . up to present , we have not explained the large scale isotropy quantified by the amplitude of the second harmonics and the small scale clustering except for @xmath108 , as well as the extension of the cosmic ray spectrum above @xmath10 ev . since we assumed that all the galaxies more luminous than a given limiting magnitude contribute to the cosmic ray flux , the number of sources is maximal and the fluctuations around the assumed non - isotropic distribution is minimal , which make the anisotropy most visible . furthermore , each source contribute at most one event in this case , it is difficult to obtain clusters which are likely to reflect the point - like sources . given this situation , we select some galaxies from our ors sample , and investigate dependence of the results on the number of selected galaxies . it is also expected that we can know the effect of fluctuation of source number within the gzk sphere on the energy spectrum above @xmath10 ev . as an example , this selection corresponds to restricting the sources of uhecrs to host galaxies of grbs , which contribute to the currently observed cosmic ray flux . we assumed that contributions to arrival distribution from sources outside 8000 km s@xmath53 from us , within which the ors is sampling the universe , is completely isotropic one . however , since we select only some galaxies in the following , point - like nature of sources has to be taken into account . thus , we distribute galaxies homogeneously in this region , and including them , we select some galaxies from our ors sample . we restrict ourselves to the limiting magnitude of @xmath112 and number weighted sources , which produce the most isotropic arrival distribution of uhecrs . it is noted that the number density of galaxies more luminous than @xmath112 in our ors sample is @xmath162 mpc@xmath7 . in figure [ fig14 ] , we show the amplitude of the first harmonics as a function of the number fraction ( nf ) of selected sources to all the ors galaxies more luminous than @xmath112 for all the @xmath140 . for each number fraction , we plot the average over all trial of source selection and realization from the simulated probability distribution with two error bars . the smaller is the statistical error due to the finite number of observed events , while the larger is both the statistical error and the cosmic variance , that is , variation between different selections of sources from our ors sample . in order to obtain the average and variance , we dial the simulated sets of events 100 times from probability distribution predicted by a specific source distribution , and the sets of sources 30 and 10 times from our ors sample for the number fraction of @xmath163 and @xmath164 respectively in the case of @xmath165 ng , but 30 times for all the number fractions in @xmath126 ng . we note that the number of sources , which contributes to the cosmic ray flux , for each set of @xmath140 differ from the others , even for the same number fraction , because of the different range of uhecrs ( see figure [ fig4 ] ) . for example , there is no source within 100 mpc for the number fraction of @xmath166 ( for the number density of @xmath167 mpc@xmath7 ) in the case of @xmath126 ng . as a general trend , anisotropy increases with decreasing the number fraction , because the arrival directions of uhecrs clumps to that of sources which is small in number . for large number fraction @xmath168 , the amplitudes approach to the values in the case that all galaxies more luminous than @xmath112 contribute to the observed cosmic ray flux , as they should . as clearly visible in figure [ fig4 ] , uhecrs can propagate the longest distance for @xmath108 , in which the deflection angle , and then the effective path length , is smallest among for another parameters . accordingly , distant sources make a substantial contribution to the arrival distribution of uhecrs , unlike in the case of stronger egmf . this is reflected in the decrease of the amplitude around the number fraction of @xmath169 for @xmath108 . except for @xmath126 ng , arrival distribution is sufficiently isotropic compared to isotropic source distribution for almost all the number fractions . the amplitude of the second harmonics is also shown in figure [ fig15 ] . dependence on the number fraction is roughly same as that of the first harmonics . for @xmath119 and @xmath120 ng , the predicted amplitude is sufficiently isotropic for the number fraction of @xmath170 . on the other hand , it appears to be inconsistent with the observation for any number fraction in the case of @xmath126 ng . figure [ fig16 ] shows @xmath171 of the two point correlation function as a function of the number fraction . increase of deviations between models and data with decreasing the number fraction is attributed to the clump of uhecrs at directions of their sources , similarly to the case of the harmonic analysis . especially , this dependence is quite noticeable for @xmath108 , where uhecrs hardly deflect so that correlation at small angle is too strong . at larger number fraction ( @xmath172 ) , it can be seen that the model of @xmath108 provide relatively better fit to the observation than another models . in figure [ fig17 ] , we show the two point correlation function predicted by a specific source scenario for @xmath108 , @xmath173 and @xmath115 with the number fraction of @xmath5 . @xmath171 is also shown . each source distribution is selected so that it predicts the smallest value of @xmath171 for respective set of @xmath140 . only for @xmath108 , another condition is also imposed that the harmonic amplitude predicted by the source model is consistent with the agasa observation within @xmath133 level . the correlation of events at small angle scale and sufficient isotropic distribution at larger scale are well reproduced for @xmath108 . there is no significant correlation for @xmath156 and @xmath115 , because of the larger deflection angle of uhecrs . in the cases of strong egmf or longer correlation length , it appears to be difficult to reproduce the strong anisotropy only at the smallest angle scale , even for the case of minimal value of @xmath171 . considering the calculated results of the first and second harmonics and the small scale anisotropy all together , the model of @xmath108 and the number fraction of @xmath5 ( the source number density of @xmath6 mpc@xmath7 ) seems to reproduce the observations better than another parameter sets . however , due to the small number of observed events , the statistics for the two point correlation function is limited . for this reason , @xmath171 does not differ very much from each other . the future experiments like the pierre auger array @xcite will decrease statistical uncertainty and provide more strong constraints to the model predictions . next we discuss dependence of the energy spectrum on the number fraction . in figure [ fig18 ] , we show the predicted energy spectra in the case of @xmath108 for the number fraction @xmath174 , @xmath169 , @xmath175 in descending order . they are normalized so as to minimize @xmath129 . the shaded regions represent 1 @xmath16 error due to the source selection from our ors galaxies more luminous than @xmath3 . as is evident from this figure , decreasing the number fraction increases fluctuation of the predicted energy spectrum , especially above @xmath10 ev . for the number fraction of @xmath175 ( the source number density of @xmath176 mpc@xmath7 ) , since there are no source within the gzk sphere , the gzk cutoff is clearly visible . the predicted energy spectrum is roughly consistent with the agasa observation within 1 @xmath16 level in the case of the number fraction of @xmath169 , where the observed isotropy and clusters are also reproduced well . however , this result should be interpreted with care . since the source number density is @xmath6 mpc@xmath7 in the case of the number fraction of @xmath169 , mean number of sources is @xmath8 within the gzk sphere . therefore , the agasa 8 events above @xmath10 ev , which do not constitute the clustered events with each other , must originate from at most a few sources . we found a source model which explain the extension of the energy spectrum . in this source model , there are two sources within the region covered by the ors ( @xmath177 mpc ) , one at @xmath178 mpc , the other at @xmath179 mpc . in figure [ fig19 ] , we show the energy spectrum predicted by this source model . the dotted line represent contribution from the nearest source . the predicted energy spectrum provide good fit to the observed one including the extension beyond @xmath9 ev . however , almost all the events above @xmath9 are generated by the nearest source as evident from figure [ fig19 ] . these events are strongly concentrated in a single center , which is inconsistent with the agasa 8 events . it seems to be difficult to reproduce the agasa observation above @xmath102 ev ( including above @xmath10 ev ) by a single scenario of uhecr origin , even for @xmath180 . recently , the hires collaboration @xcite reported the cosmic ray flux from @xmath181 ev to over @xmath10 ev including the gzk cutoff @xcite . in our numerical simulations , the sharp gzk cutoff of the energy spectrum is predicted for the number fraction of @xmath182 as shown above . the small scale correlation of events in this case is too strong for @xmath108 as is evident from figure [ fig20 ] , where the two point correlation function is shown in the same way as figure [ fig17 ] , but with the number fraction of @xmath182 . this strong correlation is reduced for @xmath156 and @xmath115 , but still inconsistent with the agasa data . finally we show in figure [ fig21 ] realizations of 57 arrival directions of uhecrs with energies of @xmath74 ev , predicted by the source model of @xmath180 of figure [ fig17 ] . the agasa 57 events in this energy range are also shown . the arrival directions are restricted in the range @xmath103 in order to compare our results with the agasa data . the arrival distribution of uhecrs seems to be isotropic on a large scale with clusters of events meaning the small scale anisotropy . the amplitudes of the first and second harmonics are consistent with the agasa , but the extension of the spectrum is not . ( mean number of simulated events above @xmath10 ev is only 1 . ) in this example , c6 doublet at @xmath183 is well reproduced . also , high intensity regions around @xmath111 mentioned in section 3.1 . are eliminated under the favor of the source selection .

we use the ors galaxy sample , which allow us to accurately quantify the contribution of nearby sources to the energy spectrum and the arrival distribution , as a source model . we find that the arrival distribution of uhecrs become to be most isotropic as restricting sources to luminous galaxies .

we present numerical simulations on the propagation of uhe protons with energies of ev in extragalactic magnetic fields over 1 gpc . we use the ors galaxy sample , which allow us to accurately quantify the contribution of nearby sources to the energy spectrum and the arrival distribution , as a source model . the sample is corrected taking the selection effect and absence of galaxies in the zone of avoidance ( ) into account . we calculate three observable quantities , cosmic ray spectrum , harmonic amplitude , and two point correlation function from our data of numerical simulations . with these quantities , we compare the results of our numerical calculations with the observation . we find that the arrival distribution of uhecrs become to be most isotropic as restricting sources to luminous galaxies . however , it is not isotropic enough to be consistent with the agasa observation , even for . in order to obtain sufficiently isotropic arrival distribution , we randomly select sources , which contribute to the observed cosmic ray flux , from the ors sample more luminous than mag , and investigate dependence of the results on their number . we show that the three observable quantities including the gzk cutoff of the energy spectrum can be reproduced in the case that the number fraction of the ors galaxies more luminous than mag is selected as uhecr sources . in terms of the source number density , this constraint corresponds to mpc . however , since mean number of sources within the gzk sphere is only in this case , the agasa 8 events above ev , which do not constitute the clustered events with each other , can not be reproduced . on the other hand , if the cosmic ray flux measured by the hires , which is consistent with the gzk cutoff , is correct and observational features about the arrival distribution of uhecrs are same as the agasa , our source model can explain both the arrival distribution and the flux at the same time . thus , we conclude that large fraction of the agasa 8 events above ev might originate in the topdown scenarios , or that the cosmic ray flux measured by the hires experiment might be better . we also discuss the origin of uhecrs below ev through comparisons between the number density of astrophysical source candidates and our result ( mpc ) .

astro-ph0210132

c

we presented the results of numerical simulations on the propagation of uhe protons with energies of @xmath0 ev injected by a discrete distribution of galaxies using the ors data sample , which is properly corrected for the selection effect and absence of galaxies in the zone of avoidance ( @xmath1 ) . we adopted strength of the egmf to be not only 1 ng but also 10,100 ng , in order to explore the possibility of reproducing the extension of the energy spectrum above @xmath10 ev . we calculated the three observable quantities , cosmic ray spectrum , harmonic amplitude , and two point correlation function . with these quantities , we made comparisons between the model predictions and the existing agasa data . at first , we explored the source model consistent with the current observations , as a function of the limiting magnitudes of galaxies . the energy spectrum for the strong egmf shows the extension beyond @xmath10 ev . however , it can not be well fitted with the observed energy spectrum , especially at @xmath137 ev where the current data have adequate statistics . on the other hand , the energy spectrum for @xmath119 ng provide good fit with the observation below @xmath136 ev , and statistical significance of deviation @xmath129 is smaller than that for the strong egmf . among this case , the extension of the energy spectrum is also reproduced for @xmath157 , although there is significant large scale anisotropy contrary to the agasa data in this case . in the case of @xmath158 , the gzk cutoff is predicted . we found that the angular image became to be isotropic and showed good correlation with agasa events as restricting sources to more luminous galaxies . as a consequence , galaxies more luminous than @xmath4 mag produce the angular image of uhecr which is most isotropic roughly irrespective of strength and correlation length of the egmf . however , it is not isotropic enough to be consistent with the observed amplitude of the second harmonics , even for @xmath112 . we further found that the small scale anisotropy is well reproduced in the case of @xmath108 because of the small deflection angle of uhecrs . next , in order to obtain sufficiently isotropic arrival distribution of uhecrs and small scale clustering even for the case of other than @xmath108 , we randomly selected sources from our ors sample , and investigate the dependence of the results on their number . we found that the arrival distribution became to be sufficiently isotropic in the case that the number fraction @xmath170 of the ors galaxies more luminous than @xmath112 is selected as uhecr sources for @xmath119 , @xmath120 ng . among this case , the small scale clustering can also be reproduced for @xmath180 better than the cases of another parameter sets . we furthermore found that the extension of the energy spectrum is explained in this case within roughly 1 @xmath16 error due to source selection from our ors sample because of the large fluctuation above @xmath10 ev . in sum , we showed that the three observable quantities including the gzk cutoff of the energy spectrum can be reproduced in the case that the number fraction @xmath5 of the ors galaxies more luminous than @xmath4 mag is selected as uhecr sources . in terms of the source number density , this constraint corresponds to @xmath6 mpc@xmath7 . as mentioned in the previous subsection , we showed that the three observable quantities including the gzk cutoff of the energy spectrum can be reproduced in the case that the number fraction @xmath5 of the ors galaxies more luminous than @xmath4 mag is selected as uhecr sources . however , we should interpret this result with care . since the agasa 8 events above @xmath10 ev do not constitute the clustered events with each other , the number of their sources within the gzk sphere must be much larger than the event number ( 8) . on the other hand , the number of sources within the gzk sphere is at most only 1 in the case of the number fraction of @xmath169 ( the source number density of @xmath184 mpc@xmath7 ) . it is suspected that cosmic rays above @xmath10 ev ( hereafter ehecrs ; extremely - high energy cosmic rays ) are strongly concentrated in a single center , even if the extension of the energy spectrum is explained . therefore , large fraction of ehecrs observed by the agasa might originate from sources other than ones of uhecr with energies of @xmath185 ev . the number density of ehecr source must be much larger than @xmath184 mpc@xmath7 . we can put forward two candidates as such ehecr production site . it is suggested that iron ions from the surfaces of young strongly magnetized neutron stars may be accelerated to @xmath10 ev through relativistic mhd winds @xcite . however , it seems to be difficult to obtain sufficiently isotropic arrival directions of ehecrs from sources localized in the galactic plane by deflection due to the galactic magnetic field @xcite . the decay of some supermassive particles , which could be produced from tds , or be certain msrps , are also considered as probable ehecrs origin . decay rate of the supermassive particles required to explain the observed ehecr flux are estimated as @xmath186 mpc@xmath7 yr@xmath53 @xcite . multiplying by the current ehecr observing time ( @xmath187 yr ) , we obtain the number density of @xmath188 mpc@xmath7 , which is sufficiently large to reproduce not clustered agasa 8 ehecrs . as for the large scale anisotropy , distribution of tds in the universe would be homogeneous . msrps are expected to be clustered in galactic halos , and thus ehecr flux will be dominated by contribution from our own galactic halo . accordingly , arrival distribution would be isotropic enough to be consistent with the current agasa observation in both cases . furthermore , these scenarios are not constrained by contribution to the cosmic ray flux at lower energy which must be smaller than observed one , since hard injection spectrum is generally predicted . for the reasons stated above , the top - down scenarios may be favored to explain large fraction of the 8 ehecrs observed by the agasa . there is a problem if all the ehecrs observed by the agasa originate from sources other than those of uhecrs . if we consider that sources of ehecrs and uhecrs precisely differ from each other , there would be no clustered event set which includes both ehecrs and uhecrs , because clustered events are expected to reflect a single point source . however , 2 ehecrs out of 8 observed by the agasa constitute the clustered events with uhecrs with energies of @xmath104 ev ( c1 and c3 in hayashida et al.(2000 ) ) . we have to interpret that the two clusters happen to be produced by chance . chance probability of more than two accidental clusterings within @xmath189 between 49 uhecrs and 8 ehecrs is quite low @xmath190 . the agasa observation seems to deviate from our prediction with @xmath191 confidence level . however , about 1 ehecr out of 8 may originate in the bottom - up scenarios . indeed , 57 cosmic rays above @xmath102 ev predicted by the source model of figure [ fig21 ] include an ehecr . in this case , since the source of this single event will be located within the gzk sphere , it is likely that this event constitutes a clustered event set with uhecrs . chance probability of more than one accidental clustering rise up to @xmath192 , which is high enough for us to interpret one of the two doublets to be produced merely by chance . thus , our scenario is consistent with the current agasa observation within 1 @xmath16 level . the event correlation between ehecrs and uhecrs would provide an important test of our conclusion with sufficient amount of data from future experiments . for example , when the event number of uhecrs above @xmath102 increases to 10 times as many as that of the current agasa observation ( 57 ) , the number of ehecrs which lie within @xmath189 from uhecrs by chance becomes @xmath193 . if future experiments observe event number of such ehecrs within this range , our scenario will be supported . here we note that the source number within the gzk sphere is at most 1 in the case of nf=@xmath169 . therefore the number of event clustering between an ehecr and an uhecr which can be explained by bottom - up scenarios is at most 1 . another test of our conclusion is distinguishing the chemical composition of primary cosmic rays which initiate air showers in the earth atmosphere . in the bottom - up scenarios , protons or nuclei are primary particles . on the other hand , photons are considered as primary in the top - down scenarios @xcite . information on the chemical composition is mainly provided by the depth of shower maximum for fluorescence observation of the air shower . there are a number of projects utilizing the fluorescence technique , such as hires @xcite , south and north auger @xcite , owl @xcite and euso @xcite . these experiment would provide information on the chemical composition and a test of our conclusion . the hires collaboration @xcite reported the cosmic ray flux from @xmath181 ev to over @xmath10 ev including the gzk cutoff @xcite . as discussed above , we showed that the three observable quantities except for ehecr events observed by the agasa can be reproduced in the case that the number fraction @xmath5 of the ors galaxies more luminous than @xmath4 mag is selected as uhecr sources . in figure [ fig22 ] , we show the predicted energy spectrum fitted to the data measured by hires - i detector in the case of @xmath180 . as easily seen , the fit is good as compared with the middle panel of figure [ fig18 ] . if the flux measured by the hires collaboration is correct and observational features about the arrival distribution are same as the agasa , our source model can explain both the arrival distribution of uhecrs and the flux at the same time . when the large - area detectors like the pierre auger array @xcite start operating , the statistical error of the observed energy spectrum will decrease . this allows us to draw a conclusion about the origin of ehecrs or whether they exist or not . cccc object & density & ratio & ref + & [ mpc@xmath7 ] & to our result & + & & ( @xmath184 mpc@xmath7 ) & + agn & @xmath195 & 100.0 & @xcite + fr - ii radio galaxy & @xmath196 & 0.03 & @xcite + bl lac & @xmath197 & 0.3 & @xcite + grb & @xmath195 & 100.0 & @xcite + dead quasar & @xmath198 & 500.0 & @xcite + colliding galaxy & @xmath199 & 0.7 & @xcite + in this subsection we discuss implications of our results , obtained by comparison of the model predictions with the existing agasa data , for the origin of uhecrs with energies of @xmath104 ev . the number densities of possible uhecr production sites and ratios to our result ( @xmath6 mpc@xmath7 ) are tabulated in table [ tbl : num ] . blast waves in agn jet could accelerate particle to a few tens of eev @xcite and similarly for agn cores . however , due to the interaction of uhecrs with very high radiation fields in and around the central engine of an agn , these maxima are unlikely to be achieved . this is consistent with our result , because the number density of agn are much larger than our results , and thus , arrival distribution may be inconsistent with the agasa if all the agns contribute to the cosmic ray flux above @xmath102 ev . among agns , the most promising acceleration sites for uhecrs are the so - called hot - spots of fr - ii radio galaxies @xcite . however , their number density seems to be too small , as compared with our result . it is unlikely that fr - ii radio galaxies are responsible for all the agasa 49 events with energies of @xmath104 ev . another possible uhecrs production sites are bl lacertae objects ( bl lacs ) @xcite . their number are larger than fr - ii radio galaxies , but still insufficient to reproduce all the 49 events . grb can be shown to in principle accelerate protons up to @xmath10 ev @xcite . the effective density of grb is determined by the grb rate @xmath200 h@xmath201 mpc@xmath7 yr@xmath53 @xcite ) and the typical time delay @xmath202 of uhecrs , which depends on the propagation distance from sources to the earth . since we are now considering uhecrs with energies of @xmath104 ev , we have to include contribution from sources outside the gzk sphere when calculating the typical time delay . we calculated the mean time delay from our numerical data assuming homogeneous grbs distribution , and obtained @xmath203 yr . this gives the grb effective density @xmath204 mpc@xmath7 . from our result , if about 1 @xmath15 of grbs produce uhecrs , arrival distribution predicted by grbs would be consistent with the agasa . the compact dynamo model has been proposed as a natural mechanism for accelerating cosmic rays in dead quasars @xcite . only 0.2 @xmath15 of dead quasars are required to contribute to the comic ray flux above @xmath102 ev . large fraction of luminous infrared galaxies ( lirgs ) are found to be interacting systems , suggesting that collisions and merging processes are responsible for triggering the huge ir light emission @xcite . in such systems , favorable environments for accelerating cosmic rays to @xmath10 ev are provided by amplified magnetic fields on the scale of tens kpc resulting from gravitational compression , as well as high relative velocities of galaxies and/or superwinds from multiple supernovae explosions @xcite . according to smialkowski et al.(2002 ) , we take the number density of such colliding galaxies as that of galaxies with huge far infrared luminosity @xmath18 . the number density is roughly equal to our result . if all the galaxies with @xmath18 are responsible for uhecrs , predicted arrival distribution would be consistent with the agasa . indeed , smialkowski et al.(2002 ) showed that arrival distribution of uhecrs predicted by lirgs is sufficiently isotropic such that statistical tests they used for large scale anisotropy was not conclusive for distinguishing between isotropic and lirgs source distribution . furthermore , they showed that the probability of occurring the clustered events are more than 10 times higher for lirgs source distribution than that for isotopic distribution . their results well agree with ours . our result is supported by a statistical analysis of clustering of uhecrs developed by dubovsky et al.(2000 ) , which allow an estimate of the minimum number density of sources . they applied their arguments to the 14 events above @xmath10 ev observed by several experiments . they obtained the minimum number density of sources @xmath205 mpc@xmath7 . since we are now considering uhecrs below @xmath10 ev , we have to apply the arguments given in their paper to the cosmic ray events below @xmath10 ev . let us apply the arguments to the 49 events with energies of @xmath185 ev observed by the agasa . according to them , the number density must be larger than @xmath206 where @xmath207 , @xmath208 , @xmath209 are the total number of events , the number of events in clusters , e - folding length of cosmic ray luminosity from a single source respectively . the value of @xmath209 can be obtained as @xmath210 mpc from figure [ fig4 ] . taking @xmath211 and @xmath212 , eq . ( [ minnum ] ) gives @xmath213 mpc@xmath7 which is consistent with our result @xmath6 mpc@xmath7 . throughout the paper , we assumed that the statistical properties of the egmf are uniform . however , simple analytical arguments based on magnetic flux freezing , and large scale structure simulations passively including the magnetic field @xcite demonstrate that the magnetic field is most likely as structured as are the baryons . the egmf as strong as @xmath214 g in sheets and filaments of large scale galaxy distribution , such as in the lsc , are compatible with existing upper limits on faraday rotation @xcite . it is suspected that the arrival distribution of uhecrs depends on the fields in the immediate environment of the observer . however , numerical simulations of uhecr propagation in inhomogeneous egmf over cosmological distances are highly time - consuming . with the assumption of homogeneous egmf , we have performed numerical simulation of spherically symmetric propagation . provided that the egmf is inhomogeneous , the propagation of uhecrs from a single point source has no longer spherical symmetry . as a result , we have to specify the earth position in the universe . we also have to choose the detector ( earth ) size so small enough for us to accurately calculate the arrival directions . in this case , the number fraction of uhecrs arriving at the earth to injected ones is extremely small . this requires the number of particle to be propagated several orders of magnitudes higher than that used in this study , which takes enormous cpu time . although the strong egmf in the lsc is compatible with the faraday ratation measures , the cosmic ray observations do not appear to support such local egmf . indeed , we showed in this study that small scale clustering can be well reproduced in the case that uhecrs propagate along nearly straight lines . if the local strong egmf affects the arrival directions of uhecrs , small scale clustering observed by the agasa will not be obtained . this difficulty can be seen from the studies by another authors . there are several groups who study the propagation of uhecr in such strong egmf in the lsc @xcite . they assume simplified source distributions which represent the lsc . the strong egmf of @xmath214 g leads to substantial deflections of uhecrs , which are better for explaining the observed isotropic arrival distribution of uhecrs . however , consistency of small scale anisotropy and also large scale isotropy predicted by their scenarios with the agasa observation is somewhat worse than that predicted by our scenario . the strong egmf in the lsc seems to be unfavored by the current cosmic ray observation , although it is not ruled out by the faraday rotation measurements . of course , since the event number of uhecrs is currently very small , we can not absolutely rule out such strong egmf in the lsc . fulture experiments would increase the significance level of statement about whether such strong egmf affects the arrival directions of uhecrs or not .

we present numerical simulations on the propagation of uhe protons with energies of ev in extragalactic magnetic fields over 1 gpc . we calculate three observable quantities , cosmic ray spectrum , harmonic amplitude , and two point correlation function from our data of numerical simulations . with these quantities , however , it is not isotropic enough to be consistent with the agasa observation , even for . in order to obtain sufficiently isotropic arrival distribution , we randomly select sources , which contribute to the observed cosmic ray flux , from the ors sample more luminous than mag , and investigate dependence of the results on their number . we show that the three observable quantities including the gzk cutoff of the energy spectrum can be reproduced in the case that the number fraction of the ors galaxies more luminous than mag is selected as uhecr sources . in terms of the source number density , this constraint corresponds to mpc . if the cosmic ray flux measured by the hires , which is consistent with the gzk cutoff , is correct and observational features about the arrival distribution of uhecrs are same as the agasa , our source model can explain both the arrival distribution and the flux at the same time .

we present numerical simulations on the propagation of uhe protons with energies of ev in extragalactic magnetic fields over 1 gpc . we use the ors galaxy sample , which allow us to accurately quantify the contribution of nearby sources to the energy spectrum and the arrival distribution , as a source model . the sample is corrected taking the selection effect and absence of galaxies in the zone of avoidance ( ) into account . we calculate three observable quantities , cosmic ray spectrum , harmonic amplitude , and two point correlation function from our data of numerical simulations . with these quantities , we compare the results of our numerical calculations with the observation . we find that the arrival distribution of uhecrs become to be most isotropic as restricting sources to luminous galaxies . however , it is not isotropic enough to be consistent with the agasa observation , even for . in order to obtain sufficiently isotropic arrival distribution , we randomly select sources , which contribute to the observed cosmic ray flux , from the ors sample more luminous than mag , and investigate dependence of the results on their number . we show that the three observable quantities including the gzk cutoff of the energy spectrum can be reproduced in the case that the number fraction of the ors galaxies more luminous than mag is selected as uhecr sources . in terms of the source number density , this constraint corresponds to mpc . however , since mean number of sources within the gzk sphere is only in this case , the agasa 8 events above ev , which do not constitute the clustered events with each other , can not be reproduced . on the other hand , if the cosmic ray flux measured by the hires , which is consistent with the gzk cutoff , is correct and observational features about the arrival distribution of uhecrs are same as the agasa , our source model can explain both the arrival distribution and the flux at the same time . thus , we conclude that large fraction of the agasa 8 events above ev might originate in the topdown scenarios , or that the cosmic ray flux measured by the hires experiment might be better . we also discuss the origin of uhecrs below ev through comparisons between the number density of astrophysical source candidates and our result ( mpc ) .

astro-ph0210132

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in this section , we present our conclusions obtained from comprehensive study on the bottom - up scenarios . for the origin of ehecrs , we conclude that large fraction of the agasa 8 events above @xmath10 ev might originate in the topdown scenarios , or that the cosmic ray flux measured by the hires experiment might be better . we also discussed the origin of uhecrs below @xmath9 ev through comparisons between the number density of astrophysical source candidates and our result ( @xmath6 mpc@xmath7 ) . at present , we can not conclude which source candidates are responsible for uhecrs below @xmath9 ev . however , our result for the source number density ( @xmath6 mpc@xmath7 ) will be useful when searching for the ultimate uhecr source . throughout the paper , we set constraints to the source models so that their predictions reproduce the current agasa observation within 1 @xmath16 error of the statistical fluctuation due to finite number of the observed events . however , if we relax the constraints to within 2 @xmath16 error , the energy spectrum ( figure [ fig9 ] and [ fig10 ] ) and the amplitude of the second harmonics ( figure [ fig12 ] ) can be reproduced in the case of @xmath215 without the source selection . in this case , since the source number density is @xmath216 mpc@xmath7 , there are @xmath217 sources within the gzk sphere . the agasa events above @xmath10 ev , which do not constitute the clustered events with each other , may also be reproduced , contrary to the case of the source number density of @xmath6 mpc@xmath7 . thus , we can not absolutely rule out the bottom - up scenarios as the origin of ehecrs . the statistics for the quantities which we used is limited by the small number of observed events , which make difficult to draw a decisive conclusion on the origin of uhecrs . however , the present working or development of large - aperture new detectors , such as hires @xcite and south and north auger @xcite will considerably decrease the statistical uncertainties . there are furthermore plans for space based air shower detectors such as owl @xcite and euso @xcite which would detect about 1000 events per year above @xmath10 ev @xcite . with the method to constrain the source model and their number density developed in this paper , these experiments will reveal the origin of uhecrs with better significance in the very near future . we would like to thank dr . t. stanev for kindly giving us the data of interaction length and inelasticity of uhe protons due to the photopion production with photons of the cosmic microwave background . this research was supported in part by giants - in - aid for scientific research provided by the ministry of education , science and culture of japan through research grant no.s14102004 and no.s14079202 .

however , since mean number of sources within the gzk sphere is only in this case , the agasa 8 events above ev , which do not constitute the clustered events with each other , can not be reproduced . on the other hand , thus , we conclude that large fraction of the agasa 8 events above ev might originate in the topdown scenarios , or that the cosmic ray flux measured by the hires experiment might be better . we also discuss the origin of uhecrs below ev through comparisons between the number density of astrophysical source candidates and our result ( mpc ) .

we present numerical simulations on the propagation of uhe protons with energies of ev in extragalactic magnetic fields over 1 gpc . we use the ors galaxy sample , which allow us to accurately quantify the contribution of nearby sources to the energy spectrum and the arrival distribution , as a source model . the sample is corrected taking the selection effect and absence of galaxies in the zone of avoidance ( ) into account . we calculate three observable quantities , cosmic ray spectrum , harmonic amplitude , and two point correlation function from our data of numerical simulations . with these quantities , we compare the results of our numerical calculations with the observation . we find that the arrival distribution of uhecrs become to be most isotropic as restricting sources to luminous galaxies . however , it is not isotropic enough to be consistent with the agasa observation , even for . in order to obtain sufficiently isotropic arrival distribution , we randomly select sources , which contribute to the observed cosmic ray flux , from the ors sample more luminous than mag , and investigate dependence of the results on their number . we show that the three observable quantities including the gzk cutoff of the energy spectrum can be reproduced in the case that the number fraction of the ors galaxies more luminous than mag is selected as uhecr sources . in terms of the source number density , this constraint corresponds to mpc . however , since mean number of sources within the gzk sphere is only in this case , the agasa 8 events above ev , which do not constitute the clustered events with each other , can not be reproduced . on the other hand , if the cosmic ray flux measured by the hires , which is consistent with the gzk cutoff , is correct and observational features about the arrival distribution of uhecrs are same as the agasa , our source model can explain both the arrival distribution and the flux at the same time . thus , we conclude that large fraction of the agasa 8 events above ev might originate in the topdown scenarios , or that the cosmic ray flux measured by the hires experiment might be better . we also discuss the origin of uhecrs below ev through comparisons between the number density of astrophysical source candidates and our result ( mpc ) .

astro-ph0509315

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we first selected cttss and haebe stars in @xmath0 ori , oriob1 , and lacob1 based on the 2mass colors . these pms stars are then utilized to trace recent star - forming activities . the young stars are found to be lined up in an age sequence between massive stars and comet - shaped clouds or bright - rimmed clouds , with the youngest stars located near the cloud surfaces . there are no pms stars far behind the i - fronts . these results support the scenario by which the lyman continuum photons of a luminous o star create expanding i - fronts that would cause the evaporation and compression of nearby clouds to form brcs or comet - shaped clouds , thereby inducing the birth of low- and intermediate - mass stars . the brcs provide us with a convenient setting in which to see that the haebe stars tend to form in the inner , denser parts of a cloud , whereas the cttss are formed near the photoevaporating cloud layers . young stars in bright - rimmed or comet - shaped clouds near a massive star are likely to have been formed by triggering . assuming a shock speed of @xmath32 km s@xmath8 , this would result in an age spread of several myrs between member stars or star groups formed in the sequence . we want to particularly thank richard f. green , director of kpno , who kindly provided us the director s discretionary time to accomplish this work . we are also grateful to the staff of the beijing astronomical observatory for their assistance during our observation runs and to the referee , hans zinnecker , for his suggestions helpful in improving the quality of this paper . this research makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation ( nsf ) . we also used the southern h - alpha sky survey atlas ( shassa ) , supported by the nsf . we acknowledge the financial support of grant nsc92 - 2112-m-008 - 047 from the national science council and 92-n - fa01 - 1 - 4 - 5 from the ministry of education of taiwan . alcal , j. m. , wachter , s. , covino , e. , sterzik , m. f. , durisen , r. h. , freyberg , m. j. , hoard , d. w. , & cooksey , k. 2004 , , 416 , 677 bertoldi , f. 1989 , , 346 , 735 bertoldi , f. & mckee , c. f. 1990 , , 354 , 529 blaauw , a. 1958 , , 63 , 186 blaauw , a. 1961 , , 15 , 265 blaauw , a. 1964 , , 2 , 213 blaauw , a. 1991 , in the physics of star formation and early stellar evolution , ed . c. j. lada & n. d. kylafis ( dordresht : kluwer ) , 125 briceo , c. , et al . 2006 , in protostars and planets v , ed . reipurth , b. , jewitt , d. , & keil , k. 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& a & k & associated with ic2118 + 4 & j05122053 - 0255523 & h(-12.1 ) & a & k & + 5 & j05141328 - 0256411 & h(-210.6 ) , o(-2.5 ) , fe , ca , he & n & k & + 6 & j05152683 - 0632010 & h(-0.3 ) & a & k & h@xmath3 emission is week , could be a wtts + 7 & j05162251 - 0756503 & h(-37.7 ) , o(-1.0 ) , ca , he & a & k & + 8 & j05181685 - 0537300 & h(-57.3 ) , o(-2.3 ) , fe , ca , he & n & k & + 9 & j05191356 - 0324126 & h(-52.1 ) , ca , he & a & k & + 10 & j05191549 - 0204529 & h(-10.7 ) , o(-3.6 ) , ca & a & k & + 11 & j05201945 - 0545553 & h(-26.9 ) , ca , he & a & k & , iras05178 - 0548 , associated with ldn1634 + 12 & j05202573 - 0547063 & h(-100.2 ) , o ? , fe , ca , he & a & k & , associated with ldn1634 + 13 & j05203142 - 0548247 & h(-19.3 ) , ca , he & a & k & , associated with ldn1634 + 14 & j05253979 - 0411020 & h(-138.9 ) , fe , ca , he & n & k & + 15 & j05262158 + 1131339 & h(-15.4 ) , o(-1.8 ) , fe , ca & - & b & + 16 & j05292393 + 1151576 & h(-40.5 ) , ca , he & a & b , k & , associated with b30 + 17 & j05300203 + 1213357 & h(-33.6 ) , ca , he & a & b , k & , iras05272 + 1211 , associated with b30 + 18 & j05301313 + 1208458 & h(-5.7 ) , ca & a & b , k & , associated with b30 + 19 & j05311615 + 1125312 & h(-21.9 ) & n & b , k & + 20 & j05315128 + 1216208 & h(-127.3 ) , o(-10.2 ) , he & a & b , k & associated with b30 + 21 & j05323207 + 1044178 & h(-96.7 ) , ca , he & - & b & + 22 & j05324305 + 1221083 & h(-13.9 ) , o(-1.3 ) , ca , he & a & b , k & , iras05299 + 1219 , associated with b30 + 23 & j05330207 + 1137114 & h(-176.8 ) , fe , ca , he & - & b & + 24 & j05391268 + 0915522 & h(-215.6 ) , ca , he & - & b & + 25 & j05432091 + 0906071 & h(-21.8 ) , o(-0.5 ) , ca , he & a & b , k & , iras05406 + 0904 , associated with b35 + 26 & j05440899 + 0909147 & h(-44.5 ) , o(-2.1 ) , fe , ca , he & a & b , k & , iras05413 + 0907 , associated with b35 + 27 & j05451493 + 0721223 & h(-5.6 ) & n & b , k & + 28 & j05452235 + 0904123 & & - & b & , iras05426 + 0903 , associated with b35 + 29 & j05515035 + 0821066 & h(-181.9 ) , ca & a & b , k & + 30 & j05534090 + 0138140 & h(-29.0 ) , o(-2.7 ) , he & - & b & , irasf05510 + 0137 , associated with ori east + 31 & j05535869 + 0144094 & h(-37.0 ) , ca , he & - & b & , irasf05513 + 0143 , associated with ori east + 32 & j21370366 + 4321172 & h(-174.8 ) , fe , ca , he & a & b , k & + 33 & j21395545 + 4313082 & h(-83.6 ) , ca & - & b & + 34 & j21535750 + 4659443 & h(-51.7 ) & - & b & + 35 & j22361978 + 4006273 & h(-63.9 ) , o(-1.8 ) , ca & - & b & associated with iras22343 + 3944 group + 36 & j22362779 + 3954066 & h(-18.4 ) & - & b & associated with iras22343 + 3944 group + 37 & j22370328 + 4005185 & h(-10.3 ) , ca ? , he ? & a & b , k & associated with iras22343 + 3944 group + 38 & j22371683 + 3952260 & h(-130.8 ) , o(-4.5 ) , ca & - & b & associated with iras22343 + 3944 group + 39 & j23104483 + 4508511 & h(-7.9 ) & n & b , k & + 40 & j23373847 + 4824119 & h(-19.2 ) & a & b , k & , associated with gal110@xmath2413 + 41 & j05042998 - 0347142 & h & a3e & k & , iras 05020 - 0351 , associated with ldn1616 + 42 & j05113654 - 0222484 & h & a3e & k & + 43 & j05305472 + 1421524 & h & f2e & k & + 44 & j05312805 + 1209102 & h , o & a2e & k & , iras05286 + 1207 , associated with b30 + 45 & j05313515 + 0951553 & h & b9e & k & + 46 & j05315724 + 1117414 & h & a0e & b & , iras05291 + 1115 + 47 & j05350960 + 1001515 & h , o ? & b9e & b & , iras05324 + 0959 + 48 & j05390921 + 0925301 & h & f7e & b , k & + 49 & j21462666 + 4744154 & h , o & b9e & k & + 50 & j21514726 + 4615115 & h & a9e & k & + 51 & j22154039 + 5215559 & h & a2e & b & + 52 & j22344101 + 4040045 & h , o , s & a2e & k & + 53 & j22363511 + 4000156 & h , o & b8e & b & associated with iras22343 + 3944 group + 54 & j05232026 + 0934432 & a0 & b , k & + 55 & j05285405 - 0606063 & me & k & , iras05264 - 0608 + 56 & j05413010 + 1418225 & c & k & + 57 & j05442880 + 0652019 & m & b & + 58 & j05464207 + 0643469 & c & b & + 59 & j05480851 + 0954012 & ce & b , k & , iras05453 + 0953 + 60 & j07323273 + 2647156 & c & k & objectfbs 0729 + 269 + 61 & j07475919 + 2052254 & ce & k & + 62 & j08231037 - 0153257 & c & k & + 63 & j08292902 + 1046241 & c & k & + 64 & j08423302 + 0621195 & m & k & + 65 & j08541870 - 1200541 & ce & k & + 66 & j09111450 - 0922053 & me & k & + 67 & j09333061 - 2216282 & m & k & + 68 & j20245404 + 2609115 & m & b & + 69 & j20291739 + 2617284 & me & b & + 70 & j20304177 + 2812340 & m & b & , iras20285 + 2802 + 71 & j20311267 + 2612270 & m & b & + 72 & j20415136 + 2752525 & m & b & + 73 & j20532040 + 2516196 & c & b & + 74 & j20551307 + 3254065 & m & b & + 75 & j20555284 + 2640515 & m & b & , iras20537 + 2629 + 76 & j21040556 + 2632111 & m & b & , iras21019 + 2620 + 77 & j21244172 + 4437134 & ce & b & , iras21228 + 4424 + 78 & j21383182 + 4542469 & ce & k & , iras21366 + 4529 + 79 & j21595030 + 3313596 & m & b & + 80 & j22024329 + 4216400 & bl lac&k & + 81 & j22055958 + 3530057 & m & b & + 82 & j22070988 + 2828374 & m & b & , irasf22048 + 2813 + 83 & j22075421 + 4105113 & m & b & , iras22057 + 4050 + 84 & j22084406 + 4855248 & m & b & , iras22067 + 4840 + 85 & j22121336 + 4646065 & c & b & iras22101 + 4631 + 86 & j22135091 + 2447203 & m & b & + 87 & j22213857 + 3335586 & c & b & + 88 & j22261658 + 4221089 & a0 & b & + 89 & j22295650 + 4546539 & ce & b & + 90 & j22313443 + 4816005 & c & k & , iras22294 + 4800 + 91 & j22314368 + 4748038 & pn & k & , iras22296 + 4732 + 92 & j22451504 + 5051534 & ce & b & , iras22431 + 5036 + 93 & j22491976 + 5154487 & m & b & iras22472 + 5138 + 94 & j22514566 + 4921137 & c & b & iras22495 + 4905 + 95 & j22521809 + 3413364 & m & b & iras22499 + 3357 + 96 & j22592372 + 4811589 & me & k & + 97 & j23023314 + 4649483 & m & b & , iras23002 + 4633 + 98 & j23113005 + 4702525 & m & b & iras23092 + 4646 + 99 & j23175960 + 4645122 & m & b & , iras23156 + 4628 + sequential star formation & yes . pms stars close to triggering & no + & sources are older than those close to brcs & + stellar distribution & pms stars are located between triggering & pms stars can be anywhere , including being far + & sources or around surfaces of brcs with no & behind the surface of a brc + & young stars embedded much behind the i - fronts & + star formation efficiency & high & low , less than a few percent . + lcccccc hd222142 & b9.5 v & 0.3 & -3.1 & 0.6 & 0.6 & ucac2 + hd222086 & b9 v & 0.5 & -2.8 & 1.0 & 1.1 & ucac2 + hd222046 & b8 vp & 0.4 & -2.7 & 1.0 & 1.0 & ucac2 + star 40 & continuum & 3.4 & -7.8 & 2.7 & 2.6 & ucac2 + lacob1a & - & -0.3 & -3.7 & - & - & hipparcos + lacob1b & - & -0.5 & -4.6 & - & - & hipparcos + and [ ] , 6300 and 6363 emission lines . star 53 is an haebe star and shows the h@xmath3 in emission but the other balmer lines in absorption.,title="fig : " ] and [ ] , 6300 and 6363 emission lines . star 53 is an haebe star and shows the h@xmath3 in emission but the other balmer lines in absorption.,title="fig : " ] 100 @xmath2 image of the trapezium region . the dots indicate cttss ( white ) and haebe stars ( black ) , labeled with the identification numbers from tables 3 and 4 . pms stars with forbidden line(s ) are bracketed . the boxes mark the fields of the h@xmath3 images shown in ( fig . [ fig : lot1 ] ) . east is to the left and north to the top . ] 100 @xmath2 and co images of the @xmath0 ori region . the symbols are the same as in figure [ fig : oriob1 ] . the distribution of pms stars extends from @xmath0 ori to b30 and b35 . east is to the left and north to the top.,title="fig : " ] 100 @xmath2 and co images of the @xmath0 ori region . the symbols are the same as in figure [ fig : oriob1 ] . the distribution of pms stars extends from @xmath0 ori to b30 and b35 . east is to the left and north to the top.,title="fig : " ] images of the ori ob1 brcs . the stars in table 3 are marked . east is to the left and north to the top . the field of view of each image is @xmath11.,title="fig : " ] images of the ori ob1 brcs . the stars in table 3 are marked . east is to the left and north to the top . the field of view of each image is @xmath11.,title="fig : " ] images of the ori ob1 brcs . the stars in table 3 are marked . east is to the left and north to the top . the field of view of each image is @xmath11.,title="fig : " ] images of the ori ob1 brcs . the stars in table 3 are marked . east is to the left and north to the top . the field of view of each image is @xmath11.,title="fig : " ] images of the ori ob1 brcs . the stars in table 3 are marked . east is to the left and north to the top . the field of view of each image is @xmath11.,title="fig : " ] images of the ori ob1 brcs . the stars in table 3 are marked . east is to the left and north to the top . the field of view of each image is @xmath11.,title="fig : " ] 100 @xmath2 , h@xmath3 and co images of the lacob1 association using the orientation of the galactic coordinates , i.e. , north is to the top and the galactic longitude increases to the left . the white plus signs indicate the 3 late - b stars , hd222142 , hd222086 , and hd222046 , in gal110@xmath2413 and the cross marks indicate the ctts candidate in the iras22343 + 3944 group , 2massj22354224 + 3959566 . the other symbols are the same as in fig . [ fig : oriob1].,title="fig : " ] 100 @xmath2 , h@xmath3 and co images of the lacob1 association using the orientation of the galactic coordinates , i.e. , north is to the top and the galactic longitude increases to the left . the white plus signs indicate the 3 late - b stars , hd222142 , hd222086 , and hd222046 , in gal110@xmath2413 and the cross marks indicate the ctts candidate in the iras22343 + 3944 group , 2massj22354224 + 3959566 . the other symbols are the same as in fig . [ fig : oriob1].,title="fig : " ] 100 @xmath2 , h@xmath3 and co images of the lacob1 association using the orientation of the galactic coordinates , i.e. , north is to the top and the galactic longitude increases to the left . the white plus signs indicate the 3 late - b stars , hd222142 , hd222086 , and hd222046 , in gal110@xmath2413 and the cross marks indicate the ctts candidate in the iras22343 + 3944 group , 2massj22354224 + 3959566 . the other symbols are the same as in fig . [ fig : oriob1].,title="fig : " ] and [ ] images of lbn437 . star 52 is associated with the nebulosity hh398 . east is to the left and north to the top . the field of view of each image is @xmath11,title="fig : " ] and [ ] images of lbn437 . star 52 is associated with the nebulosity hh398 . east is to the left and north to the top . the field of view of each image is @xmath11,title="fig : " ] image of the iras22343 + 3944 group . cttss 35 , 36 , 37 , and 38 from table 3 ( in white ) and haebe star 53 ( in black ) are labeled . the cross indicates the ctts candidate , 2massj22354224@xmath213959566 . the other symbols are the same as in fig . [ fig : oriob1 ] . east is to the left and north to the top . ]

we find that the classical t tauri stars and herbig ae / be stars tend to line up between luminous o stars and bright - rimmed or comet - shaped clouds ; the closer to a cloud the progressively younger they are . our positional and chronological study lends support to the validity of the radiation - driven implosion mechanism , where the lyman continuum photons from a luminous o star create expanding ionization fronts to evaporate and compress nearby clouds into bright - rimmed or comet - shaped clouds . these stars are a signpost of current star formation ; no young stars are seen leading the ionization fronts further into the cloud .

we present our diagnosis of the role that massive stars play in the formation of low- and intermediate - mass stars in ob associations ( the ori region , the oriob1 , and lacob1 associations ) . we find that the classical t tauri stars and herbig ae / be stars tend to line up between luminous o stars and bright - rimmed or comet - shaped clouds ; the closer to a cloud the progressively younger they are . our positional and chronological study lends support to the validity of the radiation - driven implosion mechanism , where the lyman continuum photons from a luminous o star create expanding ionization fronts to evaporate and compress nearby clouds into bright - rimmed or comet - shaped clouds . implosive pressure then causes dense clumps to collapse , prompting the formation of low - mass stars on the cloud surface ( i.e. , the bright rim ) and intermediate - mass stars somewhat deeper into the cloud . these stars are a signpost of current star formation ; no young stars are seen leading the ionization fronts further into the cloud . young stars in bright - rimmed or comet - shaped clouds are likely to have been formed by triggering , which would result in an age spread of several myrs between the member stars or star groups formed in the sequence .

0805.4492

c

while there is a consensus that the origin of the kev x - ray continuum emission from quasars is inverse compton scattering ( e.g. , see the review of reynolds & nowak 2003 ) , the extent and geometric configuration of the emission region is less clear . in the standard disk - corona model ( e.g. , haardt & maraschi 1991 ; merloni 2003 ) , it is produced in a hot , extended corona surrounding the disk . in the general relativistic mhd simulations of hirose et al . ( 2004 , also machida & matsumoto 2003 ) the region of the corona with the highest current densities lies close to the inner edge of the disk . under the assumption that these are also the regions with the highest dissipation rates for heating the corona ( see hirose et al . 2004 ) , they will dominate the x - ray emission and we would expect the x - ray source size to track the inner edge of the disk . microlensing of the x - ray source allows us to observationally measure the size of the x - ray emission region . we start with well - sampled optical light curves that allow us to determine the size of the accretion disk . morgan et al . ( 2008a ) found a clear scaling of the disk size with black hole mass that is consistent with the @xmath108 scaling of simple thin disk theory for a fixed eddington accretion rate ( shakura & sunyaev 1973 ) . we can estimate the disk size by two routes other than microlensing . first we can estimate it from the observed flux at some wavelength . size estimates from the observed flux do not depend on the black hole mass but depend only on the assumed temperature profile and the assumption that the disk radiates as a black body at that temperature . second , thin disk theory predicts the scale length through the expression we presented in the beginning of 3 . size estimates from thin disk theory depend on the black - hole mass , the eddington factor and the wavelength . the disk size from our microlensing analysis is roughly consistent with thin disk theory if the accretion efficiency is relatively low , but both the microlensing and theoretical sizes are significantly larger than that estimated from the observed optical flux of the quasar and the same disk model . this mismatch between the sizes estimated from microlensing and from the flux was first pointed out by pooley et al . one solution to this problem may be to use a shallower temperature profile than the @xmath109 of simple thin disk theory , and poindexter et al . ( 2008 ) found some evidence for a shallower profile in he 1104@xmath01805 by examining the optical / near - ir wavelength dependence of microlensing in this system . our x - ray monitoring observations of rx j1131@xmath01231 and he 1104@xmath01805 show significant flux variability in all images of both quasars . the factor of @xmath110 x - ray flux variability in image a of rx j1131@xmath01231 is interesting not only because of the high amplitude but also because it is a highly magnified saddle point image . schechter & wambsganss ( 2002 ) pointed out that in a dark matter dominated galaxy , microlensing is in a regime where images at minima and saddle points of the time - delay surface behave differently . in particular , the saddle point images should show significantly higher variability amplitudes , just as we observe in rx j1131@xmath01231 . the relatively large sizes of accretion disks in the optical relative to the typical einstein radius of the stars seems to have masked much of this effect in the optical signatures of microlensing for example , where the x - ray flux ratio @xmath111 changed by a factor of 4 during our monitoring period , the optical flux ratio changed by only a factor of 1.4 . the differences between the x - ray and optical flux ratios of he 1104@xmath01805 also imply the presence of x - ray microlensing . neither system shows evidence for soft x - ray or dust absorption that could explain the differences . while we measure the source sizes by modeling the data in detail , the essence of the measurement is comparing the amplitude of the x - ray microlensing variability to that in the optical . if the amplitude for the x - ray microlensing is larger than in the optical , then the x - ray source must be more compact , and this is what we observed in both rx j1131@xmath01231 and he 1104@xmath01805 . given the estimated black hole mass of @xmath112 ( peng et al . 2006 ) , our fits to the x - ray and optical light curves using the microlensing model described in 2.5 indicate that the x - ray emission in he 1104@xmath01805 comes from a region smaller than @xmath113 and the uv emission region has a size of @xmath114 . we note that the source sizes of he 1104@xmath01805 were derived using a bayesian analysis which requires a prior . as shown in figures 8 and 9 our upper limit on the x - ray source size is robust to prior selection but not the lower limit . obtaining a more precise x - ray size estimate requires a more extensive x - ray light curve for the system . this is somewhat challenging for he 1104@xmath01805 because the long time delay of he 1104@xmath01805 ( 162 days , morgan et al . 2008a ) and the intrinsic variability we observe here means that this lens requires observations separated by the time delay in order to correct for intrinsic variability . this is less of a problem for almost all other candidates for x - ray monitoring because they have far shorter time delays . for example , in rx j1131@xmath01231 we observe some intrinsic variability but it is significant only on time scales much longer than the delays between the a / b / c images . given the morgan et al . ( 2008b ) estimates for pg 1115 + 080 , the dai et al . ( 2009 ) results for rx j1131@xmath01231 , and our present results for he 1104@xmath01805 , the x - ray microlensing results suggest that the size of the x - ray emission arises from close to the inner edge of the disk . thus , our estimated sizes for the x - ray and uv emission regions place significant constraints on agn models that assume extended coronal envelopes around accretion disks . reducing the uncertainties in these measurements and measuring the scaling of the size with the estimated masses of the black holes requires longer x - ray time series and more systems , but there is clearly no technical barrier to making the measurements and extending them to the dependence of the size on x - ray energy . combining the data from the time series also allows us to search for extended emission from groups or clusters near the lens , which can be important for lens models ( e.g. williams et al . 2006 , fassnacht et al . 2007 ) . here we analyzed the x - ray data for the foreground cluster found near rx j1131@xmath01231 by morgan et al . 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verlag berlin heidelberg new york . also astronomy and astrophysics library . + shankar , f. , weinberg , d. h. , & miralda - escude , j. 2007 , arxiv e - prints , 710 , arxiv:0710.4488 + tsunemi , h. , mori , k. , miyata , e. , baluta , c. , burrows , d. n. , garmire , g. p. , & chartas , g. 2001 , , 554 , 496 + williams , k.a . , momchemva , i. , keeton , c.r . , zabludoff , ai . , & lhar , j. , 2006 , apj , 646 , 85 wise , m. w. , davis , j. e. , huenemoerder , houck , j. c. , dewey , d. flanagan , k. a. , and baluta , c. 1997 , _ the marx 3.0 user guide , cxc internal document _ available at http://space.mit.edu/asc/marx/ + wryzkwoski , l. , et al . , 2003 acta astron . 53 229 + yonehara , a. , mineshige , s. , fukue , j. , umemura , m. , & turner , e. l. 1999 , a&a , 343 , 41 + young , a. j. , & reynolds , c. s. 2000 , apj , 529 , 101 + clcccccc + + & & & & & & & + & & _ chandra _ & exposure & & & & + epoch & observation & observation & time & @xmath116@xmath117 & @xmath118@xmath117 & @xmath119@xmath117 & @xmath120 @xmath117 + & date & i d & ( ks ) & counts & counts & counts & counts + & & & & & & & + + 1&2004 april 12 & 4814 & 10 . & 425 @xmath16 22 & 2950 @xmath16 54 & 839 @xmath16 29 & 211 @xmath16 15 + 2&2006 march 10 & 6913 & 4.9 & 393 @xmath16 20 & 624 @xmath16 25 & 204 @xmath16 14 & 103 @xmath16 10 + 3&2006 march 15 & 6912 & 4.4 & 381 @xmath16 20 & 616 @xmath16 25 & 233 @xmath16 15 & 93 @xmath16 10 + 4&2006 april 12 & 6914 & 4.9 & 413 @xmath16 20 & 507 @xmath16 23 & 146 @xmath16 12 & 131 @xmath16 12 + 5&2006 november 10 & 6915 & 4.8 & 3708 @xmath16 61 & 1411 @xmath16 38 & 367 @xmath16 19 & 155 @xmath16 13 + 6&2006 november 13 & 6916 & 4.8 & 3833 @xmath16 62 & 1618 @xmath16 40 & 415 @xmath16 20 & 115 @xmath16 11 + & & & & & & & + + + 1&2000 june 10 & 375 & 47.4 & 1024 @xmath16 32 & 547 @xmath16 23 + 2&2006 february 16 & 6918 & 5.0 & 38 @xmath16 6 & 86 @xmath16 9 + 3&2006 march 15 & 6917 & 4.6 & 40 @xmath16 6 & 59 @xmath16 8 + 4&2006 april 09 & 6919 & 4.9 & 33 @xmath16 6 & 61 @xmath16 8 + 5&2006 october 31 & 6920 & 5.0 & 60 @xmath16 8 & 40 @xmath16 6 + 6&2006 november 08 & 6921 & 4.9 & 52 @xmath16 7 & 57 @xmath16 8 + @xmath121background - subtracted source counts for events with energies in the 0.210 kev band . the counts for images b and c for the 2004 april 12 observation of rx j1131@xmath01231 are corrected for pile - up by factors of 37% and 16% , respectively . the counts for images a and b for the 2006 november 10 observation of rx j1131@xmath01231 are corrected for pile - up by factor of 32% and 13% , respectively . the counts for images a and b for the 2006 november 13 observation of rx j1131@xmath01231 are corrected for pile - up by factors of 33% and 17% , respectively . + ccccc + + & & & & + & & & & + & & & & + & & & & + + hst & 0,0 & [email protected],[email protected] & [email protected],[email protected] & @[email protected] , [email protected] + _ chandra _ & 0,0 & [email protected] , [email protected] & [email protected] , [email protected] & @[email protected] , [email protected] + & & & & + + hst & & 0,0 & [email protected],@[email protected] & + _ chandra _ & & 0,0 & [email protected] , @[email protected] & + cccccc + + & & & & & + & & & & & + & & image a@xmath122 & image b@xmath122 & image c@xmath122 & image d@xmath122 + & & & & & + 1 & @xmath123 & 1.44@xmath124 & 1.41@xmath125 & 1.47@xmath126 & 1.95@xmath127 + & 0.22 kev flux ( 10@xmath128 erg s@xmath13 @xmath19 ) & 1.4@xmath129 & 9.1@xmath130 & 3.1@xmath131 & 0.9@xmath129 + & 210 kev flux ( 10@xmath128 erg s@xmath13 @xmath19 ) & 2.7@xmath132 & 15.7@xmath133 & 3.8@xmath134 & 0.7@xmath129 + & @xmath135 & 556/787 & 661/787 & 583/787 & 368/787 + & @xmath136 & 25/31 & 105/97 & 28/41 & 15.4/15 + & @xmath137@xmath138 & 0.76 & 0.27 & 0.95 & 0.42 + & & & & & + 2 & @xmath123 & 1.58@xmath139 & 1.63@xmath140 & 1.62@xmath141 & 1.66@xmath142 + & 0.22 kev flux ( 10@xmath128 erg s@xmath13 @xmath19 ) & 2.9@xmath143 & 5.0@xmath130 & 1.3@xmath144 & 0.8@xmath132 + & 210 kev flux ( 10@xmath128 erg s@xmath13 @xmath19 ) & 4.5@xmath145 & 7.0@xmath146 & 2.3@xmath147 & 1.1@xmath148 + & @xmath135 & 531/838 & 653/838 & 435/838 & 300/838 + & @xmath136 & 33/28 & 61/52 & 14.4/16 & 2.4/6 + & @xmath137@xmath138 & 0.24 & 0.18 & 0.57 & 0.9 + & & & & & + 3 & @xmath123 & 1.61@xmath139 & 1.73@xmath140 & 1.57@xmath149 & 1.60@xmath150 + & 0.22 kev flux ( 10@xmath128 erg s@xmath13 @xmath19 ) & 3.1@xmath151 & 5.6@xmath152 & 1.8@xmath131 & 0.8@xmath39 + & 210 kev flux ( 10@xmath128 erg s@xmath13 @xmath19 ) & 4.6 @xmath145 & 6.7@xmath153 & 3.0@xmath154 & 1.2@xmath134 + & @xmath135 & 521/838 & 555/838 & 425/838 & 292/838 + & @xmath136 & 26/27 & 42/48 & 18.5/17 & 3.8/6 + & @xmath137@xmath138 & 0.52 & 0.73 & 0.36 & 0.7 + & & & & & + 4 & @xmath123 & 1.53@xmath155 & 1.64@xmath126 & 1.70@xmath156 & 1.62@xmath157 + & 0.22 kev flux ( 10@xmath128 erg s@xmath13 @xmath19 ) & 3.0@xmath143 & 3.9@xmath158 & 1.2@xmath132 & 1.0@xmath132 + & 210 kev flux ( 10@xmath128 erg s@xmath13 @xmath19 ) & 5.1@xmath159 & 5.4@xmath160 & 1.5@xmath134 & 1.5@xmath134 + & @xmath135 & 541/838 & 548/838 & 333/838 & 350/838 + & @xmath136 & 27/29 & 40/41 & 7.7/10 & 13/9 + & @xmath137@xmath138 & 0.58 & 0.52 & 0.66 & 0.15 + & & & & & + 5 & @xmath123 & 1.59@xmath125 & 1.82@xmath161 & 1.90@xmath139 & 1.54@xmath162 + & 0.22 kev flux ( 10@xmath128 erg s@xmath13 @xmath19 ) & 29@xmath163 & 13@xmath164 & 3.4@xmath131 & 1.1@xmath144 + & 210 kev flux ( 10@xmath128 erg s@xmath13 @xmath19 ) & 35@xmath165 & 11@xmath166 & 2.8@xmath147 & 1.9@xmath134 + & @xmath135 & 771/838 & 626/838 & 502/838 & 402/838 + & @xmath136 & 72/59 & 66/63 & 34/28 & 7/11 + & @xmath137@xmath138 & 0.1 & 0.37 & 0.19 & 0.7 + & & & & & + 6 & @xmath123 & 1.51@xmath125 & 1.82@xmath124 & 1.76@xmath155 & 2.28@xmath167 + & 0.22 kev flux ( 10@xmath128 erg s@xmath13 @xmath19 ) & 30@xmath163 & 15@xmath163 & 3.2@xmath131 & 1.4@xmath131 + & 210 kev flux ( 10@xmath128 erg s@xmath13 @xmath19 ) & 36@xmath168 & 13@xmath163 & 3.6@xmath154 & 0.6@xmath169 + & @xmath135 & 768/838 & 658/838 & 489/838 & 276/838 + & @xmath136 & 65/59 & 62/70 & 29/33 & 9/8 + & @xmath137@xmath138 & 0.29 & 0.76 & 0.66 & 0.36 + & & & & & + @xmath121 model 1 consists of a power - law modified by galactic absorption . + @xmath170all errors are for 90% confidence unless mentioned otherwise with all parameters taken to be of interest except absolute normalization . + @xmath171@xmath137 is the probability of exceeding @xmath172 for @xmath173 degrees of freedom if the model is correct . + cccc + + & & & + & & & + & & image a@xmath122 & image b@xmath122 + & & & + 1 & @xmath123 & 1.59@xmath124 & 1.86@xmath126 + & 0.22 kev flux ( 10@xmath174 erg s@xmath13 @xmath19 ) & 6.9@xmath143 & 4.28@xmath143 + & 210 kev flux ( 10@xmath174 erg s@xmath13 @xmath19 ) & 10.6@xmath175 & 3.97@xmath176 + & @xmath135 & 623/790 & + & & & + 2 & @xmath123 & 1.4@xmath132 & 1.6@xmath144 + & 0.22 kev flux ( 10@xmath174 erg s@xmath13 @xmath19 ) & 2.6@xmath177 & 6.5@xmath178 + & 210 kev flux ( 10@xmath174 erg s@xmath13 @xmath19 ) & 5.8@xmath179 & 10.2@xmath180 + & @xmath135 & 192/838 & 284/1060 + & & & + 3 & @xmath123 & 1.53@xmath181 & 2.4@xmath132 + & 0.22 kev flux ( 10@xmath174 erg s@xmath13 @xmath19 ) & 3.4@xmath182&8.4@xmath183 + & 210 kev flux ( 10@xmath174 erg s@xmath13 @xmath19 ) & 5.9@xmath184 & 3.0@xmath185 + & @xmath135 & 186/838 & 195/1060 + & & & + 4 & @xmath123 & 1.76@xmath186 & 2.03@xmath187 + & 0.22 kev flux ( 10@xmath174 erg s@xmath13 @xmath19 ) & 2.9@xmath188 & 6.5@xmath189 + & 210 kev flux ( 10@xmath174 erg s@xmath13 @xmath19 ) & 3.2@xmath190 & 4.3@xmath191 + & @xmath135 & 160/838 & 224/1060 + & & & + 5 & @xmath123 & 1.59@xmath192 & 2.33@xmath193 + & 0.22 kev flux ( 10@xmath174 erg s@xmath13 @xmath19 ) & 4.5@xmath194 & 5.0@xmath195 + & 210 kev flux ( 10@xmath174 erg s@xmath13 @xmath19 ) & 6.9@xmath196 & 1.8@xmath197 + & @xmath135 & 236/838 & 165/1060 + & & & + 6 & @xmath123 & 1.61@xmath198 & 1.81@xmath199 + & 0.22 kev flux ( 10@xmath174 erg s@xmath13 @xmath19 ) & 4.4@xmath200 & 4.6@xmath201 + & 210 kev flux ( 10@xmath174 erg s@xmath13 @xmath19 ) & 6.4@xmath202 & 4.7@xmath203 + & @xmath135 & 230/838 & 222/1060 + & & & + @xmath121 model 1 consists of a power - law modified by galactic absorption . the x - ray fluxes represent unabsorbed values . + @xmath170all errors are for 90% confidence unless mentioned otherwise with all parameters taken to be of interest except absolute normalization . +

j1131 is of particular interest because of its high amplitude ( a factor of 20 ) . the differences between the x - ray and optical flux ratios of he 1104 are less dramatic , but there is no significant soft x - ray or dust absorption , implying the presence of x - ray microlensing in this system as well . combining the x - ray data with the optical light curves we find that the x - ray emitting region of he 1104 is compact with a half - light radius , where the gravitational radius is r = 3.6 10 cm , thus placing significant constraints on agn corona models .

we present results from a monitoring campaign performed with the _ chandra x - ray observatory _ of the gravitationally lensed quasars rx j1131 and he 1104 . we detect significant x - ray variability in all images of both quasars . the flux variability detected in image a of rx j1131 is of particular interest because of its high amplitude ( a factor of 20 ) . we interpret it as arising from microlensing since the variability is uncorrelated with that of the other images and the x - ray flux ratios show larger changes than the optical as we would expect for microlensing of the more compact x - ray emission regions . the differences between the x - ray and optical flux ratios of he 1104 are less dramatic , but there is no significant soft x - ray or dust absorption , implying the presence of x - ray microlensing in this system as well . combining the x - ray data with the optical light curves we find that the x - ray emitting region of he 1104 is compact with a half - light radius , where the gravitational radius is r = 3.6 10 cm , thus placing significant constraints on agn corona models . we also find that the microlensing in he 1104 favors mass models for the lens galaxy that are dominated by dark matter . finally , we better characterize the massive foreground cluster near rx j1131 , set limits on other sources of extended x - ray emission , and limit the fluxes of any central odd images to be 3050 ( 3 ) times fainter than the observed images . # 1 # 1

0806.0866

i

we have argued that the plume and long tail of m86 formed due to ram pressure stripping forces generated as m86 falls into the virgo cluster . several studies have found a similar interpretation for the formation of this feature ( e.g. , forman et al . 1979 ; fabian et al.1980 ; rangarajan et al . 1995 , however see bregman & roberts 1990 ; finoguenov et al . we concentrate on these main results : * the plume and long tail observed in the diffuse emission are created by ram pressure stripping as m86 falls into the virgo cluster . the tail is 150 kpc in projection ( a simple estimate , which assumes free - fall velocity for m86 and an nfw potential for m87 , gives a lower - limt on the true length of the tail of 380 kpc ) , making this the longest ram pressure stripped tail presently known . * based on the x - ray spectra , we detect three distinct components associated with the m86/virgo cluster system : the virgo icm , with @xmath124 kev ; the extended halo of m86 , with @xmath125 kev ; and the cooler central and stripped gas of m86 , with @xmath126 kev . the temperature structure of the tail is consistent with ram pressure stripping , where the higher entropy m86 halo gas is stripped first and deposited in the tip of the tail , and the lower entropy m86 ism is stripped more recently , constituting the base of the tail and the plume . * the large line - of - sight velocity of m86 , and its position relative to the virgo cluster , tightly constrain its orbit , especially if it is assumed that the gas tail traces the orbit . in particular , the observations are inconsistent with a radial orbit . we show that m86 is at best only marginally bound to the virgo cluster , with an inner turning radius on the order of 300 kpc as expected from its recent in - fall . our best - fitting orbital model requires that m86 be close to m87 , less than 167 kpc closer than or 263 kpc farther than m87 along our line of sight , which is consistent with the most recent distance estimates based on surface brightness fluctuations ( mei et al . 2007 ) which give a line - of - sight separation of @xmath127 mpc . * the prominent plume of gas lying 3 4north of m86 appears to have been rapidly driven from m86 by ram pressure stripping . the projected position of the plume , which does not lie directly on our best - fit model orbit for m86 , can be understood if m86 has an aspherical potential ( as suggested by optical isophotes ) . if m86 moves through the virgo icm at an inclination angle relative to the local flow , the gas at the trailing edge is more easily stripped , thereby displacing the gas from the nominal orbit of m86 itself . this model may also explain the apparent double streams of gas seen trailing m86 , as well as those in other virgo galaxies . * the apparent brightness edge to the southeast seen in _ rosat _ observations is also seen in the _ chandra _ images . the edge is well fit with a two power law gas density model , with an abrupt jump in density by a factor of @xmath128 at the edge ( consistent with no jump ) . assuming that this brightness edge is the shock generated as m86 supersonically falls into the virgo cluster , the lack of a well - defined density jump is consistent with what is expected from our orbital model , which suggests that the orientation of the mach cone would make it difficult to detect the shock edge . the financial support for this work was provided by nasa contracts nas8 - 39073 , nas8 - 38248 , nas8 - 01130 , nas8 - 03060 , the chandra science center , and the smithsonian institution . beckmann , v. , gehrels , n. , favre , p. , walter , r. , courvoisier , t. j .- l . , petrucci , p .- o . , & malzac , j. 2004 , apj , 614 , 641 binggeli , b. , popescu , c. c. , & tammann , g. a. 1993 , a&as , 98 , 297 birzan , l. , rafferty , d. a. , mcnamara , b. r. , wise , m. w. , & nulsen , p. e. j. 2004 , apj , 607 , 800 bhringer , h. , briel , u. g. , schwarz r. a. , voges , w. , hartner , g. , & trmper , j. 1994 , nature , 368 , 828 bregman , j. n. , & roberts , m. s. 1990 , apj , 362 , 468 cappellari , m. , & copin , y. 2003 , mnras , 342 , 345 crowl , h. h. , kenney , j. d. p. , van gorkom , j. h. , & vollmer , b. 2005 , aj , 130 , 65 diehl , s. , & statler , t. s. 2006 , mnras , 368 , 497 edge , a. c. 1990 , phd thesis , univ . leicester fabian , a. c. , schwarz , j. , & forman , w. 1980 , mnras , 192 , 135 finoguenov , a. , & jones , c. 2002 , apj , 574 , 74 finoguenov , a. , pietsch , w. , aschenbach , b. , & miniati , f. 2004 , a&a , 415 , 415 forman , w. , schwarz , j. , jones , c. , liller , w. , & fabian , a. c. 1979 , apj , 234 , l27 machacek , m. e. , jones , c. , & forman , w. r. 2004 , apj , 610 , 183 matsushita , k. et al . 1994 , apjl , 436 , 41 maughan , b. j. , ellis , s. c. , jones , l. r. , mason , k. o. , crdova , f. a. , & priedhorsky , w. 2006 , apj , 640 , 219 mei , s. , et al . 2007 , apj , 655 , 144 mihos , c. , harding , p. , feldmeier , j. , & morrison , h. 2005 ; apjl , 631 , 41 navarro , j. s. , frenk , c. s. , & white , s. d. m. 1995 , mnras , 275 , 720 neilsen , e. h. , & tsvetanov , z. i. 2000 , apj , 536 , 255 neto et al . 2007 , mnras , 381 , 1450 nulsen , p. e. j. 1982 , mnras , 198 , 1007 nulsen , p. e. & carter , d. 1987 , mnras , 225 , 939 osullivan , e. , vrtilek , j. m. , kempner , j. c. , david , l. p. , & houck , j. c. 2005 , mnras , 357 , 1134 rangarajan , f. v. n. , white , d. a. , ebeling , h. , & fabian , a. c. 1995 , mnras , 277 , 1047 sarazin , c. l. , kundu , a. , irwin , j. a. , sivakoff , g. r. , blanton , e. l. , & randall , s. w. 2003 , apj , 595 , 743 schekochinin , a. a. , cowley , s. c. , r. m. kulsrud r. m. , rosin , m. s. , & heinemann , t. 2007 , preprint ( astro - ph/0709.3828 ) schindler , s. , binggeli , b. , & bhringer , h. 1999 , a&a , 343 , 420 smith , r. j. , lucey , j. r. , hudson , m. j. , schlegel , d.j . , & davies . r. l. 2000 , mnras , 313 , 469 takano , s. , awaki , h. , koyama , k. , kunieda , h. , tawara , y. 1989 , nautre , 340 , 289 takeda , h. , nulsen , p. e. j. , & fabian , a. c. 1984 , mnras , 208 , 261 vollmer , b. , braine , j. , combes , f. , sofue , y. 2005 , a&a , 441 , 473 white , d. a. , fabian , a. c. , forman , w. , jones , c. , & stern , c. 1991 , apj , 375 , 35 lcccc 318&2000 - 04 - 07&m86 & s3 , s2 , i2 , i3&12.964 + 803&2000 - 05 - 19&m84 & s3 , s2 , i2 , i3&26.699 + 963&2000 - 04 - 07&m86 & s3 , s1 , s2 , i2 , i3&13.220 + 1619&2001 - 06 - 08&ngc4388 & s3 , s2 , i2 , i3&19.705 + 2882&2002 - 01 - 29&ngc4438 & s3 , s2 , i2 , i3&24.891 + 5908&2005 - 05 - 01&m84 & s3 , s1 , s2 , i2 , i3&36.299 + 5912&2005 - 03 - 09&se of m86 & i0 , i1 , i2 , i3 , s2&31.370 + 5913&2005 - 03 - 19&m86 tail tip & i0 , i1 , i2 , i3 , s2&34.744 + 6131&2005 - 11 - 07&m84 & s3 , s1 , s2 , i2 , i3&37.855 + lccccc 1&0.724@xmath129//(2.4)&0.42@xmath130&1.71@xmath131&108/91=1.18&6235 + 1&0.677@xmath132/1.291@xmath133/(2.4)&0.64@xmath134&(1.5)&90/89=1.01&6235 + 2&0.697@xmath135/(1.2)/(2.4)&0.31@xmath136&&56/57=0.98&3086 + 3&0.653@xmath137/(1.2)/(2.4)&0.50@xmath138&(1.5)&88/83=1.06&4273 + 4&0.773@xmath139/(1.2)/(2.4)&0.47@xmath140&&109/84=1.29&8630 + 5&0.854@xmath141/(1.2)/(2.4)&0.40@xmath142&&94/93=1.01&4461 + 6&0.849@xmath143/(1.2)/(2.4)&0.31@xmath144&&89/88=1.01&5059 + 7&0.860@xmath145/(1.2)/(2.4)&0.43@xmath146&&87/74=1.18&2843 + 8&0.785@xmath147/(1.2)/(2.4)&0.45@xmath148&&44/40=1.09&1749 + 9&0.924@xmath149/(1.2)/(2.4)&0.50@xmath150&&30/29=1.03&1043 + 10&1.191@xmath151/(2.4)&0.42@xmath152&&20/25=0.73&739 + 11&0.865@xmath153/1.290@xmath154/(2.4)&0.55@xmath155&&163/176=0.92&8795 + 12&0.871@xmath156/1.176@xmath157/(2.4)&0.62@xmath158&&240/187=1.29&8914 + 13&0.675@xmath159/1.256@xmath160/2.723@xmath161&0.72@xmath162&&343/293=1.17&11033 + 14&0.625@xmath163/(1.2)/(2.4)&1.17@xmath164&1.82@xmath165&459/327=1.40&42002 + 15&0.790@xmath166/(1.2)/(2.4)&0.60@xmath162&&93/90=1.03&3666 + 16&1.355@xmath167/(2.4)&0.49@xmath168&&57/59=0.96&1746 + 17&1.091@xmath169/2.422@xmath170&0.40@xmath171&&53/45=1.18&3054 + 18&1.085@xmath172/2.107@xmath173&0.22@xmath174&&118/120=0.98&4643 + 19&0.651@xmath175/1.065@xmath176/(2.4)&0.25@xmath177&&147/128=1.15&7325 + 20&1.319@xmath178/(2.4)&0.39@xmath179&&30/23=1.29&1087 + 21&1.023@xmath180/(2.4)&0.22@xmath181&&147/105=1.39&2912 + 22&0.881@xmath182/1.236@xmath183/(2.4)&0.32@xmath136&&77/75=1.03&2646 + 23&1.186@xmath184/2.712@xmath185&0.45@xmath186&&214/236=0.91&5193 + = .31 . the model is a two - temperature thermal plasma with fitted temperatures and abundance ( given in the second row of table [ tab : spectra ] ) , plus an unresolved power law component with photon index of 1.5 and a fixed thermal plasma component to model emission from the virgo icm , all with galactic absorption . the data are from two s3 observations , obs - ids 318 and 963 ( see table [ tab : obs ] ) . [ fig : m86spec ] ] ) . the x - axis gives the radius from the apparent center of curvature defined by the feature . the best fit two power law density jump model is given by the solid line . [ fig : nedge ] ] towards us . locations on the orbits where the past orbit would also appear to project 100 kpc outside the current position of m86 are shown in red ( solid lines ; the midpoint of each of these regions is marked with an asterisk ) . both regions shrink for orbits with smaller outer turning radii . as plotted , all orbits pass through the virial radius at @xmath187 kpc on the @xmath188 axis . ] ( marked with an asterisk ) . orbits are plotted from the point where they cross the virial radius ( sometimes outside the field shown ) . ] , one representative orbit is shown projected onto the smoothed 0.5 2 kev image of m86 for the remaining plausible orbits . colors indicate the outer turning radius as follows : @xmath189 mpc , yellow ; @xmath190 mpc , blue ; @xmath191 mpc , green ; @xmath60 , red . ] kpc , one of the better candidates for the orbit of m86 . centered on the orbit , at equally spaced times , circles are plotted on the plane of the sky with radii @xmath192 , where @xmath77 is the time before the present when m86 was at that location and @xmath193 is the sound speed ( @xmath194 ) . ]

we detect three main diffuse components : the virgo icm at.4 kev , the extended halo of m86 at.2 kev , and the cooler central and stripped gas of m86 at.8 kev . the tail is 150 kpc in projection , and a simple estimate gives a lower limit on the true length of the tail of 380 kpc , making this the longest ram pressure stripped tail presently known . the projected position of the plume can be understood if m86 has an aspherical potential , as suggested by optical isophotes . the large line - of - sight velocity of m86 ( 1550 with respect to m87 ) , its position relative to the virgo cluster , and the orientation of the tail tightly constrain its orbital parameters . the data are inconsistent with a radial orbit , and imply inner and outer turning radii of kpc and mpc , indicating that m86 is , at best , only weakly bound to the virgo cluster .

we present results from a mosaic of nine _ chandra _ observations of m86 and the surrounding field . we detect three main diffuse components : the virgo icm at.4 kev , the extended halo of m86 at.2 kev , and the cooler central and stripped gas of m86 at.8 kev . the most striking feature is a long tail of emission , which consists of a plume 4north of m86 and two main extensions emanating from the plume . based on the morphology and temperature structure of the tail , we conclude that it is formed by ram pressure stripping of m86 as it falls into the virgo cluster and interacts with the virgo icm , in agreement with earlier work . the tail is 150 kpc in projection , and a simple estimate gives a lower limit on the true length of the tail of 380 kpc , making this the longest ram pressure stripped tail presently known . the total gas mass in the plume ( ) and tail ( ) is about three times that in the core of m86 , which supports the scenario where most of the gas was stripped rapidly and recently . the projected position of the plume can be understood if m86 has an aspherical potential , as suggested by optical isophotes . ram pressure stripping from an aspherical potential can also explain the split `` double tails '' seen in m86 and in other virgo cluster galaxies in the field . the large line - of - sight velocity of m86 ( 1550 with respect to m87 ) , its position relative to the virgo cluster , and the orientation of the tail tightly constrain its orbital parameters . the data are inconsistent with a radial orbit , and imply inner and outer turning radii of kpc and mpc , indicating that m86 is , at best , only weakly bound to the virgo cluster .

astro-ph0507578

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kh 15d , an extraordinary pre - main - sequence eclipsing binary system , is located in the young ( 24 myr ) open cluster ngc 2264 ( @xmath11 @xmath12 760 pc ) . in 1970 , a russian circular announced the discovery of eight new variable stars in ngc 2264 ( badalian & erastova 1970 ) . kh 15d was among these , and was given the name svs 1723 . it was found to vary by 1.1 mag and was classified as an irregular variable . in 1972 , the new variables discovered by badalian & erastova ( 1970 ) were included in the 58th name - list of variable stars ( kukarkin et al . 1972 ) , and kh 15d was given the name v582 mon . prior to october 2000 , kh 15d had been observed in various surveys of the open cluster ngc 2264 . flaccomio et al . ( 1999 ) and park et al . ( 2000 ) both observed kh 15d at least once while the system was bright and included it in their catalogs , each identifying it as # 391 and # 150 , respectively . earlier surveys of ngc 2264 ( herbig 1954 ; walker 1956 ; vasilevskis , sanders , & balz 1965 ) did not identify kh 15d as a cluster member most likely because of its proximity to the b2 iii star , hd 47887 ( see fig . its light was simply lost in the bright glow of the b2 iii star . this object gained its notoriety as kh 15d when it was reported to have unusual properties in 1995 based on a project at the van vleck observatory ( vvo ) to photometrically monitor star - forming regions ( kearns & herbst 1998 ) . this object was observed to undergo eclipses that were remarkably deep ( @xmath133.5 mag in @xmath14 ) and unusually long ( @xmath1316 days in 1999/2000 ) . of central interest was the evolution of the shape and duration of the eclipses that had been observed over a 5-year period ( hamilton et al . 2001 ) . out of eclipse , the observable star in this system was determined to have a spectral type of k6/k7 ( hamilton et al . 2001 ; agol et al . 2004 ) , while during eclipse , the observed spectrum was simply an attenuated version of that out of eclipse . an international campaign to monitor this intriguing system was begun during july 2001 . the primary goal of this project was to obtain much information about the structure of the intervening material . continued photometric observations from around the world provided nearly complete coverage of three consecutive eclipses during the 2001/2002 observing season ( herbst et al . these consecutive eclipses demonstrated that , in addition to the yearly changes observed in the phased data , differences in the shape of each individual eclipse could be observed over the course of a season . the shapes of ingress and egress were successfully modeled by the steady advance or retreat of a knife edge " across a limb - darkened star . in order to match the duration of ingress and egress , however , herbst et al . ( 2002 ) determined that the occulting edge must be inclined by @xmath1315@xmath8 to the motion of the star . these authors also reported that the object s color becomes slightly bluer during eclipse , which indicates that most ( if not all ) of the light received during eclipse is due to scattering . polarization measurements made by agol et al . ( 2004 ) and gary schmidt ( private communication ) show that out of eclipse , the system exhibits low polarization consistent with zero . during eclipse , however , the polarization is observed to increase to roughly 2% across the optical spectrum . these results support the conclusion that the star is likely completely eclipsed so that the flux during eclipse is due entirely to scattered radiation , and that the obscuring material is most likely made up of relatively large grains ( @xmath1310 @xmath15 m ; agol et al . 2004 ) . high - resolution spectra obtained during the december 2001 eclipse ( hamilton et al . 2003 ) revealed that the system is still undergoing accretion and driving a bipolar outflow . recently , extended molecular hydrogen emission near 2 @xmath15 m was observed spectroscopically by deming , charbonneau , & harrington ( 2004 ) . given the spatial extent of the emission , and the observed h@xmath16 line profile , deming et al . ( 2004 ) suggest that the ambient h@xmath16 gas is being shocked by a bipolar outflow from the star and/or disk . further evidence for an extended and well - collimated outflow was provided by tokunaga et al . ( 2004 ) , who obtained broad - band and narrow - band infrared images of kh 15d , showing a jet - like h@xmath16 emission filament that extends out to @xmath17 from the object . the position angle ( @xmath1320 ) of the in - eclipse polarization is nearly parallel to this h@xmath16 filament ( agol et al . 2004 ) . many hypotheses have been proposed since 2001 to explain the evolving eclipses of kh 15d . most of these involve circumstellar material in some way . hamilton et al . ( 2001 ) , herbst et al . ( 2002 ) , winn et al . ( 2003 ) , and agol et al . ( 2004 ) all proposed the idea of an edge - on circumstellar disk with a warp that periodically passes in front of the star . barge & viton ( 2003 ) proposed that the eclipses were caused by an orbiting vortex of solid particles , and grinin & tambotseva ( 2002 ) suggested that an asymmetric common envelope in a binary system could accurately reproduce the eclipses . historical studies by winn et al . ( 2003 ) found that observations made between 1913 and 1950 were consistent with no eclipses . johnson & winn ( 2004 , hereafter jw04 ) discovered that between 1967 and 1982 , the system alternated between bright and faint states with the same period as observed today , but 180@xmath8 out of phase with the current eclipses . additionally , the eclipse depth was much smaller ( only 0.67 @xmath0 0.07 mag in @xmath14 instead of 3.5 mag ) , and when out of eclipse , the system was brighter by 0.9 @xmath0 0.15 mag than it is today ( jw04 ) . while herbst et al . ( 2002 ) first suggested the possibility of a binary companion , the light curve between 1967 and 1982 led jw04 to believe that the light from a second brighter star once contributed to the flux coming from this system , and that the second star is now completely obscured . these results have been confirmed and extended by data obtained at various observatories between 1954 and 1997 ( johnson et al . 2005 ) . models of the kh 15d system that explained the historical and modern - day light curves were put forward almost simultaneously by winn et al . ( 2004 ) and chiang & murray - clay ( 2004 ) . each model involves an eccentric pre - main - sequence binary whose motion periodically carries it behind a precessing circumbinary disk . these models are supported by the results of a recent high - resolution spectroscopic monitoring program of kh 15d : johnson et al . ( 2004 ) have observed radial - velocity variations that are consistent with a binary companion with an orbital period in agreement with the 48-day photometric period . in summary , kh 15d is now known to be a pre - main - sequence binary system with a strongly eccentric orbit of 48.38 days . the brighter component b is currently totally obscured by the circumbinary ring or disk , while only the fainter member a emerges from behind the obscuring material for just less than half the period . to explain the secular variations observed in the light curve over the past 9 years , it has been suggested that the eclipses occur whenever the motion of a star carries it behind the ring , with a period equal to that of the binary orbital period . if this ring is also precessing , it would be possible to explain the changing length of the eclipse . in this paper we present the analysis of photometric data on kh 15d obtained at vvo between 1995 and 2000 , color data obtained at the cerro tololo inter - american observatory ( ctio ) during the 2001/2002 season , and the results of the 20022004 observing campaigns as compared to those of 2001/2002 . section 2 describes the principal sources of optical photometric observations , the data reduction , and the resulting photometry for each participating observatory in the 20022004 campaigns . a comparison of individual data sets is shown in section 3 , while the results and analysis of these data are presented in section 4 . a brief discussion of our findings in light of the recent models is also presented , while a more complete interpretation is deferred to a future paper ( winn et al . 2005 , in preparation ) .

we present results from the most recent ( 20022004 ) observing campaigns of the eclipsing system kh 15d , in addition to re - reduced data obtained at van vleck observatory ( vvo ) between 1995 and 2000 . phasing nine years of photometric data shows substantial evolution in the width and depth of the eclipses . these results are interpreted and discussed in the context of the recent models for this system put forward by winn et al . ( 2004 ) and chiang & murray - clay ( 2004 ) . ( 2004 ) .

we present results from the most recent ( 20022004 ) observing campaigns of the eclipsing system kh 15d , in addition to re - reduced data obtained at van vleck observatory ( vvo ) between 1995 and 2000 . phasing nine years of photometric data shows substantial evolution in the width and depth of the eclipses . the most recent data indicate that the eclipses are now approximately 24 days in length , or half the orbital period . these results are interpreted and discussed in the context of the recent models for this system put forward by winn et al . ( 2004 ) and chiang & murray - clay ( 2004 ) . a periodogram of the entire data set yields a highly significant peak at 48.37 0.01 days , which is in accord with the spectroscopic period of 48.38 0.01 days determined by johnson et al . ( 2004 ) . another significant peak , at 9.6 days , was found in the periodogram of the out - of - eclipse data at two different epochs . we interpret this as the rotation period of the visible star and argue that it may be tidally locked in pseudosynchronism with its orbital motion . if so , application of hut s ( 1981 ) theory implies that the eccentricity of the orbit is = 0.65 0.01 . analysis of the uves / vlt spectra obtained by hamilton et al . ( 2003 ) shows that thesin of the visible star in this system is 6.9 0.3 km s . using this value ofsin and the measured rotation period of the star , we calculate the lower limit on the radius to ber , which concurs with the value obtained by hamilton et al . ( 2001 ) from its luminosity and effective temperature . here we assume that = 90 since it is likely that the spin and orbital angular momenta vectors are nearly aligned . one unusually bright data point obtained in the 1995/1996 observing season at vvo is interpreted as the point in time when the currently hidden star ( b ) made its last appearance . based on this datum , we show that star b is 0.46 0.03 mag brighter than the currently visible star a , which is entirely consistent with the historical light curve ( johnson et al . 2005 ) . finally , well - sampled and data obtained at the ctio / yale 1-m telescope during 2001/2002 show an entirely new feature : the system becomes bluer by a small but significant amount in very steady fashion as it enters eclipse and shows an analogous reddening as it emerges from eclipse . this suggests an extended zone of hot gas located close to , but above , the photosphere of the currently visible star . the persistance of the bluing of the light curve shows that its length scale is comparable to a stellar radius .

astro-ph0507578

r

the full data set now contains 6694 measurements of cousins @xmath14 magnitude covering nine seasons of observation between 1995 october and 2004 march , as well as additional color measurements . magnitudes in @xmath14 are given in table 6 and colors are given in table 7 . both tables , in full , are available electronically . in this section we describe the light and color variations and propose a rotation period for the star . we also provide some qualitative guidance to the interpretation of the variations based on the models of winn et al . ( 2004 ) and chiang & murray - clay ( 2004 ) . detailed modeling of the photometric ( and spectroscopic ) data will be done by winn et al . we turn first to a discussion of the light variations in @xmath14 , where most of the data are available . figure 8 shows the data from the last two seasons , which is the primary addition to the data set in this paper . clearly , we have obtained good coverage of a total of nine eclipses over two seasons . results indicate that the trends noticed by hamilton et al . ( 2001 ) ( reduction in amplitude of the central reversal and widening of the eclipse ) are continuing , and it would appear that the duration of the eclipse is now about one - half of the period ( compare with fig . the shapes of ingress and egress are not identical and show some level of variation , not only from eclipse to eclipse , but also from year to year . since 2001 , the duration of the eclipse has been growing by roughly 2 days year@xmath4 . however , as will be seen in section 4.1.2 , this has not always been the case . in earlier years , such as from 1998/1999 to 1999/2000 , the change in eclipse length was close to 1 day . in figure 9 , the last two seasons are compared with the seven previous ones for which modern , ccd photometry is available . some of the features and a distinct secular variation of the light curve can be seen . here , it appears that the out - of - eclipse brightness of the star has not changed by more than @xmath130.1 mag since 1995 , while the depth of the eclipse has grown by @xmath131 mag over that same interval . in fact , it appears as though the eclipse depth has been increasing at a rate of @xmath130.2 mag year@xmath4 . to determine the best estimate of the mean @xmath14 magnitude out - of - eclipse , we looked solely at the data obtained at vvo since it was the only observatory from which we had data for every year . we began by calculating a mean @xmath14 magnitude per year to see if there was any variation in the out - of - eclipse brightness with time . the phases that corresponded to the out - of - eclipse state changed as the width of the eclipse evolved with time ( discussed below ) , and are listed in table 8 . figure 10 shows the mean @xmath14 magnitudes versus observing season at vvo . the straight line represents a simple linear fit to the data . it appears as if the currently visible star might also be fading a bit , but we can not be sure whether this is a significant trend . as shown below , the increasing depth of the eclipse is accompanied by an increased time duration and a diminishing height for the central brightness reversal . the current data show that these trends , noticed previously ( see hamilton et al . 2001 ; herbst et al . 2002 ) , have continued in the last two seasons . during the first season of monitoring at vvo there was one unusually bright data point , taken on only the sixth night that the system was observed . repeated checks have shown that this is a valid datum and can not be discarded as an error . as will be shown below , its phase also corresponds to a point close to mid - eclipse . we now interpret that point as the only observation in our data set during which the relatively unobscured light from the currently invisible star ( b ) was seen directly . this point occurred close to periastron when star b was peaking above the disk for just about the last time . on that night , the system s light was only due to star b , since star a was hidden behind the disk . if this interpretation is correct , it means that the magnitude of star b is equal to or brighter than @xmath14 = 14.01 @xmath0 0.01 ( see table 6 ) . since star b might also have been partly hidden itself , we can not say for sure based on one measurement whether star b is brighter than @xmath14 = 14.01 @xmath0 0.01 , but it certainly can not be fainter . this conclusion is consistent with the historical light curve . johnson et al . ( 2005 ) show that prior to 1990 , the system was at times as much as 1 mag brighter than it appears today . if we take the difference between the combined light ( star a + star b ) and the light of star a alone to be @xmath37 mag , then the magnitude difference between star a and b is 0.45 . the mean @xmath14 magnitude out - of - eclipse based on the vvo data ( see fig . 10 ) shows that star a has a mean @xmath14 = 14.47 @xmath0 0.03 mag . assuming a minimum @xmath14 magnitude of 14.01 @xmath0 0.01 for star b , the mean brightness of star b is 0.46 @xmath0 0.03 mag brighter than star a. to make further progress we wish to phase the light curve with the appropriate period for the system , a task to which we now turn . it is important to establish the period of this system to the highest accuracy possible so that the data can be properly phased and the evolution of the light curve with time correctly displayed . it is now known that the 48-day period comes from the orbital motion within the binary . as such , the most definitive determination of the period should come from radial - velocity measurements and the spectroscopic - binary solution . this yields a period of 48.38 days with an uncertainty of about 0.01 days ( johnson et al . the problem with this method is that only a portion of the full orbit of one star can currently be seen , and it is the part near apastron which provides the least leverage on the solution . a second complication is that the visible star may suffer from a rossiter effect ( worek 1996 ) of unknown size as it enters or emerges from eclipse , depending on the inclination angle of the rotation axis to the line of sight . therefore , the data that provide the greatest leverage on the radial - velocity solution ( i.e. , those taken during late egress or early ingress ) may also be the data which are compromised in this regard . hence , we believe it is important to ask independently of the radial velocities whether the period of the system can be determined . the problem with the photometric method is , of course , that the light curve is evolving with time due to the progressive occultation by a foreground screen . this puts an additional time - dependent behavior into the system , albeit on a much longer time scale than the orbital period . to proceed , we first did a fourier transform of all of the modern photometric data using the scargle periodogram technique ( scargle 1982 ; horne & baliunas 1986 ) . this yielded a highly significant peak in the periodogram at 48.367 days ( see fig . 11 ) , which we round to 48.37 , as discussed below . this is gratifyingly close to the spectroscopic period and to the previously reported photometric period of 48.36 days ( herbst et al . 2002 ) . we attempted to refine the photometric period by focusing on a particular feature in the light curve whose phase we believe is stable and whose location we could determine from season to season . the only such feature that exists is the peak of the central reversal ( see fig . 12 ) , which we take to be the point in the orbit when the currently unseen star is closest to the edge of the obscuring cloud . assuming that this is a stable , fixed location in the orbit , if we could phase these central peaks we would have a good estimate of the period . unfortunately , it turns out that this method lacks discrimination because the location of the central peak is not sufficiently well defined by the light curves , especially the early ones where the data density is too low . a difference of 0.01 days in period is not significant and does not affect our results , as it corresponds to only 0.75 days over the 75 cycles covered by our monitoring and the early data do not constrain the time of the central peak to better than that . therefore , we find it impossible to improve on the accuracy of the period determinations with just these data . it might be possible to do this photometrically using the historical data , but any discussion of that is postponed to a later contribution ( winn et al . 2005 , in prep . ) . here we simply adopt the result of the periodogram analysis , 48.37 days , noting that it is consistent with the spectroscopic determination ; the 0.01 day difference does not affect any of the analysis or conclusions reported here . during the 20012004 observing seasons , a great deal of effort was made to observe kh 15d out - of - eclipse as well as in eclipse . significantly more data populated the bright phase of the light curve during these seasons than ever before , and small - scale variations ( @xmath130.08 mag over the course of 814 days in 2002/2003 ) are evident ( see fig . 4 and section 3.1 ) . since the visible star in the kh 15d system is a weak - lined t tauri star ( wtts ; hamilton et al . 2001 ) , it is most likely spotted in some fashion . it has been determined that this k7 star is still actively accreting ( hamilton et al . 2003 ) , and could therefore exhibit accretion hot spots on its surface , in addition to any dark , magnetically induced star spots . if this is the case , a closer look at the out - of - eclipse data from the 20012004 seasons may provide an estimate for the rotation period of the star . the analysis above indicates that systematic errors between data sets are relatively small , being at the level of 0.02 mag or less . however , when searching for the tiny amplitudes ( less than 0.1 mag ) that may characterize rotationally induced spotted - star variations , even errors of this size may make the search more difficult . therefore , we have searched each observatory s data set independently for periodicity during the out - of - eclipse phases . it is also prudent to confine the search to a single season of observation since spots are well known to evolve on time scales of less than one year . hence , one rarely finds phase coherence of spot variations extending over more than one observing season . detecting spots on wttss that are not undergoing eclipses is difficult enough , and generally only 15% or less of the stars in a cluster field will exhibit coherent periodic variations over a season s observing . in this star we have greater difficulty because during about half the observing season the star is in eclipse . nonetheless , we have found that periodogram analyses of the available data sets reveals highly significant periods in three cases ( see fig . 13 ) , as listed in table 9 . notably , two of these periods are identical to within the errors , averaging to 9.6 days . the chance of finding two exactly equal , highly significant periods in these data is vanishingly small if the periodicity is not real ; we thus identify the detected period as the likely rotation period of the visible star . it is interesting that the third significant period found in the periodograms ( 7.95 d ) is very close to the beat period between 9.6 and 48.37 days . supporting evidence for our interpretation comes from the measured @xmath2sin@xmath3 of the star . as discussed in appendix a , we derive a value of @xmath2sin@xmath3 = 6.9 @xmath0 0.3 km s@xmath4 for the visible component based on high - resolution spectra obtained out of eclipse . since sin@xmath3 is likely to be very close to 1.0 for this star ( assuming that the spin and orbital angular momenta vectors are nearly aligned ) , one can easily calculate that for a radius of @xmath5r@xmath6 ( hamilton et al . 2001 ) , the expected rotation period is 9.6 @xmath0 0.1 days , consistent with our result . both the photometry and spectroscopy of this system out - of - eclipse concur in suggesting a rotation period of 9.6 days for the visible component . to within the errors , this is a 5:1 resonance with the orbital period ( 48.37/5 = 9.67 ) , although it is not clear whether this is physically significant or just a numerical coincidence . a rotation period of 9.6 days is somewhat long for a 0.6 m@xmath6 wtts in ngc 2264 , although not unprecedented . the ( bi)modal values for stars more massive than 0.25 m@xmath6 are around 1 and 4 days . however , about 12% of the 182 cluster stars in that mass range with known rotational periods have @xmath38 days ( lamm et al . could the slightly slower than typical rotation of the visible star in the kh 15d system be caused by a tidal interaction between the components ? the effect of tidal friction on rotation can be estimated quantitatively based on the seminal theory of zahn ( 1977 ) for stars with convective envelopes . he shows that the synchronization time for a star s rotation to become tidally locked to its revolution is approximately given by @xmath39 where @xmath40 is the mass ratio , @xmath41 is the semimajor axis , @xmath21 is the stellar radius , and @xmath42 is given in years . most of the torque in a highly eccentric system will naturally occur at periastron . with @xmath43 and @xmath44 , we find a synchronization time of @xmath135 my . hence , it is not unreasonable to suggest that tidal friction is responsible for some degree of slowing of this wtts . we further note that since the orbit is rather eccentric , one would not expect to reach synchronous rotation , but only pseudosynchronous rotation . the pseudosynchronization timescale describes a near synchronization of revolution and rotation around periastron ( hut 1981 ) . hut ( 1981 ) has shown in elegant fashion that for binaries with eccentricities exceeding @xmath130.3 , as must surely be the case for kh 15d , tidal interaction near periastron is expected to produce an equilibrium angular rotation velocity of about 0.8 times the orbital angular velocity at periastron . one may write , therefore , that the pseudosynchronous rotation period ( @xmath45 ) predicted by this theory is related to the orbital period ( @xmath46 ) by @xmath47 where @xmath48 is near 0.8 for @xmath49 and is given precisely by hut ( 1981 ) . the range of particular interest for kh 15d is @xmath50 as discussed by johnson et al . ( 2004 ) , because these solutions are consistent with the radial velocities and with the inferred masses of the components based on astrophysical constraints . over this limited range , and somewhat beyond it , @xmath48 = 0.81 @xmath0 0.01 . adopting @xmath51 and @xmath46 = 48.37 @xmath0 0.01 yields a rather precise prediction for @xmath1 of 0.65 @xmath0 0.01 . this is the required orbital eccentricity if the star is in pseudosynchronous rotation and if the theory of hut ( 1981 ) is correct . remarkably , this eccentricity is very close to those inferred on the basis of two independent methods . as already noted , the orbital solution based on radial velocities , together with astrophysical constraints on the masses of the components , leads to @xmath52 , just barely outside of the present result . model fits to the light curve and its evolution over more than fifty years , by winn et al . ( 2004 ) and winn et al . ( 2005 , in prep . ) , also suggest an eccentricity of between 0.55 and 0.7 . since the rotation rate of the visible component is notably slower than that of most stars of comparable mass and age , and since it agrees so well with the predicted pseudosynchronous period , we suggest that the star has , indeed , been tidally locked into its current configuration . that , in turn , puts a rather severe limit on the possible eccentricity of the orbit , assuming that the locking has reached equilibrium and that the theory of hut ( 1981 ) is accurate in its prediction of @xmath48 . we note that the strong sensitivity of @xmath45 to @xmath1 means that there is only a very small range of measured rotation periods which would have given consistent results with the orbital solution and light - curve fitting techniques . for comparison , a normal rotation period of around 14 days for this star would have predicted a value of @xmath1 = 0.80.95 for this binary , rather extreme solutions that are inconsistent with the other results . while most of the monitoring has been in the @xmath14 band due to the brightness of the star during eclipse , we have also obtained some data at other wavelengths which reveal interesting features of the system . here we discuss the color results obtained at ctio in 2001/2002 and at the usno during several seasons . the discovery reported by herbst et al . ( 2002 ) that the star is generally bluer when fainter is confirmed , but we now have much more detailed and intriguing information on the color variations and their phase dependence . extensive @xmath20-band and @xmath10-band observations were made during the 2001/2002 season at ctio with the yale 1 m telescope ( see sections 2.8 and 3.1 for details ) and are shown in figures 14 and 15 . the solid and dashed lines in figure 14 are provided to indicate the approximate beginning of ingress and ending of egress , respectively . while the johnson magnitudes can be transformed to cousins for comparison with other data sets , there is no need to do so in this section , so we plot the results in the johnson system . the high density of color data obtained at ctio during this season reveals an interesting new feature of the behavior of kh 15d : it becomes bluer by a small but significant amount in very steady fashion as it enters eclipse and shows an analogous reddening as it emerges from eclipse . this is quite easily seen in both the time and phased versions of the light curves ( fig . 14 and 15 , respectively ) . it is also confirmed by the less dense but more temporally extended color monitoring done at the usno as described in the next section . while the general trend of bluer when fainter had been recognized for this star previously ( herbst et al . 2002 ) and has been seen in other young stars , such as uxors ( e.g. , herbst & shevchenko 1998 ) , the smooth decrease ( increase ) in @xmath53 seen during ingress ( egress ) in figure 15 is remarkable and unprecedented . before discussing its interpretation , we complete a description of the color behavior during eclipse . as both figures 14 and 15 show , the color change that occurs as the star goes into eclipse does not continue smoothly throughout the eclipse . while the data are noisy due to the low brightness of the star at those phases , it is clear that the star does not maintain a steady color with phase during eclipse . our impression of figure 15 is that there are actually three phases when the star has its bluest colors , peaking at about @xmath54 = 1.21.3 mag , or 0.30.4 mag bluer than the out - of - eclipse value of @xmath54 = 1.6 mag . these phases occur around @xmath00.17 and close to phase 0 . it is interesting that there is also a distinctive feature in the light curve at each of these three phases . at @xmath00.17 phase ( in 2001/2002 ) there is a distinct change of slope in the decline rate during ingress and the rise rate during egress . while this distinctive change of slope can be seen in the 2001/2002 light curve , it is even more noticeable in the light curves of the last two years ( see fig . 8) , where it occurs at phases of about @xmath00.20 and @xmath00.24 , respectively . the other feature in the light curve which seems to correspond to a blue extreme in the colors is the well - known central reversal near phase 0 . before discussing the interpretation of these interesting features , we turn to a description of the other major set of color data , that obtained at the usno . @xmath20 , @xmath55 , and @xmath56-band monitoring took place at the usno 1.3 m telescope throughout the 2001/2002 season , while @xmath19 , @xmath20 , @xmath55 , and @xmath56-band monitoring took place at the 1.0 m telescope during 2002/2003 ( see section 2.1 for details ) . it was determined from the first observing season that the object was simply too faint in @xmath19 to provide any reliable photometry at those wavelengths during eclipse . over the second season of monitoring , @xmath19-band measurements were obtained out - of - eclipse , in addition to the standard @xmath20 , @xmath55 , and @xmath56 observations . during 2003/2004 , only @xmath20 , @xmath55 , and @xmath56 data were obtained during three consecutive egresses . in figure 16 , we show the behavior of all of the cousins - band colors monitored at the usno during the 2002/2003 season . the trend is clearly quite similar to what was seen in the ctio data in 2001/2002 namely , there is a distinctive bluing of the system just as it enters eclipse or corresponding reddening as it emerges from eclipse . in addition , there are clearly some significant color variations out - of - eclipse which we attribute to star - spot activity on the visible star . combining the color data obtained over many seasons at the usno , we illustrate the overall trend of color with brightness in figure 17 . this confirms our impression that , out of eclipse , the star is about as red as it gets and shows relatively little color variation beyond what may be explained through star spots . as it enters ( emerges from ) eclipse the star gets bluer ( redder ) by 0.10.2 mag . near minimum light there are substantial color variations ; the star is sometimes at its bluest extreme , which is 0.30.4 mag bluer in @xmath53 than out - of - eclipse . however , sometimes it shows very little , if any , color effect . a full explanation of the color data must await improved understanding of the details of this system , which will only come from an extensive phenomenological model currently being constructed ( winn et al . 2005 , in prep ) . however , qualitative explanations for the observed trends can be proposed based on a few simple arguments . these lead to a set of questions that need to be addressed , and they suggest further observations that may clarify the situation . basically , blue colors indicate either the importance of wavelength - dependent scattering , such as from small grains or molecules , or the presence of a hotter component in the system , or both . it is likely that there is a hotter component in the system , since the currently invisible companion to the k7 star is known to be more luminous , as discussed above . all models of pre - main - sequence contraction indicate that the more massive star in a coeval pair is also more luminous and hotter , so it is reasonable to suppose that the currently invisible component of this system is also bluer than the k7 star . however , since the system was never substantially brighter in the past , even when both stars were visible , it is also true that this invisible component can not be much more massive , luminous , or hotter than the k7 star . in fact , the lack of detectable change of spectral type during minimum means there is little other than k6 or k7 light in the system , as far as a stellar component . the original interpretation proposed for the color variation by herbst et al . ( 2002 ) is that near minimum light , we see the system primarily or only by reflected light and that some small grains are involved in the reflection . this is supported by the increased polarization detected near minimum light by agol et al . the current data show , however , that there is almost certainly not a single color to which the star moves during eclipse , but rather that there is a great deal of real variability , some or all of which is phase dependent . therefore , it can not simply be that all of the light of the system is coming from distant , scattered radiation . in particular , we are impressed by the relative peak in blueness that occurs near phase zero in the color - phase plots ( fig . 15 and 18 ) . this is the time when the hotter , currently invisible , star is closest to the edge of the occulting cloud . we propose that the blue peak at this phase may be caused by this fact . we are apparently seeing a very small amount of either transmitted light or increased importance in the reflected component due to the light of this star , or , perhaps , the extension of a hot , circumstellar nebula associated with it , above the obscuring wall . in any event , we tentatively attribute the central peak in blue color and the phase - dependent variations around it as due to the orbital motion of a slightly bluer component ( than the k7 star ) relative to the edge of the occulting disk and , perhaps , relative to the principal scatterers . the blue peaks associated with phases @xmath00.17 in 2001/2002 are an entirely new feature of the light of this system revealed by the intensive color monitoring at ctio during that season and deserve some explanation . we find it interesting , as noted above , that they seem to correlate with a distinct change in slope that occurs in the decline ( rise ) in magnitude during late ingress ( early egress ) . one problem in interpreting these data is that we do not yet know how sharp the occulting edge of the cloud is . let us suppose , for the purposes of this qualitative study , that the edge is very sharp . in that case , we can identify the change of slope in decline ( rise ) rate as the point where the photosphere has just been completely covered ( has first appeared ) . the fact that the color peaks blue at that point indicates that the blue light is closely associated with the photosphere , arising just above it . we suggest , therefore , that the light in this system contains a hotter component associated with an extended chromosphere or corona of the k7 star ( and possibly its invisible companion as well ) . we have no idea whether the physical nature of this is a scaled - up solar - like chromosphere , a magnetically channeled accretion column , or something else . but the color evidence suggests an extended hotter , dense , optically thick zone located close to the photosphere of the k7 star . the persistence of the bluing of the light curve shows that it must be extended on a length scale comparable to a stellar radius . an alternative model is that one is seeing a peculiar scattering effect just as the star enters ( emerges ) from full eclipse . one could imagine , for example , that strongly forward scattered light might glance off the top of an occulting disk providing a bluish glint " at these phases . this would require , of course , wavelength - dependent scattering and , therefore , some component other than the obscuring cloud ( which produces no reddening of the transmitted light ) . if wavelength - dependent reflection is heavily involved here , then there should be some dramatic increases in polarization during these phases . it would definitely be interesting to extend the polarization study of agol et al . ( 2004 ) to a wider variety of phases . it will also be important to continue to monitor the color during these phases in future eclipses , hopefully including the @xmath57 band with larger telescopes , which will give important information on the nature of the scattering or the temperature of the emission zone .

the most recent data indicate that the eclipses are now approximately 24 days in length , or half the orbital period . a periodogram of the entire data set yields a highly significant peak at 48.37 0.01 days , which is in accord with the spectroscopic period of 48.38 0.01 days determined by johnson et al . we interpret this as the rotation period of the visible star and argue that it may be tidally locked in pseudosynchronism with its orbital motion . if so , application of hut s ( 1981 ) theory implies that the eccentricity of the orbit is = 0.65 0.01 . ( 2003 ) shows that thesin of the visible star in this system is 6.9 0.3 km s . using this value ofsin and the measured rotation period of the star , we calculate the lower limit on the radius to ber , which concurs with the value obtained by hamilton et al . ( 2001 ) from its luminosity and effective temperature . here we assume that = 90 since it is likely that the spin and orbital angular momenta vectors are nearly aligned . based on this datum , we show that star b is 0.46 0.03 mag brighter than the currently visible star a , which is entirely consistent with the historical light curve ( johnson et al . 2005 ) . finally , well - sampled and data obtained at the ctio / yale 1-m telescope during 2001/2002 show an entirely new feature : the system becomes bluer by a small but significant amount in very steady fashion as it enters eclipse and shows an analogous reddening as it emerges from eclipse . this suggests an extended zone of hot gas located close to , but above , the photosphere of the currently visible star . the persistance of the bluing of the light curve shows that its length scale is comparable to a stellar radius .

we present results from the most recent ( 20022004 ) observing campaigns of the eclipsing system kh 15d , in addition to re - reduced data obtained at van vleck observatory ( vvo ) between 1995 and 2000 . phasing nine years of photometric data shows substantial evolution in the width and depth of the eclipses . the most recent data indicate that the eclipses are now approximately 24 days in length , or half the orbital period . these results are interpreted and discussed in the context of the recent models for this system put forward by winn et al . ( 2004 ) and chiang & murray - clay ( 2004 ) . a periodogram of the entire data set yields a highly significant peak at 48.37 0.01 days , which is in accord with the spectroscopic period of 48.38 0.01 days determined by johnson et al . ( 2004 ) . another significant peak , at 9.6 days , was found in the periodogram of the out - of - eclipse data at two different epochs . we interpret this as the rotation period of the visible star and argue that it may be tidally locked in pseudosynchronism with its orbital motion . if so , application of hut s ( 1981 ) theory implies that the eccentricity of the orbit is = 0.65 0.01 . analysis of the uves / vlt spectra obtained by hamilton et al . ( 2003 ) shows that thesin of the visible star in this system is 6.9 0.3 km s . using this value ofsin and the measured rotation period of the star , we calculate the lower limit on the radius to ber , which concurs with the value obtained by hamilton et al . ( 2001 ) from its luminosity and effective temperature . here we assume that = 90 since it is likely that the spin and orbital angular momenta vectors are nearly aligned . one unusually bright data point obtained in the 1995/1996 observing season at vvo is interpreted as the point in time when the currently hidden star ( b ) made its last appearance . based on this datum , we show that star b is 0.46 0.03 mag brighter than the currently visible star a , which is entirely consistent with the historical light curve ( johnson et al . 2005 ) . finally , well - sampled and data obtained at the ctio / yale 1-m telescope during 2001/2002 show an entirely new feature : the system becomes bluer by a small but significant amount in very steady fashion as it enters eclipse and shows an analogous reddening as it emerges from eclipse . this suggests an extended zone of hot gas located close to , but above , the photosphere of the currently visible star . the persistance of the bluing of the light curve shows that its length scale is comparable to a stellar radius .

1403.4240

i

interacting supernovae ( sne ) are stellar explosions that collide with dense circumstellar material ( csm ) produced by the progenitor star . these events are raising critical new questions about the final evolutionary phases of massive stars and the mass - loss episodes that ensue before core collapse ( smith & arnett 2014 ) . type - iin and ibn sne , in particular , are interacting sne that are characterized spectroscopically by the presence of relatively narrow emission lines of h and he in their spectra ( schlegel 1990 ; filippenko 1997 ; pastorello et al . 2008 ) , which arise from dense csm that becomes illuminated by the shock between the fast moving sn ejecta and slower moving csm ( chevalier & fransson 1994 ) . as such , observations of interacting sne probe the stellar progenitor s pre - sn mass - loss history , providing valuable information on its final evolutionary episodes . various lines of evidence show that interacting sne require eruptive pre - sn mass loss that is reminiscent of luminous blue variable ( lbv ) stars , like @xmath9 car , although observations indicate a wide range of mass - loss properties ( e.g. , see the review by smith 2014 ) . the eruptions are often detectable as extragalactic transients , commonly referred to as ` sn impostors ' ( van dyk 2000 ; smith et al . 2011a ; kochanek et al . 2012 ) , which can rival the luminosity of a sn and spectroscopically mimic sne iin . although the observational distinction between interacting sne and sn impostors is not always clear , a direct link connecting these phenomena has been established for several objects . the progenitors of sn 2006jc and sn 2011ht were detected undergoing luminous outbursts 12 yr prior to their core - collapse explosions ( foley et al . 2007 ; pastorello et al . 2008 ; fraser et al . sn 2010mc ( ofek et al . 2013a ) was also detected 12 months before dramatically brightening , although for this case it appears that the precursor event may actually have been the initial phases of the sn caught unusually early ( smith , mauerhan , & prieto 2014 ) . perhaps the most interesting transient observed to have undergone multiple phases of eruptive mass loss is sn 2009ip . originally classified as a sn ( maza et al . 2009 ) , this object was actually discovered during an lbv outburst that is , as a sn impostor ( smith et al . 2010 ; foley et al . 2011 ) . several years of continued activity were followed photometrically and spectroscopically , leading up to sn 2009ip s most extreme outburst in 2012 ( mauerhan et al . 2013 ; prieto et al . 2013 ; levesque et al . 2014 ; smith et al . 2013b ; smith , mauerhan , & prieto 2014 ; pastorello et al . 2013 ; fraser et al . 2013b ; margutti et al . 2014 ; graham et al . the 2012 event was comprised of two main components : the 2012a " phase , marked by an initial peak at @xmath10 mag that lasted for just over 1 month ; and the 2012b " phase , which began with a fast 10-day rise to a second peak of @xmath11 mag , followed by a bumpy decline down to a slowly declining floor in the light curve near @xmath12 mag . based on spectral similarities with known core - collapse sne , mauerhan et al . ( 2013a ) suggested that the relatively faint 2012a phase of sn 2009ip marked the initial stages of a core - collapse sn , while the subsequent 2012b brightening was the result of interaction between this sn and dense csm ejected during the earlier lbv outbursts . levesque et al . ( 2014 ) also shared the view that the 2012b brightening was the result of interaction between the 2012a outflow and existing csm . however , several authors have suggested potential alternatives to a core collapse explosion that sn 2009ip s 2012 evolution was possibly the result of one or more nonterminal outbursts ( pastorello et al . 2013 ; fraser et al . 2013b ; margutti et al . 2014 ) , perhaps caused by the pulsational pair - instability mechanism . the motivation for nonterminal scenarios has been based largely on the fact that the total radiated energy of the light curve ( @xmath13 erg ) can be explained by an explosion energy of @xmath14 ergs ( if spherical symmetry is assumed for the csm ) , and also because the late - time data were interpreted as looking different from what is expected for radioactive decay phases . more recently , smith , mauerhan & prieto ( 2014 ; hereafter smp14 ) showed that the 2012 light curve and spectral evolution are consistent with published models for core - collapse sne , which can be initially faint ( like sn 1987a ) owing to a relatively compact progenitor radius ( i.e. , a blue supergiant , as expected for an lbv , instead of a red supergiant ) , while the late - time characteristics could be explained if the mass of synthesized @xmath15ni was half that of sn 1987a . smp14 further argued that the radiated energy did not provide an argument against core collapse , since the csm is probably aspherical , leading to an inefficient conversion of kinetic energy into radiation . in line with the spectral modeling results and interpretation of levesque et al . ( 2014 ) , which are consistent with a toroidal distribution of csm , smp14 also proposed a disk - like distribution of csm , but further argued that significant asphericity is required by the fact that broad photospheric lines are still seen at late times , even after strong csm interaction ends . this requires that a large fraction of the total solid angle of ejecta was able to expand unimpeded by csm . smp14 also pointed out that the @xmath16100-day persistence of broad photospheric lines requires a large ejecta mass of at least a few m@xmath17 , and is incompatible with a 0.1 m@xmath17 shell , which would become optically thin much more quickly . a mass of a few m@xmath17 moving at high speeds ( @xmath168000 km s@xmath18 ) directly implies @xmath19 ergs of kinetic energy . in the case of sne iin , the system geometry is critical if the total radiated energy from csm interaction is to be used to infer the kinetic energy of the sn explosion . fortunately , spectropolarimetry can yield important clues about the geometry of sne , allowing us to stringently test the hypothesis of aspherical csm . here , we report multi - epoch spectropolarimetry of the 2012 evolution of sn 2009ip , from the end of the initial 2012a phase , through the peak of 2012b , and later into its decline . the results unambiguously demonstrate that the source of bright continuum emission during the 2012b phase ( i.e. , the csm interaction zone ) was aspherical , consistent with a toroidal or disk - like distribution of csm proposed by smp14 and levesque et al . furthermore , the results indicate that the initial 2012a phase has a separate polarization component having an axis of symmetry that is distinct from 2012b , which implies that the 2012a event did not create the csm responsible for the 2012b brightening . diminishing polarization at late times , in addition to similarities in wavelength - dependent polarization across lines for sn 2009ip and other sne , provides additional evidence for a persistent underlying sn photosphere . altogether , the available evidence supports the hypothesis of a sn explosion for sn 2009ip in 2012 , and argues strongly against nonterminal explosion models for this object ( at least those proposed thus far ) .

we present spectropolarimetry of sn 2009ip throughout the evolution of its 2012 explosion . during the 2012a phase , [ firstpage ] circumstellar matter stars : evolution stars : winds , outflows supernovae : general supernovae : individual ( sn 2009ip )

we present spectropolarimetry of sn 2009ip throughout the evolution of its 2012 explosion . during the 2012a phase , when the spectrum exhibits broad p - cygni lines , we measure a-band polarization of% at a position angle of , indicating substantial asphericity for the 2012a outflow . near the subsequent peak of the 2012b phase , when the spectrum shows signs of intense interaction with circumstellar material ( csm ) , we measure% and , indicating a separate component of polarization during 2012b , which exhibits a higher degree of asphericity than 2012a and an orthogonal axis of symmetry on the sky . around 30 days past peak , coincident with a substantial bump in the declining light curve , we measure% and another significant shift in . at this point , broad photospheric lines have again become prominent and exhibit significant variations in relative to the continuum , particularly he i / na i d. by 60 days past peak the continuum polarization has dropped below 0.2% , probably declining toward a low value of interstellar polarization . the results are consistent with a scenario in which a prolate ( possibly bipolar ) explosion launched during the 2012a phase impacts an oblate ( toroidal ) distribution of csm in 2012b . previous calculations that assumed spherical symmetry for the csm have substantially underestimated the required explosion energy , since only a small fraction of the sn ejecta appears to have participated in strong csm interaction . an ejecta kinetic energy of at least ergs is difficult to avoid , supporting the interpretation that the 2012 outburst of sn 2009ip was the result of a core - collapse explosion . [ firstpage ] circumstellar matter stars : evolution stars : winds , outflows supernovae : general supernovae : individual ( sn 2009ip )

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linear polarization is expressed as the quadratic sum of the @xmath28 and @xmath29 stokes parameters , @xmath43 , and the position angle on the sky is given by @xmath44 , while carefully taking into account the quadrants in the @xmath28@xmath29 plane where the inverse tangent angle is located . since @xmath7 is a positive - definite quantity , it is significantly overestimated in situations where the signal - to - noise is low . it is typical to express the de - biased " ( or bias - corrected " ) form of @xmath7 as @xmath45 , where @xmath46 and @xmath47 are the uncertainties in the @xmath28 and @xmath29 stokes parameters . if @xmath48 , then we set a 1@xmath49 upper limit on @xmath7 of @xmath50 . in cases where @xmath51 , @xmath6 is essentially undetermined . all polarized spectra presented herein are displayed in this manner . note , however , that at low signal - to - noise ratio @xmath52 is also not a reliable function , as it has a peculiar probability distribution ( miller et al . thus , for extracting statistically reliable values of polarization within a particular waveband , we have binned the calibrated @xmath28 and @xmath29 stokes spectra separately over the wavelength range of interest before calculating @xmath7 and @xmath6 . all quoted and tabulated values in this paper were determined in this manner , although spectra are displayed as @xmath52 , so they may exhibit slight offsets from our quoted values . 0.04 for both components , implying low interstellar absorption and , hence , low galactic interstellar polarization ( see 3.1 ) . na d is seen in weak emission at the redshift of sn 2009ip.,width=316 ] interstellar polarization ( isp ) is commonly a very problematic element of polarimetric analysis , as an accurate probe of the isp from both the milky way and the host galaxy can be very difficult to obtain . fortunately , several factors indicate that the isp in the direction of sn 2009ip must be very small , and should not significantly impact our polarimetry results and the physical interpretation that follows . first , the high - resolution vlt / fors2 flux spectrum on nov . 7 , shown in figure [ fig : na ] , reveals the resolved components of galactic interstellar na i d absorption lines at 5890.1 and 5896.3 . the equivalent width ( ew ) of each component is a very small @xmath53 m , which implies a galactic @xmath54 mag ( munari & zwitter 1997 ) . according to serkowski et al . ( 1975 ) , the value of @xmath55 can be used to derive an upper limit on galactic isp . the so - called serkowski relation is given by isp @xmath56 , which implies that isp @xmath30% in the direction of sn 2009ip . second , earlier photometric estimates of the total reddening toward the host galaxy ngc 7259 and sn 2009ip indicate a low value of @xmath57 mag ( schlegel et al . 1998 ; smith et al . 2010 ; foley et al . 2011 ) , which implies that the host galaxy also does not produce substantial isp along the line of sight . this is also consistent with the lack of na d absorption at the redshift of ngc 7259 ; in fact , na d appears in weak emission , perhaps from a local h ii region or from gas excited by sn radiation , with no indication of additional absorption components . the low host extinction is not particularly surprising , given sn 2009ip s large radial distance from the center of this nearly face - on spiral galaxy . if we were to naively apply the serkowski relation to the total measured reddening , we would obtain isp @xmath58% , still a very low value . however , as shown by leonard et al . ( 2002 ) , the serkowski relation does not necessarily apply to all galaxies outside the milky way , as different dust properties can result in variable efficiencies for isp . nonetheless , the data strongly suggest a low value of total isp , which justifies our decision to make no attempt to remove it from the data , as its effect should be minor and not significantly impact our results . we revisit the subject of isp at the end of the following section . , and position angle @xmath6 for sn 2009ip during its 2012 outburst , at epochs between sep . 21 and dec . the three kuiper / spol epochs ( _ red _ ) have been averaged for clarity . the sep . 21 and 24 mmt / spol data ( _ light blue _ ) have been averaged and binned to 300 ; all other epochs are binned to 50 . note the @xmath59 offset in @xmath6 between the 2012a phase and the peak of 2012b.,width=316 ] -band ( 50505950 ) polarization for sn 2009ip during the 2012a and 2012b phases . for reference , an arbitrarily scaled version of the @xmath0-band light curve is plotted in the background . _ lower panel _ : evolution in the @xmath28@xmath29 plane . interstellar polarization is constrained to @xmath600.2% , illustrated by the black dot near the origin . the dashed lines represent the position angles @xmath61 and @xmath62 measured at the first epoch on sep . 21 and peak polarization on oct . 14 , respectively . our latest continuum measurement ( 52005500 ) for dec . 6 is marked with a red cross near the origin , consistent with our isp limit . the approximate point - reflection symmetry between 2012a and the peak of 2012b suggests two separate and roughly orthogonal components of polarization on the sky . note the temporary shift in @xmath6 associated with the bump in the light curve at @xmath1630 days past peak.,title="fig : " ] -band ( 50505950 ) polarization for sn 2009ip during the 2012a and 2012b phases . for reference , an arbitrarily scaled version of the @xmath0-band light curve is plotted in the background . _ lower panel _ : evolution in the @xmath28@xmath29 plane . interstellar polarization is constrained to @xmath600.2% , illustrated by the black dot near the origin . the dashed lines represent the position angles @xmath61 and @xmath62 measured at the first epoch on sep . 21 and peak polarization on oct . 14 , respectively . our latest continuum measurement ( 52005500 ) for dec . 6 is marked with a red cross near the origin , consistent with our isp limit . the approximate point - reflection symmetry between 2012a and the peak of 2012b suggests two separate and roughly orthogonal components of polarization on the sky . note the temporary shift in @xmath6 associated with the bump in the light curve at @xmath1630 days past peak.,title="fig : " ] figure [ fig : pol_seq ] shows the total flux spectra , @xmath7 , and @xmath6 of sn 2009ip for epochs between sep . 21 and dec . 6 . to gauge the total @xmath0-band polarization @xmath7 and @xmath6 , we first binned @xmath28 and @xmath29 separately in the wavelength range 50505950 . the extracted values are listed in table 1 . figure [ fig : pol_lc ] shows the resulting polarization light curve and the temporal evolution in the @xmath28@xmath29 plane . in addition to @xmath0-band , we also sampled continuum " regions of 52005500 and 61006200 , because they appear mostly devoid of strong line features ; these ranges are close to the respective green " and red " wavelength regions used by hoffman et al . we caution , however , that there is no location within the spectrum that is completely free of line emission / absorption during all epochs , so the regions we have selected should be regarded as pseudocontinua that avoid the strong lines . [ cols="<,>,^,^,^,^,>",options="header " , ] [ tab : p48 ] @xmath63day is with respect to the day of peak in the @xmath0 band ( jd 2456207.72 ) . + @xmath64data for oct . 5 interrupted by poor weather ; required calibration using oct . 14 standard - star observations ; to be used with caution . + the sep . 21 and 24 epochs took place near the end of sn 2009ip s 2012a phase , before the sharp rise in brightness that marks the onset of the 2012b phase . the total flux spectrum during 2012a exhibits the characteristics of sne iin , displaying intermediate - width ( @xmath161000 km s@xmath18 ) emission lines superimposed on a spectrum with broad p - cygni lines ( @xmath168000 km s@xmath18 ) that is reminiscent of more common sne ii - p ( mauerhan et al . 2013 ) . during this early epoch , sn 2009ip is polarized at @xmath160.9% with position angle @xmath2 , and it occupies quadrant iv in the @xmath28@xmath29 plane . by oct . 5 , sn 2009ip has entered the 2012b phase and the flux spectrum changes substantially ; the broad emission components have become strongly diluted by the strengthening continuum , which is quite blue , while the intermediate - width emission features have developed broad lorentzian wings , a commonly observed characteristic of sne iin and an indication of high optical depth ( chugai 2001 ; dessart et al . 2009 ; smith et al . 2008 ) , probably resulting from csm interaction . at this time , @xmath7 has changed only marginally to @xmath160.8% but the position angle has shifted dramatically to @xmath65 , moving into quadrant ii of the @xmath28@xmath29 plane . interestingly , this dramatic change in position angle indicates separate polarization components for the 2012a and 2012b phases , with distinct axes of symmetry . the lack of a correspondingly significant change in fractional @xmath7 associated with the large rise in brightness could possibly be explained by the partial cancellation of the polarization vectors from the 2012a and 2012b components , as the latter rises in luminosity . by oct . 11 , the source has risen to peak flux . the spectrum has retained the overall appearance of oct . 5 , while the continuum becomes less blue and broad - line p - cygni absorption becomes apparent for he i / na d. our lick / kast and kuiper / spol measurements on oct . 14 show that @xmath7 has risen to a maximum of @xmath161.7% and @xmath6 has reached @xmath66 . at this time , strong deficits in polarization are seen for the intermediate - width emission components of h@xmath67 and , to a lesser extent , h@xmath68 . this is likely to be the result of dilution from the strong , intrinsically unpolarized emission lines in the outer csm . meanwhile , a slight increase in @xmath7 is seen at 56005800 , suggesting a potential association with broad he i @xmath695876 or na d p - cygni lines . figure [ fig : qu_full ] ( top panels ) shows the stokes spectra and the data distribution in the @xmath28@xmath29 plane for the oct . 14 lick epoch , binned to 100 . for reference , we also show scaled logarithmic flux spectra in the same figure , which has been normalised with a low - order spline ( avoiding the strongest emission features for the spline nodes ) . on oct . 14 , near peak brightness , the entire optical spectrum of sn 2009ip occupies a compact portion of the @xmath28@xmath29 plane , in quadrant ii . the points form a slightly elongated cluster that shows a continuous trend in wavelength , with the bluest points exhibiting the lowest position angle in the @xmath28@xmath29 plane . the cluster as a whole exhibits a small but non - negligible spread in position angle , which corresponds to a range of @xmath70 on the sky . the dilution in polarization associated with intermediate - width h@xmath67 emission is apparent as a protrusion from the cluster of data points which roughly points toward the origin . note that our binning causes the line to be unresolved , and this affects the strength and position angle of the protrusion ; the unbinned data show the protrusion extending very close to the origin . in total polarization @xmath7 , we see broad , shallow variations that appear to be associated with broad absorption components of h@xmath67 and he i / na d blueward of 5876 . it is interesting to note that the scaled flux spectrum included in figure [ fig : qu_full ] shows that the broad p - cygni emission features from fast ejecta , first seen during 2012a , are still present throughout the peak of 2012b ; this has important physical consequences for the energetics of sn 2009ip ( see 4 ) . by nov . 67 , roughly 30 days past peak , the continuum has faded substantially and broad p - cygni lines have once again become prominent in the flux spectrum . he i / na d absorption has deepened , and the intermediate - width component of h@xmath67 has developed an absorption component on top of the broad underlying feature , perhaps part of its own p - cygni profile . interestingly , this epoch coincides with the appearance of a temporary albeit substantial bump in the declining light curve . 7 vlt / fors2 spectropolarimetry data are shown in detail in the lower panels of figure [ fig : qu_full ] . at this time , the @xmath0-band polarization has dropped to @xmath160.7% and the position angle has shifted substantially to @xmath1650@xmath31 . the enhancement of polarization near he i / na i absorption feature has become more pronounced and sharp ; this feature is also apparent in lick data from nov . 6 , shown in figure [ fig : pol_seq ] . meanwhile , the sharp dip in polarization produced by the dilution from unpolarized intermediate - width balmer lines is no longer apparent . we examine the polarization enhancements of two specific line features in figure [ fig : qu_line1 ] , which show the stokes parameters plotted as a function of velocity , with respect to the he i @xmath695876 and h@xmath67 rest wavelengths . on nov . 7 , the enhanced polarization of he i / na d is substantially blueshifted to a velocity of 13,000 km s@xmath18 ( if it is associated with he ) and exhibits a velocity width of @xmath161500 km s@xmath18 . the peak is also blueshifted by @xmath161500 km s@xmath18 with respect to the flux minimum of the absorption line . the enhanced he i / na d feature forms a linear - shaped loop that roughly traces the average polarization axis of the system for that date . there also appears to be an enhancement in fractional polarization for the absorption component blueward of the intermediate - width h@xmath67 emission feature ( at @xmath71 km s@xmath18 ) . the origin of this absorption feature is unclear . it could be an absorption component of a p - cygni profile for the intermediate - width h@xmath67 component , or it could be the result of blueshifted absorption for he i @xmath696678 . if it is from h@xmath67 p - cygni , then this enhanced polarization feature does not appear blueshifted as in the case of the broad he i / na d absorption . in the @xmath28@xmath29 plane , the track across this potential h@xmath67/he i feature appears to be roughly consistent with the overall axis of symmetry . there also appears to be some indication of polarization enhancement for blend of absorption components seen at the higher velocities of @xmath72 km s@xmath18 and larger , which are probably from h@xmath67 . overall , the broad emission component of h@xmath67 appears to make a loop in the @xmath28@xmath29 plane . averaging all of our measurements from kuiper / spol on nov . 12 and 14 , we detect @xmath160.7% polarization in the @xmath0 band , similar to the value of the preceding vlt / fors2 epoch on nov . 7 . the lick / kast data solely from nov . 14 show a value of polarization similar to the nov.1214 combined average of the kuiper / spol data . the polarized spectra are not shown in figure [ fig : pol_seq ] , to avoid cluttering the figure , although their broadband measurements are presented in figure [ fig : pol_lc ] . interestingly , although the overall degree of polarization has not changed substantially between nov . 6 and 14 , the position angle has shifted again back toward the axis of symmetry of the 2012b peak . it thus appears that the bump in the light curve on nov . 67 is associated with another component of polarization , perhaps related the 2012a luminosity source . a few weeks later , on dec . 57 , we detect weak polarization in an average of three separate measurements with bok / spol , obtaining @xmath73 and only an upper limit for the continuum of @xmath74% . the last vlt / fors2 measurement takes place on dec . 6 , for which we obtain @xmath75% and @xmath76% . for the december epochs the position angle has changed significantly with the diminishing polarization , moving into quadrant iii with @xmath77 . the flux spectrum during this late epoch shows that the continuum has become redder , while the broad p - cygni features are still present . he i / na d absorption has become a double - dipped profile . figure [ fig : qu_line2 ] shows that by dec . 6 the enhanced polarization of this feature has shifted redward , and is probably associated with the bluer component of the double - dipped profile . a complicated blend of multiple absorption and perhaps emission features appears blueward of h@xmath67 at this time , and also exhibits evidence for enhanced polarization , roughly along the average axis of symmetry . examining more closely the temporal evolution of sn 2009ip in the @xmath28@xmath29 plane , shown in figure [ fig : pol_lc ] ( lower panel ) , the range of possible isp values constrained by the value of @xmath55 ( see 3.1 ) are illustrated by the radius of the black spot centered on the origin . it seems plausible that the path traced by @xmath28 and @xmath29 during dec . is the result of a migration back to the point of isp , somewhere near the origin . indeed , our latest measurement of the continuum polarization yielded @xmath74% from bok / spol for dec . 57 , and @xmath78% from vlt / fors2 on dec . 6 ( @xmath79% , @xmath80 ) , which is consistent with the isp limits we have estimated . an alternative , and less likely possibility , is that @xmath28 and @xmath29 are destined to drift back to the location in quadrant iv occupied by our earliest mmt / spol measurements in september ( i.e. , that the 2012a phase is intrinsically unpolarized , and instead reflects the location of isp ) . but such a large value of isp ( @xmath811% ) seems implausible given the constraints on isp indicated by the low values of @xmath55 and ew(na d ) ; the structure in @xmath7 for the september epochs also does not follow a serkowski law , which is inconsistent with the 2012a polarization being the result of isp . furthermore , it would be a rather remarkable coincidence for the position angle of isp to be orthogonal to the polarization axis of sn 2009ip at peak . therefore , the evidence is strong that our earliest polarization detections from mmt / spol in september reveal true polarization intrinsic to the source during the 2012a phase , and that the isp is within @xmath58% of the origin , and likely @xmath82% , as indicated by our latest continuum measurement . as one can see , any value of isp within this allowable range will affect our results only slightly , and will not change the fact that the 2012a and 2012b phases appear to have two separate components of polarization that will remain roughly orthogonal between 2012a and the peak of 2012b , no matter where the isp lies within the range illustrated by figure [ fig : pol_lc ] ( lower panel ) .

around 30 days past peak , coincident with a substantial bump in the declining light curve , we measure% and another significant shift in . at this point , broad photospheric lines have again become prominent and exhibit significant variations in relative to the continuum , particularly he i / na i d. by 60 days past peak the continuum polarization has dropped below 0.2% , probably declining toward a low value of interstellar polarization .

we present spectropolarimetry of sn 2009ip throughout the evolution of its 2012 explosion . during the 2012a phase , when the spectrum exhibits broad p - cygni lines , we measure a-band polarization of% at a position angle of , indicating substantial asphericity for the 2012a outflow . near the subsequent peak of the 2012b phase , when the spectrum shows signs of intense interaction with circumstellar material ( csm ) , we measure% and , indicating a separate component of polarization during 2012b , which exhibits a higher degree of asphericity than 2012a and an orthogonal axis of symmetry on the sky . around 30 days past peak , coincident with a substantial bump in the declining light curve , we measure% and another significant shift in . at this point , broad photospheric lines have again become prominent and exhibit significant variations in relative to the continuum , particularly he i / na i d. by 60 days past peak the continuum polarization has dropped below 0.2% , probably declining toward a low value of interstellar polarization . the results are consistent with a scenario in which a prolate ( possibly bipolar ) explosion launched during the 2012a phase impacts an oblate ( toroidal ) distribution of csm in 2012b . previous calculations that assumed spherical symmetry for the csm have substantially underestimated the required explosion energy , since only a small fraction of the sn ejecta appears to have participated in strong csm interaction . an ejecta kinetic energy of at least ergs is difficult to avoid , supporting the interpretation that the 2012 outburst of sn 2009ip was the result of a core - collapse explosion . [ firstpage ] circumstellar matter stars : evolution stars : winds , outflows supernovae : general supernovae : individual ( sn 2009ip )

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the most natural explanation for linear polarization of a sn is thomson scattering by free electrons , either from the sn photosphere or within the zone of intense csm interaction , which includes the forward shock , the reverse shock , and the cold dense shell ( cds ) in between . for most sne iin , including sn 2009ip , evidence of electron scattering is also indicated by the broad lorentzian wings typically seen at the bases of the intermediate - width emission - line profiles ( chugai et al . 2001 ; smith et al . 2008 ; dessart et al . 2009 ) . but in the case of scattered photons emerging from a spherically symmetric distribution of material , the sum of all electric vectors will cancel out and yield zero net polarization . thus , the detection of net polarization from any sn directly implies aspherical structure , either intrinsic or imposed from partial obscuration of the polarized surface by intervening material ( see wang & wheeler 2008 for a review on sn polarization ) . core - collapse sne of type ii - p have been observed to be weak sources of polarization while in their plateau phases , which implies that the outer layer of ejecta is roughly spherical in some cases . however , near the end of their plateaus , sne ii - p can exhibit brief but significant increases in polarization ( leonard et al . 2000 , 2006 ; chornock et al . 2010 ) , because as the ejecta cool and recombine the photosphere recedes from the spherical outer layers of h - rich material into more aspherical he - rich and metal - rich layers deeper inside the ejecta . thus , to first order , sne ii - p can be characterized by a single component of photospheric polarization that scales inversely with the decreasing luminosity . sne iin , on the other hand , appear to exhibit a high degree of polarization while in their brightest phases , at least for the few objects that have been studied in sufficient detail ( e.g. , leonard et al . 2001 ; hoffman et al . this implies that csm interaction luminosity must be a major source of the net polarization from sne iin . in this case , since both the sn photosphere and the csm interaction zone are potential sources of polarized photons , changes in the relative luminosities of these components can lead to variations in net polarization , even if the fractional polarization and position angles of each component remain constant with time . below , we propose this to be the case for sn 2009ip . sn 2009ip s photospheric component is made evident by its spectropolarimetric similarities with the type iib sn 1993j , shown in figure [ fig:93j ] . near peak brightness , both sne exhibit a comparable degree of polarization across the optical band , with sn 2009ip being stronger in the continuum , and they both display remarkably similar wavelength - dependent variations across their polarization spectra , particularly evident at wavelengths of 52007000 . in the case of sn 1993j , these variations are associated with the broad p - cygni lines of h@xmath67 and he i@xmath39na d , and the same is probably true for sn 2009ip . the variations are produced by the depolarizing effect of line scattering ( trammell et al . 1993 ; hflich 1995 ; hflich et al . 1996 ; tran et al . this is not to be confused with the intrinsically unpolarized recombination emission from the outer optically thin csm that we see in sn 2009ip , which dilutes the polarized continuum and results in relatively narrow absorption " features of polarization for the h@xmath67 and h@xmath68 lines . rather , true depolarization is important for the broad emission lines that develop in the ionised ejecta above the electron - scattering photosphere of the sn . the persistence of these lines in sn 2009ip for @xmath16100 days implies a massive amount of high - velocity material ( a few m@xmath17 ) , consistent with a sn outflow ( see smp14 ) . csm is also a potential contributor to the polarization properties of sn 1993j ( hflich et al . 1996 ; tran et al . 1997 ) , via electron scattering within a sn / csm interaction zone and/or the scattering of photons by dust . after all , the continuum polarization of sn 1993j being entirely due to an aspherical ejecta photosphere is somewhat difficult to reconcile with the evolution of a highly spherical radio remnant revealed by vlbi ( bietenholz , bartel , & rupen 2003 ) , although this structure might only trace the morphology of the outermost h - rich layers , not the more asymmetric he - rich layers potentially responsible for the polarized continuum . still , the source did exhibit evidence for pre - existing csm at early times , in the form of narrow emission - line features exhibiting small velocity widths of @xmath16170 km s@xmath18 , indicative of an ambient stellar wind ( benetti et al . 1994 ) . however , these features were less pronounced than those of sn 2009ip and lasted for a shorter amount of time , indicating a much less dense csm . sn 1993j s x - ray properties were also indicative of csm interaction ( leising et al 1994 ) , while its radio evolution indicated a changing pre - sn mass - loss rate in the range @xmath83@xmath84 yr@xmath18 ( van dyk et al . 1994 ) , which , although roughly 100 times weaker than the pre - sn mass - loss rate inferred for sn 2009ip ( ofek et al . 2013b ) , could generate enough csm to influence the object s polarization properties . therefore , like sn 2009ip , sn 1993j could have two components of polarization photospheric and csm interaction . in the case of sn 2009ip , however , it appears rather obvious that csm interaction is the dominant source of polarization near photometric peak . the opposite could be true for sn 1993j : its polarization could be dominated by an aspherical explosion and only moderately influenced by the csm component . in this regard , a noteworthy difference between the two sne is that near peak brightness sn 1993j exhibits more variation than sn 2009ip in @xmath6 as a function of wavelength , suggesting that sn 2009ip has a more highly ordered axis of symmetry in 2012b resulting from its luminous and highly aspherical csm interaction zone . by 5060 days after peak , however , both sne exhibit remarkable similarity in @xmath7 and @xmath6 as a function of wavelength . it appears that as csm interaction fades after the peak of 2012b and the broad p - cygni lines return by nov . 6 , the polarization characteristics of sn 2009ip begin to look more like a sn photosphere again . it is thus interesting that the source makes a pronounced shift in position angle on nov . 6 , associated with the obvious bump in the light curve ( see figure [ fig : pol_lc ] ) , which could represent the temporary brightening of the photospheric component of polarization that dominated the 2012a phase . taken at face value , sn 2009ip s degree of peak polarization for the 2012a and 2012b phases ( from @xmath1% to @xmath85% ) indicates respective axial ratios of @xmath600.85 and @xmath600.7 for the aspherical source ( @xmath8615% and @xmath8630% asphericity ) , if we assume that polarization translates directly to the apparent geometry via comparison with the oblate electron - scattering atmosphere models of hlfich ( 1995 ) . however , the true physical axial ratios could be substantially more aspherical than these limits , for two key reasons : ( 1 ) inclination angle , and ( 2 ) partial cancellation between the 2012a and 2012b polarization vector components . if both the 2012a peak and the late decline of the 2012b phase ( from the nov . 67 bump onward ) are dominated by the sn photosphere component , as appears to be the case , then partial cancellation could be particularly important for the 2012b peak . indeed , the @xmath59 shift in position angle between the earliest 2012a observation and the peak of the 2012b phase implies two separate components of polarization that are roughly orthogonal to one another . since orthogonal polarization vectors cancel , the degree of intrinsic polarization for the 2012b component must be higher than it appears ( i.e. , even more aspherical ) , because the orthogonality of the separate 2012a vector component , if still present during 2012b , will partially cancel the 2012b component . we can estimate the true intrinsic polarization of the 2012b peak component as follows . if we rotate the @xmath28@xmath29 values from figure [ fig : pol_lc ] such that they are aligned with the axis of symmetry at maximum polarization ( @xmath87 ) , which roughly traces the average axis of symmetry for the entirety of 2012b , then the majority of polarization during the 2012b phase is shifted onto the positive @xmath28 axis , while the orthogonal 2012a polarization gets shifted onto the negative @xmath28 axis . figure [ fig : rsp ] shows the evolution of the resulting rotated stokes parameters . the @xmath88 curve represents variations along the main axis of symmetry , while @xmath89 traces deviations from the average axis of symmetry . the result implies that if the 2012a component maintains its orthogonal contribution to the total electric vector during 2012b , then the separation between the 2012a and 2012b components will approximately define the true degree of intrinsic polarization for the 2012b peak , which , therefore , could be as high as @xmath162.6% . in this case , comparison with the models of hlfich ( 1991 ) would imply a more highly aspherical axial ratio of @xmath900.6 for the 2012b component ( @xmath8640%50% asphericity ) . considering the additional effect of a @xmath91 inclination angle , hypothetically , it is possible that the intrinsic geometry of the 2012b component is a highly flattened one . below we discuss a plausible geometric scenario for sn 2009ip s 2012 evolution , facilitated by figures [ fig : cartoon1 ] and [ fig : cartoon2 ] . ) . the plot is meant to illustrate the full possible degree of intrinsic polarization for the 2012b component ( @xmath162.6% ) , after considering the effect of the partial cancellation , roughly orthogonal 2012a vector component ( see 4.1.2).,width=316 ] for the 2012b component of polarization the situation appears relatively clear . since csm interaction dominates the luminosity during this phase , and since the associated polarization source exhibits a rather steady and well - defined axis of symmetry , the net polarization must reflect the physical structure of the dense csm , which in this case could represent a toroidal geometry ( a disk or ring ) . toroidal geometry for the interacting csm has already been suggested for sn 2009ip by levesque et al . ( 2014 ) , based on spectral modeling and analysis of the balmer emission lines . those authors found that the h@xmath67 emission during the peak of 2012b requires a total radiating area of @xmath1620,000 au@xmath92 , while the balmer decrement requires a high csm density of @xmath93 @xmath94 , for case - b recombination ( note that such a high density would naturally explain the absence of forbidden emission lines in sn 2009ip s spectrum ) . the combination of high density and large area implies a flattened geometry ( i.e. , a disk / ring ) , possibly as thin as 10 au . alternatively , a lower density csm of @xmath95 @xmath94 in a limb - brightened spherical shell configuration was also proposed by levesque et al . ( 2014 ) as an additional possibility , although less favourably because it requires that the optical depth of h@xmath68 be lower than for h@xmath67 , which would be unusual . independently , smp14 also favoured disk - like geometry for the csm based on energetic arguments and on the persistence of broad p - cygni lines even after the phase of intense csm interaction had declined , which implies that a large fraction of the ejecta did not decelerate and , thus , must not have participated in strong csm interaction ( toroidal geometry would allow a large fraction of the ejected mass to bypass strong csm interaction in directions orthogonal to the csm plane ) . our spectropolarimetric results are consistent with toroidal geometry for the csm around sn 2009ip , and contradict models that invoke spherical distributions of csm . in this case , the axial ratio of the polarized emission source at the peak of 2012b ( constrained to @xmath96 , and probably @xmath600.6 ; see 4.1.2 ) is consistent with toroidal geometry tilted at some intermediate inclination angle with respect to our line of sight . the spectropolarimetric evolution is _ inconsistent _ with some physical scenarios previously proposed as possibilities for sn 2009ip s 2012 evolution . since it is the csm geometry that determines the polarization properties at the peak of the interaction phase , then the earlier eruption that produced such csm should reflect the same geometry . thus , the orthogonal position angle shift we observe between 2012a and the peak of 2012b is not compatible with the interpretation that these respective phases represent the launching and collision of successive shells of csm ( e.g. , from pair - instability eruptions ) , a possibility suggested by other authors ( pastorello et al . 2013 ; margutti et al . 2014 ) , since such a scenario should result in similar axes of symmetry for the two phases , not orthogonal geometries . rather , the orthogonality between the 2012a and 2012b events implies a physically distinct origin for each of the associated outflows . in addition , the large shift in polarization and position angle between the 2012b peak and the subsequent bump in the declining light curve on nov . 67 also suggests that the bump is the result of a polarized luminosity component that is separate from that of the 2012b peak for example , the sn photospheric component brightening again as the csm interaction component fades away . this is inconsistent with the interpretation that the bump in the light curve is the result of a fluctuating central source that variably illuminates the csm , such as activity from a central surviving star , as proposed by martin et al . ( 2013 ) . toroidal csm geometry would not be unique to sn 2009ip ; it has been proposed before for other sne iin , specifically in the cases of sn 1988z ( chugai & danziger 1994 , their model b ) , sn 1998s ( leonard et al . 2000 ) , and sn 1997eg ( hoffman et al . this type of geometry is also unsurprising in the context of sn 2009ip s stellar progenitor , since rings and tori are common phenomena around lbvs , b[e ] supergiants , and other evolved massive stars ( smith , bally , & walawender 2007 ; smith et al . not at all clear , however , is the connection of such geometry to the erratic behaviour of sn 2009ip over the last decade . it is possible that dense equatorial csm is the result of binary - influenced mass loss , as has been suggested to explain the toroidal csm of b[e ] supergiants . a connection between such objects and sn 2009ip was speculated upon by clark et al . ( 2013 ) in the case of lha 115-s 18 , a b[e ] supergiant exhibiting erratic long - term variability that is reminiscent of lbvs . it is thus interesting to note that the radial dimensions of b[e ] disks ( @xmath97@xmath98 au ; zickgraf et al . 1986 ) are comparable to the size estimates for sn 2009ip s toroidal csm ( smith et al . 2013 ; smp14 ) . represents the angle subtended by the csm from the point of view of the explosion.,width=316 ] and [ fig : qu_line2]).,width=316 ] the origin of the polarization for the 2012a phase is less clear . since the spectrum of sn 2009ip on sep . 2124 resembles that of more common core - collapse sne , the simplest explanation might be electron scattering within the photosphere of the early sn , which has yet to impact the dense csm lying farther out . in this case , the axial ratio of @xmath99 and the orthogonal geometric axis with respect to the peak of the csm interaction phase would suggest a prolate / bipolar shape for the 2012a outflow . interestingly , bipolar geometry has been suggested previously for other cases of highly polarized core - collapse sne ( e.g. , see wang et al . 2001 ) . alternatively , net polarization from the 2012a phase could also arise if the near side of the soon - to - be - shocked toroidal csm is partially blocking the waist of the sn photosphere ( figure [ fig : cartoon1 ] , inset ) , which could result in a polarization axis that is orthogonal to 2012b if the polarized poles of the photosphere remain relatively unobscured . finally , scattering of the sn photons by dust in the outer csm could provide another source of polarized photons . after all , infrared data obtained during the 2012a phase show strong evidence for circumstellar dust at a radius of @xmath16120220 au ( smith et al . we note that the strength of sn 2009ip s blue continuum detected at the same time indicates that the central source is probably not completely enshrouded by the dusty component , which is consistent with the toroidal geometry inferred for the csm . however , if dust scattering from the dense csm were an important source of polarized flux during 2012a , we would expect the geometric axis during this phase to reflect that of 2012b rather than being orthogonal to it . thus , electron scattering within the sn photosphere appears to be the most plausible explanation as the dominant source of polarized photons during 2012a , with net polarization either being the result of bipolar geometry for the photosphere or partial blocking of its waist by the toroidal csm . if strong csm interaction is confined to a toroidal geometry , then large amounts of high - velocity sn ejecta could expand relatively unimpeded . this is already indicated by the persistence of the broad p - cygni lines ( smp14 ) , but could also explain some of the higher - order effects we see in the spectropolarimetric data . for example , the sharp blueshifted enhancement in polarization associated with the he i / na d feature seen on nov . 67 ( figure [ fig : qu_line1 ] ) is an indication of high - velocity material . this feature has a blueshifted velocity of 13,000 km s@xmath18 , while the position angle across the feature approximately follows along the main axis of symmetry of this epoch in the @xmath28@xmath29 plane . the fact that the peak of the enhanced polarization feature is not coincident with the flux minimum of the absorption line implies that the enhancement can not simply be the result of absorption of unpolarized or less polarized flux ( which would increase the fractional polarization at that wavelength ) . rather , the net blueshift probably results from an intervening layer of fast he - rich ( or na - rich ) material that lies near the outer edge of the ejecta and is _ partially _ absorbing the inner polarized continuum . from the point of view of the observer , such partial blocking can increase the net polarization over that range of velocities by interfering with the cancellation of orthogonal polarization vectors distributed across the polarized source ( e.g. , also see kasen et al . the high - velocity he / na d - rich material was probably launched during the sn in 2012a phase , while the csm responsible for the 2012b phase was likely to have been created by the lbv progenitor eruptions during the years prior ( e.g. , see graham et al . 2014 , their figure 7 ) . a toroidal or disk - like distribution of csm around sn 2009ip has important consequences for the kinetic energy of the explosion that is inferred from the total radiated energy measured during the 2012b csm - interaction phase . taking the 2012a explosion time of @xmath100 days , suggested by smp14 , and the fastest ejecta velocity of 13,000 km s@xmath18 indicated by the blue edge of the h@xmath67 p - cygni line during 2012a , implies a radial distance of @xmath16350 au from the point of explosion to the inner edge of the dense csm ; this is consistent with the limits on the minimum radius of the dust component inferred from infrared measurements during 2012a ( @xmath86120 au ; smith et al . 2013b ) , and with the 300 au radial estimates by levesque et al . the latter authors showed that the csm need only be @xmath1610 au thick to explain the h@xmath67 luminosity in the toroidal scenario . for a 10 au toroidal scale height , the 300350 au distance from the explosion would imply a very small subtended angle of @xmath101 for the csm from the point of view of the explosion . such a configuration inclined at an angle of 3545@xmath31 with respect to our line of sight ( from edge - on ) would appear as an ellipse on the sky having an axial ratio that is consistent with the geometric constraints placed by the value of peak polarization during 2012b ( see 4.1.2 ) . for such a small subtended angle of csm , the fraction of the total explosion solid angle ( @xmath102/4@xmath103 ) intercepted by csm will be only 23% ( @xmath6010% conservatively ) . this minor amount of interacting area will result in an inefficient conversion of the total kinetic energy of the sn into radiation . thus , the @xmath104 ergs of kinetic energy inferred from the radiated energy of the explosion by fraser et al . ( 2013 ) and margutti et al . ( 2014 ) , both of whom assume a spherical csm configuration in their calculations , must be a significant underestimate , by 1 dex or more . a kinetic energy of @xmath19 ergs , as suggested by smp14 , seems more likely , given the demand for aspherical csm by spectropolarimetry . one must also keep in mind that the shape of the explosion is an influential factor as well . a bipolar explosion , which we have shown is a plausible geometry for the 2012a outflow , will intersect even less area of the toroidal csm . if the material is clumpy , then the effective intersecting area could be even lower than we have estimated , implying an even lower efficiency conversion of kinetic energy into radiation .

when the spectrum exhibits broad p - cygni lines , we measure a-band polarization of% at a position angle of , indicating substantial asphericity for the 2012a outflow . near the subsequent peak of the 2012b phase , when the spectrum shows signs of intense interaction with circumstellar material ( csm ) , we measure% and , indicating a separate component of polarization during 2012b , which exhibits a higher degree of asphericity than 2012a and an orthogonal axis of symmetry on the sky . previous calculations that assumed spherical symmetry for the csm have substantially underestimated the required explosion energy , since only a small fraction of the sn ejecta appears to have participated in strong csm interaction . an ejecta kinetic energy of at least ergs is difficult to avoid , supporting the interpretation that the 2012 outburst of sn 2009ip was the result of a core - collapse explosion .

we present spectropolarimetry of sn 2009ip throughout the evolution of its 2012 explosion . during the 2012a phase , when the spectrum exhibits broad p - cygni lines , we measure a-band polarization of% at a position angle of , indicating substantial asphericity for the 2012a outflow . near the subsequent peak of the 2012b phase , when the spectrum shows signs of intense interaction with circumstellar material ( csm ) , we measure% and , indicating a separate component of polarization during 2012b , which exhibits a higher degree of asphericity than 2012a and an orthogonal axis of symmetry on the sky . around 30 days past peak , coincident with a substantial bump in the declining light curve , we measure% and another significant shift in . at this point , broad photospheric lines have again become prominent and exhibit significant variations in relative to the continuum , particularly he i / na i d. by 60 days past peak the continuum polarization has dropped below 0.2% , probably declining toward a low value of interstellar polarization . the results are consistent with a scenario in which a prolate ( possibly bipolar ) explosion launched during the 2012a phase impacts an oblate ( toroidal ) distribution of csm in 2012b . previous calculations that assumed spherical symmetry for the csm have substantially underestimated the required explosion energy , since only a small fraction of the sn ejecta appears to have participated in strong csm interaction . an ejecta kinetic energy of at least ergs is difficult to avoid , supporting the interpretation that the 2012 outburst of sn 2009ip was the result of a core - collapse explosion . [ firstpage ] circumstellar matter stars : evolution stars : winds , outflows supernovae : general supernovae : individual ( sn 2009ip )

1703.02566

c

we present submillimeter array 880 @xmath0 m polarization observations of six massive dense cores in the dr21 filament . with the complementary archival polarimetric observations from scupol of the jcmt @xcite , we are able to characterize the magnetic field properties from the filament to the cores . our main results are the following : 1 . the sma dust polarization shows complex magnetic field structures in the massive dense cores , in contrast to the ordered parsec - scale magnetic fields of the filament . significant depolarization effect is found toward the center of core , and the variation in the sma polarization angles is @xmath1 3040@xmath36 in the cores , again both indicating complex magnetic field structures in the cores . the major axis of core appears to be either parallel or perpendicular to the large - scale magnetic fields inferred from the jcmt polarization map . however , the major axis of the cores shows no preference of alignment to the small - scale magnetic fields inferred from the sma polarization map . the transition from the either - parallel - or - perpendicular alignment to the random alignment suggests that in the formation of massive dense cores , the magnetic fields below 0.1 pc scales become less important as compared to gravity than the magnetic fields above 0.1 pc scales . 3 . our analysis of angular dispersion functions of sma polarization segments yields plane - of - sky magnetic field strengths of 1.7 mg in cyg - n44 and about 0.5 mg in other four cores . most of the cores have the angular dispersion functions similar to the dispersion of random magnetic field . the derived number of turbulent cells and the derived ratio of turbulent magnetic fields to ordered magnetic fields are both much greater than unity , indicating that the magnetic fields in the cores are dominated by turbulent components . the virial parameters show that in the filament , the gravitational energy @xmath122 is dominant over magnetic @xmath124 and kinematic @xmath123 energies , and the gravitational collapse can transfer the @xmath122 of the filament to the @xmath123 and @xmath124 of the cores , resulting in the relations of @xmath112 and @xmath120 in the cores . the virial parameters reveal an overall picture of weakly magnetized cores in a strongly magnetized filament , suggesting that the kinematics arising from gravitational collapse must become more important than magnetic fields during the evolution from filament to massive dense cores . part of the data were obtained in the sma legacy project : filaments , magnetic fields , and massive star formation ( pi : qizhou zhang ) . t. c. c. acknowledges the support of the smithsonian predoctoral fellowship and the university consortium of alma - taiwan ( ucat ) graduate fellowship . t. c. c. and s. p. l. are thankful for the support of the ministry of science and technology ( most ) of taiwan through grants 102 - 2119-m-007 - 004-my3 , 104 - 2119-m-007 - 021 , 105 - 2119-m-007 -022 -my3 , and 105 - 2119-m-007 -024 . q. z. acknowledges the support of the si scholarly studies awards `` are magnetic fields dynamically important in massive star formation ? '' j. m. g. acknowledges the support from the micinn ( spain ) aya2014 - 57369- c3 grant and the mecd ( spain ) prx15/00435 travel grant . k. q. acknowledges the support from national natural science foundation of china ( nsfc ) through grants nsfc 11473011 and nsfc 11590781 . ccccccccc 2011 jul 09 & subcompact & 7 & single & mwc349a & uranus & 3c279 & 3c279 & cyg - n38 + 2011 jul 12 & subcompact & 6 & single & mwc349a & uranus & 3c279 & 3c279 on 2011 jul 13 & cyg - n48 , cyg - n53 + 2011 jul 13 & subcompact & 7 & single & mwc349a & mwc349a & 3c279 & 3c279 & cyg - n38 , cyg - n48 , cyg - n53 + 2012 jul 03 & compact & 7 & single & mwc349a & titan & 3c279 , 3c84 & 3c279 on 2012 jul 04 & cyg - n38 , cyg - n48 + 2012 jul 04 & compact & 7 & single & mwc349a & titan & 3c279 & 3c279 & cyg - n38 , cyg - n48 + 2012 jul 05 & compact & 7 & single & mwc349a & titan & 3c279 , 3c84 & 3c84 & cyg - n38 , cyg - n48 + 2012 aug 07 & subcompact & 6 & single & mwc349a & uranus & 3c279 & 3c84 on 2012 aug 08 & cyg - n38 , cyg - n48 + 2012 aug 08 & subcompact & 6 & single & mwc349a & uranus & 3c84 & 3c84 & cyg - n38 , cyg - n48 + 2012 aug 09 & subcompact & 6 & single & mwc349a & uranus & 3c84 & 3c84 on 2012 aug 08 & cyg - n38 , cyg - n48 + 2014 jun 19 & compact & 7 & dual & mwc349a & neptune & 3c279 , 3c454.3 & 3c454.3 & cyg - n43 , cyg - n51 + 2014 jun 21 & compact & 7 & dual & mwc349a & neptune & 3c454.3 & 3c454.3 on 2014 jun 19 & cyg - n43 , cyg - n51 + 2015 jun 08 & subcompact & 7 & dual & mwc349a & titan & 3c279 & 3c279 & cyg - n53 + 2015 jun 12 & subcompact & 7 & dual & mwc349a & neptune & 3c279 , 3c454.3 & 3c279 & cyg - n43 + 2015 jun 19 & subcompact & 7 & dual & mwc349a & titan & 3c279 & 3c279 & cyg - n51 + lcccccccccc cyg - n38 & 20:38:59.11 & 42:22:25.96 & & 9.4/0 & & 3.6 @xmath131 2.9 & 65 & & 15/1.6 & dr21(oh)-w + cyg - n43 & 20:39:00.60 & 42:24:34.99 & & 0/3.1 & & 4.6 @xmath131 3.5 & 55 & & 10/1.6 & w75s - fir1 + cyg - n44@xmath132 & 20:39:01.20 & 42:22:48.50 & & 4.7/0 & & 3.9 @xmath131 3.4 & 56 & & 20/3.1 & dr21(oh ) + cyg - n48 & 20:39:01.34 & 42:22:04.89 & & 7.5/0 & & 3.3 @xmath131 3.0 & 63 & & 13/1.7 & dr21(oh)-s + cyg - n51 & 20:39:02.40 & 42:24:59.00 & & 0/3.5 & & 4.4 @xmath131 3.4 & 54 & & 8.9/1.6 & w75s - fir2 + cyg - n53 & 20:39:02.96 & 42:25:50.99 & & 1.5/2.1 & & 4.4 @xmath131 3.0 & 60 & & 14/1.9 & + ccccccccccccc cyg - n38 & 4.3 @xmath77 0.3 & 11.5 @xmath77 0.4 & 7.8 @xmath77 0.6 & 64 @xmath77 3 & & -27.0 @xmath77 3.7 & 85.0 @xmath77 5.1 & -50.0 @xmath77 36.2 & & 59 @xmath77 4 & 2.2 @xmath77 0.2 & 1.1 @xmath77 0.1 + cyg - n43 & 1.2 @xmath77 0.1 & 14.3 @xmath77 0.3 & 5.7 @xmath77 0.4 & 61 @xmath77 2 & & -74.4 @xmath77 1.7 & -44.5 @xmath77 24.4 & -24.0 @xmath77 38.1 & @xmath1 -31 & 16 @xmath77 1 & 0.7 @xmath77 0.1 & 0.4 @xmath77 0.03 + cyg - n44 & 21.4 @xmath77 0.3 & 11.1 @xmath77 0.5 & 9.4 @xmath77 0.1 & 69 @xmath77 2 & & 13.3 @xmath77 3.7 & 78.2 @xmath77 5.9 & 47.6 @xmath77 30.1 & @xmath1 63 & 167 @xmath77 2 & 5.3 @xmath77 0.2 & 2.5 @xmath77 0.1 + cyg - n44 mm1 & 2.0 @xmath77 0.1 & @xmath133 4.3 @xmath77 0.1 & @xmath133 3.2 @xmath77 0.1 & @xmath133 25 @xmath77 1 & & 52.3 @xmath77 1.3 & & & & 16 @xmath77 1 & @xmath134 3.8 @xmath77 0.2 & @xmath134 4.8 @xmath77 0.4 + cyg - n44 mm2 & 0.2 @xmath77 0.1 & @xmath133 2.5 @xmath77 0.1 & @xmath133 2.1 @xmath77 0.1 & @xmath133 16 @xmath77 1 & & 16.0 @xmath77 9.6 & & & & 2 @xmath77 1 & @xmath134 1.0 @xmath77 0.5 & @xmath134 2.1 @xmath77 0.1 + cyg - n48 & 7.5 @xmath77 0.3 & 14.3 @xmath77 0.2 & 7.2 @xmath77 0.4 & 69 @xmath77 2 & & -71.5 @xmath77 1.0 & -59.2 @xmath77 9.3 & -60.8 @xmath77 44.0 & @xmath1 -72 & 102 @xmath77 4 & 3.3 @xmath77 0.2 & 1.5 @xmath77 0.1 + cyg - n51 & 3.3 @xmath77 0.2 & 16.7 @xmath77 0.3 & 7.4 @xmath77 0.3 & 75 @xmath77 2 & & 7.5 @xmath77 0.7 & -84.9 @xmath77 8.9 & 89.3 @xmath77 35.3 & & 45 @xmath77 3 & 1.2 @xmath77 0.1 & 0.5 @xmath77 0.03 + cyg - n53 & 1.9 @xmath77 0.1 & 4.0 @xmath77 0.3 & 2.6 @xmath77 0.1 & 22 @xmath77 1 & & -14.3 @xmath77 3.4 & 73.7 @xmath77 22.2 & -23.5 @xmath77 18.3 & & 26 @xmath77 1 & 8.3 @xmath77 0.2 & 12.2 @xmath77 0.2 + [ phy_table ] cccccccc cyg - n38 & 26 @xmath77 12 & 3.8 @xmath77 2.4 & -1.9 @xmath77 1.6 & 4.7 @xmath77 0.1 & 1.5 @xmath77 0.2 & 0.56 @xmath77 0.19 & @xmath1 0.69 + cyg - n43 & 26 @xmath77 31 & 2.8 @xmath77 5.3 & 2.5 @xmath77 6.6 & 4.5 @xmath77 0.3 & 1.6 @xmath77 0.4 & 0.42 @xmath77 0.41 & @xmath1 0.51 + cyg - n44 & 22 @xmath77 5 & 2.0 @xmath77 0.2 & 0.8 @xmath77 0.4 & 5.2 @xmath77 0.5 & 2.2 @xmath77 0.7 & 1.71 @xmath77 0.55 & @xmath1 1.75 + cyg - n48 & 15 @xmath77 3 & 4.5 @xmath77 1.2 & 0.1 @xmath77 0.4 & 7.4 @xmath77 2.2 & 1.2 @xmath77 0.2 & 0.48 @xmath77 0.10 & @xmath1 0.59 + cyg - n51 & 22 @xmath77 6 & 2.9 @xmath77 0.6 & 0.1 @xmath77 0.7 & 5.7 @xmath77 0.6 & 1.6 @xmath77 0.2 & 0.46 @xmath77 0.08 & @xmath1 0.56 + dr21 filament@xmath132 & 151 @xmath77 21 & @xmath1 0.16 & & @xmath1 1 & @xmath1 0.8 & @xmath1 0.62 & @xmath1 0.94 + [ phy_table2 ] ccccccccccc cyg - n38 & 0.34 & 1.5 & 0.9 & 7.5 & 2.7 & 0.27 & 2.4 & 1.4 & 0.19 & 3.0 + cyg - n43 & 0.34 & 1.6 & 1.2 & 8.0 & 2.4 & 0.18 & 1.0 & 5.7 & 0.99 & 12.4 + cyg - n44 & 0.42 & 2.2 & 1.6 & 9.0 & 2.4 & 0.14 & 2.3 & 1.2 & 0.20 & 2.6 + cyg - n48 & 0.34 & 1.2 & 0.7 & 6.0 & 3.0 & 0.50 & 4.3 & 0.6 & 0.06 & 1.3 + cyg - n51 & 0.34 & 1.6 & 1.1 & 8.0 & 2.4 & 0.18 & 1.6 & 2.5 & 0.42 & 5.4 + dr21 filament & 0.30@xmath132 & 0.8 & 3.0@xmath135 & 4.6 & 0.5 & 0.02 & 3.4@xmath136 & 0.04 & 0.28 & 0.36 + [ phy_table3 ] m toward the dr21 filament @xcite . the contours show the total dust continuum emission with levels of 5% , 10% , 15% , 20% , 30% , ... , 90% of the peak . the red and orange segments represent the polarization detections at s / n above 3 and between 23 , respectively . the segments show the magnetic field direction with its length proportional to the polarization percentage . the triangles mark the positions of the millimeter sources in @xcite . left and right panels : the sma dust polarization maps at 880 @xmath0 m toward six massive cores in the dr21 filament . in the maps of cyg - n38 , cyg - n43 , cyg - n48 , cyg - n51 , and cyg - n53 , the contour levels are -5 , -3 , 3 , 5 , 10 , 20 , ... , 70 times the rms noises of the maps . the cyg - n44 map is the sma subcompact , compact and extended map in @xcite , which shows contours at 4% , 8% , 18% , 28% , ... , 98% of the peak . the polarized intensity is shown in gray image with the scale bar at top - left corner of the figure in units of jy beam@xmath11 . the blue segments show the sma polarizations of s / n @xmath137 3 with the directions of magnetic fields and the lengths proportional to the polarization percentage . in each panel , the synthesized beam is plotted as a filled grey ellipse . the size of the sma panels is 32@xmath9 , equal to the diameter of sma primary beam at 880 @xmath0 m . ] m continuum maps of the cyg - n38 , cyg - n44 , and cyg - n48 . ( a ) the gray scale in units of jy beam@xmath11 and the contours show the combined dust stokes @xmath6 emission . the contours are plotted at 5% , 10% , 15% , 25% , ... , 95% of the peak . the dotted circles represent the sma primary beams of the sources . the synthesized beam of the combined map is plotted as a filled grey circle . the red , orange , and blue segments are the segments in figure 1 with equal length ( please note that we do not combine the jcmt and sma stokes @xmath7 and @xmath8 maps ) . ( b ) the structures selected by dendrograms overlaid on the jcmt and sma combined map . the contours show the boundries of the structures , and the ellipses are plotted using the major fwhm , minor fwhm , and @xmath21 computed by dendrograms . for each source , the red ( or orange if s / n between 23 ) and blue segments show the orientations of @xmath37 and @xmath35 , respectively . ] , @xmath37 , and @xmath35 . the widths of the shadow zones are the means of the error bars in @xmath37 and @xmath35 . in order to present the correlation , some of the position angles are shifted by 180@xmath12 . ] \rangle$ ] , binned in 1@xmath685 for a nyquist sampling of the 3@xmath94@xmath9 beam . the dots represent the mean values of the data , and the error bars show the standard deviations of the mean values . the gray boxes display the interquartile ranges of the data . the blue line shows the best fit to the data ( equation 5 ) , and the red line shows the ordered component @xmath138 of the best fit . the dotted vertical and horizontal lines note the beam size and the expected value for random magnetic fields , respectively . bottom panels : the dots represent the correlated component of the best fit to the data . the red line shows the correlation due to the beam ( equation 18 in @xcite @xcite ) , and the blue line shows the turbulent component @xmath139 ( equation 10 ) of the best fit . the dashed line marks the zero value . ] ine - of - sight magnetic field strength against volume density of molecular cloud . the red circles and red square denote the massive cores and the dr21 filament in this work . the triangles denote the zeeman observations in @xcite . note that despite the zeeman observations are probing similar density scales , the spatial scales of the zeeman observations are about 10 times larger than our observations . the dotted line represents the model of maximum magnetic field strength scaling with volume density as @xmath140 proposed in @xcite along with its uncertainty shown as the shadow zone . the solid line represents the single power - law fit of the massive cores in the dr21 filament . [ fig_b_den ]

we present submillimeter array 880 m dust polarization observations of six massive dense cores in the dr21 filament . the dust polarization shows complex magnetic field structures in the massive dense cores with sizes of 0.1 pc , in contrast to the ordered magnetic fields of the parsec - scale filament . the major axes of the massive dense cores appear to be aligned either parallel or perpendicular to the magnetic fields of the filament , indicating that the parsec - scale magnetic fields play an important role in the formation of the massive dense cores . however , the correlation between the major axes of the cores and the magnetic fields of the cores is less significant , suggesting that during the core formation , the magnetic fields below 0.1 pc scales become less important than the magnetic fields above 0.1 pc scales in supporting a core against gravity . our analysis of the angular dispersion functions of the observed polarization segments yields the plane - of - sky magnetic field strengths of 0.41.7 mg of the massive dense cores . we estimate the kinematic , magnetic , and gravitational virial parameters of the filament and the cores . the virial parameters show that in the filament , the gravitational energy is dominant over magnetic and kinematic energies , while in the cores , the kinematic energy is dominant . our work suggests that although magnetic fields may play an important role in a collapsing filament , the kinematics arising from gravitational collapse must become more important than magnetic fields during the evolution from filaments to massive dense cores .

we present submillimeter array 880 m dust polarization observations of six massive dense cores in the dr21 filament . the dust polarization shows complex magnetic field structures in the massive dense cores with sizes of 0.1 pc , in contrast to the ordered magnetic fields of the parsec - scale filament . the major axes of the massive dense cores appear to be aligned either parallel or perpendicular to the magnetic fields of the filament , indicating that the parsec - scale magnetic fields play an important role in the formation of the massive dense cores . however , the correlation between the major axes of the cores and the magnetic fields of the cores is less significant , suggesting that during the core formation , the magnetic fields below 0.1 pc scales become less important than the magnetic fields above 0.1 pc scales in supporting a core against gravity . our analysis of the angular dispersion functions of the observed polarization segments yields the plane - of - sky magnetic field strengths of 0.41.7 mg of the massive dense cores . we estimate the kinematic , magnetic , and gravitational virial parameters of the filament and the cores . the virial parameters show that in the filament , the gravitational energy is dominant over magnetic and kinematic energies , while in the cores , the kinematic energy is dominant . our work suggests that although magnetic fields may play an important role in a collapsing filament , the kinematics arising from gravitational collapse must become more important than magnetic fields during the evolution from filaments to massive dense cores .

1511.04184

c

* we have presented the first measurements of the rest - frame 1040 kev xlf of agns at @xmath0 based on a sample of 94 sources selected at comparable observed - frame energies ( 824 kev ) . our study takes advantage of the unprecedented sensitivity at these energies that is achieved by the _ nustar _ survey program . * we find that different models of the @xmath12 function , used to account for selection biases in our measurements , make significantly different predictions for the total number of sources in our sample , leading to slight differences in our binned estimates of the xlf . the @xcite model predicts fewer agns than observed in our sample , possibly due to a higher @xmath106 , whereas the @xcite model , which predicts more sources with @xmath126 @xmath2 , is in better agreement with the observed samples . * our results are also sensitive to our assumed x - ray spectral model . stronger reflection ( @xmath127 , compared to our baseline assumption of @xmath128 ) at all luminosities can bring the @xcite model predictions into better agreement with our _ nustar _ sample . however , with @xmath127 the @xcite model over - predicts the number of sources in our sample by @xmath207% . * our results are consistent with the strong evolution of the agn population seen in lower energy studies of the xlf ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , characterized by a shift in the luminosity function toward higher luminosities at higher redshifts . however , the models that successfully describe the high - redshift population detected by _ nustar _ tend to over - predict the local ( @xmath214 ) xlf measured by _ swift_/bat , indicating some evolution of the agn population that is not fully captured by the current models . nonetheless , as our sample is limited to luminous ( @xmath215 ) x - ray sources at @xmath193 , we defer an investigation of different parametric descriptions of the evolution of the xlf to future studies . * forthcoming x - ray spectral analysis of the _ nustar _ survey should enable us to measure @xmath12 and @xmath61 for the brightest sources , break the degeneracy between the @xmath12 function and the average reflection strength , and refine our estimates of the xlf . including lower - energy _ nustar _ detections may enable us to probe a factor @xmath72 deeper . the ongoing _ nustar _ survey program will also increase our sample size and improve our estimates of the xlf . this work made use of data from the _ nustar _ mission , a project led by the california institute of technology , managed by the jet propulsion laboratory , and funded by the national aeronautics and space administration . we thank the _ nustar _ operations , software and calibration teams for support with the execution and analysis of these observations . this research has made use of the _ nustar _ data analysis software ( nustardas ) jointly developed by the asi science data center ( asdc , italy ) and the california institute of technology ( usa ) . we acknowledge financial support from : erc advanced grant feedback at the university of cambridge ( ja , acf ) ; a cofund junior research fellowship from the institute of advanced study , durham university ( ja ) ; the science and technology facilities council ( stfc ) grants st / i001573/1 ( dma and adm ) , st / k501979/1 ( gbl ) , and st / j003697/1 ( pg ) ; the leverhulme trust ( dma ) ; the caltech kingsley visitor program ( dma , ac ) ; nsf award ast 1008067 ( drb ) ; nasa grants 11-adap11 - 0218 and go3 - 14150c ( fc ) ; an alfred p. sloan research fellowship and a dartmouth class of 1962 faculty fellowship ( rch ) ; conicyt - chile grants basal - cata pfb-06/2007 ( feb , et ) ; fondecyt 1141218 ( feb ) and 1120061 ( et ) ; embiggen " anillo act1101 ( feb , et ) ; the ministry of economy , development , and tourism s millennium science initiative through grant ic120009 , awarded to the millennium institute of astrophysics , mas ( feb ) ; nasa nustar subcontract 44a-1092750 and nasa adp grant nnx10ac99 g ( wnb , bl ) ; asi / inaf grant i/037/12/0011/13 ( ac , lz ) ; and nasa earth and space science fellowship program grant nnx14aq07h ( mb ) .

we present the first direct measurements of the rest - frame 1040 kev x - ray luminosity function ( xlf ) of active galactic nuclei ( agns ) based on a sample of 94 sources at , selected at 824 kev energies from sources in the _ nustar _ extragalactic survey program . however , different models of the intrinsic distribution of absorption , which are used to correct for selection biases , give significantly different predictions for the total number of sources in our sample , leading to small , systematic differences in our binned estimates of the xlf . adopting a model with a lower intrinsic fraction of compton - thick sources and a larger population of sources with column densities furthermore , the models that successfully describe the high - redshift population seen by _ nustar _ tend to over - predict previous , high - energy measurements of the local xlf , indicating that there is evolution of the agn population that is not fully captured by the current models .

we present the first direct measurements of the rest - frame 1040 kev x - ray luminosity function ( xlf ) of active galactic nuclei ( agns ) based on a sample of 94 sources at , selected at 824 kev energies from sources in the _ nustar _ extragalactic survey program . our results are consistent with the strong evolution of the agn population seen in prior , lower - energy studies of the xlf . however , different models of the intrinsic distribution of absorption , which are used to correct for selection biases , give significantly different predictions for the total number of sources in our sample , leading to small , systematic differences in our binned estimates of the xlf . adopting a model with a lower intrinsic fraction of compton - thick sources and a larger population of sources with column densities or a model with a stronger compton reflection component ( with a relative normalization of at all luminosities ) can bring extrapolations of the xlf from 210 kev into agreement with our _ nustar _ sample . ultimately , x - ray spectral analysis of the _ nustar _ sources is required to break this degeneracy between the distribution of absorbing column densities and the strength of the compton reflection component and thus refine our measurements of the xlf . furthermore , the models that successfully describe the high - redshift population seen by _ nustar _ tend to over - predict previous , high - energy measurements of the local xlf , indicating that there is evolution of the agn population that is not fully captured by the current models .

1610.06932

i

galaxy gas reservoirs are the raw fuel for star formation and thus play a key role in galaxy evolution . . therefore , understanding the extent to which environment governs galaxy gas content is a fundamental ingredient to understanding galaxy assembly as a whole . several studies have highlighted the link between star formation and environment through the color - density relation , which translates into the physical understanding that galaxies in dense regions have lower star formation rates ( sfrs ) and typically older ages than those in the field @xcite . likewise , galaxies in dense environments show gas deficiencies @xcite while the most gas - rich galaxies are often found in the least dense environments @xcite . there are multiple possible connections between galaxy gas supply and the surrounding environment . for example , the low cold gas content among galaxies in dense environments can be attributed to mechanisms that cut off gas replenishment ( i.e. , starvation ; @xcite ) or directly remove gas ( e.g. , tidal , ram - pressure , or viscous stripping ; @xcite , @xcite , @xcite ) . in the absence of these processes , galaxies acquire gas from their surroundings over time . fresh gas infall is needed to explain the roughly constant star formation history of the milky way @xcite , as well as the heavy element abundances in its stellar populations @xcite . regular ( and possibly overwhelming ) gas infall also explains the high gas content and exponential stellar mass growth of many dwarf galaxies in the local universe @xcite , and there are multiple examples of early - type galaxies that appear to be ( re)growing gas and stellar disks @xcite . while galaxies can acquire new gas through hierarchical merging @xcite , a more subtle but extremely important alternative mechanism is the smooth accretion of the igm , i.e. `` cosmological accretion . '' traditional theory suggests that as gas enters a dark matter halo , it shock heats to the halo s virial temperature before slowly cooling onto the galaxy @xcite . below a halo mass threshold , the cooling timescale may be short enough that infalling gas can avoid shock heating to the virial temperature @xcite . this cold mode " of accretion is thought to take the form of gas streams that penetrate into halos along cosmic filaments , depositing cool gas onto galaxies much more rapidly than the traditional hot " mode . direct detection of cool gas streams associated with cold mode accretion is difficult since this gas is expected to be in a low - density , warm - hot ionized state that lacks detectable emission at low redshift @xcite . however , a number of high - redshift studies have detected gas through lyman-@xmath14 emission or absorption with properties consistent with cold - mode accretion @xcite , and some absorption features consistent with pristine gas infall have also been reported at low redshift ( e.g. , @xcite ) . further evidence comes from observations of neutral atomic hydrogen ( h ) emission around nearby galaxies . high - velocity clouds have been observed around many galaxies in the local group , particularly the milky way , and some of these clouds may have external origins @xcite . key group halo mass scales theoretically associated with changes in accretion can be related to observed trends in galaxy properties . the halo mass scale below which cold - mode accretion is expected to dominate over hot - mode accretion ( @xmath15 ; @xcite ) matches the observed gas - richness threshold scale " @xcite , where gas - dominated galaxies become the norm . the scale above which cold - mode accretion is no longer present ( @xmath16 ; @xcite ) matches the bimodality mass , " which marks a transition between star - forming and quenched " galaxies @xcite . more recent simulations suggest that cold - mode accretion may be less important than previously thought , with infalling streams likely getting disrupted in the inner halo before reaching the central galaxy @xcite . however , this effect is at least somewhat balanced by a faster cooling rate for gas accreted via the hot mode . recent work has often emphasized a picture wherein galaxy gas reservoirs are largely governed by dark matter halos and their internal environments : gas accretion rates are expected to be closely tied to the masses of dark matter halos , as are many processes that deplete gas content ( e.g. , ram pressure stripping ; @xcite ) . however , there is evidence that galaxy properties may also depend on the environment beyond the halo virial radius . a number of different physical mechanisms have been proposed that either remove gas or slow the infall of gas in dark matter halos in overdense regions . such environments may have higher rates of flyby interactions ( involving ejected satellites " or splashback galaxies " ) , wherein a galaxy enters a more massive halo , loses its gas content , and then escapes the inner regions , at least temporarily @xcite . additionally , @xcite suggest that the igm in large - scale structure leads to ram pressure stripping of hot halo gas ( particularly at @xmath17 ) , reducing the potential of galaxies to replenish their cold gas supply . halo gas accretion rates may also be lessened by competition between dark matter halos @xcite , or by longer cooling times caused by earlier heating from the gravitational collapse of cosmic structure @xcite and/or early active galactic nucleus ( agn ) feedback @xcite . in this work , we present the first 21 cm data release for the resolved spectroscopy of a local volume ( resolve ) survey , a new multi - wavelength volume - limited census of galaxies in the local universe that has a large dynamic range of group halo masses ( @xmath18 ) and large - scale structure densities ( factor of @xmath19 variation ) , and probes galaxy masses down to the dwarf galaxy regime ( baryonic mass @xmath20 ) . resolve and its h census are ideally suited for environmental studies of global h - to - stellar mass ratios enabling us to address multiple key questions relating to the physical processes governing galaxy fuel supplies : how does gas content scale with halo mass ? does this scaling behave differently for centrals and satellites ? does the observed gas deficiency previously observed in large groups and clusters also occur in more moderately sized dark matter halos ? in [ sec : ch4:data ] , we describe the resolve survey and its 21 cm census , followed by a discussion of the metrics in [ sec : ch4:discussion ] we interpret our findings from the point of view of the physical processes occurring within and around group dark matter halos and large - scale structure . we summarize our conclusions in [ sec : ch4:conclusion ] .

we present the h mass inventory for the resolved spectroscopy of a local volume ( resolve ) survey , a volume - limited , multi - wavelength census of galaxies spanning diverse environments and complete in baryonic mass down to dwarfs of . this first 21 cm data release provides robust detections or strong upper limits ( 1.4 510 of stellar mass ) for% of resolve . we identify a rare population of gas - poor centrals in low - mass halos primarily located within.5 the virial radius of more massive ( ) halos ,

we present the h mass inventory for the resolved spectroscopy of a local volume ( resolve ) survey , a volume - limited , multi - wavelength census of galaxies spanning diverse environments and complete in baryonic mass down to dwarfs of . this first 21 cm data release provides robust detections or strong upper limits ( 1.4 510 of stellar mass ) for% of resolve . we examine global atomic gas - to - stellar mass ratios ( ) in relation to galaxy environment using several metrics : group dark matter halo mass , central / satellite designation , relative mass density of the cosmic web , and distance to nearest massive group . we find that at fixed , satellites have decreasing with increasing starting clearly at , suggesting the presence of starvation and/or stripping mechanisms associated with halo gas heating in intermediate - mass groups . . on larger scales trends are less sensitive to the abundance matching method . at fixed , the fraction of gas - poor centrals increases with large - scale structure density . in overdense regions , we identify a rare population of gas - poor centrals in low - mass halos primarily located within.5 the virial radius of more massive ( ) halos ,

1610.06932

c

we have presented the first major release of 21 cm data for the resolve survey , a multi - wavelength , volume - limited census of galaxies in the local universe complete into the dwarf mass regime and spanning diverse environments . the census currently provides detections and strong upper limits for @xmath294% of resolve . we have combined this h census with metrics designed to characterize galaxy environments on the scales of galaxy groups ( dark matter halo mass ) and the surrounding cosmic web ( large - scale structure density and group separation ) . we have used this data set to investigate how both halo mass and large - scale environment independently influence the atomic gas content of the @xmath1 galaxy population . our key results are as follows : * by comparing gas fractions of satellites as a function of stellar mass in different halo mass regimes , we find systematic gas deficiency in groups as low mass as @xmath86 , ( see [ sec : ch4:mhalo_gs ] , [ sec : ch4:cosmic_variance ] , fig . [ fig : medgs_mstars_mbary_3panel ] , fig . [ fig : ch4:medgs_mstars_mbary_sep_springfall ] ) . * while we find mostly consistent behavior among satellites independent of how we estimate halo mass , an analogous gas fraction stellar mass halo mass analysis applied to central galaxies yields results strongly dependent on the integrated group property ( stellar or baryonic mass ) used in halo abundance matching . we caution that halo abundance matching inevitably builds in relationships for central galaxies ( see [ sec : ch4:mhalo_gs ] , fig . [ fig : medgs_mstars_mbary_3panel ] ) . * the fraction of gas - poor ( @xmath97 ) , centrals grows with increasing large - scale structure density ( see [ sec : ch4:dmdens_gs ] , fig . [ fig : ch4:msmhalo_dmdens_gs_all ] ) . * gas - poor , @xmath99 centrals at high @xmath92 often reside alone within their halos , but they tend to cluster within @xmath125 of the nearest group . this result is not driven by fragmentation in group finding , but may indicate a need to revisit the definition of halo boundaries ( see [ sec : ch4:gs_groupdist ] , [ sec : ch4:gs_largeenv ] , fig . [ fig : ch4:largermsgroupdist_gs ] ) . * relationships between @xmath8 and large - scale environment are generally independent of whether halo masses are estimated based on stellar or baryonic mass , although the statistical significance of the observed trends is sometimes slightly weaker when using baryonic mass - based halo mass estimates . we argue that analysis based on stellar mass tends to highlight ram - pressure / viscous stripping interpretations , as opposed to tidal stripping and starvation interpretations , because the latter affects both stellar and gas mass ( see [ sec : ch4:lss_mhalodef ] ) . * the results of this work address several of our key questions about the relationship between gas content and environment as presented in [ sec : ch4:intro ] : we find evidence for gas - deficiency of satellites down to @xmath210@xmath126 halos , which is possibly linked to the emergence of stable hot gas atmospheres in halos at this mass scale . the hint of gas deficiency down to @xmath91 may reflect the build - up of hot halo atmospheres from the inner halos outward . the influence of the group environment may not be limited to galaxies residing within the group itself , as we find evidence that low halo mass ( often singleton ) galaxies may have their gas content depleted by interactions with more massive halos . large - scale structure appears to have a substantial influence on gas content , such that large - scale overdensities have higher fractions of gas - poor centrals , which could be attributed to a number of physical processes . a number of questions remain unanswered , some of which were raised by this study . can we assess the detailed relationship between gas fraction , stellar mass , and group halo mass for central galaxies without built - in biases from halo mass estimation ? does satellite gas deficiency begin below @xmath10 ? can we constrain whether variations in gas content across environment are caused by gas starvation or direct gas removal processes ? some of these questions will be the subject of future work with resolve , while others may require future surveys to address . . although we are still working toward a complete physical interpretation of the trends reported in this paper , our results highlight the importance of considering the multi - scale environments of galaxies when developing a complete picture of galaxy assembly .

we examine global atomic gas - to - stellar mass ratios ( ) in relation to galaxy environment using several metrics : group dark matter halo mass , central / satellite designation , relative mass density of the cosmic web , and distance to nearest massive group . the fraction of gas - poor centrals increases with large - scale structure density . in overdense regions ,

we present the h mass inventory for the resolved spectroscopy of a local volume ( resolve ) survey , a volume - limited , multi - wavelength census of galaxies spanning diverse environments and complete in baryonic mass down to dwarfs of . this first 21 cm data release provides robust detections or strong upper limits ( 1.4 510 of stellar mass ) for% of resolve . we examine global atomic gas - to - stellar mass ratios ( ) in relation to galaxy environment using several metrics : group dark matter halo mass , central / satellite designation , relative mass density of the cosmic web , and distance to nearest massive group . we find that at fixed , satellites have decreasing with increasing starting clearly at , suggesting the presence of starvation and/or stripping mechanisms associated with halo gas heating in intermediate - mass groups . . on larger scales trends are less sensitive to the abundance matching method . at fixed , the fraction of gas - poor centrals increases with large - scale structure density . in overdense regions , we identify a rare population of gas - poor centrals in low - mass halos primarily located within.5 the virial radius of more massive ( ) halos ,

0909.2051

i

stellar - mass black hole x - ray binaries ( bhxrbs ) and active galactic nuclei ( agns ) are both powered by accretion onto a black hole ( bh ) . in many cases these systems emit radiation over several decades of frequency and possess relativistic jets @xcite . the above similarities in the basic generation of energy and observational properties have led to the paradigm that these two systems are fundamentally similar , with characteristic time and size scales linearly proportional to the mass of the central bh ( @xmath010 m@xmath1 for bhxrbs and @xmath2 to @xmath3 m@xmath1 for agns ) . although this paradigm has given rise to the expectation that we might test models of agns with observations of bhxrbs , such an approach is unjustified until detailed , possibly quantitative connections between bhxrb systems and agns become well - established . the comparison of bhxrbs and agns is complicated by the fact that a single agn usually does not show the entire range of properties that we wish to compare . for example , seyfert galaxies are the agns that most resemble bhxrbs , but their radio jets tend to be weak and non - relativistic ( e.g. * ? ? ? * ) . on the other hand , in radio - loud agns with strong , highly variable nonthermal radiation ( blazars ) , the doppler beamed emission from the jet at most wavelengths masks the thermal emission from the accretion disk and its nearby regions . one well - established property of bhxrbs is the connection between accretion state and events in the jet . in these objects , transitions to high - soft x - ray states are associated with the emergence of very bright features that proceed to propagate down the radio jet @xcite . similarly , an accretion disk - jet connection was established in agns by @xcite , who reported a relationship between x - ray and radio events in the radio galaxy 3c 120 ( redshift of 0.033 ) . during @xmath0 3 yr of monitoring of this object , four dips in the x - ray flux , accompanied by spectral hardening , preceded the appearance of bright superluminal knots in the radio jet . this fanaroff - riley class i radio galaxy has a prominent radio jet that displays strong variability in flux and jet structure @xcite . the jet lies at an angle @xmath4 to our line of sight , significantly wider than is typically the case for blazars @xcite . at optical and x - ray frequencies , 3c 120 possesses properties similar to seyfert galaxies and bhxrbs , e.g. , a prominent iron emission line at a rest energy of 6.4 kev @xcite . hence , most of the x - rays are produced in the immediate environs of the accretion disk : the corona , a hot wind , or the base of the jet . since the superluminal knots are disturbances propagating down the jet , a link between decreases in x - ray production and the emergence of new superluminal components demonstrates the existence of a strong disk - jet connection . in this paper we present the results of extensive multi - frequency monitoring of 3c 120 between 2002 and 2007 at x - ray energies ( 2.4 - 10 kev ) , optical @xmath5 and @xmath6 bands , and radio frequencies 37 and 14.5 ghz , as well as imaging with the very long baseline array ( vlba ) at 43 ghz . we use these data to obtain quantitative support for the disk - jet connection claimed by @xcite . times of ejections " are defined as the extrapolated time of coincidence of a moving knot with the position of the ( presumed quasi - stationary ) core in the vlba images . @xcite have found that ejection times are generally associated with an increase in flux at 37 ghz . therefore , the 37 ghz flux should be anti - correlated with the x - ray flux if decreases in x - ray production are linked to ejections . here , we confirm the existence of this anti - correlation and test for a relation between the amplitude of the x - ray dips and that of the associated 37 ghz flares . another similarity between bhxrbs and seyfert galaxies lies in their x - ray power spectral densities ( psds ) . the psd corresponds to the power in the variability of flux on different timescales . the x - ray psds of seyfert galaxies can be fit by piece - wise power laws with a break @xcite . this is generally similar to that of bhxrbs although in many cases the latter have more than one break and sharp peaks due to quasi - periodic oscillations . we use our data set to verify that the x - ray psd of 3c 120 also has a break , as inferred by @xcite , who calculated the psd from somewhat less extensive observations that partially overlap with ours . the bulk of the optical continuum from non - blazar agns is thought to emanate from the accretion disk @xcite . in order to test this , we cross - correlate the optical flux variations of 3c 120 with those at x - ray energies . however , the coefficients of raw correlations may be artificially low due to the uneven sampling present in the data . in light of this , we use simulated light curves , based on the underlying psd , to estimate the significance of the derived coefficients of both the x - ray / optical correlation and x - ray/37 ghz anti - correlation found in the 3c 120 data . in 2 we present the observations and data reduction procedures , while in 3 we describe the power spectral analysis and its results . in 4 we cross - correlate the x - ray and 37 ghz light curves and quantitatively investigate the relation between the x - ray dips , radio flares and ejections , as well as discuss the x - ray / optical correlation . in 5 we discuss and interpret the results , focusing on the implications regarding the accretion disk - jet connection and the source of the optical emission in 3c 120 . 6 presents conclusions , including comparison of 3c 120 with bhxrbs

we present the results of extensive multi - frequency monitoring of the radio galaxy 3c 120 between 2002 and 2007 at x - ray ( 2 - 10 kev ) , optical ( r and v band ) , and radio ( 14.5 and 37 ghz ) wave bands , as well as imaging with the very long baseline array ( vlba ) at 43 ghz . over the 5 yr of observation , significant dips in the x - ray light curve the x - ray power spectral density of 3c 120 shows a break , with steeper slope at shorter timescale and the break timescale is commensurate with the mass of the central black hole based on observations of seyfert galaxies and black hole x - ray binaries . these findings provide support for the paradigm that black hole x - ray binaries and both radio - loud and radio - quiet active galactic nuclei are fundamentally similar systems , with characteristic time and size scales linearly proportional to the mass of the central black hole . the x - ray and optical variations , we discus physical scenarios for the disk - jet connection that are consistent with our observations .

we present the results of extensive multi - frequency monitoring of the radio galaxy 3c 120 between 2002 and 2007 at x - ray ( 2 - 10 kev ) , optical ( r and v band ) , and radio ( 14.5 and 37 ghz ) wave bands , as well as imaging with the very long baseline array ( vlba ) at 43 ghz . over the 5 yr of observation , significant dips in the x - ray light curve are followed by ejections of bright superluminal knots in the vlba images . consistent with this , the x - ray flux and 37 ghz flux are anti - correlated with x - ray leading the radio variations . furthermore , the total radiative output of a radio flare is related to the equivalent width of the corresponding x - ray dip . this implies that , in this radio galaxy , the radiative state of accretion disk plus corona system , where the x - rays are produced , has a direct effect on the events in the jet , where the radio emission originates . the x - ray power spectral density of 3c 120 shows a break , with steeper slope at shorter timescale and the break timescale is commensurate with the mass of the central black hole based on observations of seyfert galaxies and black hole x - ray binaries . these findings provide support for the paradigm that black hole x - ray binaries and both radio - loud and radio - quiet active galactic nuclei are fundamentally similar systems , with characteristic time and size scales linearly proportional to the mass of the central black hole . the x - ray and optical variations are strongly correlated in 3c 120 , which implies that the optical emission in this object arises from the same general region as the x - rays , i.e. , in the accretion disk - corona system . we numerically model multi - wavelength light curves of 3c 120 from such a system with the optical - uv emission produced in the disk and the x - rays generated by scattering of thermal photons by hot electrons in the corona . from the comparison of the temporal properties of the model light curves to that of the observed variability , we constrain the physical size of the corona and the distances of the emitting regions from the central bh . in addition , we discus physical scenarios for the disk - jet connection that are consistent with our observations .

0909.2051

c

the physical cause of the connection between events in the central engine and the jet of bhxrbs and agns is currently a matter of considerable speculation . if the jet is magnetically launched from the accretion disk @xcite , then there must be a link between the magnetic state at the base of the jet and the accretion state in the inner disk . one scenario , proposed for bhxrbs by @xcite and @xcite , involves a change in the magnetic field configuration in the inner disk from a turbulent condition in the high - soft state ( when the x - ray flux is relatively higher and softer ) to mainly poloidal in the low - hard x - ray state . the turbulence is needed for viscous heating , which in the bhxrb case leads directly to bright x - ray emission with a soft spectrum . in an agn it causes strong ultraviolet emission , which is compton scattered in the corona to a hard x - ray spectrum . if the field switches from chaotic to mainly poloidal , which @xcite suggest can occur by random episodes of near - alignment of the field in the relatively small number of turbulent cells in the inner disk , then the radiation in the inner disk will be quenched at the same time as energy flow into the jet is promoted . the transition back to the turbulent , radiative inner disk of the high - soft state would need to involve a surge of energy injected into the jet in order to send a shock wave @xcite down the jet . perhaps global magnetic reconnection could cause this , but no detailed mhd model has been published to date . alternatively , it is possible that the corona , " where the x - ray emission seen in agn supposedly arises from compton up - scattering of softer accretion - disk photons , might be the base of the jet @xcite . if this is the case , then the x - ray flux will be related to the number of electrons residing there and available for scattering to create x - rays . the mass loading of the jet should also affect the asymptotic lorentz factor of the flow downstream if the jet is magnetically driven ( e.g. * ? ? ? * ) . the same decrease in electron number that causes a drop in scattered x - ray emission near the disk would lead to a time - delayed increase in the speed of the jet downstream . the flatter - spectrum nonthermal x - ray emission from the downstream jet would then play a larger relative role in the x - ray emission , causing the observed hardening of the spectrum during the dips . the increase in flow speed of the jet could form a shock wave , seen as a superluminal radio knot . it is difficult to speculate why the mass loading should change , since we do not understand the processes by which material from the disk and/or ergosphere are injected into the base of the jet . however , observations of the microquasar grs 1915 + 105 suggest that outflow of matter from the disk switches from mainly a wind to the jets @xcite . in an agn with a magnetically driven jet , it may be the case that lower mass injection into the jet actually enhances the jet emission owing to an increase in the flow speed driving a shock wave down the jet , as described above . the strong correlation between the x - ray and optical variations in 3c 120 implies that the emission at both wave bands arises from the same general region . since the x - rays originate in the corona , the optical emission is probably thermal emission from the accretion disk @xcite . we can reject the alternative hypothesis that the main component of optical emission is synchrotron radiation from the jet . in that case , the emission should be significantly polarized , contrary to observations showing the optical linear polarization to be @xmath70 @xcite . furthermore , the anti - correlation of the x - ray and 37 ghz emission ( the latter of which is produced in the jet ) implies that any optical synchrotron emission from the jet should also anti - correlate with the x - ray flux , contrary to the strong observed correlation . although the x - rays are predominantly produced by inverse compton ( ic ) scattering of the thermal optical / uv seed photons from the accretion disk by hot , but non - relativistic , electrons in the corona , the optical / uv emission and the x - rays are tied together by another mechanism : some of the optical / uv radiation is produced by heating of the accretion disk by x - rays produced in the above process ( feedback " mechanism ) . the amplitude of the short timescale ( @xmath0days ) variations in the x - ray light curve is larger than that in the optical . this can happen if a significant fraction of the optical emission is due to heating of the disk by x - rays , since this reprocessing may smooth out the short timescale variations . feedback can make the time delay more difficult to define by producing a fraction of the optical / uv photons with different temporal properties from that of the direct emission . there is a weak correlation between the x - ray spectral index and the x - ray flux , indicating that the spectrum becomes harder during a decrease in the production of x - rays ( fig [ baseline1sig ] ) . this kind of pivoting " has been seen before @xcite . the x - rays may be produced mainly by up - scattering of uv photons and not optical photons , consistent with the correlation found by @xcite between the x - ray and uv variations in 3c 120 . this could occur if the flux of optical photons reaching the corona is much smaller than that of uv photons . such a scenario is likely if the corona is small such that the region where the uv photons are generated is much closer to the corona than the region where the majority of the optical photons are produced . any disturbance propagating outwards in the accretion disk will cause a change in the uv flux ( and a resultant nearly immediate change in the x - ray emission ) followed by a similar change in the optical flux . the sign of the time delay will switch if the disturbance propagates inwards . the observed mean time delay between x - ray and optical variations may be due to such propagation time delays . if we adopt typical parameters such as @xmath0 0.1 for accretion efficiency , l / l@xmath71 @xmath0 0.3 @xcite , and l@xmath72 2@xmath73 @xmath74 ergs / sec @xcite and neglect general relativistic effects , the region in the accretion disk where the emission peaks in the extreme uv / soft x - ray range ( @xmath75 nm ) should be very close to the innermost stable orbit ( @xmath0 5 @xmath76 , where @xmath76 is the gravitational radius of the black hole ) . the region where the emission peaks in the optical ( @xmath77 nm ) lies at @xmath0 1000@xmath76 . for 3c 120 , with a bh mass of @xmath0 5@xmath78 m@xmath1 , 1000 @xmath76 is equivalent to @xmath04 light days . we consider a model that includes both time delays and coupling of emission from the corona and disk . we have performed a theoretical calculation to produce multi - wavelength light curves from a disk - corona system . we assume that ( 1 ) the temperature of the disk changes with its radial distance from the center according to t@xmath79 @xcite , ( 2 ) each annulus radiates as a perfect black - body , ( 3 ) the x - rays are produced in a spherical region ( corona ) close to the center of the disk by inverse - compton scattering of the disk photons that reach the corona , and ( 4 ) lower energy radiation ( uv - optical ) is produced both by blackbody radiation in the disk and reheating of the disk by the x - rays from the corona . for simplicity , we assume that the energy distribution of electrons is uniform throughout the volume of the corona . the fraction of the uv - optical photons that reach the corona are up - scattered to x - rays and a part of the x - rays re - heat the disk to produce additional thermal photons . we treat the x - ray production in the corona as a reflection that increases the energy of the radiation . the computer code that we use for the model also follows the travel time of photons from different radii of the disk to the corona and _ vice versa_. the temporal nature of the emission from the corona and the part of the disk close to it are very similar owing to the small light travel time . figure [ theory0 ] shows the variation of the total uv and optical intensity emitted by an annulus at radius @xmath80 of thickness @xmath81 , i.e. , @xmath82 versus @xmath80 . this shows that the annulus that produces the largest amount of uv radiation ( region uv " ) lies @xmath05 @xmath76 from the center , and for optical emission ( region op " ) it is at @xmath075 @xmath76 . this distance is much smaller than what would be expected if most of the optical radiation were to come from radii near where the planck curve @xmath83 peaks at r band . these latter radii lie @xmath04 light - days ( 1000 @xmath76 ) from the center , while regions close to the center are at higher temperature , and therefore emit at a higher blackbody intensity at all wavelengths . although @xmath83 increases monotonically with decreasing radii , @xmath82 peaks at a radius @xmath075 @xmath76 at r band . we use a computer code to model this disk - corona system and then introduce a disturbance in the temperature of the accretion disk that propagates at a speed @xmath00.1@xmath84 from the center toward the outside or _ vice versa_. due to the disturbance , the temperature at a given annulus varies with time according to a gaussian profile . this causes a flare in the emission of the entire system at all wavelengths , although the flare starts and peaks at different times at different wavelengths . we produce these light curves at x - ray , uv , and optical bands , including delays from internal light - travel time . the nature of the flare and relation between flares at multiple wave bands depend on the speed and direction of propagation of the disturbance since emission from different annuli of the disk have different wavelength dependence . the top panel of figure [ theory1 ] shows the x - ray and optical light curves from the above calculation when the disturbance propagates toward smaller radii . as a result , the emission from the outer disk flares before that closer to the bh . therefore , the optical variation leads that in the x - rays . in this simulation , the time delay between the peaks of the x - ray and optical light curves @xmath04 days . in 3c 120 , the time delay is centered on 0.5 day with an uncertainty of @xmath85 days , hence the direction of the time delay can not be specified with certainty . the correlation function in figure [ xop_small ] also shows a relatively broad peak centered on zero , with a similar uncertainty in the time delay . the cross - correlation function for longterm light curves sometimes show a broad peak due to changes in the direction and magnitude of the time delay over the timespan of the light curves . if the broad peak in these correlation functions is due to the above - mentioned reason , it may indicate a dichotomy in the speed of propagation of the disturbances and their directions , i.e. , the uncertainty corresponds to an actual range of time delays . this also constrains the size of the corona . for example , if the corona were spread such that the regions op and uv were at the same distance from the corona , then these regions would contribute equally to the flux of seed photons that are up - scattered to x - rays . in that case , the x - ray flares would be much broader than observed and no optical / x - ray time delay would be present . this is contrary to the observation of relatively sharp x - ray flares . in addition , although overall we find a short mean time delay of @xmath86 day ( i.e. , if the uncertainty does not correspond to an actual range of time delays but rather is consistent with zero ) , in some of the individual flares the time delay is longer ( @xmath025 days ; see top panel of figure [ xop_tw ] ) . also , if optical and uv photons were up - scattered to soft and hard x - rays , respectively , a significant soft - hard " time delay would be expected . but from figure [ softhard ] , it is clear that the soft - hard time lag can not be more than 0.25 day , which is essentially unobservable with the longterm light curves . from the above discussion , we conclude that the corona is situated close to the center of the accretion disk , and its size is such that the flux of photons reaching the corona from region op is negligible with respect to that from region uv . based on the solid angle subtended , the coronal radius should be less than 40@xmath76 for the flux from region op to be less than 10% of that from region uv . in figure [ theory1 ] , the two panels show results for different levels of feedback ( the fraction of the x - rays produced in the corona that reflect toward and re - heat the disk ) . the top panel has feedback fraction equal to zero , i.e. , none of the x - rays re - heat the disk . we can see from the figure that , as feedback is introduced , the resulting time delay becomes smaller and less precise . figure [ theory2 ] shows the light curves when the disturbance is propagating outwards from the bh . in this case , as expected , the x - ray variations lead those in the optical ( by similar amount as in figure [ theory1 ] ) for the same propagation speed . the panels show , as above , that including feedback makes the time delay shorter . hence , feedback from the corona may also contribute to the range of time delays that we see in the data . in another possible scenario , the x - ray variability is caused by intrinsic changes in the hot electrons in the corona and the uv - optical changes are due to feedback , i.e. , there is no intrinsic variability in the accretion disk . in this case , the x - ray / optical time delay will solely be due to light travel time from the corona to the accretion disk . this will produce time lags of a small fraction of a day @xcite , which is too small to observe with the sampling of the data used in this work . the observed essentially zero time lag between the long - term x - ray and optical light curves ( @xmath67 days ) and smaller variability amplitude in the short - term optical light curve than that in the x - rays are consistent with the above scenario . in fact the steepening of the x - ray spectrum and decrease in the mean x - ray flux level after 2006.0 ( see fig . [ baseline1sig ] ) suggest a long - term steepening of the energy distribution of electrons in the corona . but the longer x - ray / optical time delay over a significant portion of the dataset ( figure [ xop_tw ] ) and comparable x - ray / optical b - band variability amplitude in the long - term light curves @xcite with b - band variations sometimes leading , indicate that propagation of disturbances in the accretion disk must produce at least part of the x - ray / optical variability in this radio galaxy . figure [ cartoon ] shows a sketch of the accretion disk - corona system as derived in this paper . the black filled circle is the position of the bh , the temperature of the accretion disk is shown by gray scale with lighter color meaning higher temperature , and the larger circular area filled with dots is the corona . region uv " and region op " are shown as thick solid lines on the accretion disk . the radius of the corona and the distance of the relevant emission regions from the bh are shown in units of @xmath76 . from the above model and the correlation results , we conclude that most , if not all , of the optical emission in 3c 120 is produced in the accretion disk . the x - rays are produced by scattering of ( mostly ) uv radiation in the corona . optical / uv emission due to re - heating of the disk by the x - rays is also a possible ongoing mechanism that may cause the spread of the time delay . the presence of sharp x - ray flares and the x - ray / optical time delay of weeks in some individual flares indicate that the corona must lie sufficiently close to the bh that the flux of seed photons reaching the corona is dominated by uv light . the light curve during the dip at x - ray and optical wave bands between 2006 october and 2007 april , displayed in figure [ xop_commondips ] , is very well - sampled . it is evident that the optical flux starts to decrease after @xmath0mjd @xmath87 , @xmath88 days earlier than the decrease starts in the x - rays . the minimum in optical occurs @xmath040 days earlier than that in the x - rays as well . this indicates that the decrease was caused by a disturbance propagating from the outer radii of the accretion disk toward the bh . if this disturbance is a thermal fluctuation propagating inward , then it should have an effective speed @xmath89 @xmath90 to cause a time delay of @xmath040 days . this is one order of magnitude higher than the sound speed for a gas pressure dominated disk of temperature @xmath91 @xmath92 k. therefore , the above disturbance can not be transmitted by sound waves @xcite unless the relevant regions of the disk are dominated by radiation pressure , which can not be ruled out in 3c 120 given its high accretion rate , nearly the eddington value ( 0.3 @xmath93 ) . on the other hand , this scenario is consistent with the model proposed by @xcite , in which large scale alignment of poloidal magnetic field in the inner accretion disk from random fluctuations causes the decrease in the x - ray flux . such alignment occurs at a timescale @xmath94 , where @xmath95 is the radius to thickness ratio of the disk , @xmath96 is a constant @xmath010 @xcite , and @xmath97 is the disk dynamical timescale at radius @xmath5 . this alignment timescale , for a @xmath98 bh , is few seconds , which translates to @xmath050 days for a @xmath99 bh in 3c 120 . model light curves of @xcite also contain short timescale , small amplitude fluctuations on top of the big flares and dips caused by small - scale alignment of the poloidal magnetic field , similar to that observed in the light curves of 3c 120 presented in this paper .

this implies that , in this radio galaxy , the radiative state of accretion disk plus corona system , where the x - rays are produced , has a direct effect on the events in the jet , where the radio emission originates . are strongly correlated in 3c 120 , which implies that the optical emission in this object arises from the same general region as the x - rays , i.e. , in the accretion disk - corona system .

we present the results of extensive multi - frequency monitoring of the radio galaxy 3c 120 between 2002 and 2007 at x - ray ( 2 - 10 kev ) , optical ( r and v band ) , and radio ( 14.5 and 37 ghz ) wave bands , as well as imaging with the very long baseline array ( vlba ) at 43 ghz . over the 5 yr of observation , significant dips in the x - ray light curve are followed by ejections of bright superluminal knots in the vlba images . consistent with this , the x - ray flux and 37 ghz flux are anti - correlated with x - ray leading the radio variations . furthermore , the total radiative output of a radio flare is related to the equivalent width of the corresponding x - ray dip . this implies that , in this radio galaxy , the radiative state of accretion disk plus corona system , where the x - rays are produced , has a direct effect on the events in the jet , where the radio emission originates . the x - ray power spectral density of 3c 120 shows a break , with steeper slope at shorter timescale and the break timescale is commensurate with the mass of the central black hole based on observations of seyfert galaxies and black hole x - ray binaries . these findings provide support for the paradigm that black hole x - ray binaries and both radio - loud and radio - quiet active galactic nuclei are fundamentally similar systems , with characteristic time and size scales linearly proportional to the mass of the central black hole . the x - ray and optical variations are strongly correlated in 3c 120 , which implies that the optical emission in this object arises from the same general region as the x - rays , i.e. , in the accretion disk - corona system . we numerically model multi - wavelength light curves of 3c 120 from such a system with the optical - uv emission produced in the disk and the x - rays generated by scattering of thermal photons by hot electrons in the corona . from the comparison of the temporal properties of the model light curves to that of the observed variability , we constrain the physical size of the corona and the distances of the emitting regions from the central bh . in addition , we discus physical scenarios for the disk - jet connection that are consistent with our observations .

0909.2051

i

this paper presents well - sampled , 5-yr - long light curves of 3c 120 between 2002 and 2007 at x - ray , optical , and radio wavebands , as well as monthly images obtained with the vlba at 43 ghz . we have calculated the broad - band x - ray power spectral density ( psd ) of 3c 120 . the x - ray and radio light curves were decomposed into individual dips and flares , respectively , and the properties of the contemporaneous dips and flares were compared . that comparison , as well as , the x - ray / radio correlation analysis were used to find a connection between events in the jet and the accretion disk . we have also cross - correlated the x - ray and optical light curves and have determined the significance of the correlations with simulated light curves based on the psd . using a numerical model , we have produced x - ray and optical light curves from the accretion disk - corona system . from the comparison of the temporal properties of the simulated light curves to that of the observed variability , we infer the physical size of the corona and the distances of the emitting regions from the central bh . our main conclusions are as follows : + ( 1 ) the x - ray psd of 3c 120 is best fit by a bending power - law model where there is a smooth change in the slope above a break frequency . the best fit value of break frequency for 3c 120 is @xmath100 hz , which agrees very well with the relation between break timescale , bh mass and accretion rate obtained by @xcite spanning a range of bh mass from 10 @xmath101 to @xmath102 @xmath101 . this indicates that the accretion process in 3c 120 is similar to that of the bhxrbs . + ( 2 ) the x - ray and 37 ghz variations are anti - correlated with the x - ray leading the radio by @xmath0120 days . the anti - correlation remains even if the large x - ray dips and radio flares after 2006 are excluded . + ( 3 ) almost all x - ray dips are followed by the ejection of a new knot in the vlba images . this and the anti - correlation mentioned in ( 2 ) imply that decrease in the x - ray production is linked with increased speed in the jet flow , causing a shock front to form and move downstream . this property of 3c 120 is also similar to the galactic black hole systems where transitions to high - soft x - ray states are associated with the emergence of very bright features that proceed to propagate down the radio jet . + ( 4 ) we derive a distance @xmath00.5 pc from the corona ( where the x - rays are produced ) to the vlba 43 ghz core region using the average time delay between the start of the x - ray dips and the time of ejection " of the corresponding superluminal knots . + ( 5 ) the x - ray and optical variations in 3c 120 are very strongly correlated ( see also @xcite ) . this correlation , absence of significant optical polarization , and anti - correlation of x - ray and 37 ghz variations ( the latter of which are produced in the jet ) , together imply that the optical emission is blackbody radiation from the accretion disk . + ( 6 ) the x - rays are produced by scattering of ( mostly ) uv radiation in the corona . comparison of simulated light curves from a disk - corona system and the observed variation imply that the corona must lie sufficiently close to the bh that the flux of seed photons reaching the corona is dominated by uv light .

are followed by ejections of bright superluminal knots in the vlba images . we numerically model multi - wavelength light curves of 3c 120 from such a system with the optical - uv emission produced in the disk and the x - rays generated by scattering of thermal photons by hot electrons in the corona . from the comparison of the temporal properties of the model light curves to that of the observed variability , we constrain the physical size of the corona and the distances of the emitting regions from the central bh . in addition

we present the results of extensive multi - frequency monitoring of the radio galaxy 3c 120 between 2002 and 2007 at x - ray ( 2 - 10 kev ) , optical ( r and v band ) , and radio ( 14.5 and 37 ghz ) wave bands , as well as imaging with the very long baseline array ( vlba ) at 43 ghz . over the 5 yr of observation , significant dips in the x - ray light curve are followed by ejections of bright superluminal knots in the vlba images . consistent with this , the x - ray flux and 37 ghz flux are anti - correlated with x - ray leading the radio variations . furthermore , the total radiative output of a radio flare is related to the equivalent width of the corresponding x - ray dip . this implies that , in this radio galaxy , the radiative state of accretion disk plus corona system , where the x - rays are produced , has a direct effect on the events in the jet , where the radio emission originates . the x - ray power spectral density of 3c 120 shows a break , with steeper slope at shorter timescale and the break timescale is commensurate with the mass of the central black hole based on observations of seyfert galaxies and black hole x - ray binaries . these findings provide support for the paradigm that black hole x - ray binaries and both radio - loud and radio - quiet active galactic nuclei are fundamentally similar systems , with characteristic time and size scales linearly proportional to the mass of the central black hole . the x - ray and optical variations are strongly correlated in 3c 120 , which implies that the optical emission in this object arises from the same general region as the x - rays , i.e. , in the accretion disk - corona system . we numerically model multi - wavelength light curves of 3c 120 from such a system with the optical - uv emission produced in the disk and the x - rays generated by scattering of thermal photons by hot electrons in the corona . from the comparison of the temporal properties of the model light curves to that of the observed variability , we constrain the physical size of the corona and the distances of the emitting regions from the central bh . in addition , we discus physical scenarios for the disk - jet connection that are consistent with our observations .

astro-ph0204245

i

there has been outstanding progress in solar neutrino research in the last several years . the large water cherenkov detectors superkamiokande ( sk ) @xcite and the sudbury neutrino observatory ( sno ) @xcite have begun to measure the high - energy solar neutrinos from @xmath7b decay in real time with a high counting rate . the results from these two neutrino telescopes of a new generation add significant information to the existing results from the chlorine @xcite and gallium @xcite radiochemical experiments and the kamiokande experiment @xcite . the elastic scattering results of sk combined with the charged current results from sno indicate that , in addition to electron neutrinos , active neutrinos of other flavors are reaching the earth from the sun . the combined analysis of results of all these experiments gives convincing evidence that part of the electron neutrinos formed in thermonuclear reactions in the sun change their flavor on their way to the earth . further measurement of the details of flavor conversion for solar neutrinos requires a new generation of neutrino telescopes that will be sensitive to the spectrum below 2 mev , a region that contains the proton - proton @xmath8 and cno continua as well as the @xmath9be and @xmath10 lines . although there are many promising ideas for real - time low - energy neutrino detectors @xcite , at the present time only the radiochemical gallium experiments are able to measure and monitor this part of the solar neutrino spectrum . the 233-kev threshold of the reaction @xmath11ga@xmath12ge @xcite enables one to measure the @xmath2 neutrinos , the principal component of the solar neutrino spectrum . if we exclude exotic hypotheses , the rate of the @xmath2 reaction is directly related to the solar luminosity and is insensitive to alterations in the solar models that influence the subsequent reactions in the solar fusion chain . the neutrino capture rate in @xmath13ga predicted by the standard solar model ( ssm ) @xcite is @xmath14 snu , with the main contribution of 69.7 snu from the @xmath2 neutrinos atoms of the neutrino absorbing isotope . contributions by @xmath9be and @xmath7b neutrinos are 34.2 snu and 12.1 snu , respectively . the insensitivity of ga to variation in the solar model is seen in the independently calculated result of 127.2 snu @xcite for the total capture rate . from the results of the sno and sk experiments we now have a high accuracy measurement of the @xmath7b flux that reaches the earth and its electron neutrino component . in the near future it is expected that the kamland experiment @xcite will greatly restrict the range of possible electron neutrino mixing parameters . this data , combined with results from the borexino experiment @xcite , will give us a good measurement of the @xmath9be flux from the sun . by subtracting the @xmath9be and @xmath7b components from the total signal in the ga experiment , we will obtain a measurement of a fundamental astrophysical parameter the neutrino flux from the proton - proton fusion reaction . there will be a slight contamination from the cno and @xmath10 neutrinos but this can be removed with the information from the cl experiment . a rough estimate of the @xmath2 neutrino flux using the information that we have now is presented in the next to last section . since in the immediate future only the ga experiments provide this measurement , it is very important that both sage @xcite and gallex s successor gno @xcite continue to operate so as to improve the accuracy of their results . the experimental layout and procedures , including extraction of germanium from gallium , counting of @xmath13ge , and data analysis , are described in detail in our article `` measurement of the solar neutrino capture rate with gallium metal '' in physical review c @xcite . that article gives the sage results for the period january 1990 through december 1997 . since it contains a complete description of the experiment and the analysis techniques , we refer the reader who wishes further detail to that publication . here we briefly discuss the main principles of the experiment , give the statistical analysis of the data from 19982001 , present new results for some systematic uncertainties , and conclude with the current implications of the sage result for solar and neutrino physics .

we present the results of measurements of the solar neutrino capture rate in gallium metal by the russian - american gallium experiment sage during slightly more than half of a 22-year cycle of solar activity . ( syst . ) snu . this represents only slightly more than half of the predicted standard solar model rate of 128 snu . we give the results of new runs beginning in april 1998 and the results of combined analysis of all runs since 1990 during yearly , monthly , and bimonthly periods . using a simple analysis of the sage results combined with those from all other solar neutrino experiments , we estimate the electron neutrino flux that reaches the earth to be/(-s ) . assuming that neutrinos oscillate to active flavors the neutrino flux emitted in the solar fusion reaction is approximately/(-s ) , in agreement with the standard solar model calculation of/(-s )

we present the results of measurements of the solar neutrino capture rate in gallium metal by the russian - american gallium experiment sage during slightly more than half of a 22-year cycle of solar activity . combined analysis of the data of 92 runs during the 12-year period january 1990 through december 2001 gives a capture rate of solar neutrinos with energy more than 233 kev of ( stat . ) ( syst . ) snu . this represents only slightly more than half of the predicted standard solar model rate of 128 snu . we give the results of new runs beginning in april 1998 and the results of combined analysis of all runs since 1990 during yearly , monthly , and bimonthly periods . using a simple analysis of the sage results combined with those from all other solar neutrino experiments , we estimate the electron neutrino flux that reaches the earth to be/(-s ) . assuming that neutrinos oscillate to active flavors the neutrino flux emitted in the solar fusion reaction is approximately/(-s ) , in agreement with the standard solar model calculation of/(-s )

1308.3580

r

maser features of pz cas are spatially distributed over a region of 200 @xmath48 200 square mas . we identified 52 maser spots that are assembled into 16 maser features . those maser features were arranged in 11 maser groups , which are labeled _ a _ to _ k _ , as shown in figure [ fig:05 ] . the groups _ a _ to _ e _ , and _ g _ , _ h _ , and _ i _ have a radial velocity range between @xmath49 and @xmath50 km s@xmath4 . the groups _ f _ , _ j _ , and _ k _ , which have been detected at one epoch , have a radial velocity of @xmath51 , @xmath52 , and @xmath53 km s@xmath4 , respectively . the radial velocities of the identified maser spots are close to the stellar systemic velocity ( _ [email protected]@xmath10.68 km s@xmath4 ) . groups _ a _ and _ b _ located to the north and southeast of the spatial distribution , respectively , are bright and have complicated structures while the other groups ( _ c _ to _ k _ ) have a rather simple structure . for the following annual parallax analysis , we selected 16 maser spots among 52 using the following two criteria . ( 1 ) maser spots were detected with the image s / n greater than or equal to 7 . ( 2 ) the maser spot was detected at eight epochs or more . all the selected maser spots belong to either group _ a _ or _ b _ by chance . in the first step of the annual parallax analysis we performed a levenberg - marquardt least - squares model fitting of the maser motions in the same way as that described by @xcite using the peak positions of the selected maser spots . we adopted the astrometric error as mentioned in section [ sec:03 - 03 ] and a tentative value of a morphology uncertainty ( a positional uncertainty due to maser morphology variation ) of @xmath55as in the fitting , equivalent to 0.1 au by assuming the distance of 2 kpc to the source . figures [ fig:06 ] and [ fig:07 ] show the images and the fitting results of all the selected maser spots . the stellar annual parallax , @xmath56 , was determined by the combined fitting with the levenberg marquardt least - squares analysis for all the selected spots . the obtained stellar annual parallax was [email protected] mas at this stage . if we carefully look at figure [ fig:07 ] , the maser spots do not seem to be properly identified with the image peak positions because multiple maser spots are spatially blended . this is caused when the multiple maser spots , whose size is typically 1 au @xcite , are closely located comparing with the synthesized beam size of @xmath57 mas in this case , equivalent to 2.6 au at the distance of pz cas . to identify an individual maser spot properly , especially for blended structures , we performed aips jmfit for the 2d multiple gaussian component fitting of the emissions . here we refer to a maser spot that can be identified with the image peak position as an isolated maser spot , and to a maser spot that can not be identified with a single peak position because of the insufficient spatial resolution as a blended component . if we can identify 2d gaussian components using jmfit , instead of sad that automatically searches multiple spots , in the brightness distribution , we refer to such spots as identified spots . figure [ fig:08 ] provides an example of the annual parallax least - squares fitting for a maser spot using either the image peak position or the 2d gaussian peak . table [ tbl:04 ] lists our combined fitting results using the image peak only for the isolated spots , only for the blended components , and for all those involved in the two groups . we also tried to make another combined fitting using the gaussian peak only for the isolated spots , only for the blended but identified spots with jmfit , and all of them , as listed in the bottom row in table [ tbl:04 ] . the combined fitting results for the isolated spots show little difference between the cases of image peak and gaussian peak . however , the fitting result for the blended spots with jmfit peak positions is definitely changed from that with the image peak for the blended components and becomes closer to that obtained with the isolated spots . if a maser spot is recognized as an isolated spot , in other words , if a maser cloud is spatially resolved into multiple spots in the image , the image peak position can be treated as the maser position . because this can not be the case for the maser spots of pz cas , we adopted the gaussian peak positions in our least - squares model fitting . the model fitting results obtained from the individual spots are listed in table [ tbl:05 ] . from the combined fitting analysis by using all the selected maser spots , we obtained the stellar annual parallax of 0.356 @xmath1 0.011 mas with assumptions of the above astrometric error and morphology uncertainty at this stage . although h@xmath0o maser features around rsgs are good tracers for astrometry @xcite , the morphology of the maser spots observed with the high - resolution vlbi is no longer negligible for the precise maser astrometry . these monitoring observations of pz cas have been conducted so often for two years that we can investigate the contribution of the morphology uncertainty to the maser astrometry . figure [ fig:09 ] shows the position residuals of the 16 selected maser spots after removing the stellar annual parallax of 0.356 mas , proper motion , and initial position estimated for each of the spots . the standard deviation of the residuals is 93 and 110 @xmath44as for right ascension and declination , respectively . assuming that those errors have the statistical characteristics of a gaussian distribution , the morphology uncertainty is 59 ( = @xmath58 ) and 105 ( = @xmath59 ) @xmath44as for right ascension and declination , respectively , where 72 and 33 @xmath44as are the astrometric errors discussed in section 3.3 . it is unlikely that the morphology uncertainty has different values between right ascension and declination , so we adopted 105 @xmath44as as the morphology uncertainty to be on the safer side . based on the trigonometric parallax of 0.356 mas , 105 @xmath44as is 0.29 au at pz cas . we conducted the combined fitting with all the maser spots whose positions were determined with jmfit and obtained @xmath56 of @xmath60 mas at this stage . note that the above error of the annual parallax is a result of considering the random statistical errors from the image s / n and the randomly changing maser spot position , as well as a common positional shift to all the maser spots at a specific epoch due to the astrometric error . because the majority of the maser spots and features in the current parallax measurement are associated with the maser group _ a _ , the obtained stellar annual parallax could be affected by a time variation of the specific maser features at a certain level . assuming that all the 13 maser spots belonging to group _ a _ have an identified systematic error , the annual parallax error can be evaluated to be @xmath61 mas . however , if we assume that maser spots belonging to a certain maser feature have a common systematic error but that some of them have their own time variations , the annual parallax error should be estimated to be ranging somewhere between 0.011 and 0.040 mas . to evaluate the contributions of such a systematic error , we carried out monte carlo simulations introduced by @xcite for our astrometric analysis . first we prepared the imitated data set of the 16 maser spots with position changes added by considering the fixed stellar annual parallax and the maser proper motions . second we added an artificial positional offset due to the image s / n , the astrometric accuracy , and the morphology uncertainty to each of the maser spot positions . the positional offset caused by the image s / n was given to each of the maser spots at each epoch independently . the positional offset due to the astrometric error was common to all the maser spots at a specific epoch but randomly different between the epochs . in this paper , we assumed that the positional offset due to the morphology uncertainty was common to all the maser spots belonging to a specific maser feature at a specific epoch , but randomly different between the features and the epochs . we assumed the standard deviation of the maser morphology uncertainty was 105 @xmath44as , equivalent to the intrinsic size of 0.29 au . in a single simulation trial , we obtained the stellar annual parallax for the imitated data set . thirdly we carried out 200 trials in order to obtain the standard deviation of the stellar annual parallax solutions . the resultant standard deviation was 0.026 mas which can be treated as the annual parallax error in our astrometric analysis . the resultant estimate of the stellar annual parallax was 0.356 @xmath1 0.026 mas , corresponding to @xmath5 kpc . similar to the cases seen in other rsgs ( vy cma , @xcite ; s per , @xcite ; vx sgr , @xcite ; @xcite ; nml cyg , @xcite , @xcite ) , the maser features around pz cas are widely distributed over a @xmath62 square mas ( corresponding to @xmath63 square au at a distance of 2.81 kpc ) while the velocity of the features ( @xmath64 to @xmath65 km s@xmath4 ) is distributed more closely to the stellar systemic velocity than those found in other rsgs are . it is likely that the detected maser groups are located at the tangential parts of the shell - like circumstellar envelope , whose 3d velocity has a small line - of - sight velocity . we determined the proper motions of all detected maser spots were identified at least in two epochs . table [ tbl:06 ] lists maser spots whose proper motions and positions were calculated with the stellar annual parallax determined above . using the proper motion data listed in tables [ tbl:05 ] and [ tbl:06 ] , we then conducted the least - squares fitting analysis to obtain the position of pz cas and the stellar proper motion based on the spherically expanding flow model @xcite . the obtained stellar proper motion in right ascension and declination , @xmath663.7 @xmath1 0.2 mas yr@xmath4 and @xmath672.0 @xmath1 0.3 mas yr@xmath4 , respectively . the astrometric analysis result for pz cas is listed in table [ tbl:07 ] . the proper motions of the detected maser spots together with the stellar position indicated by the cross mark are shown in figure [ fig:10 ] .

we present the very long baseline interferometry ho maser monitoring observations of the red supergiant , pz cas , at 12 epochs from 2006 april to 2008 may . we fitted maser motions to a simple model composed of a common annual parallax and linear motions of the individual masers . the maser motions with the parallax subtracted were well modeled by a combination of a common stellar proper motion and a radial expansion motion of the circumstellar envelope . we obtained an annual parallax of 0.356 0.026 mas and a stellar proper motion of and mas yr eastward and northward , respectively . the annual parallax corresponds to a trigonometric parallax of kpc . by rescaling the luminosity of pz cas in any previous studies using our trigonometric parallax , we estimated the location of pz cas on a hertzsprung - russell diagram and found that it approaches a theoretically evolutionary track around an initial mass of . the sky position and

we present the very long baseline interferometry ho maser monitoring observations of the red supergiant , pz cas , at 12 epochs from 2006 april to 2008 may . we fitted maser motions to a simple model composed of a common annual parallax and linear motions of the individual masers . the maser motions with the parallax subtracted were well modeled by a combination of a common stellar proper motion and a radial expansion motion of the circumstellar envelope . we obtained an annual parallax of 0.356 0.026 mas and a stellar proper motion of and mas yr eastward and northward , respectively . the annual parallax corresponds to a trigonometric parallax of kpc . by rescaling the luminosity of pz cas in any previous studies using our trigonometric parallax , we estimated the location of pz cas on a hertzsprung - russell diagram and found that it approaches a theoretically evolutionary track around an initial mass of . the sky position and the distance to pz cas are consistent with the ob association , cas ob5 , which is located in a molecular gas super shell . the proper motion of pz cas is close to that of the ob stars and other red supergiants in cas ob5 measured by the _ hipparcos _ satellite . we derived the peculiar motion of pz cas of 1.5 , 4.4 , and 4.4 km s . this peculiar motion has rather a large component , unlike those of near high - mass star - forming regions with negatively large motions . the uniform proper motions of the cas ob5 member stars suggest random motions of giant molecular clouds moving into local potential minima in a time - dependent spiral arm , rather than a velocity field caused by the spiral arm density wave .

astro-ph0210555

r

infrared reflection nebulosity is associated with two distinct regions of ionized gas ( fig . 1 ) : w75 n ( a ) at position @xmath31 @xmath53 and w75 n ( b ) at position @xmath31 @xmath53 ( e.g. haschick et al . 1981 , moore et al . 1988 ) . shock - excited emission ( figs . 2 & 3 ) is present in the north - east ( near @xmath31 @xmath53 ) and along the co emission boundaries ( see also davis et al . 1998a , b ) . our images also show that faint , patchy emission extends nearly an arcminute ( 0.6 pc at a distance of 2 kpc ) beyond the south - west co flow ( @xmath31 @xmath53 ) . the continuum subtracted h@xmath41 mosaic is shown in fig . 2 . following the nomenclature used by davis et al . ( 1998a , b ) for the south - west portion of the h@xmath41 flow , all previously known h@xmath41 knots and filaments are marked with solid lines . these are labeled sw a to sw h in the south - west flow , c a and c b in the central region , and ne a to ne f in the north - east flow . additionally , figs . 2 & 3 reveal faint diffuse h@xmath41 emission beyond the tip of the south - west flow and within the north - east flow . these new features are marked with dashed lines and labeled sw i to sw k and ne g to ne faint , diffuse h@xmath41 features as well as the filamentary structure of the emission in knots ne d , ne e , & ne f are confirmed by observations obtained in 2002 august . figure 3 presents an overlay of the continuum subtracted [ feii ] emission ( contours ) on the h@xmath41 ( greyscale ) images from the 2002 august observations . [ feii ] line emission is only detected close to the uc hii regions in w75 n b and near the exciting star of w75 n a. no [ feii ] emission is detected in the outer flow regions . the non - detection of [ feii ] far from the protostars does not appear to be due to higher extinction since we clearly detect 2.12@xmath50 m emission beyond the co outflow boundaries and we detect [ feii ] emission near the cloud core where the column density is higher . a chain of h@xmath41 knots , apparently unrelated to the main flow , are detected near @xmath31 @xmath54 ( fig . this jet is outside of the co and infrared mosaic fields . the knots may be associated with a jet from a young star north of the main complex discussed in this paper . a high - velocity co outflow , centered near w75 n ( b ) , measures 3 pc from end - to - end ( projected length ) and extends well beyond the infrared reflection nebula ( figs . 1 & 4 ) . red and blue - shifted co emission exists both in the north - east and south - west . the co mosaic did not include areas to the north - west and south - east so it is unclear if high - velocity co exists in these regions . the boundaries and flux density of the co outflow are well determined on the red - shifted side of the line , however , at velocities between 0 and 5.6 the dr 21 cloud ( @xmath55 ) confuses the identification of the outflow structure . nine millimeter continuum peaks showing the locations of warm dust emission are identified in fig . 5 & table 1 ( w75 n : mm 1 through w75 n : mm 9 ) . mm 1 mm 4 are near the origin of the outflow activity and lie @xmath56 from the w75 n ( b ) reflection nebulosity to the north and west . mm 5 is associated with the more extended hii region , w75 n ( a ) , while mm 6 mm 9 are not associated with any previously known sources . infrared counterparts do not exist for the millimeter sources ( except mm 5 ) suggesting that these sources are too deeply embedded to be detected at 2@xmath50 m . figure 5 also shows the @xmath0 resolution image from shepherd ( 2001 ) for comparison . the @xmath0 resolution resolved the individual millimeter cores mm 14 but resolved out the more extended emission associated with mm 5 and mm 6 . millimeter cores mm 79 were outside of the primary beam of the shepherd ( 2001 ) observations and thus , were not detected . figure 5 also compares the mm 5 millimeter source with narrow - band @xmath52continuum emission and k@xmath2 broad - band emission in w75 n ( a ) . the central star of w75 n ( a ) ( spectral type b0.5 ; haschick et al . 1981 ) is clearly visible in the infrared and is surrounded by a @xmath57 shell of thermal dust emission . diffuse reflection nebulosity is centered on the star and a wisp of emission is visible just east of the star ( @xmath31 @xmath53 ) . compact , high - velocity co emission appears to originate from the uc hii regions vla 1 ( ba ) & vla 3 ( bb ) and from mm 2 ( figs . 6 , 7 , & 8) . the @xmath58 resolution is not sufficient to determine if vla 2 , located only @xmath59 north of vla 3 ( bb ) , is also associated with high - velocity co gas . a detailed discussion of each of the proposed outflows is given below . * the outflow from vla 1 ( ba ) : * vla 1 ( ba ) is a thermal jet source associated with and oh masers ( baart et al . 1986 , torrelles et al . it is embedded in the mm 1 core detected in 1 & 3 mm continuum emission ( shepherd 2001 ) . the spectral type of the powering source is unknown since the observed centimeter continuum emission is likely due to the ionized jet rather than emission from an ionization - bounded uc hii region . red - shifted emission to the north - east of mm 1 can be traced to the jet - like ionized flow from vla 1 ( ba ) . figure 7 presents a @xmath27 image of the integrated co emission from the flow as well as a position - velocity diagram from a slice along the proposed flow axis ( p.a . a ridge of co emission extends to the north - east with projected velocity greater than 25 ( relative to @xmath5 ) almost an arcminute from the uc hii region . high - velocity co emission is also centered on the uc hii regions ( position offset @xmath60 in the pv diagram of fig . 7 ) . a @xmath0 resolution image ( fig . 6 , top left ) shows that this red - shifted emission near the base of the outflow appears to be produced by vla 1 ( ba ) as well as vla 3 ( bb ) and possibly vla 2 . the @xmath0 resolution of fig . 6 resolves out much of the extended emission in the flow leaving only compact clumps visible along the flow axis . the p.a . is similar to the elongation of the ionized emission in vla 1 ( ba ) ( p.a . @xmath61 ) and a line of masers detected along the jet ( torrelles et al . the molecular flow is also seen in fig . 1 as a well - collimated , red - shifted lobe extending to the north - east from the mm 1 core . the outflow is shown as one - sided in figs . 6 & 7 because only one side of the flow is detected . the counterflow may exist however it may be too extended to image at this high - resolution or it may be expanding into a less dense medium that would not create appreciable co emission . * the outflow from vla 3 ( bb ) : * vla 3 ( bb ) is a compact uc hii region in mm 1 with a central star of spectral type b0.5 to b0 . it is associated with a single maser and compact 1 & 3 mm continuum emission . a lower limit on the mass of warm gas and dust within 2000 au of the protostar is 5 m ( shepherd 2001 ) . figure 6 illustrates that compact red - shifted emission to the east and blue - shifted emission to the west of mm 1 can be traced to vla 3 ( bb ) with p.a . @xmath62 . there are no obvious features in the extended emission that correspond to an outflow with this orientation , however , the co mosaic did not extend to the north - west or south - east so a large - scale outflow could have been missed ( fig . 1 ) . the molecular gas morphology does not seem to be correlated with that of the ionized gas or masers near the source : the ionized gas is slightly elongated along p.a . 149and the maser is located near the southern boundary of the ionized gas . * the outflow from mm 2 : * mm 2 is a molecular core identified by compact , warm dust emission at 1 & 3 mm and maser emission ( torrelles et al 1997 , shepherd 2001 ) . the mass of the core is @xmath63 m. no ionized gas has been detected indicating that the spectral type is less than a b2 star or high accretion is preventing the formation of a uc hii region . high - velocity , blue - shifted emission ( 13 to 36 projected velocity relative to @xmath5 ) can be traced from the mm 2 core to the south - east ( p.a . figure 8 presents a @xmath27 image of the integrated emission from the flow as well as a position - velocity diagram from a slice along the proposed flow axis . the velocity of the jet relative to @xmath64 increases away from the position of mm 2 and remains well collimated . diffuse emission at velocities greater than @xmath65 is due to the w75 n & dr 21 clouds . figure 6 shows the more compact emission in the flow . three clumps of high - velocity gas are detected extending away from mm 2 along with faint emission at the location of the core . the compact clumps appear to trace a shell of dense gas surrounding the outflow axis . the molecular outflow is identified as one - sided because the red - shifted counterflow was not detected . the diffuse millimeter core mm 4 is located along the axis of the proposed mm 2 outflow . although no or oh maser emission has been detected toward mm 4 , nor has centimeter or 1 mm continuum emission been detected , there is diffuse warm dust emission traced by 3 mm continuum . thus , mm 4 may harbor an embedded protostar . assuming the mm 4 core is heated internally , the lack of maser activity , compact warm dust emission at 1 mm , and the absence of ionized gas emission at centimeter wavelengths suggest that mm 4 is a low - mass protostar ( shepherd 2001 ) . with the current resolution and sensitivity , we can not determine if the mm 4 protostar is contributing to the observed flow dynamics . the proposed position angles of the outflowing gas ( illustrated by arrows in figs . 6 , 7 , & 8) are 51 for vla 1 ( ba ) , 101 for vla 3 ( bb ) , and 124 for mm 2 . the position angle of the parsec - scale outflow detected in and co ( fig . 1 ) is 62.5 . although the orientation of the vla 1 ( ba ) outflow is similar to that of the parsec - scale flow , it does not appear likely that vla 1 ( ba ) is the powering source . assuming the vla 1 ( ba ) flow is symmetric , a blue - shifted counterflow is expected in the south - west , not a red - shifted flow . thus , our observations do not not identify the source responsible for the 3 pc outflow which dominates the large - scale morphology and kinematics of the region . the mass associated with co line emission is calculated following the method proposed by scoville et al . the co excitation temperature near the millimeter continuum emission varies from about 35 to 75 k with @xmath66 k being the median value near the mm 1 peak ( davis et al . rotational temperatures derived from ch@xmath67cn in the cloud core vary from 47 to 78 k , consistent with the davis et al . estimates ( kalenski et al . 2000 ) . we assume the gas is in lte , at a temperature of 50 k , with [ co]/ [ ] = @xmath68 , and [ co]/ [ ] = 71 at the galacto - centric distance of 8.5 kpc ( wilson & rood 1994 ) . the co optical depth as a function of velocity and position is calculated using single dish and spectra taken at three positions within the w75 n region ( fig . we assume is optically thin at all velocities which is probably valid in the line wings ; however , is likely to be optically thick near the line core . in channels where no emission is detected , we assume the co is optically thin . the co channel images ( fig . 4 ) show that the emission near @xmath5 is almost entirely resolved out by the interferometer . if high - velocity ( @xmath4 ) structures exist that are larger than the largest angular scale that can be imaged ( @xmath69 ) , then our mass estimate represents a lower limit . because multiple , overlapping flows are present , it is not possible to obtain a reasonable estimate of the inclination of each flow . thus , we assume an inclination angle of 45 which minimizes errors introduced by inclination effects . table 2 summarizes the physical properties of the molecular gas in the combined outflows originating within mm 1 and from the blue - shifted mm 2 outflow lobe . the total flow mass @xmath70 is given by @xmath71 where @xmath72 is the flow mass in velocity channel @xmath73 corrected for optical depth . the momentum @xmath74 is given by @xmath75 and the kinetic energy e by @xmath76 where @xmath77 is the central velocity of the channel relative to @xmath5 . the characteristic flow timescale @xmath78 is @xmath79 , where the intensity - weighted velocity @xmath80 is given by @xmath81 ( cabrit & bertout 1990 ) and @xmath82 is the flow radius . the mass outflow rate @xmath83 is @xmath84 and the force f is @xmath85 . assuming d=2 kpc , the total molecular mass in outflowing gas ( @xmath86 relative to @xmath5 ) is @xmath87 m. the values presented in table 2 are derived assuming all flows have the same systemic velocity . this is a reasonable assumption for the driving sources of the combined mm 1 outflows since the observed uc hii regions are embedded within the same molecular clump and have a projected separation of only 0.5 to @xmath88 ( 1000 - 2000 au at a distance of 2 kpc ) . the source driving the outflow from the mm 2 molecular core has a projected separation of about @xmath23 ( 10,000 au or 0.05 pc ) from mm 1 . it is possible that mm 2 could have a slightly different systemic velocity from mm 1 that we can not detect in our images or single dish spectra . if the systemic velocity of the mm 2 core is different by a factor of @xmath89 from the assumed velocity of 10 , then the error in the momentum estimates will be proportional to @xmath90 and mechanical energy to @xmath91 . the combined mm 1 outflows have a total mass of at least 165 m and energy , e @xmath92 ergs . the mm 2 outflow has a total mass @xmath93 m , e @xmath94 ergs . the co mosaic did not extend in the south - east direction of the mm 2 flow , thus , the full outflow was not imaged and age and @xmath95 should be considered a lower limit . despite the uncertainties , the flow masses and energies are consistent with those for outflows driven by young , early b stars . this is in agreement with the estimated spectral types of the stars powering the uc hii regions in mm 1 ( b2 to o9 ; hunter et al . 1994 ; torrelles et al . 1997 ; shepherd 2001 ; slysh et al . 2002 ) . the mass of gas and dust associated with warm dust being heated by the central protostars is estimated from the millimeter continuum emission using @xmath96 where d is the distance to the source , @xmath97 is the continuum flux density due to thermal dust emission at frequency @xmath98 , and @xmath99 is the planck function at temperature t@xmath100 ( hildebrand 1983 ) . assuming a gas - to - dust ratio of 100 , the dust opacity per gram of gas is taken to be @xmath101 cm@xmath44 g@xmath30 where @xmath103 is the opacity index ( see kramer et al . 1998 ; and the discussion in shepherd & watson 2002 ) . this value of @xmath104 agrees with those derived by hildebrand ( 1983 ) and kramer et al . ( 1998 ) to within a factor of 2 . the opacity index @xmath105 appears to be appropriate between wavelengths of 650 microns and 2.7 mm for sub - micron to millimeter - sized grains expected in warm molecular clouds and young disks ( pollack et al . we assume the emission is optically thin and the temperature of the dust can be characterized by a single value . using values of @xmath106 k and @xmath105 , we find the total mass of gas and dust associated with the 2.7 mm continuum emission is approximately 475 m ( table 1 ) . our results are consistent with those of shepherd ( 2001 ) and watson et al . ( 2002 ) to within the errors .

we present to resolution 3 mm continuum and line emission and near infrared k , , and [ feii ] images toward the massive star forming region w75 n. the co emission uncovers a complex morphology of multiple , overlapping outflows . nine cores of millimeter - wavelength emission highlight the locations of embedded protostars in w75 n. the total mass of gas & dust associated with the millimeter cores ranges from 340 m to 11 m. the infrared reflection nebula and shocked emission have multiple peaks and extensions which , again , suggests the presence of several outflows . diffuse emission extends about 0.6 parsecs beyond the outer boundaries of the co emission while the [ feii ] emission is only detected close to the protostars .

we present to resolution 3 mm continuum and line emission and near infrared k , , and [ feii ] images toward the massive star forming region w75 n. the co emission uncovers a complex morphology of multiple , overlapping outflows . a total flow mass of m extends 3 pc from end - to - end and is being driven by at least four late to early - b protostars . more than 10% of the molecular cloud has been accelerated to high velocities by the molecular flows ( relative to ) and the mechanical energy in the outflowing gas is roughly half the gravitational binding energy of the cloud . the w75 n cluster members represent a range of evolutionary stages , from stars with no apparent circumstellar material to deeply embedded protostars that are actively powering massive outflows . nine cores of millimeter - wavelength emission highlight the locations of embedded protostars in w75 n. the total mass of gas & dust associated with the millimeter cores ranges from 340 m to 11 m. the infrared reflection nebula and shocked emission have multiple peaks and extensions which , again , suggests the presence of several outflows . diffuse emission extends about 0.6 parsecs beyond the outer boundaries of the co emission while the [ feii ] emission is only detected close to the protostars . the infrared line emission morphology suggests that only slow , non - dissociative j - type shocks exist throughout the pc - scale outflows . fast , dissociative shocks , common in jet - driven low - mass outflows , are absent in w75 n. thus , the energetics of the outflows from the late to early b protostars in w75 n differ from their low - mass counterparts they do not appear to be simply scaled - up versions of low - mass outflows . # 1#2#3#1#2#3 # 1#2#3 = 500 = 500 =

astro-ph0210555

c

the total molecular mass of outflowing gas from the mm 1 and mm 2 combined flows ( @xmath86 relative to @xmath5 ) is @xmath3 m. hunter et al . ( 1994 ) found @xmath107 with a rough scaling performed to take into account an optical depth correction . however , their image covered only the inner region of the flow so their estimate should be considered a lower limit . based on single dish observations of co(j=32 ) , davis et al ( 1998a ) estimated a total flow mass of @xmath108 , uncorrected for optical depth effects . this mass estimate is extremely high for an optically thin approximation . examination of their fig . 11 , t@xmath109 vs. ( @xmath110 ) , shows that the blue - shifted lobe has an order of magnitude increase in the integrated flux at the velocity of dr 21 ( 2.5 ) . it appears that their single - dish map may have been significantly contaminated by emission from the dr 21 cloud , which introduced uncertainties in the mass and kinematics estimates . ridge & moore ( 2001 ) estimated the outflow mass of the red - shifted lobe only to be 273 based on a co(j=21 ) single dish image corrected for optical depth . the mass of blue - shifted gas was not estimated by ridge & moore due to the contamination by the dr 21 cloud . this value is significantly higher than our estimate and may be due to missing extended emission in the interferometer image , especially at low velocities . despite this problem , interferometric imaging also provided benefits : it was easier to distinguish between outflow gas and the dr 21 cloud and to identify flows from multiple sources in the cluster . the total cloud core mass of w75 n has been estimated to be 18002500 based on observations at submillimeter wavelengths ( moore , mountain , & yamashita , 1991 ) and 1200 based on cs(j=76 ) emission ( hunter et al . 1994 ) . the gravitational binding energy of the cloud , @xmath111 , is 12@xmath112 ergs , where we take the radius @xmath113 pc ( moore et al . 1991 ) and @xmath114 is a constant which depends on the mass distribution ( @xmath115 for @xmath116 ) . more than 10% of the molecular cloud is participating in the outflow and the combined outflow energy is roughly half the gravitation binding energy of the cloud . the observed w75 n outflows are injecting a significant amount of mechanical energy into the cloud core and may help prevent further collapse of the cloud . our co(j=10 ) images suggest that high - velocity gas is associated with at least two uc hii regions : vla 1 ( ba ) and vla 3 ( bb ) and an embedded source in the millimeter core mm 2 . the position angles of the individuals outflows are not aligned , ranging from 51 to 124 . the morphology is diffuse and patchy both in the north - east and south - west . the irregular morphology of the infrared reflection nebula with fingers of nebulosity radiating out from the mm 1/mm 2 millimeter cores supports the conclusion that multiple energetic outflows are carving large cavities in the molecular cloud . low surface brightness emission extends well beyond the co outflow while [ feii ] emission is only detected close to the protostellar cluster . it is generally believed that [ feii ] line emission associated with low - mass outflows requires the presence of fast , dissociative shocks that disrupt dust grains and release heavy elements just behind a jump - shock ( j - shock ) boundary . emission , on the other hand , appears to be produced in slow , non - dissociative j - type shocks ( e.g. hollenbach & mckee 1989 ; smith 1994 ; gredel 1994 ; beck - winchatz et al . continuous - shocks ( c - shocks ) can not easily produce emission from ionized species such as [ feii ] nor can they produce the observed column densities typically seen in toward herbig haro objects from low - mass protostars ( gredel 1994 ) . in fact , nisini et al . ( 2002 ) find that there appears to be no correlation between and [ feii ] emission in outflows from low - mass ysos which supports the interpretation that physically different mechanisms are responsible for producing and [ feii ] emission . in a sample of herbig haro objects produced by jets from low - mass protostars , both and [ feii ] is found toward all sources and the morphology of and [ feii ] emission is similar on large scales although it differs in the detail ( gredel 1994 ; reipurth et al . these observations indicate that jets from low - mass protostars produce both fast , dissociative regions where [ feii ] emissions arises and slower , non - dissociative regions where emission arises . in contrast , [ feii ] emission toward w75 n is only detected close to the central sources and does not show a jet - like morphology as in outflows from low- and intermediate - mass young stellar objects ( e.g. lorenzetti et al . 2002 ; nisini et al . 2002 ; reipurth et al . the outflows from w75 n appear to exhibit only slow , non - dissociative j - type shocks which produce copious emission throughout the outflow region but the fast , dissociative shocks responsible for [ feii ] emission are absent in the outer regions of the flow . instead , the diffuse [ feii ] line emission in w75 n is coincident with the brightest k@xmath2-band reflection nebulosity . one possibility may be that the [ feii ] emission traces photo - dissociation regions ( pdrs ) along cloud surfaces illuminated by the massive protostars in the mm 1 core . this situation is also observed in the orion bar pdr ( e.g. walmsley et al . 2000 ) suggesting that the w75 n nebula may exhibit similar excitation conditions to those in orion . the and [ feii ] line emission in w75 n does not conform to what is expected for shock - excited emission resulting from the interaction between a well - collimated jet and diffuse molecular gas . in this respect , the physical characteristics of the w75 n flows differ from their low - mass counterparts which produce collimated jets observed in both and [ feii ] emission . many previous authors have assumed that only vla 1 ( ba ) was in an outflow stage based on the elongated morphology of the ionized gas , the presence of maser emission along the uc hii region axis , and because the position angles of the ionized gas and the co emission were similar . maser emission is also associated with vla 2 and vla 3 ( bb ) as well as mm 3 and mm 2 , however , outflowing material could not be traced to specific sources . assuming a single primary driving source for the co gas , davis et al . ( 1998b ) suggested that the south - west co red - shifted lobe and morphology supports a bow - shock entrainment scenario for a molecular outflow driven by a jet from a single massive star . our co and millimeter continuum observations do not support this theory that a single source drives the high - velocity co gas . further , our infrared observations suggest that the w75 n outflows are not likely to be scaled - up versions of jet - driven outflows from low - mass protostars . a question remains unanswered by this work : what source powers the 3 pc flow at p.a . the flow mass is @xmath117 m , the dynamical age is roughly @xmath118 years , and the mass loss rate @xmath119 to @xmath120 m@xmath121 yr@xmath30 . the flow parameters are consistent with those produced by an early b protostar . hutawarakorn et al . ( 2002 ) have modeled the oh maser position - velocity data and find evidence for a massive disk centered on vla 2 ( m@xmath122 m with p.a . = 155 , roughly perpendicular to the outflow axis ) . a high - velocity , time - variable oh maser cluster is coincident with vla 2 suggesting an outflow origin . further , recent observations with the very long baseline array ( vlba ) show that a clump of strong maser emission with high velocity dispersion is centered on vla 2 ( torrelles et al . 2003 ) . thus , the oh and maser activity suggests vla 2 is producing a powerful outflow . although our observations did not have adequate resolution to isolate high - velocity gas toward vla 2 , we have determined that vla 1 ( ba ) , vla 3 ( bb ) , and mm 2 are not likely to drive the 3 pc flow that dominates the region dynamics . thus , it is possible that vla 2 may drive the large - scale flow . follow - up observations at a resolution less than @xmath88 will be required to determine if , in fact , vla 2 drives the 3 pc flow . based on the size and velocity of the co outflows from the w75 n ( b ) uc hii regions , the region is @xmath123 years old . w75 n ( a ) is more evolved than the sources in mm 1 and the exciting star of w75 n ( a ) has no detectable high - velocity gas associated with it . the star , detected in the infrared , is centered within a shell of warm dust emission and an extended hii region ( hashick et al . 1981 ) . figure 10 shows a color - color diagram using data from the 2mass point source catalog for stars within @xmath124 of mm 1 that were detected at all three bands . the locus of main - sequence stars is represented by the thick , curved line ( bessell & brett 1988 , koornneef 1983 ) while the two diagonal lines show reddening vectors up to @xmath125 of dust ( adopting the @xmath126 extinction law from cardelli , clayton , & mathis 1989 ) . sources within the reddening vectors have colors consistent with main - sequence stars reddened by foreground dust . those to the right of the reddening vectors demonstrate excess emission at @xmath127 m , consistent with the presence of circumstellar material . the infrared colors of the w75 n ( a ) exciting star are consistent with those of a main - sequence star reddened by foreground dust . in comparison , the two bright stars to the south - east and south - west of mm 1 ( irs 2 and irs 3 ) have excess emission at @xmath127 m consistent with the presence of circumstellar material . the protostars within mm 1 and mm 2 are not detectable at infrared wavelengths . n represents a region of clustered star formation which appears to be forming mid to early - b stars which exist at a range of developmental stages . vla 1 ( ba ) appears to have a well - collimated , outflow based on the ionized gas morphology imaged by torrelles et al . ( 1997 ) and the presence of a relatively well - collimated , red - shifted co lobe which extends about 0.5 pc north - east of the source . however , the spectral type of the protostar is unknown since the ionized gas appears to be due to thermal jet emission . the well - collimated outflow which appears to be produced by the embedded source in mm 2 is not detected at centimeter wavelengths . either the powering source is not an early - b star ( e.g. it does not have sufficient ionizing radiation to produce a detectable uc hii region ) or accretion onto the protostar is sufficiently high that it prevents the formation of a uc hii region ( see e.g. churchwell 1999 and references therein ) . there is no evidence for well - collimated flows ( collimation ratios , length / width , @xmath128 ) from the remaining embedded sources ( early - b protostars ) or in the large - scale morphology of the co , , & [ feii ] emission . the lack of highly - collimated flows from the known , early - b protostars in w75 n suggests that it may be difficult for massive stars to collimate outflowing material . although a few mid to early - b protostars appear to be powering ionized jets , their molecular outflows tend to be complex and poorly collimated ( see , e.g. , the review by shepherd 2002 and references therein ) . to our knowledge , there is no well - collimated _ molecular _ outflow powered by a massive protostar ( spectral type early - b to o ) and most do not appear to have ionized outflow components that are well - collimated ( e.g. ridge & moore 2001 , shepherd , claussen , & kurtz 2001 ; churchwell 1999 ) . poorly collimated flows could be due to several factors : * confusion from multiple outflow sources in a cluster ( e.g. w75 n : this work ; or dr 21 : garden et al . 1991 ) ; * large flow precession angles ( e.g. pv ceph : reipurth , bally , & devine 1997 , gomez , kenyon , & whitney 1997 ; or iras 20126@xmath524104 : shepherd et al . 2000 ) ; * the presence of a strong wide - angle wind ( e.g. orion i : greenhill et al . 1998 ; or g192.163.82 : shepherd , claussen & kurtz 2001 ) ; and/or * the molecular flow represents only the truncated base of a much larger flow ( e.g. hh 8081 : yamashita et al . 1989 , rodrguez et al . 1994 ; or g192.163.82 : devine et al . 1999 ) . our observations of w75 n supports the interpretation that massive protostars may not be able to produce well - collimated molecular outflows . this conclusion does not rule out the possibility that an underlying , neutral jet may still exist as part of the outflow from the massive protostars in w75 n. high - resolution observations in shock tracers such as sio(j=10,v=0 ) or sio(j=21,v=0 ) may be able to determine whether collimated neutral jets are present in w75 n.

more than 10% of the molecular cloud has been accelerated to high velocities by the molecular flows ( relative to ) and the mechanical energy in the outflowing gas is roughly half the gravitational binding energy of the cloud . the infrared line emission morphology suggests that only slow , non - dissociative j - type shocks exist throughout the pc - scale outflows . fast , dissociative shocks , common in jet - driven low - mass outflows , are absent in w75 n. thus , the energetics of the outflows from the late to early b protostars in w75 n differ from their low - mass counterparts they do not appear to be simply scaled - up versions of low - mass outflows . # 1#2#3#1#2#3 # 1#2#3 = 500 = 500 =

we present to resolution 3 mm continuum and line emission and near infrared k , , and [ feii ] images toward the massive star forming region w75 n. the co emission uncovers a complex morphology of multiple , overlapping outflows . a total flow mass of m extends 3 pc from end - to - end and is being driven by at least four late to early - b protostars . more than 10% of the molecular cloud has been accelerated to high velocities by the molecular flows ( relative to ) and the mechanical energy in the outflowing gas is roughly half the gravitational binding energy of the cloud . the w75 n cluster members represent a range of evolutionary stages , from stars with no apparent circumstellar material to deeply embedded protostars that are actively powering massive outflows . nine cores of millimeter - wavelength emission highlight the locations of embedded protostars in w75 n. the total mass of gas & dust associated with the millimeter cores ranges from 340 m to 11 m. the infrared reflection nebula and shocked emission have multiple peaks and extensions which , again , suggests the presence of several outflows . diffuse emission extends about 0.6 parsecs beyond the outer boundaries of the co emission while the [ feii ] emission is only detected close to the protostars . the infrared line emission morphology suggests that only slow , non - dissociative j - type shocks exist throughout the pc - scale outflows . fast , dissociative shocks , common in jet - driven low - mass outflows , are absent in w75 n. thus , the energetics of the outflows from the late to early b protostars in w75 n differ from their low - mass counterparts they do not appear to be simply scaled - up versions of low - mass outflows . # 1#2#3#1#2#3 # 1#2#3 = 500 = 500 =

astro-ph0210555

i

w75 n represents an example of clustered , massive star formation . the cluster covers a wide range of evolutionary stages ; from stars with no apparent circumstellar material to deeply embedded protostars actively powering massive outflows . the co outflow measures more than 3 pc from end - to - end and is produced by at least four individual sources . emission extends well - beyond the co boundaries while [ feii ] emission is only located close to the protostellar cluster . the co , & [ feii ] morphology does not conform to what is expected for shock - excited emission resulting from the interaction between a well - collimated jet and diffuse molecular gas . the irregular morphology of the infrared reflection nebula with fingers of nebulosity radiating out from the millimeter cores supports the conclusion that multiple energetic outflows are carving large cavities in the molecular cloud . more than 10% of the molecular cloud is outflowing material and the combined outflow energy is roughly half the gravitational binding energy of the cloud . thus , the observed w75 n outflows are injecting a significant amount of mechanical energy into the cloud core and may help prevent further collapse of the cloud . research at the owens valley radio observatory is supported by the national science foundation through nsf grant number ast 99 - 81546 . star formation research at owens valley is also supported by nasa s origins of solar systems program , grant nagw-4030 , and by the norris planetary origins project . this paper is partly based on observations made with the italian telescopio nazionale galileo ( tng ) operated on the island of la palma by the centro galileo galilei of the inaf ( istituto nazionale di astrofisica ) at the spanish observatorio del roque de los muchachos of the instituto de astrofisica de canarias . the arnica and nics observations were performed in service mode by the tng staff , we especially acknowledge the help of francesca ghinassi , juan carlos guerra , and antonio magazz . this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation . baart , e.e . , cohen , r.j . , davies , r.d . , norris , r.p . , rowland , p.r . 1986 , mnras , 219 , 145 baffa , c. , comoretto , g. , gennari , s. , lisi , f. , oliva , e. , biliotti , v. , checcucci , a. , gavrioussev , v. , giani , e. , ghinassi , f. , hunt , l. k. , maiolino , r. , mannucci , f. , marcucci , g. , sozzi , m. , stefanini , p. , & testi , l. 2001 , a&a , 378 , 722 beck - winchatz , b. , bhm , k .- h . , & noriega - crespo , a. 1996 , aj , 111 , 346 bessell , m. s. , & brett , j. m. 1988 , pasp , 100 , 1134 cabrit , s. & bertout , c. 1990 , apj , 348 , 530 cabrit , s. , ferreira , j. , & raga , a. c. 1999 , a&a , 343 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moore , t. j. t. 1989 , apj , 347 , 894 @xmath129 mm 1 eastern outflow emission measured at velocities 2.2 to 4.8 and 15.2 to 36 . + mm 1 western outflow emission measured at velocities 8.2 to 4.8 and 15.2 to 36.0 . + mm 2 outflow emission measured between 26.4 and 2.2 . * figure 1 . * integrated co red - shifted ( red lines ) and blue - shifted ( blue lines ) emission contours from 36.0 to 17.8 and 0.4 to 26.4 , respectively . the images have an rms of 23.5 with a peak of 56.0 in the red - shifted emission image and 100.6 in the blue - shifted emission image . contours begin at 10% of the peak emission and continue at increments of 20% . the synthesized beam is @xmath24 at p.a . @xmath130 . line @xmath52 continuum emission is shown as grey scale displayed as the square root of the intensity with a peak of @xmath131 erg @xmath132s@xmath30arcsec@xmath133 . w75 n ( a ) is located at position @xmath31 @xmath53 and w75 n ( b ) at position @xmath31 @xmath53 . uc hii regions embedded in the core of mm 1 are shown as filled triangles while the millimeter cores mm 29 are shown as open circles . the large open circle ( mm 5 ) is coincident with the infrared emission associated with w75 n a. the solid black line delineates the boundaries of the co mosaic . * figure 2 . * continuum - subtracted line mosaic of w75 n. the image is displayed on a linear scale from 0.6 to a peak intensity of @xmath134 erg @xmath132 s@xmath30 . individual knots of emission are labeled ne a through i , c a & b , and sw a through k. features observed by davis et al . ( 1998a , b ) are identified by solid lines , previously undetected features which are more diffuse are shown as dashed lines . large dashed boxes outline the fields shown in fig . figure 3 . * continuum - subtracted emission shown in grey scale with [ feii ] emission shown as contours . the [ feii ] contours begin at @xmath135 and continue with a spacing of @xmath136 . the left panel shows the central and north - east outflow regions . the strong , diffuse [ feii ] emission is coincident with the w75 n ( a ) and ( b ) reflection nebulae . the right panel shows the south - west outflow . [ feii ] contours coincident with point sources are due to imperfect continuum subtraction . * figures 4a & 4b . * co channel images at 2.6 spectral resolution between 32.1 and @xmath137 . the central velocity is indicated in the upper right of each panel . the lsr velocity is 10 . the rms is 0.13 and the peak emission is 16.9 . in the first 12 and last 12 panels , contours are plotted from @xmath138 , 8 , 12 , 16 , 20 @xmath139 and continue with a spacing of @xmath140 . in the central 6 panels ( 8.7 to 4.3 ) , contours begin at @xmath141 and continue with a spacing of @xmath142 . panels at velocities 32.1 & 27.7 show the synthesized beam in the bottom right corner ( @xmath24 at p.a . @xmath130 ) and a scale size of 0.9 pc . the plus symbol in each panel represents the location of the peak emission in mm 1 . no other emission was detected outside of this velocity range . * figure 5 . * the bottom left image shows continuum emission at 2.7 mm . no other continuum sources were detected within the mosaic field . the image has an rms of 3.6 . contours begin at @xmath143 and continue with a spacing of @xmath144 . the greyscale is plotted on a linear scale from 7.2 to 265 . the synthesized beam in the lower right corner is @xmath28 at p.a . uc hii regions in the center of mm 1 are identified by filled triangles , mm 24 are shown as open circles . a scale size of 0.15 pc is represented by a bar in the lower left corner . the bottom right inset shows 3.3 mm continuum emission obtained with @xmath145 resolution ( figure 1 from shepherd 2001 ) . upper panels show the mm 5 millimeter source compared with narrow - band @xmath52continuum emission and wide - band 2.12@xmath50 m emission in w75 n ( a ) ( from fig . * figure 6 . * the relationship between compact , high velocity co emission , infrared emission , millimeter continuum peaks , and uc hii regions in w75 n ( b ) . red- and blue - shifted co emission ( upper panels ) is plotted from 20.4 to 36.0 and 5.6 to 23.8 , respectively . the rms in both images is 0.5 ; contours are plotted from 3 , 2 , 3 , 4 @xmath139 and continue at spacings of 1 @xmath139 . millimeter core positions for mm 24 are shown as filled circles , uc hii regions embedded in mm 1 are represented as filled triangles . proposed outflows are identified by arrows from uc hii regions vla 1 ( ba ) , vla 3 ( bb ) , and mm 2 . the synthesized beam ( @xmath146 at p.a . @xmath147 ) is shown in the top right image and a scale size of 0.1 pc is represented by a bar in the top left image . the bottom two images show the k@xmath2 and emission relative to the proposed outflows . both images are displayed as the square root of the intensity . * figure 7 . * * top : * integrated emission ( zeroth moment ) from 17.8 to 36.0 . the rms in the image is 1.2 , contours are plotted from 4 to @xmath142 with increments of @xmath148 and then from 20 to @xmath149 with increments of @xmath135 . greyscale is plotted from @xmath150 to a peak of 56.0 . millimeter cores are identified as filled circles , uc hii regions by filled triangles . the synthesized beam in the bottom left corner is @xmath151 at p.a . @xmath130 . * bottom * position - velocity plot along the length of the high - velocity , red - shifted outflow . contours are plotted at 2 , 5 , 10 , 15 , 20 , 30 , 40 , 50 , 70 , & 90% of the peak . * figure 8 . * * top : * integrated emission ( zeroth moment ) from 5.6 to 26.4 . the rms in the image is 0.96 , contours are plotted from 4 to @xmath142 with increments of @xmath148 , greyscale is plotted from @xmath150 to a peak of 20.0 . millimeter cores are identified as filled circles , uc hii regions by filled triangles . the synthesized beam in the bottom right corner is @xmath151 at p.a . @xmath130 . * bottom * position - velocity plot along the length of the high - velocity , blue - shifted outflow . contours are plotted at 3 , 5 , 7 , 9 , 20 , 40 , 60 , 80 , & 100% of the peak . * * co(j=10 ) optical depth as a function of velocity based on single - dish observations with the kitt peak 12 m telescope . optical depth is derived for three positions within the outflow : in the north - east lobe ( top ) ; centered on the mm 1 core ( center ) ; and in the south - west lobe ( bottom ) . co emission was measured in each channel image of the interferometer mosaic and an optical depth correction was made to the mass estimate based on the location and velocity of the emission . * figure 10 . * * left : * three color image using data from the two micron all sky survey ( 2mass ) . the image is @xmath152 on a side . the j - band image at 1.25@xmath50 m is shown as blue , h - band at 1.65@xmath50 m is green , & k@xmath2-band at 2.17@xmath50 m is red . the @xmath52 symbol represents the location of the mm 1 peak . * right : * a color - color diagram using data from the 2mass point source catalog for stars within @xmath124 of mm 1 that were detected at all three bands . the locus of main - sequence stars is represented by the thick , curved line while the two diagonal lines show reddening vectors up to @xmath125 of dust .

a total flow mass of m extends 3 pc from end - to - end and is being driven by at least four late to early - b protostars . the w75 n cluster members represent a range of evolutionary stages , from stars with no apparent circumstellar material to deeply embedded protostars that are actively powering massive outflows .

we present to resolution 3 mm continuum and line emission and near infrared k , , and [ feii ] images toward the massive star forming region w75 n. the co emission uncovers a complex morphology of multiple , overlapping outflows . a total flow mass of m extends 3 pc from end - to - end and is being driven by at least four late to early - b protostars . more than 10% of the molecular cloud has been accelerated to high velocities by the molecular flows ( relative to ) and the mechanical energy in the outflowing gas is roughly half the gravitational binding energy of the cloud . the w75 n cluster members represent a range of evolutionary stages , from stars with no apparent circumstellar material to deeply embedded protostars that are actively powering massive outflows . nine cores of millimeter - wavelength emission highlight the locations of embedded protostars in w75 n. the total mass of gas & dust associated with the millimeter cores ranges from 340 m to 11 m. the infrared reflection nebula and shocked emission have multiple peaks and extensions which , again , suggests the presence of several outflows . diffuse emission extends about 0.6 parsecs beyond the outer boundaries of the co emission while the [ feii ] emission is only detected close to the protostars . the infrared line emission morphology suggests that only slow , non - dissociative j - type shocks exist throughout the pc - scale outflows . fast , dissociative shocks , common in jet - driven low - mass outflows , are absent in w75 n. thus , the energetics of the outflows from the late to early b protostars in w75 n differ from their low - mass counterparts they do not appear to be simply scaled - up versions of low - mass outflows . # 1#2#3#1#2#3 # 1#2#3 = 500 = 500 =

1208.5698

i

the main contributors to the uv emission from any stellar system are the hottest stars . indeed blue horizontal branch ( hb ) stars are well known to be among the hottest stellar populations in globular clusters ( gcs ) and contribute substantially to the uv radiation observed from old stellar systems ( welch & code , 1972 ) . later on , two other sub - classes of post - hb stars were found to be important contributors to far - uv ( @xmath0 , @xmath31600 ) radiation ( e.g. , greggio and renzini 1990 ; dorman et al . 1995 , hereafter dor95 ; han et al . the hottest hb stars ( extreme hb , ehb ) have such a small envelope mass that most of their post - he - core burning phase takes place at high effective temperature ( ) , during the so called `` agb - manqu phase '' , and these stars never return to the asymptotic giant branch ( agb ) . another group of uv - bright stars is that of post - early agb stars , which after a brief return to the agb , spend the bulk of their helium shell burning phase at high . in systems with only red hb a small floor level of @xmath0 is provided by post - agb stars , which evolve to the agb phase with an higher envelope mass where they undergo thermal pulses and eventually lose their envelopes moving at higher temperatures at constant luminosity . the relative contributions of the various types of stars and the factors that might lead to larger or smaller populations of uv - bright stars have remained an open question ( greggio and renzini 1990 ; dor95 ; lee et al . 2002 ; rich et al . 2005 ; sohn et al . 2006 ) . in distant extragalactic systems one can ordinarily observe only the integrated light of unresolved stellar populations , from which the hope is to gain knowledge about the underlying stellar population . galactic globular clusters ( ggcs ) play an important role in understanding the integrated uv colors of extragalactic systems , especially the so called `` uv - upturn '' observed in the spectral energy distributions of elliptical galaxies ( code & welch 1979 ; de boer 1982 ; bertola et al . 1982 ; greggio & renzini 1990 ; oconnell 1999 ) . first of all , gcs are the closest example in nature to a single stellar population ( ssp ) : a system of coeval stars with similar chemical composition dex ) spread in the iron abundance and ( possibly ) age : @xmath4 centauri ( norris et al . 1996 , lee et al . 1999 , ferraro et al . 2004 ) and terzan 5 ( ferraro et al . 2009 ) . ] . moreover ggcs span a large range of metallicities , a small range of ages , and perhaps some range of helium abundance . hence they can be used to test the stellar evolution theory , which in turn is one of the basic ingredients of the models used to interpret the integrated light of distant galaxies . ggcs are relatively nearby objects ( more than @xmath5 are located at distances @xmath6kpc ) , so their populations can be easily resolved . with typically more than 100,000 stars , even relatively short - lived evolutionary stages are sampled . we can directly observe the properties of individual stars and measure the population ratios for objects in different evolutionary stages . in particular we can study the impact of hot and bright populations ( as the agb - manqu stars ) on the integrated uv light of ggcs and then use them as crucial local templates for comparison with integrated properties of distant extragalactic systems . in fact comparing features in the color - magnitude diagrams ( cmds ) of well known and resolved ggcs with integrated quantities can lend important _ model independent _ insights into the nature of extragalactic systems . integrated uv photometry of ggcs has previously been obtained by the _ orbiting astronomical observatory _ ( oao 2 ; welch & code 1980 ) , _ astronomical netherlands satellite _ ( ans ; van albada , de boer & dickens 1981 ) , _ ultraviolet imaging telescope _ ( uit ; hill et al . 1992 ; landsman et al . 1992 ; parise et al . 1994 ; whitney et al . 1994 ) , and _ international ultraviolet explorer _ ( iue ; castellani & cassatella 1987 ) . using a large , but heterogeneous , collection of data obtained with some of these telescopes along with population synthesis models , dor95 showed how the uv colors varied with parameters like metallicity and how they compare with elliptical galaxies . they showed how the uv colors of ggcs could plausibly be produced by hot hb stars and their progeny . at the time of dor95 , uv photometry of individual stars in ggcs was available for only a few clusters . that situation has changed dramatically . our group alone has already published hst uv photometry for a dozen of ggcs ( see ferraro et al . 1997 , ferraro et al . 1998 , ferraro et al . 1999 , ferraro et al . 2001 , ferraro et al . 2003 , lanzoni et al . 2007 , dalessandro et al . 2008 , rood et al . 2008 ) and obtained data for an additional 32 clusters in hst cycle 16s ( go11975 , pi : ferraro ; see contreras et al . 2012 , sanna et al . 2012 and references therein ) . more recently , we have secured observations of 44 ggcs during three observing cycles with the _ galaxy evolution explorer _ ( galex ) . this is the largest homogeneous sample ever collected for ggcs in uv so far . in schiavon et al . ( 2012 ; hereafter paper i ) we presented photometry and cmds for these clusters . here we present integrated uv magnitudes and colors ( 2 ) for each cluster , and we describe ( 3 ) how they are affected by hb class , metallicity , age , and possibly structural parameters ( mass , density , central relaxation time , etc . ) . in 4 we compare our data with observations of gcs in m31 and m87 .

we present ultraviolet ( uv ) integrated colors of 44 galactic globular clusters ( ggcs ) observed with the galaxy evolution explorer ( galex ) in both and bands . this allows us to determine how the integrated uv colors are driven by hot stellar populations , primarily horizontal branch stars and their progeny . we also investigate how the uv colors vary with parameters like metallicity , age , helium abundance and concentration .

we present ultraviolet ( uv ) integrated colors of 44 galactic globular clusters ( ggcs ) observed with the galaxy evolution explorer ( galex ) in both and bands . this data - base is the largest homogeneous catalog of uv colors ever published for stellar systems in our galaxy . the proximity of ggcs makes it possible to resolve many individual stars even with the somewhat low spatial resolution of galex . this allows us to determine how the integrated uv colors are driven by hot stellar populations , primarily horizontal branch stars and their progeny . the uv colors are found to be correlated with various parameters commonly used to define the horizontal branch morphology . we also investigate how the uv colors vary with parameters like metallicity , age , helium abundance and concentration . we find for the first time that gcs associated with the sagittarius dwarf galaxy have colors systematically redder than ggcs with the same metallicity . finally , we speculate about the presence of an interesting trend , suggesting that the uv color of gcs may be correlated with the mass of the host galaxy , in the sense that more massive galaxies possess bluer clusters .

1209.3788

i

the stellar mass of a galaxy is intricately connected to that galaxy s environment @xcite , metal abundance @xcite , star formation history @xcite , dark matter halo mass @xcite , and just about any other principal characteristic one cares to consider . yet , we rely on estimates of stellar masses that are potentially rife with systematic errors . those estimates hinge on our poor knowledge of a galaxy s star formation history and are further predicated on two aspects of stellar evolution that are poorly understood : stars behavior during the phase(s ) of their life at which they are at their most luminous and the initial distribution of stellar masses ( the initial mass function or imf ) . despite these various complications , we utilize simple models to estimate stellar masses because dynamical measurements are technically difficult to obtain and complicated by the presence of dark matter . even when a dynamical mass estimate is available , modeling is required to determine the relative contributions of stars and dark matter to the total mass . given that any apparent failure of such models impugns our understanding of either stellar evolution or the imf , and therefore affects many aspects of our study of the extragalactic universe , testing these models on the simplest possible stellar systems is paramount . discrepancies between models and observations , when found , are commonly attributed to deviations in the imf from the adopted prescription ( for some recent examples see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) rather than to either the star formation history or stellar evolutionary models . direct measurements of the initial mass function are difficult for various reasons ( see * ? ? ? * for a review ) , particularly over the full range of environments and conditions . various standard " descriptions of the imf are often used to span the range of possibility although given the simple mathematical descriptions used for the imf it is not evident that such an approach is complete . some of the imfs in widest use include the original power - law description by @xcite , which is generally acknowledged to be a poor fit to current data for nearby regions but remains in use as a benchmark @xcite , the multisegmented power - law @xcite , and forms closer to log normal @xcite . it is often quite difficult to distinguish between multisegmented and log - normal variants @xcite . among the most direct measurements of the imf , the evidence currently points to a universal imf that is a power law with index close to salpeter s original value for stellar masses above a few solar masses and log normal or shallower for lower mass stars @xcite , despite hints of variations in other , more extreme , environments or epochs that are observationally less accessible ( for examples see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in summary , the range of standard imfs , let alone the potential for variations across different environments , results in stellar mass uncertainties of at least a factor of several , which is unsatisfactory when testing models whose purpose is to measure differences in galaxy stellar masses to comparable or better precision . to avoid the problems associated with testing these models against the observed properties of galaxies , with their complex stellar populations and ever present dark matter , we will test whether the models can reproduce the properties of local stellar clusters . this approach is not new . the challenge in implementing such a test is finding populations of clusters for which one can dynamically measure the cluster masses and also sample the relevant parameter ranges , principally cluster age , but also metallicity . to date , @xmath4% of the local clusters with kinematic measurements , from which masses can be derived , are old , log(age [ yrs ] ) @xmath5 @xcite . the remainder tend to be extremely young and therefore subject to questions about whether they are dynamically relaxed @xcite . because systematic effects can bias the estimated masses either high or low as a group , a population of clusters all at one age does not provide a strong test of the models . to test the evolutionary predictions of models , including the effects of dynamical evolution , investigators have turned to the populations of clusters in galaxies outside the local group @xcite . however , distance quickly diminishes our ability to measure the internal properties of clusters , particularly age . here , we seek , using local group clusters , to measure the evolution of the stellar mass - to - light ratio , @xmath2 , for a set of clusters with well measured structural properties , ages , and chemical abundances , and to determine if models of a simple stellar population with a universal imf can produce a match to that evolution . a large compilation of local group stellar cluster data was published by @xcite . the particular focus of that study was on the radial surface brightness profiles of the clusters and emphasis was placed on homogenizing the data obtained from various sources , thereby making it useful for subsequent studies as well . in addition , when available , they collated velocity dispersions and produced dynamical models . however , as we alluded to before , out of the 153 clusters presented in that study , measurements of the internal kinematics exist for only 57 , and , of those , only 6 are younger than 10 gyrs old . they compared their dynamically measured @xmath2 to those derived from stellar population models , using both a variety of imfs and two different evolution codes @xcite . although the mean ratio of @xmath2 from their dynamical models to that from their preferred stellar population models is @xmath6 ( formally 2.5@xmath7 discrepant with a ratio of 1 ) , they do not stress this as a significant disagreement , presumably because they appreciate that systematic errors in their mass scale could be @xmath820% . subsequently , @xcite alleviated the apparent discrepancy by showing that due to the internal dynamical evolution of the clusters , which causes the preferential loss of low mass stars , the measured values of @xmath2 are expected to be lower than those calculated from stellar population models . nevertheless , even if the models , once one includes dynamical evolution , are in quantitative agreement for this set of clusters , this result provides support for the models only at a single age . to expand the age range of the sample of clusters with dynamically measured values of @xmath2 and define a homogenous sample for study , we undertook to measure the velocity dispersions of 22 local group stellar clusters . here we present our measurements , using integrated spectra , of the internal velocity dispersions of 20 of those clusters that span @xmath9 ( for two we failed to obtain a measurement ) . of those , we use the 18 that are also in the compilation of @xcite for our subsequent analysis . in 2 we discuss the required data , both that drawn from @xcite and our own observations . we present the observational details , the data reduction , and our measurements of the internal velocity dispersions . in 3 we then convert these velocity dispersion measurements to mass estimates . in 4 , we present and discuss the behavior of @xmath2 with age , and evaluate the possible effects of dynamical evolution and binary stars on these results . in 5 we focus on our preferred hypothesis for the origin of the failure of the simple stellar population models to describe the behavior of @xmath2 with age the existence of at least two distinct imfs . we summarize this study in 7 .

the nature of this failure , in which is at first underestimated and then overestimated with age , invalidates potential simple solutions involving a rescaling of either the measured masses or modeled luminosities . independent of further conjectures regarding the origin of this problem , this result highlights a basic failing of our understanding of the integrated stellar populations of these systems .

we present velocity dispersion measurements of 20 local group stellar clusters ( log(age [ yrs ] ) ) from integrated light spectra and examine the evolution of the stellar mass - to - light ratio , . we find that the clusters deviate from the evolutionary tracks corresponding to simple stellar populations drawn from standard stellar initial mass functions ( imfs ) . the nature of this failure , in which is at first underestimated and then overestimated with age , invalidates potential simple solutions involving a rescaling of either the measured masses or modeled luminosities . a range of possible shortcomings in the straightforward interpretation of the data , including subtleties arising from cluster dynamical evolution on the present day stellar mass functions and from stellar binarity on the measured velocity dispersions , do not materially affect this conclusion given the current understanding of those effects . independent of further conjectures regarding the origin of this problem , this result highlights a basic failing of our understanding of the integrated stellar populations of these systems . we propose the existence of two distinct initial mass functions , one primarily , but not exclusively , valid for older , metal poor clusters and the other for primarily , but not exclusively , younger , metal rich clusters . the young ( log(age [ yrs]).5 ) clusters are well - described by a bottom - heavy imf , such as a salpeter imf , while the older clusters are better described by a top - heavy imf , such as a light - weighted kroupa imf , although neither of these specific forms is a unique solution . the sample is small , with the findings currently depending on the results for four key clusters , but doubling the sample is within reach .

1209.3788

i

using determinations of the velocity dispersions of 18 stellar clusters within the local group that span 7 @xmath3 log ( age [ yrs ] ) @xmath3 10.2 , we trace the evolution of the stellar mass - to - light ratio of simple stellar populations . we find that the observed behavior does not match simple theoretical expectations , and that the failure is such that global scalings of the masses , luminosities , or universal initial mass function can not reconcile the two . the effect of the internal dynamical evolution of the clusters on @xmath2 goes in the correct sense to alleviate the discrepancy , but fails to produce results that the sufficiently large . this is confirmed both by using models of the dynamical evolution @xcite and direct measures of the stellar mass function in nearby clusters @xcite . contamination by binaries is also discussed , but seems problematic due to fine tuning problems . the data can be explained if there are two populations of clusters , drawn from different initial mass functions . specifically , we find that one imf is primarily , but not exclusively , appropriate for older , metal poor clusters and the other for primarily , but not exclusively , for younger , metal rich clusters . the young ( log(age [ yrs])@xmath39.5 ) clusters are well - described by a bottom - heavy imf , such as a salpeter imf , while the older clusters are better described by a top - heavy imf , such as a light - weighted kroupa imf , although neither of these specific forms is a unique solution . of course , the sample is currently small and there are only four clusters in the key age range . we are in the process of enlarging the sample , although there are not many intermediate age clusters available for such study with the current technology . there are also a variety of effects , including the dynamical evolution described above , whose magnitude is estimated using models ; therefore , significant departures from those models can also be used to explain the observations . claims for variations in the initial mass function are usually treated with significant skepticism . this is not because we have a basic understanding of the initial mass function that predicts universality , but is rather due to a fondness for occam s razor . in fact , certain previous claims of variations in the imf are in the same sense as the effect seen here . for example , @xcite found evidence for greater numbers of low mass stars in younger galactic populations and @xcite inferred top heavy star formation at earlier times on the basis of galaxy evolution models . whether these findings are quantitatively consistent with what we present is unclear , but certainly worth exploring to determine if a consistent picture can emerge . it is certainly the case that allowing for the possibility of varying imfs tremendously complicates what one can constrain in extragalactic astronomy . even if there are only two imfs , the variation between those as a function of age , environment , star formation rate , or whatever else drives the dichotomy provides numerous new degrees of freedom to any simulation or model . of course , some have already appealed to such effects to alleviate conflicts between models and data , but multiple imfs not only enables one to address what were previously frustrating conflicts , but requires one to reassess what were previously apparent successes . even worse , without knowing the underlying physical cause for the two classes of imfs claimed to be responsible for the observations presented here , we can not claim that there are only two variants . unfortunately , this is now an added complication that we must face or at least include as a source of systematic error in any study involving galaxy luminosities , color , or stellar mass determinations . dz acknowledges financial support from nsf grant ast-0907771 and nasa adap nnx12ae27 g and thanks the max planck institute for astronomy for its hospitality during the completion of this study . r. c. acknowledges support from nsf through career award 0847467 .

we present velocity dispersion measurements of 20 local group stellar clusters ( log(age [ yrs ] ) ) from integrated light spectra and examine the evolution of the stellar mass - to - light ratio , . we find that the clusters deviate from the evolutionary tracks corresponding to simple stellar populations drawn from standard stellar initial mass functions ( imfs ) . we propose the existence of two distinct initial mass functions , one primarily , but not exclusively , valid for older , metal poor clusters and the other for primarily , but not exclusively , younger , metal rich clusters . the young ( log(age [ yrs]).5 ) clusters are well - described by a bottom - heavy imf , such as a salpeter imf , while the older clusters are better described by a top - heavy imf , such as a light - weighted kroupa imf , although neither of these specific forms is a unique solution .

we present velocity dispersion measurements of 20 local group stellar clusters ( log(age [ yrs ] ) ) from integrated light spectra and examine the evolution of the stellar mass - to - light ratio , . we find that the clusters deviate from the evolutionary tracks corresponding to simple stellar populations drawn from standard stellar initial mass functions ( imfs ) . the nature of this failure , in which is at first underestimated and then overestimated with age , invalidates potential simple solutions involving a rescaling of either the measured masses or modeled luminosities . a range of possible shortcomings in the straightforward interpretation of the data , including subtleties arising from cluster dynamical evolution on the present day stellar mass functions and from stellar binarity on the measured velocity dispersions , do not materially affect this conclusion given the current understanding of those effects . independent of further conjectures regarding the origin of this problem , this result highlights a basic failing of our understanding of the integrated stellar populations of these systems . we propose the existence of two distinct initial mass functions , one primarily , but not exclusively , valid for older , metal poor clusters and the other for primarily , but not exclusively , younger , metal rich clusters . the young ( log(age [ yrs]).5 ) clusters are well - described by a bottom - heavy imf , such as a salpeter imf , while the older clusters are better described by a top - heavy imf , such as a light - weighted kroupa imf , although neither of these specific forms is a unique solution . the sample is small , with the findings currently depending on the results for four key clusters , but doubling the sample is within reach .

0707.3069

i

in various domains of physics a description in terms of fields is frequently used . hydrodynamics represents a first example in which some fields ( densities , velocities , ... ) are introduced for describing the properties of a coarse grained entity the so - called fluid particle . later , field theory ( ft ) has been used as a simple and intuitive tool to predict the behaviour of complex systems in the domain of soft matter physics @xcite . these ft are essentially phenomenological and rely on hamiltonian functionals introduced in an ad hoc manner . they focus on a mesoscopic scale description and they are based on a more or less explicit coarse graining procedure . in this context , hamiltonians are introduced to describe large classes of phenomena having similar properties though different in their microscopic details . this further suggests another type of problems where a ft is extensively used i.e. the description of critical phenomena . here also the ft is based on the assumption that a detailed microscopic knowledge of the system is not relevant to describe its universality class @xcite . and well suited approximations to describe systems with long range correlations or interactions are introduced . in relation , field theory is also used to describe systems with the long ranged coulomb interactions . in this case , ft is constructed using the hubbard - stratonovich transform of the standard partition function @xcite . better known as the sine - gordon transform in the case of the coulomb potential , it has given rise to considerable literature @xcite . these approaches give an exact description of the systems properties on a microscopic level . in this respect , they are distinct from the soft matter like descriptions based on a coarse graining procedure . the sine - gordon approaches introduce an auxiliary field and intricate couplings between fluctuating fields . in our opinion , this auxiliary field is essentially a mathematical tool , difficult to associate with any physical quantity . as a result finding meaningful approximations is rather counterintuitive and the application of such approaches requires that one be rather cautious @xcite . + in contrast to these approaches , our main goal is to show that it is possible to write a ft directly in terms of fields using methods similar to those used in quantum field theory ( qft ) . namely , we show that it is possible to build the theory around a field , which is a real quantity having a simple physical meaning . moreover we will show that our ft construction is not only simple and intuitive but also leads to a complete description at microscopic level . in this paper , we consider systems at equilibrium . + the paper is organized as follows . in the next section we present the main requirements which a ft must verify . in section [ sec : definingh ] , we give the hamiltonian on which the ft is based : it contains two terms of different nature . this leads to investigate the feynman expansion of a purely local hamiltonian with an infinite number of coupling constants . this is developed in section [ ssec : int_representation ] where some important specific aspects of the expansion are shown . in section [ sec : interactinggas ] we calculate the partition function in the presence of an interaction pair potential . in the next section we establish an exact mapping between our ft and the standard statistical mechanics given in terms of mayer expansion @xcite . in section [ sec : discussion ] we illustrate on several examples how our approach may lead to new aspects in statistical physics . finally , in section [ sec : conclusion ] we give some conclusions and perspectives .

we propose a formally exact statistical field theory for describing classical fluids with ingredients similar to those introduced in quantum field theory . it has been shown that there exists a mapping between this approach and the standard statistical mechanics given in terms of mayer function expansion . some perspectives of the theory are given .

we propose a formally exact statistical field theory for describing classical fluids with ingredients similar to those introduced in quantum field theory . we consider the following essential and related problems : ) how to find the correct field functional ( hamiltonian ) which determines the partition function , ) how to introduce in a field theory the equivalent of the indiscernibility of particles , ) how to test the validity of this approach . we can use a simple hamiltonian in which a local functional transposes , in terms of fields , the equivalent of the indiscernibility of particles . the diagrammatic expansion and the renormalization of this term is presented . this corresponds to a non standard problem in feynman expansion and requires a careful investigation . then a non - local term associated with an interaction pair potential is introduced in the hamiltonian . it has been shown that there exists a mapping between this approach and the standard statistical mechanics given in terms of mayer function expansion . we show on three properties ( the chemical potential , the so - called contact theorem and the interfacial properties ) that in the field theory the correlations are shifted on non usual quantities . some perspectives of the theory are given .

0707.3069

c

from standard text books @xcite , we know that the so - called classical statistical mechanics contains two basic properties governed by quantum physics . namely , the thermal de broglie wavelength , @xmath12 , and the indiscernibility of particles which originates from @xmath179 distinct particles a @xmath180 coefficient in the partition function . these elements are not related to the interaction potential . in the present paper , we have shown that a simple local functional together with a renormalization procedure can reproduce these two properties . this procedure is not modified when an interaction pair potential is introduced in the hamiltonian and consequently we can then demonstrate that the theory is equivalent to the usual statistical mechanics . we have shown that the local functional leads , in perturbation theory , to a simple combinatory of the fields . in each monomial term , the @xmath76 fields are equivalent and their permutation is associated with the coefficient @xmath77 . in other words , the local functional transposes to the ft the indiscernibility of particles . one characteristic of our ft is that we have been able to introduce a renormalization procedure through which all the results are finite and independent from , arbitrary lattice spacing , although there exists an infinity of coupling constants . due to renormalization , the expression @xmath51\}$ ] is formal and we must consider that this quantity is defined by its series expansion around the activity and that some terms in this expansion are cancelled by counter terms ; these are independent of the interaction potential , showing that they have no physical meaning but are originated only by a mathematical procedure . achieving a microscopically faithful description shows that a simple ft is not necessarily associated with a coarse graining and can have a level of description equivalent to that of the standard statistical mechanics , in contrast to the common conceptions of this type of approach @xcite . indeed , the measure we have used does not require the introduction of any normalization constant in the partition function , necessary in the case of a coarse grained approach . + we can also compare this ft with other microscopically exact field theoretical descriptions . considering a field approach without using as a starting point the standard partition function , we deal with a renormalization that does not exist for field theories based on the hubbard stratonovich transform . on the other hand , our field is extremely simple and has an obvious physical meaning . this contrasts with the hubbard stratonovich type approaches , where we have to work in a complex plane with an auxiliary field for which it is rather difficult to introduce appropriate physical approximations . we also emphasize that ft is distinct from the dft . both approaches are based on the existence of a functional of the density . however , in the two formalisms , the correlations are treated in different ways @xcite . in the dft , the form of the functional includes all correlations and fluctuations and we know that this functional exists but we ignore its exact form . minimizing this functional yields the equilibrium density distribution . in contrast , in ft the functional is known and simple . the core of the ft formalism is to gradually account for the fluctuations when calculating quantities for the system in a perturbative expansion . one part of @xmath13 $ ] is @xmath23 $ ] which is formally like the free energy of the ideal system . a similar term @xmath181 $ ] is introduced in dft , however it is important to point out the differences between @xmath23 $ ] and @xmath181 $ ] . @xmath23 $ ] is a functional of a field i.e. a fluctuating quantity where as , at the minimum , @xmath181 $ ] is a function of the mean value of the fluid density . moreover , we have mentionned earlier that @xmath51\}$ ] is essentially a formal expression . this illustrates one specificity of the ft : the fluctuations of the ideal term which basically represent the entropy must be considered on the same footing as the fluctuations related to the interaction pair potential . + in this respect , although our ft is equivalent to standard statistical mechanics , the two approaches focus on different aspects of the correlations . this is the case when comparing standard approaches , but the discussion will be extended below for the case of our ft . we are convinced that having at disposal distinct formulations for a given quantity is indeed useful , possibly for acquiring a broader understanding . hereafter we illustrate on three examples how ft leads to a new point of view on traditional quantities . + in liquid state theory there are three classical expressions of the chemical potential . one of them corresponds to @xcite @xmath182 a second traditional expression is given by @xcite @xmath183;\mathbf{r})+v^{ext}(\mathbf{r})=\beta\mu\end{aligned}\ ] ] where @xmath184;i)$ ] is the single - particle direct correlation function @xcite . finally , we also have a relation based on a charging process of the interaction potential @xcite @xmath185 where @xmath186 is the pair distribution function @xcite as a function of the charging parameter @xmath187 . we note that all these expressions emphasize properties related to the potential , whether calculating the correlations of a quantity involving the interaction , or calculating the single - particle direct correlation function or alternatively considering a charging process of the interaction . the field theoretical description leads to a new expression which can be obtained by writing that the field is a dummy variable in the functional integral . this leads to the so called dyson relations @xcite and we obtain @xmath188 here the term related to the interactions is rather simple , it expresses the mean potential at a given point without taking into account the correlations . all correlations and fluctuations appear in the calculation of the average of the logarithm of the density field . this contrasts with a simple term like the logarithm of the average density , which appears in standard statistical mechanical expressions or in the dft . as a consequence , differences in the description and a different organisation of the perturbation expansion in the ft , suggest that one should be able to elaborate new approximations . + let us consider now the so - called contact theorem which establishes an exact relation between the pressure @xmath189 existing in a bulk phase and the value of the density profile @xmath190 at the wall enclosing the bulk material . this corresponds to @xmath191 in so far as this relation is concerned , discussing the derivation of this theorem is an opportunity to emphasize the conceptual differences between the various approaches . we mention the kinetic theory of gases , in which this relation is the consequence of the mechanical equilibrium at the interface . in the case of dft , the derivation is straightforward as we only need to write a displacement of the external potential : the interface , in two different ways . another derivation @xcite is obtained by integrating the bgy equations . in this case , a _ subtle _ integration of the correlations through the interface leads to the relation . within our field theoretical framework , the key element is the local functional which is essential at different levels . it is crucial to obtain the density contact value present in the contact theorem @xcite , but it is also necessary to cancel supplementary terms which appear in the demonstration . in this respect , specific relations of the field theory are also required , namely the dyson type relations @xcite . + now , in a third example , we illustrate one of the main aspects of the ft , i.e. the existence of an intricate coupling between counting ( entropy ) and interaction . let us study the interfacial properties of ionic fluids . from the point of view of the interactions , we know that the important quantity is the charge , the difference of densities of each species . however , this system can also be viewed as a peculiar mixture which has a specific condition due to electroneutrality . from this point of view , we have two terms in the ideal functional describing the indiscernibility for each ion . thus the natural fields are the densities describing each ion . in @xcite , we show , in the specific instance where the natural fields for the ideal and for the interaction term are distinct , that the perturbation theory leads to a coupling of the charge and of the total density field due to the local ideal functional . this has direct consequences . + for the simple neutral interface , we show that there exists a depletion for the quadratic fluctuations of the charge . then , the entropic coupling between the charge field and the total density field predicts a non trivial profile on the total density @xcite . we can verify that the contact value of this total density profile satisfies the exact condition of the contact theorem , for the pressure calculated at the same level of approximation . we have used this phenomenon to analyse the anomalous behaviour of the differential capacitance as a function of the temperature @xcite which has been thoroughly discussed recently in experiments @xcite , numerical simulation @xcite and theoretical approaches @xcite . the interest of our analysis is that it provides a simple interpretation and understanding for this phenomenon , associating the decrease in the capacitance with the depletion of the ionic density at the interface at low temperature and providing the physical origin of this depletion . moreover , the more detailed account of these entropic effects is fundamental in the case of asymmetric , in valence , electrolytes . in @xcite , we have tested our ft by comparing with the results of numerical simulations @xcite and shown that the theory accounts for all main qualitative properties of the phenomenon , in comparison with other approaches @xcite which although currently more quantitative fail to take certain features into consideration .

we can use a simple hamiltonian in which a local functional transposes , in terms of fields , the equivalent of the indiscernibility of particles . then a non - local term associated with an interaction pair potential is introduced in the hamiltonian . we show on three properties ( the chemical potential , the so - called contact theorem and the interfacial properties ) that in the field theory the correlations are shifted on non usual quantities .

we propose a formally exact statistical field theory for describing classical fluids with ingredients similar to those introduced in quantum field theory . we consider the following essential and related problems : ) how to find the correct field functional ( hamiltonian ) which determines the partition function , ) how to introduce in a field theory the equivalent of the indiscernibility of particles , ) how to test the validity of this approach . we can use a simple hamiltonian in which a local functional transposes , in terms of fields , the equivalent of the indiscernibility of particles . the diagrammatic expansion and the renormalization of this term is presented . this corresponds to a non standard problem in feynman expansion and requires a careful investigation . then a non - local term associated with an interaction pair potential is introduced in the hamiltonian . it has been shown that there exists a mapping between this approach and the standard statistical mechanics given in terms of mayer function expansion . we show on three properties ( the chemical potential , the so - called contact theorem and the interfacial properties ) that in the field theory the correlations are shifted on non usual quantities . some perspectives of the theory are given .

1209.4416

i

in this study we consider the problem of parameter - free identification of a class of dynamical systems . the approach we propose is derived from a general method for the reconstruction of the constitutive relations in systems described by partial differential equations ( pdes ) which was initially introduced in @xcite and further developed in @xcite , see also @xcite the idea is that , given an autonomous evolution equation @xmath0 for some quantity @xmath1 ( defined in a finite or infinite dimension with @xmath2 denoting time ) , one seeks to optimally reconstruct the flux function @xmath3 , so that the system outputs best match , in a suitably defined sense , with the measurements available . as shown schematically in figure [ fig : f ] , the originality of this approach is that the function @xmath3 is reconstructed directly as a _ continuous _ object , rather than employing a truncated polynomial or other galerkin expansion . in @xcite we reviewed the mathematical foundations and some computational aspects of this approach applied to the reconstruction of state - dependent transport coefficients in a class of systems described by pdes . in the present investigation we adapt this method to the problem of identification of the propagator function @xmath4 , @xmath5^t$ ] , in a finite - dimensional dynamical system @xmath6 with the state vector @xmath7^t \in \rr^n$ ] . to fix attention , instead of working with an abstract formulation , we will focus on a specific problem concerning a three - dimensional ( @xmath8 ) model characterized by oscillatory dynamics with a stable limit cycle . in many real - life physical problems with infinite - dimensional state spaces and evolution described by pdes such systems arise as reduced - order models providing low - dimensional approximate description in the neighborhood of fixed points and limit cycles . in some cases propagator @xmath9 may be derived from the description of the full plant based on first principles . in general , however , the reduced - order model is inferred from experimental or numerical data . such reduced models are of paramount importance as test - beds for the development of our understanding of system dynamics . they are also useful as low - cost surrogates guiding optimization and real - time control design for expensive full - scale models . in all cases , typical model identification is generally performed in three steps : ( 1 ) selection of the state space @xmath10 which is large enough to capture the behaviour of interest and at the same time sufficiently small to allow one to exploit the analytical / numerical advantages of the surrogate plant ; ( 2 ) structure identification of the propagator @xmath11 , e.g. , determination of the polynomial degree of its components @xmath12 , @xmath13 ; and ( 3 ) parameter identification , e.g. , inference of the polynomial coefficients from time - resolved trajectories @xmath14 . these different steps are illustrated schematically in figure [ fig : f]a . the challenge of this approach is to find the right balance between the robustness of the model identification , requiring only a few tunable parameters , and a good accuracy for which a larger number of parameters is typically needed . identification problems can also be solved using variational techniques and this is the approach we will pursue in the present study , cf . figure [ fig : f]b . similar methods have been developed for a broad range of problems in both the finite and infinite - dimensional setting , including flow control in fluid mechanics @xcite , data assimilation in meteorology @xcite and geophysics @xcite to mention just a few application areas . the related problem of state estimation is usually solved using various filtering approaches such as the kalman filter @xcite . we introduce now our model . the oscillatory fluctuation is parameterized by @xmath15 where @xmath16 is the imaginary unit , @xmath17 is the amplitude of the fluctuation ( `` @xmath18 '' means `` equal to by definition '' ) and @xmath19 the corresponding phase , while the base - flow deformation is characterized by a single parameter @xmath20 . following the mean - field theory @xcite , we make the following assumptions about the structure of the system : 1 . in the plane @xmath21 the system exhibits an unstable fixed point at the origin and an attracting limit cycle , 2 . the state variable @xmath20 is `` slaved '' to @xmath22 and @xmath23 , i.e. , @xmath24 , and 3 . the dynamics is phase - invariant , i.e. , the descriptor system depends only on @xmath25 . [ ass1 ] as regards the time @xmath26 , we will assume that @xmath27 $ ] for some @xmath28 . as a general form of a dynamical system consistent with assumption [ ass1 ] we will consider [ eq : descriptorsystemb ] @xmath29 or , equivalently [ eq : descriptorsystema ] @xmath30 where @xmath31 and @xmath32 . subsequently , we will also use the notation @xmath33^t$ ] and @xmath34 $ ] , where @xmath35 } r(t)$ ] . we note that the equations governing @xmath22 and @xmath23 , or equivalently @xmath25 and @xmath36 , do not depend on @xmath20 . equations and describe the dependency of a slow variable on the fluctuation amplitude , and the usefulness of these algebraic equations will become clear in the context of the mean - field models discussed in section [ toc : meanfieldsystem ] . in and the functions @xmath37 , @xmath38 , are assumed sufficiently regular to make the systems well posed ( the question of the regularity of functions @xmath39 , @xmath38 , will play an important role in our approach and will be addressed in detail further below ) . without loss of generality , we will also assume that @xmath40 . system , or , is complemented with the initial condition , respectively , @xmath41^t$ ] and @xmath42 , @xmath43 . dynamical systems of the type or arise commonly as a result of various rigorous and empirical model - reduction strategies in diverse application areas such as fluid mechanics @xcite , thermodynamics @xcite and phase transitions @xcite . the main contribution of this work is development of a computational technique allowing one to reconstruct functions @xmath44 , @xmath45 and @xmath46 in in a very general form based on some measurements . the key idea is to formulate a least - squares minimization problem in which one of the functions @xmath39 , @xmath38 , is the control variable . then , a variational gradient - based approach can be employed to find the optimal solution in a suitable function space . in the present investigation , we will consider system as a reduced - order model of hydrodynamic instabilities in open shear flows obtained using a suitable galerkin projection to fix attention without losing generality . although this problem is very well - studied , our method provides a systematic refinement of the state - of - the - art mean - field model , which is the second main contribution of this study . details of this problem are introduced in the next section . in the following section we develop our model identification approach , whereas in section [ toc : results ] we present a number of computational results concerning identification of the model for the system considered in section [ toc : modelidentification ] . then , in section [ toc : discussion ] , we analyze the computational performance of our method and discuss the improvements it offers over the predictions of some standard models applied to the problem in question . summary and conclusions are deferred to section [ toc : conclusions ] , whereas in appendices [ toc : pod ] , [ toc : regularity ] and [ toc : perturbation ] we collect some technical results .

we propose a general framework for parameter - free identification of a class of dynamical systems . here , the propagator is approximated in terms of an arbitrary function of the state , in contrast to a polynomial or galerkin expansion used in traditional approaches . the computational aspect of the identification method is thoroughly validated showing that good reconstructions can also be obtained in the absence of of accurate initial approximations .

we propose a general framework for parameter - free identification of a class of dynamical systems . here , the propagator is approximated in terms of an arbitrary function of the state , in contrast to a polynomial or galerkin expansion used in traditional approaches . the proposed formulation relies on variational data assimilation using measurement data combined with assumptions on the smoothness of the propagator . this approach is illustrated using a generalized dynamic model describing oscillatory transients from an unstable fixed point to a stable limit cycle and arising in nonlinear stability analysis as an example . this 3-state model comprises an evolution equation for the dominant oscillation and an algebraic manifold for the low- and high - frequency components in an autonomous descriptor system . the proposed optimal model identification technique employs mode amplitudes of the transient vortex shedding in a cylinder wake flow as example measurements . the reconstruction obtained with our technique features distinct and systematic improvements over the well - known mean - field ( landau ) model of the hopf bifurcation . the computational aspect of the identification method is thoroughly validated showing that good reconstructions can also be obtained in the absence of of accurate initial approximations . * keywords : * hydrodynamic instabilities , reduced - order models , mean - field models , variational data assimilation , adjoint - based optimization , * ams subject classifications : * 93a30 , 65k10 , 76d25

1605.08422

i

in this work we consider time - independent schrdinger equation to calculate vibrational spectra of molecules . the goal is to find smallest eigenvalues and corresponding eigenfunctions of the hamiltonian operator . the key assumption that we use is that potential energy surface ( pes ) can be approximated by a small number of sum - of - product functions . this holds , e.g. if pes is a polynomial . we discretize the problem using the discrete variable representation ( dvr ) scheme @xcite . the problem is that the storage required for each eigenvector grows exponentially with dimension @xmath2 as @xmath3 , where @xmath4 is number of grid points in each dimension . even for the dvr scheme where @xmath5 grid points in each dimension is often sufficient to provide very accurate results we would get @xmath6 pb of storage for a 12 dimensional problem . this issue is often referred to as the _ curse of dimensionality_. to avoid exponential growth of storage we use _ tensor train _ ( tt ) decomposition @xcite to approximate the operator and the eigenfunctions in the dvr representation , which is known to have exponential convergence rate . it is important to note that the tt - format is algebraically equivalent to the matrix product state format ( mps ) , which has been used for a long time in quantum information theory and solid state physics to approximate certain wavefunctions @xcite ( dmrg method ) , see the review @xcite for more details . prior research @xcite has shown that the eigenfunctions often can be well approximated in the tt - format , i.e. they lie on a certain low - dimensional non - linear manifold . the key question is how to utilize this a priori knowledge in computations . we propose to use well - established iterative methods that utilize matrix inversion and solve corresponding linear systems inexactly along the manifold to accelerate the convergence . our main contributions are : * we propose a concept of a _ manifold preconditioner _ that explicitly utilizes information about the size of the tt - representation . we use the manifold preconditioner for a tensor version of _ locally optimal block preconditioned conjugate gradient _ method ( lobpcg ) @xcite . we will refer to this approach as _ manifold - preconditioned lobpcg _ ( mp lobpcg ) . the approach is first illustrated on computation of a single eigenvector ( section [ sec : mp1 ] ) and then extended to the block case ( section [ sec : mpb ] ) . * we propose tensor version of simultaneous inverse iteration ( also known as block inverse power method ) , which significantly improves accuracy of the proposed mp lobpcg . similarly to the manifold preconditioner the inversion is done using the a priori information that the solution belongs to a certain low - parametric manifold . we will refer to this method as _ manifold - projected simultaneous inverse iteration _ ( mp sii ) . the approach is first illustrated on computation of a single eigenvector ( section [ sec : iii1 ] ) and then extended to the block case ( section [ sec : iib ] ) . * we calculate vibrational spectra of acetonitrile molecule ch@xmath0cn using the proposed approach ( section [ sec:12 ] ) . the results are more accurate than those of the smolyak grid approach @xcite but with much less storage requirements , and more accurate than the recent memory - efficient h - rrbpm method @xcite , which is also based on tensor decompositions . we note that the smolyak grid approach does not require pes to be approximated by a small number of sum - of - product functions .

we propose a new algorithm for calculation of vibrational spectra of molecules using tensor train decomposition . under the assumption that eigenfunctions lie on a low - parametric manifold of low - rank tensors we suggest using well - known iterative methods that utilize matrix inversion ( lobpcg , inverse iteration ) and solve corresponding linear systems inexactly along this manifold . as an application , we accurately compute vibrational spectra ( 84 states ) of acetonitrile molecule chcn on a laptop in one hour using only mb of memory to represent all computed eigenfunctions .

we propose a new algorithm for calculation of vibrational spectra of molecules using tensor train decomposition . under the assumption that eigenfunctions lie on a low - parametric manifold of low - rank tensors we suggest using well - known iterative methods that utilize matrix inversion ( lobpcg , inverse iteration ) and solve corresponding linear systems inexactly along this manifold . as an application , we accurately compute vibrational spectra ( 84 states ) of acetonitrile molecule chcn on a laptop in one hour using only mb of memory to represent all computed eigenfunctions .

1603.09591

c

are shown here for reference . see text for details . colour coding indicates region , as defined by @xcite : red , oph a ; orange , oph a@xmath168 ( low - column - density region surrounding oph a ) ; dark green , oph b1 ; light green , oph b2 ; blue , oph c ; dark purple , oph e ; light purple , oph f. solid black line indicates adiabatic track ; dashed back line indicates isothermal track . the shaded region indicates the hypothesised ` starless core desert'.,scaledwidth=47.0% ] it is notable that there is only one core in the l1688 region which is both gravitationally dominated and virially unbound , and that this one core , b2-mm16 , has an uncertainty on its virial ratio such that the core is consistent with in fact being prestellar . we hypothesise that this parameter space ( @xmath84 ; @xmath90 ) may be largely inaccessible to starless cores - a ` starless core desert ' of sorts . it may be difficult to assemble a starless core with sufficient mass to be gravitationally - dominated , while simultaneously maintaining an internal linewidth sufficiently large that the core remains virially unbound . the absence of virially - unbound and gravitationally - dominated starless cores further hints at a formation mechanism for prestellar cores in which starless cores initially form as pressure - confined objects , and those which are sufficently virially bound then evolve to become gravitationally - bound prestellar cores , perhaps in the manner described in this model . in order to test this hypothesis , further measurements of the virial balance of starless cores are needed . if the gravitationally - dominated and virially - unbound quadrant of the virial plane is in fact significantly underpopulated compared to the other quadrants i.e. if the hypothesised ` starless core desert ' is not a result of the small counting statistics in the l1688 core sample this would lend support to the suggestion that starless cores may initially form as pressure - confined objects . this model can be usefully compared to numerical simulations of cores collapsing under external pressure . such simulations typically assume that cores obey a bonnor - ebert density distribution , and typically involve the perturbation of a system which is initially in equilibrium ( e.g. @xcite ; @xcite ) . this is a somewhat different approach to our model , which considers cores as obeying a plummer - like density distribution , and models the evolution of cores which are initially in a non - equilibrium ( i.e. virially unstable ) state . @xcite modelled the evolution of an initially stable bonnor - ebert sphere undergoing a steady increase in external pressure , in order to study protostellar collapse induced by external compression . they found that while the compression of their core is slow ( i.e. when the external pressure on their core increases on a timescale much greater than the sound - crossing time of the core ) , the core evolves quasistatically . during the prestellar stage of the core s evolution the outer boundary of the core is pushed inward qualitatively similar to the contraction of pressure - dominated and virially bound cores in our model and a modest , approximately uniform , inward velocity field is set up . however , @xcite found that when cores are strongly compressed ( i.e. the external pressure increases on a timescale shorter than the sound - crossing time ) , a compression wave is driven into the core , leaving behind it an inward velocity field which can become supersonic if the core compression is strong enough . this is dissimilar to our model , which assumes quasistatic core evolution throughout . our model is thus qualitatively similar to numerical simulations of the collapse under slow compression of pressure - confined cores @xcite . whether the environments in the molecular clouds studied in this work allow quasistatic core evolution is not clear . however , @xcite noted that their simulations in which core compression is slow the quasistatic case produce results which match observational constraints on starless cores , suggesting that core evolution may be quasistatic in at least some cases . this analysis shows that a virially - bound and pressure - confined starless core will not necessarily evolve to become gravitationally bound , and thus can not be considered to be a prestellar core . those of our cores which have no route to becoming gravitationally bound may be evolving toward or oscillating slightly about virial equilibrium . a core can only be definitively considered prestellar ( i.e. about to form a protostar ) if it is gravitationally unstable . pressure confinement alone is not necessarily sufficient . it must be emphasised that the core properties measured by @xcite and listed as initial conditions in table [ tab : ics ] are substantially uncertain . the majority of the cores have virial ratios consistent at the 3-@xmath40 level with their being virialised , and the evolutionary tracks described above are accurate only if measurements of the core properties are precisely accurate . these evolutionary scenarios should be viewed as representative of a core with the described properties , rather than a prediction specific to the core being observed .

we hypothesise a ` starless core desert ' in this quadrant of the virial plane , which may result from cores initially forming as pressure - confined objects . we conclude that a virially - bound and pressure - confined core will not necessarily evolve to become gravitationally bound , and thus can not be considered prestellar . a core can only be definitively considered prestellar ( collapsing to form an individual stellar system ) if it is gravitationally unstable .

we propose an analytical model for the quasistatic evolution of starless cores confined by a constant external pressure , assuming that cores are isothermal and obey a spherically - symmetric density distribution . we model core evolution for plummer - like and gaussian density distributions in the adiabatic and isothermal limits , assuming larson - like dissipation of turbulence . we model the variation in the terms in the virial equation as a function of core characteristic radius , and determine whether cores are evolving toward virial equilibrium or gravitational collapse . we ignore accretion onto cores in the current study . we discuss the different behaviours predicted by the isothermal and adiabatic cases , and by our choice of index for the size - linewidth relation , and suggest a means of parameterising the magnetic energy term in the virial equation . we model the evolution of the set of cores observed by in the l1688 region of ophiuchus in the ` virial plane ' . we find that not all virially - bound and pressure - confined cores will evolve to become gravitationally bound , with many instead contracting to virial equilibrium with their surroundings , and find an absence of gravitationally - dominated and virially - unbound cores . we hypothesise a ` starless core desert ' in this quadrant of the virial plane , which may result from cores initially forming as pressure - confined objects . we conclude that a virially - bound and pressure - confined core will not necessarily evolve to become gravitationally bound , and thus can not be considered prestellar . a core can only be definitively considered prestellar ( collapsing to form an individual stellar system ) if it is gravitationally unstable . [ firstpage ] stars : formation methods : analytical ism : clouds

1506.02905

i

fluctuation relations are central to our present understanding of statistical mechanics . their long and distinguished history goes back to at least the studies by callen and welton @xcite , green @xcite and kubo @xcite , which were inspired by the works of einstein on the brownian movement @xcite and of johnson @xcite and nyquist @xcite on noise in electrical circuits . the derivation by jarzynski of a rather general non - equilibrium work relation @xcite , linking the average of the exponential of the work being performed on a system with the equilibrium free energy difference between initial and final equilibrium states of the system , is of particular interest . subsequently , crooks @xcite obtained the jarzynski equality from a relation between the probability of a given amount of work being performed on a system and the probability that the system performs the same amount of work on its surroundings if the time - reversed protocol is undertaken . such heightened interest in non - equilibrium work relations has not only been fuelled by novel theoretical advances in out - of - equilibrium dynamics , but also by experimental progress in preparing and probing non - equilibrium evolution ( see @xcite for reviews on the subject ) . in the present paper , we propose a relatively simple yet realistic experiment based on a proposal by crooks @xcite , which would allow for a direct test of the crooks - tasaki fluctuation relation . the experimental system we consider consists of a normal - metal / insulator / superconducting ( nis ) junction between a superconductor and a normal metal , which is initially short - circuited and is subjected to a given voltage protocol ( see below ) . we establish that for the proposed protocol , the full work distribution - function has non - gaussian character with a non - standard decay exponent . we also compute the first two moments of such distribution , which can be determined experimentally by measuring the average heat released and its variance . in order to obtain a closed expression for the characteristic function of the work distribution , we derive an equivalence between the dynamics of an nis junction and the one of an assembly of two - level systems subjected to a circularly polarized field . using this mapping , the work distribution is determined . for realistic parameters of experimentally available nis junctions as _ e.g. _ those of ref . @xcite , our findings show that at cryogenic temperatures , even the tiny amounts of heat released will result in a measurable volume change for a probe connected to the junction . the structure of the paper is as follows : sect . [ secper ] places the recent developments briefly outlined above into their proper historical context and reviews the theoretical tools necessary to study work - fluctuation relations at the quantum level . in sect . [ sechm ] , we introduce the hamiltonian of the nis junction and describe in detail the work protocol applied to the system . in sect . [ secdw ] , we use results that are derived in [ secmap ] and [ secgenfun ] to compute both the average work dissipated as well as its fluctuations and the full work distribution . [ apb ] contains an extension of the results presented in [ secgenfun ] and [ secaptun ] contains a discussion of a method of measurement of the tunnelling amplitude that describes the nis junction . section [ seciso ] contains the main result of our paper , where we compute the numerical value of the average heat released on a nis junction such as the ones discussed in ref . . we leave to [ appim ] the discussion of the experimental techniques that can be used to measure such a quantity . in particular , we show that the heat that is released can be measured by determining the volume change of a probe that absorbs it . we provide estimates of the relative volume change , which should be measurable using capacitive methods @xcite . finally , in sect . [ secconc ] , we present our conclusions . for increased readability , most technical details have been relegated to the appendices .

we propose an experimental setup to measure the work performed in a normal - metal / insulator / superconducting ( nis ) junction , subjected to a voltage change and in contact with a thermal bath . we compute the performed work and argue that the associated heat release can be measured experimentally . our results allow for a direct experimental test of the crooks - tasaki fluctuation relation .

we propose an experimental setup to measure the work performed in a normal - metal / insulator / superconducting ( nis ) junction , subjected to a voltage change and in contact with a thermal bath . we compute the performed work and argue that the associated heat release can be measured experimentally . our results are based on an equivalence between the dynamics of the nis junction and that of an assembly of two - level systems subjected to a circularly polarised field , for which we can determine the work - characteristic function exactly . the average work dissipated by the nis junction , as well as its fluctuations , are determined . from the work characteristic function , we also compute the work probability - distribution and show that it does not have a gaussian character . our results allow for a direct experimental test of the crooks - tasaki fluctuation relation . email : ` @nanotech.dtu.dk ` email : ` [email protected] ` email : ` .kirchner@correlated - matter.com `

1011.1939

i

coordinated networks of mobile robots are already in use for environmental monitoring and warehouse logistics . in the near future , autonomous robotic teams will revolutionize transportation of passengers and goods , search and rescue operations , and other applications . these tasks share a common feature : the robots are asked to provide service over a space . one question which arises is : when a group of robots is waiting for a task request to come in , how can they best position themselves to be ready to respond ? the distributed _ environment partitioning problem _ for robotic networks consists of designing individual control and communication laws such that the team divides a large space into regions . typically , partitioning is done so as to optimize a cost function which measures the quality of service provided over all of the regions . _ coverage control _ additionally optimizes the positioning of robots inside a region as shown in fig . [ fig : cover_example ] . this paper describes a distributed partitioning and coverage control algorithm for a network of robots to minimize the expected distance between the closest robot and spatially distributed events which will appear at discrete points in a non - convex environment . optimality is defined with reference to a relevant `` multicenter '' cost function . as with all multirobot coordination applications , the challenge comes from reducing the communication requirements : the proposed algorithm requires only short - range gossip " communication , i.e. , asynchronous and unreliable communication between nearby robots . territory partitioning and coverage control have applications in many fields . in cyber - physical systems , applications include automated environmental monitoring @xcite , fetching and delivery @xcite , construction @xcite , and other vehicle routing scenarios @xcite . more generally , coverage of discrete sets is also closely related to the literature on data clustering and @xmath0-means @xcite , as well as the facility location or @xmath0-center problem @xcite . partitioning of graphs is its own field of research , see @xcite for a survey . territory partitioning through local interactions is also studied for animal groups , see for example @xcite . a broad discussion of algorithms for partitioning and coverage control in robotic networks is presented in @xcite which builds on the classic work of lloyd @xcite on optimal quantizer selection through centering and partitioning . " the lloyd approach was first adapted for distributed coverage control in @xcite . since this beginning , similar algorithms have been applied to non - convex environments @xcite , unknown density functions @xcite , equitable partitioning @xcite , and construction of truss - like objects @xcite . there are also multi - agent partitioning algorithms built on market principles or auctions , see @xcite for a survey . while lloyd iterative optimization algorithms are popular and work well in simulation , they require synchronous and reliable communication among neighboring robots . as robots with adjacent regions may be arbitrarily far apart , these communication requirements are burdensome and unrealistic for deployed robotic networks . in response to this issue , in @xcite the authors have shown how a group of robotic agents can optimize the partition of a convex bounded set using a lloyd algorithm with gossip communication . a lloyd algorithm with gossip communication has also been applied to optimizing partitions of non - convex environments in @xcite , the key idea being to transform the coverage problem in euclidean space into a coverage problem on a graph with geodesic distances . distributed lloyd methods are built around separate partitioning and centering steps , and they are attractive because there are known ways to characterize their equilibrium sets ( the so - called centroidal voronoi partitions ) and prove convergence . unfortunately , even for very simple environments ( both continuous and discrete ) the set of centroidal voronoi partitions may contain several sub - optimal configurations . we are thus interested in studying ( discrete ) gossip coverage algorithms for two reasons : ( 1 ) they apply to more realistic robot network models featuring very limited communication in large non - convex environments , and ( 2 ) they are more flexible than typical lloyd algorithms meaning they can avoid poor suboptimal configurations and improve performance . there are three main contributions in this paper . first , we present a discrete partitioning and coverage optimization algorithm for mobile robots with unreliable , asynchronous , and short - range communication . our algorithm has two components : a _ motion protocol _ which drives the robots to meet their neighbors , and a _ pairwise partitioning rule _ to update territories when two robots meet . the partitioning rule optimizes coverage of a set of points connected by edges to form a graph . the flexibility of graphs allows the algorithm to operate in non - convex , non - polygonal environments with holes . our graph partition optimization approach can also be applied to non - planar problems , existing transportation or logistics networks , or more general data sets . second , we provide an analysis of both the convergence properties and computational requirements of the algorithm . by studying a dynamical system of partitions of the graph s vertices , we prove that almost surely the algorithm converges to a pairwise - optimal partition in finite time . the set of pairwise - optimal partitions is shown to be a proper subset of the well - studied set of centroidal voronoi partitions . we further describe how our pairwise partitioning rule can be implemented to run in anytime and how the computational requirements of the algorithm can scale up for large domains and large teams . third , we detail experimental results from our implementation of the algorithm in the player / stage robot control system . we present a simulation of 30 robots providing coverage of a portion of a college campus to demonstrate that our algorithm can handle large robot teams , and a hardware - in - the - loop experiment conducted in our lab which incorporates sensor noise and uncertainty in robot position . through numerical analysis we also show how our new approach to partitioning represents a significant performance improvement over both common lloyd - type methods and the recent results in @xcite . the present work differs from the gossip lloyd method @xcite in three respects . first , while @xcite focuses on territory partitioning in a convex continuous domain , here we operate on a graph which allows our approach to consider geodesic distances , work in non - convex environments , and maintain connected territories . second , instead of a pairwise lloyd - like update , we use an iterative optimal two - partitioning approach which yields better final solutions . third , we also present a motion protocol to produce the sporadic pairwise communications required for our gossip algorithm and characterize the computational complexity of our proposal . preliminary versions of this paper appeared in @xcite and @xcite . compared to these , the new content here includes : ( 1 ) a motion protocol ; ( 2 ) a simplified and improved pairwise partitioning rule ; ( 3 ) proofs of the convergence results ; and ( 4 ) a description of our implementation and a hardware - in - the - loop experiment . in section [ sec : prelim ] we review and adapt coverage and geometric concepts ( e.g. , centroids , voronoi partitions ) to a discrete environment like a graph . we formally describe our robot network model and the discrete partitioning problem in section [ sec : algorithm ] , and then state our coverage algorithm and its properties . section [ sec : convergence ] contains proofs of the main convergence results . in section [ sec : results ] we detail our implementation of the algorithm and present experiments and comparative analysis . some conclusions are given in section [ sec : conclusion ] . in our notation , @xmath1 denotes the set of non - negative real numbers and @xmath2 the set of non - negative integers . given a set @xmath3 , @xmath4 denotes the number of elements in @xmath3 . given sets @xmath5 , their difference is @xmath6 . a set - valued map , denoted by @xmath7 , associates to an element of @xmath3 a subset of @xmath8 .

the algorithm has two components : ( 1 ) a motion protocol to ensure that neighboring robots communicate at least sporadically , and ( 2 ) a pairwise partitioning rule to update territory ownership when two robots communicate . by studying an appropriate dynamical system on the space of partitions of the graph vertices , we prove that territory ownership converges to a pairwise - optimal partition in finite time . this new equilibrium set represents improved performance over common lloyd - type algorithms . additionally , we detail how our algorithm scales well for large teams in large environments and how the computation can run in anytime with limited resources . finally , we report on large - scale simulations in complex environments and hardware experiments using the player / stage robot control system .

we propose distributed algorithms to automatically deploy a team of mobile robots to partition and provide coverage of a non - convex environment . to handle arbitrary non - convex environments , we represent them as graphs . our partitioning and coverage algorithm requires only short - range , unreliable pairwise `` gossip '' communication . the algorithm has two components : ( 1 ) a motion protocol to ensure that neighboring robots communicate at least sporadically , and ( 2 ) a pairwise partitioning rule to update territory ownership when two robots communicate . by studying an appropriate dynamical system on the space of partitions of the graph vertices , we prove that territory ownership converges to a pairwise - optimal partition in finite time . this new equilibrium set represents improved performance over common lloyd - type algorithms . additionally , we detail how our algorithm scales well for large teams in large environments and how the computation can run in anytime with limited resources . finally , we report on large - scale simulations in complex environments and hardware experiments using the player / stage robot control system .

1410.3104

i

the last years have witnessed the development of heterogeneity in clusters and datacenters . two main reasons have led to this situation today . the first one is due to the maintenance and evolution of the components in the datacenters : different generations of computers are commonly seen in production datacenters since the owners are not changing everything at each update . the second reason is driven by the idea that heterogeneity might be the key to achieving energy - proportional computing @xcite , especially for high - performance computing applications . many recent studies alert dramatically on the energy consumption of the datacenters . for instance , koomey s report @xcite claims that today s datacenters are consuming nearly 2% of the global energy , and up to half of that is spent on cooling - related activities @xcite . this results generally in very poor power usage effectiveness ( pue ) . in this paper , we study the multi - objective resource management problem for heterogeneous datacenters . besides the performance criterion , we also consider the energy consumption of the servers and their thermal impact on the datacenter cooling . the aim of our work is to optimize these objectives and to explore their tradeoffs . in particular , the energy consumption is partly due to the cooling efficiency in the datacenter @xcite , which is related to both the physical placement of the servers and the scheduling strategies when jobs dynamically enter and leave the system . the latter also affects the performance and the energy consumed by the servers . server placement in a computer room has been relatively less studied , especially its impact on the cooling efficiency . the reason for this lack of attention is mainly due to the fact that , when servers are homogeneous , their relative positions have no impact on the performance and computing energy . however , server placement can have an impact on the cooling infrastructure . the main observation is that one server might contribute to the temperature raise at the inlets of the other servers , due to the recirculation of heat in a datacenter . such mutual influence can be modeled by a heat distribution matrix among the servers . if one wants to keep the inlet temperature under a given threshold , the supplied air temperature has to be decreased accordingly by the cooling system , which in turn increases its energy consumption . in the presence of heterogeneous servers with different power consumptions and hence heat dissipation , the problem of find the optimal placement becomes complicated and , to the best of our knowledge , has not been studied . since it is not feasible to change dynamically the positions of the servers in a datacenter , we focus on static placement to minimize the cooling cost induced by different configurations . with a given server placement , the traditional problem of job scheduling in the heterogeneous environment remains . many previous work ( e.g. , @xcite ) considered only the performance criterion and hence focused on the jobs execution times . in order to address the power consumption issue in datacenters , however , application scheduling must employ a multi - objective approach by considering performance , energy and cooling together . to account for the fact that a scheduler has no future knowledge ( jobs arrive over time ) , we need an online scheduling strategy . instead of designing different independent algorithms , we design a greedy online scheduling framework that can be adapted easily by redefining the cost function , from a single objective to two or more objectives . to tackle the energy - performance tradeoff , we further introduce a fuzzy - based priority approach , which allows to explore the potential improvement in one objective while relaxing the other objective up to an acceptable range . this approach can be extended to incorporate more than two objectives in the framework . its principle is not limited to the case at hand and can potentially be applied to other multi - objective optimization problems . the main contributions of this paper are the following : * a static server placement heuristic to reduce the cooling cost for the servers in a datacenter . * a greedy scheduling framework and several cost functions to tackle single - objective scheduling ( for performance , energy , and cooling ) . * a fuzzy - based priority approach to handle the tradeoff between two conflicting objectives , and its extension to multi - objective optimization . these proposals are supported by extensive simulations conducted using real hardware specifications and software benchmarks , as well as experimentally verified cooling model and heat distribution matrix @xcite . specifically for the hardware , a server system with high packing density and integrated cooling support is chosen for the experiments , which we believe represents well an emerging class of highly integrated energy - efficient servers . the results demonstrate the flexibility of our scheduling framework and confirm the effectiveness of the fuzzy - based approach for exploring the energy - performance tradeoff in heterogeneous datacenter environments . our static server placement heuristic is also shown to provide much improved thermal distribution leading to significant reduction in cooling cost . the rest of this paper is organized as follows . section [ sec : statement ] formally states the system model and the scheduling problem . section [ sec : gmp ] describes our greedy server placement heuristic . section [ sec : scheduling ] presents the job scheduling framework , various cost functions and the fuzzy - based priority approach . the simulation results are shown in section [ sec : evaluation ] . section [ sec : related ] reviews some related work , and section [ sec : conclusion ] summarizes the paper and addresses future directions .

this leads to improved energy usage in a heterogeneous datacenter including the cooling of the computer rooms . we propose a heuristic to solve the server placement problem and we design a generic greedy framework for the online scheduling problem . we derive several single - objective heuristics ( for performance , energy , cooling ) and a novel fuzzy - based priority mechanism to handle their tradeoffs . finally , we show results using extensive simulations fed with actual measurements on heterogeneous servers . datacenter heterogeneity ; online scheduling ; server placement ; cooling ; multi - objective optimization .

we propose in this paper to study the energy- , thermal- and performance - aware resource management in heterogeneous datacenters . witnessing the continuous development of heterogeneity in datacenters , we are confronted with their different behaviors in terms of performance , power consumption and thermal dissipation : indeed , heterogeneity at server level lies both in the computing infrastructure ( computing power , electrical power consumption ) and in the heat removal systems ( different enclosure , fans , thermal sinks ) . also the physical locations of the servers become important with heterogeneity since some servers can ( over)heat others . while many studies address independently these parameters ( most of the time performance and power or energy ) , we show in this paper the necessity to tackle all these aspects for an optimal resource management of the computing resources . this leads to improved energy usage in a heterogeneous datacenter including the cooling of the computer rooms . we build our approach on the concept of heat distribution matrix to handle the mutual influence of the servers , in heterogeneous environments , which is novel in this context . we propose a heuristic to solve the server placement problem and we design a generic greedy framework for the online scheduling problem . we derive several single - objective heuristics ( for performance , energy , cooling ) and a novel fuzzy - based priority mechanism to handle their tradeoffs . finally , we show results using extensive simulations fed with actual measurements on heterogeneous servers . datacenter heterogeneity ; online scheduling ; server placement ; cooling ; multi - objective optimization .

1407.3554

r

if @xmath17 and @xmath18 are knots in @xmath15 , then @xmath1 . the proposition is trivial if one of @xmath17 or @xmath18 is the unknot , so suppose that both are non - trivial knots . assume also that @xmath22 . let @xmath232 be the `` swallow - follow '' torus in @xmath625 which swallows the @xmath18 summand and follows the @xmath17 summand ( see figure 6 ) . we apply theorem 3.23 by setting @xmath626 , noting that one component of @xmath627 is homeomorphic to @xmath628 , which will correspond to @xmath363 . what needs to be shown is that the untelescoped minimal splitting @xmath28 can be isotoped so that it meets @xmath232 only in essential simple closed curves , and such that each component of @xmath629 is separating . by its definition as a swallow - follow torus , @xmath232 is isotopic to @xmath630 , where @xmath55 is the decomposing annulus of the connected sum in @xmath626 , and @xmath181 the sub - annulus of @xmath631 which lies in the component of @xmath632 corresponding to @xmath628 . by proposition 1.21 , @xmath28 can be isotoped to intersect @xmath55 only in essential simple closed curves , and since each boundary component of @xmath629 is then a standard meridional curve of @xmath633 , every component of @xmath629 is separating in @xmath628 ( otherwise we could obtain a non - separating surface in @xmath15 ) . the hypotheses of theorem 3.23 ( which assume conventions 3.1 , 3.3 , and 3.9 ) can then be satisfied by isotoping @xmath232 sufficiently close to @xmath630 . now @xmath596 is the component of @xmath627 which is _ not _ homeomorphic to @xmath628 , but is instead homeomorphic to @xmath634 , where @xmath635 is the link in @xmath15 which has @xmath18 as one component , and a meridian @xmath636 of @xmath18 as its other component , and @xmath637 under this correspondence ( see figure 6 ) . furthermore , the slope in which @xmath28 has been made to intersect @xmath638 is the standard longitudinal slope determined by the meridian disk @xmath639 with @xmath640 and @xmath641 . thus the slope of the trivial dehn filling of @xmath642 which yields @xmath643 meets each component of @xmath644 exactly once , and theorem 3.23 applies to @xmath645 , yielding @xmath646 ( in yellow ) is seen as situated in @xmath647 , and @xmath364 is indicated with dashed lines lying on the `` swallow - follow '' torus @xmath232 . in the second diagram , @xmath596 is reimbedded in @xmath648 , and in the final diagram we see @xmath596 and @xmath364 as they look after inverting the image of @xmath232 under this reimbedding.,scaledwidth=95.0% ] this proof also works if the knots @xmath17 and @xmath18 are embedded in homology spheres ( or any pair of compact @xmath0-manifolds in which every closed embedded surface is separating ) . in general , however , it is important to keep in mind the delicacy theorem 3.23 ( and corollary 3.25 ) , whose assumptions are encoded in conventions 3.1 , 3.3 and 3.9 . in particular , the assumption of convention 3.3 that @xmath232 and @xmath28 are well - configured can not always be satisfied , as can be shown using straightforward examples in @xmath649 , where @xmath122 is a closed genus @xmath650 surface . thus corollary 3.25 can not be applied to prove the following plausible conjecture in the case @xmath651 in any obvious way . suppose @xmath175 is a compact @xmath0-manifold and @xmath232 is a separating , incompressible , orientable , genus @xmath652 surface properly embedded in @xmath175 . if @xmath363 and @xmath596 are the components of @xmath627 , then @xmath653 . similarly , the need for @xmath232 and @xmath28 to be well - configured is what keeps us from applying theorem 3.23 and corollary 3.25 to prove the analogue of theorem 4.1 for satellite knots . theorem 4.1 has some relation to the `` rank - genus conjecture '' for knot complements in @xmath15 . if we define @xmath654 to be the minimal number of generators for @xmath655 , then the rank - genus conjecture states : for all knots @xmath5 , @xmath656 . since a genus @xmath652 heegaard splitting of a knot complement induces a @xmath652-generator presentation of @xmath655 , it is clear that @xmath657 , but it remains unknown whether it is possible for this inequality to be strict . the rank - genus conjecture for closed @xmath0-manifolds is known to be false @xcite , even when restricted to the class of hyperbolic @xmath0-manifolds @xcite . this suggests that the rank - genus conjecture also fails for knot complements , and a pair of knots in @xmath15 whose tunnel number degenerated enough to violate theorem 4.1 would have given a counterexample , since the following analogue of theorem 4.1 for rank is trivial ( thanks to richard weidmann for pointing out the simple line of proof below ) . @xmath658 for any knots @xmath2 . @xmath659 is an amalgamated free product @xmath660 which retracts onto each of its factors . the fact that theorem 4.1 is true indicates that the class of knot pairs which experience high tunnel number degeneration is not a good place to look for counterexamples to the rank - genus conjecture after all . it might even be seen as a small vote in favor of the possibility that the rank - genus conjecture is valid for knot complements in @xmath15 .

we conclude for any pair of knots , where denotes the tunnel number of . it is not difficult to see that , although it takes some work to find examples where equality is achieved in this bound , , . it is known that for any pair of non - trivial knots in , and more generally that . in the case that and are small , it is known that ( the hard part of this is to show that ) , in fact this equation holds even under the assumption that and are meridionally small . another impressive lower bound is , which holds for any pair of non - trivial knots in ( in fact a more general analogue involving iterated connected sums is derived in ) . in this paper , we prove that for any pair of knots .

we prove a theorem which bounds heegaard genus from below under special kinds of toroidal amalgamations of-manifolds . as a consequence , we conclude for any pair of knots , where denotes the tunnel number of . the tunnel number of a knot can be defined by the equation , where denotes heegaard genus and is an open regular neighborhood of . in more intuitive terms , the tunnel number of a knot is the minimal number of `` tunnels '' that must be drilled through in order to make the resulting manifold a handlebody . the behavior of under the operation of connected sum has been studied extensively . it is not difficult to see that , although it takes some work to find examples where equality is achieved in this bound , , . it is also known that for some pairs of knots , , , and that the degeneration can be arbitrarily large , . perhaps most difficult is the task of finding lower bounds on . it is known that for any pair of non - trivial knots in , and more generally that . in the case that and are small , it is known that ( the hard part of this is to show that ) , in fact this equation holds even under the assumption that and are meridionally small . another impressive lower bound is , which holds for any pair of non - trivial knots in ( in fact a more general analogue involving iterated connected sums is derived in ) . in this paper , we prove that for any pair of knots . this bound was previously unknown , although there are many examples which show it to be best possible , including those of and . the proof is centered around the rather involved construction of so - called _ doppelgnger _ surfaces . in rough outline , the strategy of our proof is as follows . suppose without loss of generality that and let be realized via the satellite construction with as the companion and as the pattern . this means that lies in , and if is the standard unknotted embedding of the solid torus , then . if is a thin generalized heegaard surface of , then can be isotoped to intersect in a particularly nice way . taking into account certain information contained in the intersection , we can then construct the previously mentioned _ doppelgnger surface _ inside of a solid torus which , in certain important respects , imitates the placement of the surface in . as a result , forms a generalized heegaard surface of which amalgamates to a surface of lower genus than the amalgamation of . this yields the desired lower bound . in section 1 we introduce the notion of a _ generalized compression body _ , which form the basic pieces of and , and prove a series of essential cutting and pasting lemmas about them . section 2 then describes and works out the basic topology of so - called _ spoke graphs _ and _ spoke surfaces _ , which form the building blocks of the doppelgnger surface . section 3 then constructs in detail and proves that it has the desired properties , culminating in the main technical result of the paper , theorem 3.23 . in section 4 the bound is proved ( theorem 4.1 ) , and some topics related to it are briefly discussed . throughout this paper , denotes a _ closed _ regular neighborhood of in , , and , or equivalently , . we assume throughout that behaves well with respect to intersection , so that . if is a topological space , denotes the number of components of . an embedding of manifolds is said to be _ proper _ if is transverse to and . a _ proper isotopy _ is a homotopy through proper embeddings ( note that this does _ not _ imply that the boundary remains fixed ) . as an informal aid to the reader , topological spaces which are allowed to have multiple connected components will usually be denoted in calligraphic font , e.g. , , , whereas connected topological spaces will usually be denoted in standard font , e.g. , , .

1403.5074

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first order methods have recently been widely applied to solve convex optimization problems in a variety of areas including machine learning and signal processing . in particular , proximal gradient algorithms ( a.k.a . forward - backward splitting algorithms ) and their accelerated variants have received considerable attention ( see @xcite and references therein ) . these algorithms are easy to implement and suitable for solving high dimensional problems thanks to the low memory requirement of each iteration . moreover , they are particularly suitable for composite optimization , that is when a convex objective function is the sum of a smooth and a non - smooth component . this class of optimization problems arises naturally in regularization schemes where one component is a data fitting term and the other a regularizer , see for example @xcite . interestingly , proximal splitting algorithms separate the contribution of each component at every iteration : the proximal operator defined by the non smooth term is applied to a gradient descent step for the smooth term . in practice it is often relevant to consider situations where the latter operation can not be perfomed _ exactly_. for example the case where the proximal operator is known only up - to an error have been considered in @xcite . in this paper we are interested in the complementary situation where it is the gradient of the smooth term to be know up - to an error . more precisely , we consider the case where only stochastic estimates of the gradient are available and develop stochastic versions of proximal splitting methods . this latter situation is particularly relevant in statistical learning , where we have to minimize an expected objective function from random samples . in this context , iterative algorithms , where only one gradient estimate is used in each step , are often referred to as online learning algorithms . more generally , the situation where only stochastic gradient estimates are available is important in stochastic optimization , where iterative algorithms can be seen as a form of stochastic approximation . finally , stochastic gradient approaches are considered in the incremental optimization of an objective function which is the sum of many terms , e.g. the empirical risk in machine learning @xcite , see section [ ss : amm ] for a detailed discussion . in the next section we describe our contribution in the context of the state of the art . the study of stochastic approximation methods originates in the classical work of @xcite , and assumes the objective function to be smooth and strongly convex ; the related literature is vast ( see e.g. @xcite and references therein ) . an improvement of the original stochastic approximation method , based on averaging of the trajectories and larger step - sizes , is proposed by @xcite and @xcite . more recently , one can recognize two main approaches to solve general nonsmooth convex stochastic optimization . the first one uses different versions of mirror descent stochastic approximation , based on projected subgradient averaging techniques @xcite . similar methods have been extensively studied also in the machine learning community in the context of online learning , where the proof of convergence of the average of the iterates is often based on regret analysis and , the so called , online - to - batch conversion @xcite . the second line of research is based on stochastic variants of accelerated proximal gradient descent @xcite . the algorithm we consider is also a stochastic extension of proximal gradient descent , but corresponds to its basic version with no acceleration . indeed , as discussed below , a main question we consider is if accelerated methods yield any advantage in the stochastic case . the fobos algorithm in @xcite is the closest approach to the one we consider , the main two differences being 1 ) we consider an additional relaxation step which may lead to accelerations , and especially 2 ) we do not consider averaging of the iterates . this latter point is important , since averaging can have a detrimental effect . indeed , non - smooth problems often arise in applications where sparsity of the solution is of interest , and it is easy to see that averaging prevent the solution to be sparse @xcite . moreover , as noted in @xcite and @xcite , averaging can have a negative impact on the convergence rate in the strongly convex case . indeed , in this paper we improve the error bound in @xcite in this latter case . our study is developed in an infinite dimensional setting , where we focus on almost sure convergence of the iterates and non asymptotic bounds on their expectation . considering iterates convergence is standard in optimization theory and often considered in machine learning when sparsity based learning is studied @xcite . the theoretical analysis in the paper is divided in two parts . in the first , we study convergence in expectation in the strongly convex case , generalizing the results in ( * ? ? ? * section 3 ) to the nonsmooth case . we provide a non - asymptotic analysis of stochastic proximal gradient descent where the bounds depend explicitly on the parameters of the problem . interestingly , we obtain , in the strongly convex case , the same @xmath0 error bound that can be obtained from the optimal rate of convergence for function values as achieved by accelerated methods , see e.g. @xcite . this result ( confirmed by numerical simulations ) suggests that , unlike in the deterministic setting , in stochastic optimization acceleration does not have an impact on the rate of convergence . in the second part , we establish almost sure convergence . our results generalize to the composite case the analysis of the stochastic projected subgradient algorithm in a hilbert space @xcite ( see also @xcite ) . our analysis is based on a novel extension of the analysis of proximal methods with exact gradient , based on considering random quasi - fejr sequences @xcite . this approach allows to consider assumptions on the stochastic estimates of the gradients which are more general than those considered in previous work , and does not require boundedness of the iterates . we note that a recent technical report @xcite also analyzes a stochastic proximal gradient method ( without the relaxation step ) and its accelerated variant . almost sure convergence of the iterates ( without averaging ) is proved under uniqueness of the minimizer , but under assumptions different from ours : continuity of the objective function thus excluding constrained smooth optimization and boundedness the iterates . convergence rates for the iterates without averaging are derived , but only for the accelerated method . finally , we note that convergence of the iterates of stochastic proximal gradient has been recently obtained from the analysis of convergence of stochastic fixed point algorithms presented in the recent preprint @xcite . however , this latter results is derived from summability assumptions on the errors of the stochastic estimates which are usually not satisfied in the machine learning setting . the paper is organized as follows . in section [ sec : psae ] we introduce composite optimization and the stochastic proximal gradient algorithm , along with some relevant special cases . in section [ s : alconv ] , we study convergence in expectation and almost surely that we prove in section [ sec : proofs ] . section [ s : exp ] describes some numerical tests comparing the stochastic projected gradient algorithm with state of the art stochastic first order methods . the proofs of auxiliary results are found in appendix [ s : bg ] . [ [ notation - and - basic - definitions ] ] * notation and basic definitions * + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + throughout , @xmath1 is a probability space , @xmath2 , and @xmath3 is a real separable hilbert space . we use the notation @xmath4 and @xmath5 for the scalar product and the associated norm in @xmath3 . the symbols @xmath6 and @xmath7 denote , respectively , weak and strong convergence . the class of lower semicontinuous convex functions @xmath8-\infty,+\infty\right]$ ] such that @xmath9 , is denoted by @xmath10 . the proximity operator of @xmath11 is @xmath12 throughout this paper , we assume implicitly that the closed - form expressions of the proximity operators to be available . we refer to @xcite for the closed - form expression of a wide class of functions , see @xcite for examples in machine learning . given a random variable @xmath13 , we denote by @xmath14 $ ] its expected value , and by @xmath15 the @xmath16-field generated by @xmath13 . the conditional expectation of @xmath13 given a @xmath16-algebra @xmath17 is denoted by @xmath18 $ ] . the conditional expectation of @xmath13 given @xmath19 is denoted by @xmath20 $ ] . a filtration of @xmath21 is an increasing sequence @xmath22 of sub-@xmath16-algebras of @xmath21 . a @xmath3-valued random process is a sequence of random variables @xmath23 taking values in @xmath3 . the shorthand notation ` a.s . ' stands for ` almost sure ' .

we prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems , where a convex objective function is given by the sum of a smooth and a possibly non - smooth component . we consider the iterates convergence and derive non asymptotic bounds in expectation in the strongly convex case , as well as almost sure convergence results under weaker assumptions . our approach allows to avoid averaging and weaken boundedness assumptions which are often considered in theoretical studies and might not be satisfied in practice .

we prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems , where a convex objective function is given by the sum of a smooth and a possibly non - smooth component . we consider the iterates convergence and derive non asymptotic bounds in expectation in the strongly convex case , as well as almost sure convergence results under weaker assumptions . our approach allows to avoid averaging and weaken boundedness assumptions which are often considered in theoretical studies and might not be satisfied in practice . proximal methods , forward - backward splitting algorithm , stochastic optimization , online learning algorithms .

math9903176

i

the plancherel measure is probability measure defined on the set @xmath5 of irreducible representations @xmath6 of any finite group @xmath7 . concretely , the measure of a representation @xmath6 is @xmath8 . it is called plancherel because the fourier transform @xmath9 is an isometry just like in the classical plancherel theorem . in this paper we will be dealing with plancherel measures for @xmath10 and their asymptotics as @xmath4 . the set @xmath11 is labeled by partitions @xmath3 of @xmath1 or , equivalently , by young diagrams with @xmath1 squares . we denote the plancherel measure by @xmath12 and recall that the dimension @xmath13 is given by several classical formulas such as the hook formula . logan and shepp @xcite and , independently , vershik and kerov @xcite ( see also the paper @xcite which contains complete proofs of the results announced in @xcite ) discovered the following measure concentration phenomenon for the plancherel measures for @xmath10 as @xmath4 . take a diagram @xmath3 , scale it in both directions by a factor of @xmath14 so that to obtain a shape of unit area , and rotate it by @xmath15 like in figure [ fig1 ] . the boundary of this shape is a polygonal line which is thickened in figure [ fig1 ] . in this way the plancherel measure @xmath16 becomes a measure on the space of continuous functions . it was shown in @xcite that as @xmath4 , this measure converges to the delta measure at the following function @xmath17 whose graph is drawn in figure [ fig2 ] . the constant 2 in means that the first part of @xmath3 should behave like @xmath18 as @xmath4 . indeed , it was shown in @xcite that @xmath19 in probability ( in @xcite the inequality @xmath20 was obtained ) . this constant 2 corresponds to the constant 2 in the ulam problem about the length of the longest increasing subsequence in a random permutation ; it was also obtained by different means in @xcite . about the history of the ulam problem see @xcite and vast literature cited there . the next term in the asymptotic of the plancherel measure was computed by kerov in @xcite who showed that the plancherel measure behaves like @xmath21 where @xmath22 is the following gaussian random process @xmath23 here @xmath24 are the tchebychef polynomials of the second kind @xmath25 and @xmath26 are independent standard normal variables . observe that near the endpoints @xmath27 the formula becomes inadequate because the series diverges at the endpoints . for more information about the behavior of the plancherel typical partition in the bulk of the limit shape the reader is referred to the recent paper @xcite . the behavior of the plancherel measure near the edges of @xmath28 $ ] has been the subject of intense recent studies and numerical experiments , see @xcite and references therein . it has been conjectured by baik , deift , and johansson that this behavior , suitably scaled , is identical to the behavior of the eigenvalues of a random hermitian matrix near the edge of the wigner semicircle . more precisely , consider a random @xmath29 matrix @xmath30 such that the real and imaginary parts @xmath31 are independent normal variables with mean 0 and variance @xmath32 . let @xmath33 be the eigenvalues of @xmath34 . introduce the variables @xmath35 @xmath36 then as @xmath4 the @xmath35 s have a limit distribution which was studied in @xcite and other papers . in particular , the correlation functions of this random point process have determinantal form with the airy kernel , see for example @xcite . the distributions of individual @xmath35 s were obtained by tracy and widom in @xcite ; they involve certain solutions of the painlev ii equation . similarly , let @xmath37 be a partition and set ( note the difference with in the exponent of @xmath1 ) @xmath38 baik , deift , and johansson conjectured that the limit distribution of the @xmath39 s exists and coincides with that of the @xmath35 s . they verified this conjecture for the distribution of @xmath40 and @xmath41 in @xcite and @xcite , respectively , using very advanced analytic methods . the aim of this paper is to give a direct combinatorial proof of proof of the following result . consider the points @xmath42 as a random measure on @xmath43 with masses 1 placed at the points @xmath39 , @xmath44 . consider its laplace transform @xmath45 this is a random process on @xmath46 . define @xmath47 similarly . denote expectation by angle brackets . [ t1 ] in the @xmath4 limit , all mixed moments of the random variables @xmath48 exist and are identical to those of @xmath47 , that is , @xmath49 for any @xmath50 and any numbers @xmath51 . from theorem [ t1 ] one obtains the following result about the distribution of the individual rows of a plancherel typical partition @xmath3 [ t1 ] in the @xmath4 limit , the joint distribution of @xmath52 is identical to the joint distribution of @xmath53 for any fixed @xmath54 . in our proof of theorem [ t1 ] we use the equivalence of two points of view on topological surfaces ( or algebraic curves ) . one way to think about a surface is to imagine it glued from polygons by identifying sides of polygons in pairs . such a representation is a combinatorial structure called a _ map _ on a surface . in connection with quantum gravity , it has been long known that maps are most intimately related to random matrices , see e. g. @xcite for an elementary introduction . another equally classical way of representing a surface is to realize it as a ramified covering the sphere @xmath55 , or in other words , as a riemann surface of an algebraic function of one complex variable . it is classically known that every problem about the combinatorics of covering has a translation into a problem about permutations which arise as monodromies around the ramification points . the two sides of have a combinatorial interpretation as asymptotics of certain maps and coverings , respectively . we produce a correspondence between the two enumeration problems and show that its deviation from being a bijection is negligible in the @xmath4 limit . the two sides of are also very directly connected to intersection theory on the moduli spaces @xmath56 of genus @xmath57 curves with @xmath58 marked points . namely , we show in section [ brown ] that our enumeration problem for maps ( or coverings ) is related to kontsevich s combinatorial model @xcite for intersection numbers on @xmath56 by , essentially , a reparametrization . this reparametrization involves passage times for the standard brownian motion . as a consequence , our enumeration asymptotics derived in theorem [ t3 ] , differs from the unique boxed formula of @xcite by replacing the laplace transform variables by their square roots . it follows that the limit is a close relative of the so called @xmath58-point function for the intersection numbers of the @xmath59-classes on @xmath56 . this can be used to compute the @xmath58-point function , see @xcite . it is tempting to speculate that both sides of must be certain riemann integral sums for the corresponding integrals over @xmath56 and the only difference between them is that one discretizes @xmath56 using maps and the other using coverings . for another application of asymptotics of coverings to evaluation of integrals over certain moduli spaces see @xcite . another connection between coverings and moduli spaces was obtained in @xcite . the reader would be hardly surprised to learn that our main technical tool on the symmetric group side are the jucys murphy elements @xcite . in recent years , they have become all purpose heavy duty technical tools in representation theory of @xmath10 , see for example @xcite . the observation that in the @xmath4 the spectral measures ( in the regular representation ) of these elements becomes the wigner semicircle was made by p. biane in @xcite . the existence of a connection between plancherel measures and random matrices has been actively advocated by s. kerov , see e.g. @xcite . the simplest evidence of such a connection is the fact that the so called transition distribution for the limit shape @xmath60 coincides with the wigner semicircle . random matrices also enter the representation theory of symmetric groups via the free probability theory . for a detailed discussion of the interplay between symmetric groups and free probability see the paper @xcite by p. biane . our results explain , at least to some extend , this connection . an analytic proof of the baik johansson conjecture was found subsequently in @xcite and , independently , in @xcite . this approach is based on an exact formula for the so - called correlation functions of the poissonized plancherel measure . same formula allows to analyze the local structure of a plancherel typical partition in the bulk of the limit shape , see @xcite . this exact formula for correlation functions is a special case of the result obtained in @xcite . the results of @xcite were considerably generalized in @xcite . the author would like to thank a. eskin for numerous discussions and p. biane for explaining the connection to brownian motion . the author was supported by nsf for under grant dms9801466 .

we prove the conjecture of baik , deift , and johansson which says that with respect to the plancherel measure on the set of partitions of , the rows of behave , suitably scaled , like the 1st , 2nd , 3rd , and so on eigenvalues of a gaussian random hermitian matrix as . our proof is based on an interplay between maps on surfaces and ramified coverings of the sphere . we also establish a connection of this problem with intersection theory on the moduli spaces of curves .

we prove the conjecture of baik , deift , and johansson which says that with respect to the plancherel measure on the set of partitions of , the rows of behave , suitably scaled , like the 1st , 2nd , 3rd , and so on eigenvalues of a gaussian random hermitian matrix as . our proof is based on an interplay between maps on surfaces and ramified coverings of the sphere . we also establish a connection of this problem with intersection theory on the moduli spaces of curves .

1607.08119

i

a common technique in theoretical and applied kinematics is the use of a point model for the group @xmath0 of rigid body displacements . one prominent example is the projectivised dual quaternion model of @xmath0 which exhibits particularly nice geometric and algebraic properties @xcite . in this article , we revisit some fundamental concepts related to this model , the transformation group generated by coordinate changes in the moving and the fixed frame and the kinematic images of dyads with revolute and prismatic joints . while numerous necessary conditions on these objects are well - known , we contribute sets of provably sufficient conditions . our characterisation of the transformation group generated by coordinate changes in fixed and moving frame ( ) is based on the pencil of quadrics spanned by the study quadric and null cone . these are quadrics corresponding to dual quaternions of real norm and purely dual norm , respectively . admissible transformations fix each member of this pencil and , in addition , preserve the two families of rulings on a further quadric in a subspace of dimension three . this leads to the important distinction between `` left '' and `` right '' rulings . at this point we also introduce a further invariant , the `` fiber projectivity '' , which will be crucial in our latter characterisation of dyads with prismatic joints in . the relative position of two rigid bodies can be constrained by a link or a sequence of links . fixing one of the two bodies , the collection of all possible poses ( position and orientation ) of the other is called a _ constrained variety . _ these are important objects in the study of open and closed kinematic chains , in linkage synthesis or analysis and other fields . in , we characterise constraint varieties generated by dyads of two revolute joints ( `` rr dyads '' ) as regular ruled quadrics in the study quadric that contain four complex rulings of the null cone . in we extend this result to dyads containing one prismatic and one revolute joint ( `` rp dyads '' and `` pr dyads '' ) . it is tempting to view them as limiting cases of rr dyads where one joint axis becomes `` infinite '' ( lies in the plane at infinity ) . indeed , their kinematic image is a regular ruled quadric in the study quadric that intersects the null cone in two complex lines and a real transversal line . nonetheless , this viewpoint is not complete because of the possibility of commuting r and p joints ( `` cylindrical joints '' ) . a closer investigation leads us to a more refined concept involving the fiber projectivity which allows to distinguish between the rp , the pr , and the cylindrical case . we conclude this paper with an application of our results to a recently presented non - injective extension of the classical kinematic map @xcite . here , commuting rp dyads appear naturally as kinematic images of straight lines . we use this to prove that the extended kinematic image of a straight line is , in general , a vertical darboux motion . some parts of this paper , mostly and the computations in the appendix , overlap with a previously published conference paper @xcite . the investigation on the group of admissible transformation in , the characterisation of rp and pr dyads in , and the relation of straight lines in extended kinematic image space to vertical darboux motions in are new .

preserve the two families of rulings of an exceptional three - dimensional quadric . the constraint variety of a dyad with two revolute joints is a regular ruled quadric in a three - space that contains a `` null quadrilateral '' . keywords : kinematic map , dual quaternion , study quadric , null cone , revolute joint , prismatic joint , fiber projectivity , vertical darboux motion .

we provide necessary and sufficient conditions for admissible transformations in the projectivised dual quaternion model of rigid body displacements and we characterise constraint varieties of dyads with revolute and prismatic joints in this model . projective transformations induced by coordinate changes in moving and/or fixed frame fix the quadrics of a pencil and preserve the two families of rulings of an exceptional three - dimensional quadric . the constraint variety of a dyad with two revolute joints is a regular ruled quadric in a three - space that contains a `` null quadrilateral '' . if a revolute joint is replaced by a prismatic joint , this quadrilateral collapses into a pair of conjugate complex null lines and a real line but these properties are not sufficient to characterise such dyads . we provide a complete characterisation by introducing a new invariant , the `` fiber projectivity '' , and we present examples that demonstrate its potential to explain hitherto not sufficiently well understood phenomena . keywords : kinematic map , dual quaternion , study quadric , null cone , revolute joint , prismatic joint , fiber projectivity , vertical darboux motion .

1607.08119

c

we provided necessary and sufficient geometric conditions on the transformation group induced by coordinate changes in the fixed and moving frame and on the kinematic image of 2r , rp , and pr dyads . while many properties of these objects are already known , sufficiency of certain collections of conditions seems to be new . we payed proper attention to the case of commuting joints ( which is trivial for rr dyads ) , highlighted the role of left and right rulings , and introduced the fiber projectivity . it is important in our characterisation of rp and pr spaces but also for the kinematic images of darboux motions , as illustrated in and .

we provide necessary and sufficient conditions for admissible transformations in the projectivised dual quaternion model of rigid body displacements and we characterise constraint varieties of dyads with revolute and prismatic joints in this model . projective transformations induced by coordinate changes in moving and/or fixed frame fix the quadrics of a pencil and

we provide necessary and sufficient conditions for admissible transformations in the projectivised dual quaternion model of rigid body displacements and we characterise constraint varieties of dyads with revolute and prismatic joints in this model . projective transformations induced by coordinate changes in moving and/or fixed frame fix the quadrics of a pencil and preserve the two families of rulings of an exceptional three - dimensional quadric . the constraint variety of a dyad with two revolute joints is a regular ruled quadric in a three - space that contains a `` null quadrilateral '' . if a revolute joint is replaced by a prismatic joint , this quadrilateral collapses into a pair of conjugate complex null lines and a real line but these properties are not sufficient to characterise such dyads . we provide a complete characterisation by introducing a new invariant , the `` fiber projectivity '' , and we present examples that demonstrate its potential to explain hitherto not sufficiently well understood phenomena . keywords : kinematic map , dual quaternion , study quadric , null cone , revolute joint , prismatic joint , fiber projectivity , vertical darboux motion .

0705.1384

i

the notion of pathwidth of a matroid has received some recent attention in the matroid theory literature @xcite , @xcite . this notion has long been studied in the coding theory literature , where it is used as a measure of trellis complexity of a linear code @xcite , @xcite , @xcite . however , there appears to be no standard coding - theoretic nomenclature for this notion . it has been called the state complexity of a code in @xcite , but the use of this term there conflicts slightly with its use in @xcite . so to avoid ambiguity , we will give it a new name here _ trellis - width _ which acknowledges its roots in trellis complexity . the relationship between matroid pathwidth and code trellis - width can be made precise as follows . to an arbitrary linear code @xmath4 over a finite field @xmath0 , we associate a matroid , @xmath5 , which is simply the vector matroid , over @xmath0 , of any generator matrix of the code . recall that in coding theory , a matrix @xmath6 is called a generator matrix of a code @xmath4 , if @xmath4 is the rowspace of @xmath6 . consequently , the matroid @xmath5 does not depend on the actual choice of the generator matrix , and so is a characteristic of the code @xmath4 . the code @xmath4 may in fact be viewed as a representation over @xmath0 of the matroid @xmath5 . the trellis - width of @xmath4 is simply the pathwidth of @xmath5 ; we will give the precise definition of matroid pathwidth in section [ pw_section ] . it has repeatedly been conjectured in the coding theory literature that computing the trellis - width of a linear code over a fixed finite field @xmath0 is np - hard @xcite , @xcite , ( * ? ? ? * section 5 ) . this would imply that the corresponding decision problem ( over a fixed finite field @xmath0 ) given a generator matrix for a code @xmath4 over @xmath0 , and a positive integer @xmath1 , deciding whether or not the trellis - width of @xmath4 is at most @xmath1 is np - complete . this decision problem has been given various names `` maximum partition rank permutation '' @xcite , `` maximum width '' @xcite and `` trellis state - complexity '' @xcite . an equivalent statement of the trellis - width conjecture above is the following : given a matrix @xmath7 over @xmath0 , the problem of computing the pathwidth the vector matroid @xmath8 $ ] is np - hard . in this paper , we prove the above statement for any fixed field @xmath0 , not necessarily finite . our proof is by reduction from the problem of computing the pathwidth of a graph , which is known to be np - hard @xcite , @xcite . thus , in particular , computing the trellis - width of a linear code over @xmath0 is np - hard , which settles the aforementioned coding - theoretic conjecture . the situation is rather different if we weaken the trellis - width decision problem above by _ not _ considering the integer @xmath1 to be a part of the input to the problem . in other words , for a fixed finite field @xmath0 , and a _ fixed _ integer @xmath9 , consider the following problem : + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ given a length-@xmath10 linear code @xmath4 over @xmath0 , decide whether or not @xmath4 has trellis - width at most @xmath1 . + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ the equivalent decision problem for matroid pathwidth would be to decide ( for a fixed finite field @xmath0 and integer @xmath9 ) whether or not a given @xmath0-representable matroid has pathwidth at most @xmath1 . based on results from the structure theory of matroids @xcite , we strongly believe that these problems are solvable in polynomial time . in the process of studying matroids of bounded pathwidth , we observe that for any finite field @xmath11 and integer @xmath9 , the class , @xmath12 , of @xmath13-representable matroids having pathwidth at most @xmath1 , is minor - closed and has finitely many excluded minors . as a relatively easy exercise , we show that the list of excluded minors for @xmath14 consists of with ground set @xmath15 and rank function @xmath16 to be @xmath17 for @xmath18 . therefore , what we consider to be matroids of pathwidth one would be matroids of pathwidth two in @xcite , @xcite . ] @xmath19 , @xmath20 , @xmath21 and @xmath22 . unfortunately , the problem of finding excluded - minor characterizations of @xmath12 for @xmath23 becomes difficult very quickly . we give a list of excluded minors for @xmath24 , which is probably not complete . the rest of the paper is organized as follows . in section [ prelim_section ] , we lay down the definitions and notation used in the paper . in section [ np_section ] , we prove that , for any fixed field @xmath0 , the problem of computing the pathwidth of an @xmath0-representable matroid is np - hard , and therefore , so is the problem of computing the trellis - width of a linear code over @xmath0 . finally , in section [ bounded_pw_section ] , we consider the class of matroids @xmath12 . we give the complete lists of excluded minors for @xmath14 and the corresponding family of linear codes over @xmath13 having trellis - width at most one . we also give a partial list of excluded minors for @xmath24 .

, we show that the problem of determining the pathwidth of a representable matroid is np - hard . , we also consider the class of-representable matroids of pathwidth at most , and correspondingly , the family of linear codes over with trellis - width at most . these are easily seen to be minor - closed . since these matroids ( and codes ) have branchwidth at most , a result of geelen and whittle shows that such matroids ( and the corresponding codes ) are characterized by finitely many excluded minors . we provide the complete list of excluded minors for , and give a partial list for . matroids , pathwidth , linear codes , trellis complexity , np - hard . 05b35 , 94b05

we relate the notion of matroid pathwidth to the minimum trellis state - complexity ( which we term trellis - width ) of a linear code , and to the pathwidth of a graph . by reducing from the problem of computing the pathwidth of a graph , we show that the problem of determining the pathwidth of a representable matroid is np - hard . consequently , the problem of computing the trellis - width of a linear code is also np - hard . for a finite field , we also consider the class of-representable matroids of pathwidth at most , and correspondingly , the family of linear codes over with trellis - width at most . these are easily seen to be minor - closed . since these matroids ( and codes ) have branchwidth at most , a result of geelen and whittle shows that such matroids ( and the corresponding codes ) are characterized by finitely many excluded minors . we provide the complete list of excluded minors for , and give a partial list for . matroids , pathwidth , linear codes , trellis complexity , np - hard . 05b35 , 94b05

astro-ph0310044

r

the physical parameters of the veelr filaments are tabulated in table 1 . the recession velocities of the filaments shown in column 5 are those of h@xmath0 . as the spectral resolution of our spectra , @xmath26 , is too low to allow accurate measurement of the velocity dispersion of the emission - lines , we list the values for clearly resolved , high signal - to - noise data in column 6 . instrumental broadening of the emission line was roughly corrected using the following simple equation : @xmath27 , where @xmath28 is the observed emission - line width and @xmath29 is the instrumental line width . column 7 of table 1 shows the names of individual clouds as given by yos02 . the electron densities @xmath30 were obtained from the intensity ratios of [ ] @xmath126717/ [ ] @xmath126731 under the assumption that the ionized gas temperature is 10@xmath31 k ( osterbrock 1989 ) . we found that the [ ] @xmath126731 lines of most filaments of the veelr are too weak , relative to the [ ] @xmath126717 line , to allow accurate determination of @xmath30 : that is , the @xmath30s of the veelr filaments are lower than @xmath32 @xmath33 . the emission - line intensity ratios of [ ] @xmath125007/h@xmath25 , [ ] @xmath126584/h@xmath0 , [ ] @xmath126717+@xmath126731/h@xmath0 and [ ] @xmath126300/h@xmath0 are summarized in table 2 . the velocity field of the veelr is shown in figure 3 . the velocities of almost all the filaments measured are blue - shifted relative to the systemic velocity of the galaxy . the velocities show a very wide range ( @xmath34 km s@xmath3 ) from @xmath35 km s@xmath3 to over @xmath36 km s@xmath3 . the overall velocity field of the veelr is quite complicated and could be dominated by significant turbulent motion . there is no smooth velocity gradient across the region . although we measured only a fraction of the filaments in the region , several kinematic groups seem to be represented ( see figure 4 ) . first , a string of relatively low velocity , @xmath35 km s@xmath3 @xmath37 km s@xmath3 , filaments ( hereafter referred to as the `` lv filaments '' ) was found along a line originating at around pa 65@xmath38 and @xmath39 ( 14.2 kpc ; m2 - 10 ) northeast from the nucleus and extended along pa 55@xmath38 . second , a group of high velocity , @xmath40 km s@xmath3 @xmath41 km s@xmath3 , filaments ( hereafter referred to as the `` hv filaments '' ) are distributed over the region . the hv filaments can be broken down into the following three groups : the `` ne - hv filaments , '' the `` n - hv filaments , '' and the `` w - hv filaments . '' the ne - hv filaments are a bow - like string of filaments that extend from the cloud at pa 65@xmath38 , @xmath42 ( around m2 - 14 ) to the north along pa 10@xmath38 . the n - hv filaments are a group of clouds at pa 40@xmath38 , @xmath43 ( around m1 - 5 and m2 - 6 ) , pa 32@xmath38 , @xmath44 ( m1 - 9 and m1 - 10 ) and pa 45@xmath38 , @xmath45 ( m1 - 11 and m2 - 11 ) . the w - hv filaments consist of a bright , dumbbell - like cloud , corresponding to the `` c26 '' of yos02 , located at pa 95@xmath38 and @xmath46 ( m1 - 1 , m1 - 2 and m2 - 5 ) , and a bright cloud at pa 70@xmath38 and @xmath47 ( m2 - 9 ) , corresponding to `` c25 '' of yos02 . third , there is a group of very high velocity clouds / filaments ( hereafter referred to as the `` vhv clouds '' ) around the region where pa@xmath48 , @xmath49 ( m1 - 7 , m1 - 8 , m2 - 7 and m2 - 8 ) . the typical radial velocity of the vhv clouds is @xmath50 km s@xmath3 , and one of these clouds even has a velocity of @xmath51 km s@xmath3 . the vhv clouds are embedded in a string of filaments that extend from pa 50@xmath38 , @xmath52 toward the north - northeast ( pa 15@xmath38 ) . this string of filaments contains the n - hv filaments and the vhv clouds . the morphology of this string suggests that the vhv clouds are part of one stream . if this were the case , the high velocity motion of the vhv clouds could be interpreted as a projection effect of the helical motion of a outflow stream . however , the helical motion velocity of the stream would then reach up to 200 km s@xmath3 , which is too fast to maintain the shape of the stream unless there is a very strong confinement force , such as a strong magnetic field . thus , the greater fraction of their high velocities can not be interpreted as a projection of a helical motion of the stream . instead , the vhv clouds must be accelerated radially by some as yet undetermined mechanism . these names for the groups ( the `` lv filaments , '' `` ne - hv filaments , '' `` n - hv filaments , '' `` w - hv filaments , '' and `` vhv clouds '' ) are given in column 8 of table 1 . in addition , the spectra of the ne plume kpc to the northeast of the galaxy ( e.g. , pogge 1988 ; colina 1992 ; petitjean and durret 1993 ; veilleux et al . the configuration of the extra - planar emission - line region of ngc 4388 was illustrated in figure 2 of yos02 . ] and the galaxy disk are labeled as `` nep '' and `` disk '' in column 8 of table 1 . the positions and possible extensions of these filament / cloud groups are overlaid on the velocity field of the veelr in figure 4 . figure 5 shows a position velocity diagram for the veelr . the horizontal axis of this diagram represents the distance from the nucleus in units of kpc . data points for different filaments / clouds groups are shown as different symbols in this diagram ( figure 5 ) . the groups of filaments mentioned above can be seen to be well separated in position velocity space . the emission - line spectra of the veelr filaments are characterized by forbidden line enhancement and are very different from those of extragalactic regions . figure 6 shows some examples of the spectra and figures 79 show diagnostic diagrams for optical emission - lines ( veilleux & osterbrock 1987 ) . two different ionization model loci are over - plotted in figures 79 . the dotted lines represent a power - law photoionization model calculated with the photoionization code cloudy ( cloudy 94.00 : ferland 1996 ) . we used a simple power - law continuum with a spectral index @xmath0 of @xmath53 as the incident light , assuming a plane parallel cloud geometry with an electron density @xmath30 of 30 @xmath33 and solar metal abundance . the dotted - dashed lines are the loci of the shock ionization model of dopita and sutherland ( 1995 ) . the loci shown here are for a shock only model with no pre - existing magnetic field . figures 79 show that the emission - line ratios of almost all the filaments are consistent with a power - law photoionization model with solar metal abundance , suggesting that the filaments have approximately solar abundance and are ionized by the power - law ionizing continuum emerging from the nucleus of ngc 4388 . this result is consistent with the conclusions regarding the ionization mechanism of the veelr reported in previous studies ( yos02 ; ciroi et al . the ionization parameter @xmath54 , which is the ratio of the number density of ionizing photons to that of electrons , of a typical filament of the veelr was estimated to be of the order of @xmath55 from the diagrams ( figure 79 ) . the filaments showing relatively high @xmath54 ( @xmath56@xmath55 ) tend to be distributed near the nucleus ( i.e ne - plume and inner n - hv filaments ) , whereas low @xmath54 ( @xmath57@xmath58 ) filaments are located far from the nucleus ( outer n - hv filaments and vhv filaments ) . this also supports the agn photoionization hypothesis . some filaments show low excitation spectra . low excitation emission - lines , such as [ ] and [ ] , are enhanced in the spectra of the w - hv filaments ( `` c26 '' ) . on the other hand , [ ] is relatively weak ( [ ] /h@xmath25 @xmath59 1 ) in these filaments , in contrast to other high excitation filaments . the emission - lines of the w - hv filaments are also considerably broad ( see the bottom right panel of figure 6 ) . the data points for these regions are distributed around the model locus of the shock model of dopita and sutherland ( 1995 ) with a shock velocity of 200 300 km s@xmath3 . these findings strongly suggest that the w - hv filaments are excited by shocks . the w - hv filaments exist outside the ionization cone of the ngc 4388 nucleus ( falcke , wilson , and simpson 1998 ; veilleux et al . 1999a , yos02 ) . yos02 remarked that the excitation mechanism of these `` out of the cone '' filaments is a mystery , pointing out that there is no counterpart to c26 in the broad - band images ( v and r@xmath60 images ) , so that it is not plausible that this filament is a bright region at the outskirts of the galaxy disk . shock may also contribute to the excitation of the other filaments . figure 10 shows the [ ] /h@xmath0 ratios of the veelr filaments as a function of velocity . this figure clearly shows that the [ ] line is enhanced in the vhv clouds ( see also the upper right panel of figure 6 ) . this velocity excitation coupling indicates that shocks , induced by the rapid motion , can also play a role in excitation of the filaments . ciroi et al . ( 2003 ) carried out a detailed analysis of the ionization of the veelr and the sw cone ( falcke , wilson & simpson 1998 ; yos02 ) using a composite model of photoionization and shock heating . they used the photometric data of yos02 for analysis of the veelr . the ionization parameters they obtained for the veelr filaments were distributed in the range 10@xmath61 10@xmath62 . these values are consistent with our results , although they are slightly lower . this subtle discrepancy may be attributed to the contribution of shock heating to ionization of the filaments . ciroi et al . ( 2003 ) suggested that shock heating gives rise to the ionization of the filaments , and derived shock velocities in the range @xmath63 150 km s@xmath3 . note that these values are almost consistent with the shock velocities suggested in the present study for the low excitation clouds of the veelr .

in addition to photoionization , shock heating probably contributes to the ionization of the gas . in particular , the filaments outside the ionization cone of the seyfert nucleus are mainly excited by shocks . the predicted shock velocity is 300 km s , which is comparable to the velocities of the filaments .

we report here the results of deep optical spectroscopy of the very extended emission - line region ( veelr ) found serendipitously around the seyfert 2 galaxy ngc 4388 in the virgo cluster using the subaru telescope . the h recession velocities of most of the filaments of the region observed are highly blue - shifted with respect to the systemic velocity of the galaxy . the velocity field is complicated , and from the kinematic and morphological points of view , there seem to be several streams of filaments : low velocity filaments , with radial velocities with respect to the systemic velocity of ngc 4388 km s , high velocity ( km s ) filaments , and a very high velocity ( km s ) cloud complex . the emission - line ratios of the veelr filaments are well explained by power - law photoionization models with solar abundances , suggesting that the seyfert nucleus of ngc 4388 is the dominant ionization source of the veelr and that the veelr gas has moderate metallicity . in addition to photoionization , shock heating probably contributes to the ionization of the gas . in particular , the filaments outside the ionization cone of the seyfert nucleus are mainly excited by shocks . the predicted shock velocity is 300 km s , which is comparable to the velocities of the filaments . we conclude that the veelr was formerly the disk gas of ngc 4388 , which has been stripped by ram pressure due to the interaction between the hot intra - cluster medium ( icm ) and the galaxy . the velocity field and the morphology of the veelr closely resemble snapshots from some numerical simulations of this process . in the case of ngc 4388 , the ram pressure - stripped gas , which is normally seen as extended filaments , happens to be exposed and ionized by the radiation from the agn , and so can be seen as optical emission - line gas .

astro-ph0310044

c

yos02 discussed the origin of the gas of the veelr from a morphological point of view , and concluded that there are two possibilities for the origin of the veelr : it is either the tidal debris of a past minor merger , or the disk gas of ngc 4388 stripped by the ram pressure of the hot icm . here , we examine these two scenarios using our new observational results , and discuss the origin of the veelr gas . as suggested in yos02 , ngc 4388 might have experienced at least one minor merger in the past . a minor merger affects the dynamics of the primary galaxy and leaves some imprints on its morphology ( hernquist & mihos 1995 ; mihos et al . peculiar morphological characteristics of ngc 4388 , such as its boxy bulge and central bar , and the faint hump and tail that extend outside the disk , could have formed as a result of the dynamic disturbance induced by a minor merger ( yos02 ) . if the veelr were the tidal debris of a merger of a gas - rich dwarf galaxy and ngc 4388 , the gas in the dwarf should have been stripped by the tidal force of ngc 4388 and the stripped gas would have been left near the path of the dwarf s fall . if this were the case , the velocity of the veelr gas relative to ngc 4388 should not exceed the infall velocity of the merging dwarf . however , the measured velocities of the veelr filaments are @xmath64 @xmath65 km s@xmath3 , and some filaments show much higher radial velocities , up to @xmath36 km s@xmath3 . these velocities are well beyond the escape velocity of ngc 4388 ( @xmath66 km s@xmath3 , where @xmath67 is taken to be 180 km s@xmath3 , following veilleux et al . 1999b ) and so are too high to apply the tidal debris scenario . in addition , the turbulent nature of the velocity field of the veelr is not consistent with the minor merger hypothesis . the tidal tails found in and around merging galaxies have smooth velocity fields and mild velocity gradients of the order of 1 10 km s@xmath3 kpc@xmath3 in general ( e.g. , smith 1994 ; hibberd et al . 1994 ; hibberd and yun 1999 ) . for example , the magellanic stream , the nearest example of tidal debris , has a velocity gradient of @xmath68 km s@xmath3 over a few tens of kpc ( mathewson , cleary & murray 1974 ) . the velocity field of the magellanic stream is also smooth and its kpc - scale velocity dispersion does not exceed @xmath69 km s@xmath3 . on the other hand , the veelr is highly turbulent ( see figures 3 , 4 ) . the velocities of the filaments range over 700 km s@xmath3 and abrupt velocity changes , with magnitudes of up to @xmath68 km s@xmath3 , are seen over the region . further , the emission - line spectra of the veelr filaments suggest that the metallicity of the veelr gas is almost at the solar value : there is no evidence that the gas is metal - poor . this is inconsistent with the hypothesis that the veelr gas was dragged out of a merged gas - rich dwarf galaxy , because a typical gas - rich dwarf galaxy has a metal abundance of 1/10 solar ( cf . vlchez & iglesias - pramo 2003 ) . these results seem to disfavor the minor merger hypothesis . as mentioned above , ngc 4388 might have experienced a minor merger in the past ( cf . yos02 ) , which may have given rise to part of the veelr . however , it is difficult to explain most of the spectroscopic properties of the veelr gas only with the minor merger hypothesis . therefore , we concluded that it is unlikely that the majority of the veelr gas is tidal debris from a past minor merger . the characteristics of the veelr described above can be naturally explained by the ram pressure stripping hypothesis . as noted in yos02 , the morphology of the veelr strongly resembles some snapshots from the inclined collision models of ram pressure stripping simulations conducted by abadi et al . ( 1999 ) , quilis et al . ( 2000 ) , vcbd , and ss01 . the one - sided elongation of the veelr suggests that ngc 4388 has a large transverse velocity toward the southwest . the h@xmath0 gas of the inner disk of the galaxy is abruptly truncated at a distance of 5 kpc from the nucleus on the western side , while on the eastern side of the galaxy faint ionized gas extends to the outside of the stellar disk ( figure 1a of yos02 ) . the gas distribution is also asymmetric in the same manner as the h@xmath0 gas ( cayatte et al . this peculiar gas distribution supports the hypothesis that the galaxy is moving in a southwesterly direction with a large transverse velocity and the disk gas is blown out by ram pressure induced by this galactic motion . the velocity field of the veelr can also be interpreted in the context of the ram pressure stripping scenario . while the recession velocity of ngc 4388 is approximately 1500 km s@xmath3 larger than the systemic velocity of the virgo cluster , the galaxy is thought to be located at the vicinity of the cluster core . thus , ngc 4388 is moving in the virgo cluster icm with a line - of - sight velocity of @xmath70 km s@xmath3 relative to the icm . hence , the blue - shifted velocity field of the veelr can be explained naturally : the collision between the galaxy and the hot icm strips the disk gas and the gas is blown in the direction opposite to the motion of the galaxy . assuming that the direction of the extension of ram pressure - stripped gas is almost the same as the direction of the icm wind in other words , the stripped gas is blown along the wind direction and that the inclination angle of the veelr with respect to our line of sight is 45@xmath13 , the transverse velocity is also @xmath71 km s@xmath3 and the total infalling velocity of ngc 4388 toward the virgo cluster center reaches @xmath72 km s@xmath3 . turbulent nature of the velocity field of the veelr can also be explained by high speed collision between the galaxy and the hot icm . strong ram pressure from the icm should induce turbulent motion in the stripped gas stream . as described above , there seem to be a number of groups of kinematically related filaments in the veelr : the lv filaments , the hv filaments , and the vhv clouds . vcbd presented some results of a series of numerical simulations based on inclined collision models of ram pressure stripping . edge - on snapshots of a model of vcbd with an inclination angle of 45@xmath13 and a colliding velocity of @xmath73 km s@xmath3 show that the disk gas of the primary galaxy forms two streams as it is stripped . one of the streams begins at the disk edge at the nearside of the icm wind and the other at the far side of the wind . the latter stream is removed from the disk more rapidly than the former . thus , it is suggested that the lv filaments correspond to the former stream , while the hv and vhv clouds are embedded in the latter . in addition , ram pressure stripping scnenario has no problem in explaining high metallicity of the veelr gas . it is natural for the extended gas to have the same metallicity , approximately solar value , to the galaxy disk , if the gas is stripped from the galaxy by ram pressure . therefore , the new spectroscopic data presented here led us to the conclusion that it is most likely that the veelr gas is the disk gas of ngc 4388 stripped by the ram pressure of the hot icm . a spatial coincidence between the veelr and the soft x - ray gas around ngc 4388 , which was found recently by detailed analysis of _ chandra _ archival data ( iizuka , kunieda & maeda 2003 ) also supports the ram pressure stripping hypothesis . if this is the case , we have detected ram pressure - stripped gas in the form of warm ( @xmath74 k ) ionized gas ( the veelr ) very far away from a cluster galaxy . the ionization of the stripped gas by a powerful agn , together with the deep imaging capability of an 8-m class telescope , have made it possible to detect this faint structure . although there have been many observational studies of ram pressure stripping phenomena ( e.g. , cayatte et al . 1990 ; gavazzi et al . 1995 ; phookun & mundy 1995 ; ryder et al . 1997 ; kenney & koopmann 1999 ; vollmer et al . 2000 ; vollmer , braine et al . 2001 ; bureau & carignan 2002 ) , the present study is the first to have revealed the detailed morphology and kinematics of the ram pressure - stripped gas over a few tens of kpc kpc ) warm ionized gas around the two irregular galaxies in the cluster of galaxies abell 1367 , and concluded that these are ram pressure - stripped material . this material is twice as large as the veelr of ngc 4388 , but its detailed morphology and the kinematics are not known . ] . in fact , the situation of ngc 4388 is rather special , in that the majority of the stripped gas happens to pass into the ionizing radiation cone of the seyfert nucleus , and as a consequence a part of the stripped gas is ionized and visible as optical emission - line gas . the case of ngc 4388 provides a rare opportunity to investigate the warm phase of ram pressure - stripped gas in detail . we discuss the veelr in the context of the ram pressure stripping hypothesis in the following sections . in this section , we briefly discuss the fate of the veelr gas and examine the possibility of star formation in the veelr . the discovery of the veelr indicates that some part of the ram pressure - stripped gas survives throughout the stripping process and does not evaporate for a significantly long time ( @xmath75 yr ) kpc and @xmath68 km s@xmath3 , respectively . assuming that the inclination angle of the veelr is 45@xmath38 , we estimated the age of the veelr as @xmath75 yr ] . vcbd pointed out that the disk gas of the galaxy would be stripped in the form of an ensemble of relatively dense cloudlets , each of which would be dense enough to prevent its evaporation in the hot icm during ram pressure stripping . those cloudlets would survive in the hot icm for a long time ( @xmath76 yr ) . according to vcbd , the stripped cloudlets would cool radiatively and become denser with time , so that molecules would be formed in their cores . ss01 also pointed out that the radiative cooling of ram pressure - stripped gas could be important in cases in which the stripped gas density is higher than a critical density , which is determined by the strength of the ram pressure . they estimated that the critical density would be of the order of @xmath77 @xmath33 for the virgo cluster ( ss01 ) . although our spectroscopic results did not provide a definite value for the electron densities of the veelr filaments ( they are too low to be derived from [ ] emission line ratios ) yos02 estimated the r.m.s . electron density of each filament to be @xmath78 @xmath33 from h@xmath0 photometry . hence , assuming a typical volume filling factor of interstellar ionized gas , @xmath79 ( e.g. , robinson et al . 1994 ) , for the veelr filaments , we estimate the local densities of the line emitting clouds to be @xmath80 @xmath33 . this is high enough to make radiative cooling dominant in the thermal balance of the stripped gas . the filamentary structure of the veelr also suggests that radiative cooling and thermal instability cause the stripped gas to condense . in the veelr , there are a number of filaments that could be ionized by the radiative shock induced by a collision between the disk ism and the hot icm . although the main ionization source should be the nuclear power - law radiation , shock waves accompanied with rapid motion could be responsible for the ionization of some hv filaments and vhv clouds . in fact , for some vhv clouds that are distant from the nucleus , low ionization emission - lines , such as [ ] or [ ] , tend to be enhanced , suggesting that shock heating plays some role in their ionization . successive shocks would condense the filaments significantly . therefore , the physical state of the veelr filaments allows them to form molecules internally , and to eventually form stars . recently , gerhard et al . ( 2002 ) found an intergalactic compact star - forming region near ngc 4388 . the location of the region is about 20 kpc north of the disk of ngc 4388 . although it is far away from the main stream of the veelr , it is worth noting that its distance from the galaxy is comparable to that of the extension of the veelr . this region might be a gas clump that has split off from the main stream of the veelr . if this is the case , this region is the first known example of star formation within ram pressure - stripped gas . our data suggest that ram pressure - stripped gas can survive for a long time after stripping and it might be dense enough to cool radiatively . as mentioned above , stars might be formed in such cool gas . it is , however , no better than a speculation . in order to obtain some conclusive results on intracluster star formation and its relationship with ram pressure - stripping phenomenon , deep observations of neutral gas , or co molecule , would be crucial . we compared the deep h@xmath0 and [ ] images of ngc 4388 taken by yos02 with radio observations to investigate how the active star formation of ngc 4388 affects the extra - planar plasma evolution . irwin et al . ( 1999 ) conducted vla 20 cm and 6 cm observations of ngc 4388 as a part of a series of studies of extended radio plasma around edge - on galaxies . they found very extended , faint radio emission on both sides of the disk of the galaxy at 20 cm . the morphology of this emission is peculiar : it has a `` cracked '' x - shape . it extends in three directions from the disk ( to the northwest , southeast , and southwest ) but not in the northeasterly direction , which is the direction of extension of the veelr . the radio images of irwin et al . are overlaid on the h@xmath0 image from yos02 in figure 11b . we found faint extra - planar spurs in the h@xmath0 image of ngc 4388 ( figure 11d ) . the directions of these spurs agree well with the direction of the extended radio emission . on the northeastern side of the galaxy , the bright ne plume and the veelr prevent the identification of such faint structures . irwin et al . ( 1999 ) also found , at 6 cm , a striking extension originating on the eastern side of the disk ( 10 east of the nucleus ) and extending northwards . the size of this extension is comparable to that of the ne - hv filaments , whereas it is located between the complex of the ne - hv filaments and the vhv clouds and the ne plume ( see figure 11c ) . in other words , the extra - planar radio plasma and the optical emission - line gas seem to be anti - correlated in spatial distribution . this raises the question of the significance of this spatial anti - correlation . the faint radio emission seen at 20 cm and the northeastern extension detected at 6 cm may be parts of a large x - shaped , starburst - driven superwind ( chevalier & clegg 1985 ; heckman , armus & miley , 1990 ; strickland & stevens 2000 ) from the disk of ngc 4388 . to the northeastern side of the outflow , the radio - emitting plasma may be accelerated by the turbulent motion of the ram pressure - stripped ionized gas through some particle acceleration mechanisms such as fermi acceleration or shock acceleration ( cf . webb et al . 2003 ; references are therein ) . the spatial anti - correlation between the emission - line gas and the radio - emitting plasma suggests an interaction between the two components . this effect might change the energy distribution of the radio - emitting plasma toward high energy , causing the spectral index of the northeast extension to become harder than the other wind plasma . thus , the counterpart of the northeast extension may be lost in the low energy band ( i.e. , 20 cm ) . the interaction between the veelr gas and the starburst superwind may also accelerate the veelr gas . the vhv clouds are located just outside of the northeast top of the 6-cm radio emission . this spatial coincidence supports the above suggestion . in other words , parts of the ne - hv filaments may be accelerated by the superwind and form the vhv clouds . this interaction would induce shock - waves in the vhv clouds and the shocks would excite the gas . the shock - like excitation property of the vhv clouds which was mentioned in section 4.2 is naturally explained by this scenario . an extended x - shaped structure has also been found in soft x - ray emission . the _ rosat _ hri image of ngc 4388 , reduced by colbert et al . ( 1998 ) , shows an x - shaped structure . although the scale of this emission is considerably smaller than the radio emission , the position angles of the legs of the `` x ' 's are in good agreement . the size and the luminosity of the hri emission is comparable to those of the hri emissions of the starburst galaxy ngc 2146 ( armus et al . recently , the extra - planar soft x - ray emission is found to be more extended toward the south of the galaxy at very faint level by a deep x - ray image of ngc 4388 taken by _ ( iizuka , kunieda , & maeda 2003 ) . as mentioned in section 5.1.2 . , the largest component of this faint x - ray emission is extended toward the north - eastern direction , which is attributed to the ram pressure stripping . the southern extension of this faint x - ray emission is seen like an extension of the central `` x '' shaped x - ray emission of _ rosat_. these x - ray characteristics also suggest that a superwind blows from the ngc 4388 disk and interacts with the veelr or the hot icm wind . the disk radio emission of ngc 4388 should be a result of active star - forming regions in the galaxy disk emission but also by many chimney - like structures , whch would be formed by supernovae explosions in the disk ( cf . norman and ikeuchi 1989 ) , seen in the faint level of the emission - line image ( see figure 5 of yos02 ) . ] . ss01 pointed out that the disk gas of the primary galaxy is significantly compressed in the early phase of ram pressure stripping . the mechanism of the compression is as follows : initially the disk gas is moved slightly in the direction of the icm wind , but then the offset gas experiences the gravitational force of the dark - matter halo and tends to fall back to the galactic plane . its motion is now in the opposite direction to the icm wind , so that the icm wind and the gravitational force compress the disk gas from both sides of the disk . this is the situation for a face - on collision , i.e. , one in which the galaxy is exposed to the icm wind face - on . in the case of an inclined collision , the disk gas is also compressed in the disk plane by ram pressure . vcbd have also discussed gas compression of this kind , occurring before prompt stripping . further , a third process , the gas `` annealing '' process discussed by ss01 , may be efficient in compressing the inner disk . in this process , angular momentum transport by spiral waves induced in the ram pressure stripping event leads to simultaneous expansion of the outer disk and compression of the inner disk . the models of ss01 suggest that by the time the outer disk has been stripped , the inner disk is significantly compressed . a combination of the above processes must lead to strong compression of the disk gas of ngc 4388 . vcbd estimated the compression factor of the gas surface density to be as high as 1.5 for the case of an edge - on collision . other studies have also suggested that gas compression by a factor of 2 3 should occur in the early phases of ram pressure stripping ( e.g. , fujita and nagashima 1999 ; ss01 ) . this high compression of disk gas should cause active star formation in the disk . assuming a schmidt law , where @xmath81 is the star formation rate per unit area and @xmath82 is the gas surface density . ] ( schmidt 1959 ) with a slope @xmath83 ( kennicutt 1998 ) , we find that the star formation rate ( sfr ) increases by a factor of up to 3 5 . in fact , the sfr of the ngc 4388 disk , estimated from the h@xmath0 emission , is @xmath84 m@xmath11 yr@xmath3 , which is consistent with the above value if we assume that the sfr was @xmath77 m@xmath11 yr@xmath3 before collision with the icm . finally , we discuss the global structure of the extra - planar emission - line region around ngc 4388 . the following emission - line regions are found in and around ngc 4388 : ( 1 ) disk regions , ( 2 ) the ne plume and the sw cone ( see figure 2 of yos02 ) , ( 3 ) faint extra - planar spurs ( figure 11d ) , and ( 4 ) the veelr . here , we propose an evolutionary scenario in which the above emission - line regions can be related to each other . in this scenario we assume that the prime mover of the evolution of the interstellar medium ( ism ) of ngc 4388 is the fast collision between the galaxy and the hot icm of the virgo cluster . initially , ngc 4388 was captured by the virgo cluster during the cluster s mass assembly process and started to fall into the central region of the cluster . once the galaxy began to experience ram pressure from the cluster icm , the ram pressure ( and the opposing gravitational force ) compressed the disk gas . this would have taken place @xmath85 yr before the galaxy reached the central region of the cluster . this gas compression caused a starburst in the disk . successive bursts of supernovae and stellar winds from clusters of young massive stars heated the ism , causing it to expand into intra - cluster space : i.e. , a starburst superwind was formed . at the same time , the outer disk gas of ngc 4388 began to be stripped by ram pressure . when the galaxy had passed through the cluster center , the ram pressure gradually started to decline and the stripped gas rotated slowly in the rotation direction of the host galaxy as a result of its angular momentum . ngc 4388 probably collided with the icm to the southwestern side of the disk . as the disk rotation and the ram pressure stripping force had the same direction on the western side of ngc 4388 , the western disk gas was the first to be dragged out of the galaxy . at the eastern side of the disk , where the directions of the disk rotation and the ram pressure force were opposite to each other , the disk gas lost its angular momentum due to deceleration by the ram pressure . this disk gas thus started to fall in toward the nucleus . in fact , this gas infall might have excited the nuclear activity , although the triggering mechanism of agn is not known in detail and this is just one of several possible hypotheses . recently , minor merger events have been proposed as a promising mechanism for triggering agn activity ( taniguchi 1999 ; kendall , magorrian & pringle 2003 ) . as pointed out in yos02 , the disk of ngc 4388 bears the marks of a past minor merger . hence , a minor merger might have occurred and triggered the agn at about the same time that ngc 4388 passed near the cluster center . to the northeast of the galaxy , the stripped gas formed an elongated filamentary structure as a result of the combination of its rotation and the ram pressure forces it experienced . according to vcbd , the stripped gas forms highly elongated structures like the veelr @xmath75 yr after the time when the ram pressure force reaches its maximum . therefore , ngc 4388 passed through the cluster central region @xmath75 yr ago and is now receding from the center of the virgo cluster . the interaction between the stripped gas and the starburst superwind accelerated the gas and changed the energy spectrum of the radio - emitting plasma . the radio jet from the agn of ngc 4388 was possibly accompanied by a warm gas outflow , and veilleux et al . ( 1999a ) suggested that this outflow might have formed the ne plume . however , we do not believe that the agn outflow was the primary factor in forming the ne plume , because ( 1 ) there is a large discrepancy between the pa of the radio jet and that of the ne plume , ( 2 ) the ne plume has a highly disturbed morphology compared to the winds seen in other agn wind cases , and ( 3 ) the velocity of the ne plume is comparable to that of the ne - hv filaments . in addition , the morphology of the ne plume resembles that of the ne - hv filaments . therefore , we conclude that most of the structure of the ne plume was formed by ram pressure stripping ( cf . corbin , baldwin & wilson 1988 ; petitjean & durret 1993 ) . the agn outflow possibly contributed to the formation of the ne plume , but if so its contribution must have been small . in the above scenario , the primary cause of the various phenomena occurring in ngc 4388 is the fast collision of the galaxy with the hot icm . we summarize the structure of the emission - line regions around ngc 4388 as a schematic drawing in figure 12 . the various phenomena in ngc 4388 the agn , the starburst , and the ram pressure stripping will last for only a comparatively short time . after another several tens of millions of years , these activities will cease or decay significantly . as the velocities of many veelr filaments exceed the escape velocity of ngc 4388 , most of the gas in the veelr will escape into intracluster space . on the other hand , the gas that is presently in the galaxy disk will remain there , because the ram pressure force acting on it will decay . therefore , ngc 4388 will be observed as an ` anemic ' spiral galaxy with no peculiar activity several tens of millions of years from now .

the velocity field is complicated , and from the kinematic and morphological points of view , there seem to be several streams of filaments : low velocity filaments , with radial velocities with respect to the systemic velocity of ngc 4388 km s , high velocity ( km s ) filaments , and a very high velocity ( km s ) cloud complex .

we report here the results of deep optical spectroscopy of the very extended emission - line region ( veelr ) found serendipitously around the seyfert 2 galaxy ngc 4388 in the virgo cluster using the subaru telescope . the h recession velocities of most of the filaments of the region observed are highly blue - shifted with respect to the systemic velocity of the galaxy . the velocity field is complicated , and from the kinematic and morphological points of view , there seem to be several streams of filaments : low velocity filaments , with radial velocities with respect to the systemic velocity of ngc 4388 km s , high velocity ( km s ) filaments , and a very high velocity ( km s ) cloud complex . the emission - line ratios of the veelr filaments are well explained by power - law photoionization models with solar abundances , suggesting that the seyfert nucleus of ngc 4388 is the dominant ionization source of the veelr and that the veelr gas has moderate metallicity . in addition to photoionization , shock heating probably contributes to the ionization of the gas . in particular , the filaments outside the ionization cone of the seyfert nucleus are mainly excited by shocks . the predicted shock velocity is 300 km s , which is comparable to the velocities of the filaments . we conclude that the veelr was formerly the disk gas of ngc 4388 , which has been stripped by ram pressure due to the interaction between the hot intra - cluster medium ( icm ) and the galaxy . the velocity field and the morphology of the veelr closely resemble snapshots from some numerical simulations of this process . in the case of ngc 4388 , the ram pressure - stripped gas , which is normally seen as extended filaments , happens to be exposed and ionized by the radiation from the agn , and so can be seen as optical emission - line gas .

astro-ph0310044

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using the subaru telescope , we carried out deep optical spectroscopic observations of the very extended emission - line region ( veelr ) found around the seyfert 2 galaxy ngc 4388 in the virgo cluster . the h@xmath0 recession velocities of most of the filaments in the veelr are highly blue - shifted relative to the systemic velocity of the galaxy . the velocity field is complicated and the range of velocities is considerably broad ( @xmath34 km s@xmath3 ) . there are a number of kinematically and morphologically distinct groups of filaments . we classified the filaments into the following groups : the low velocity ( `` lv '' ) filaments , the high velocity ( `` hv '' ) filaments , and the very high velocity ( `` vhv '' ) clouds . the hv filaments consist of the following spatially separated subgroups : the n - hv filaments , the ne - hv filaments , and the w - hv filaments . the emission - line ratios of the veelr filaments are well explained by power - law photoionization models with solar abundances , suggesting that the seyfert nucleus of ngc 4388 is the dominant ionization source of the veelr and that the veelr gas has moderate metallicity . shock heating also contributes to the ionization of some filaments . in particular , the western part of the hv filaments ( the `` w - hv filaments '' ) may be excited predominantly by shocks . we conclude that the veelr was formerly the disk gas of ngc 4388 , which has been stripped from the disk by the ram pressure caused by the interaction between the hot intra - cluster medium ( icm ) and the galaxy . the velocity field and the morphology of the veelr closely resemble snapshots taken from some numerical simulations of this situation . in the case of ngc 4388 , the ram pressure - stripped gas , which would ordinarily be seen as extended filaments , happens to be exposed and ionized by the agn light , and so can be seen as optical emission - line gas . this special situation makes it possible to study in detail environmental effects , especially ram pressure stripping by the hot icm , on the evolution of cluster galaxies and intracluster medium . finally , we point out that filamentary / clumpy structure of the veelr suggests that ram pressure - stripped gas may be cooled radiatively and be condensed to dense , small clouds as being extended into the inter - galactic space . in other words , most of the debris of ram pressure - stripping could be found as an ensumble of small filaments , if the filaments are not ionized by some energetic source like agns . thus high spatial resolution , deep survey may be important to make statistics of the ram pressure - stripping phenomena and its impact to the galaxy evolution . we are grateful to the staff of the subaru telescope for their kind help with the observations . we wish to thank curt struck for his useful comments and the referee for a constructive report . in addition , m. y. thanks the staff of okayama astrophysical observatory for their encouragement during the course of this work . this study was carried out using the facilities at the astronomical data analysis center , national astronomical observatory of japan . this research made use of nasa s astrophysics data system abstract service . this work was financially supported in part by the japan society for the promotion of science ( grant - in - aid for scientific research no . 14204018 ) . lccrrrcc m1 - 1 & 9.5 & 150 & 14.6 & -364 @xmath86 & 200 & c26 & w - hv + m1 - 2 & 10.5 & 160 & 11.1 & -251 @xmath87 & 530 & c26 & w - hv + m1 - 4 & 7.6 & 230 & 3.3 & -294 @xmath88 & 180 & c1 & n - hv + m1 - 5 & 8.6 & 450 & 21.1 & -183 @xmath86 & & c2+c3 & n - hv + m1 - 6 & 11.0 & 310 & 6.6 & -280 @xmath87 & & c11 & n - hv + m1 - 7 & 11.6 & 190 & 3.6 & -576 @xmath89 & & c15 & vhv + m1 - 8 & 13.2 & 260 & 4.6 & -564 @xmath87 & & c16 & vhv + m1 - 9 - 1 & 13.7 & 50 & 0.3 & -376 @xmath90 & & c18 & n - hv + m1 - 9 - 2 & 13.9 & 160 & 2.5 & -300 @xmath87 & & c18 & n - hv + m1 - 10 & 14.7 & 150 & 2.8 & -415 @xmath89 & & c19 & n - hv + m1 - 11 & 15.9 & 310 & 4.9 & -292 @xmath89 & 80 & c22 & n - hv + m1 - 12 & 18.5 & 110 & 0.7 & -20 @xmath91 & 320 & part of of1 & lv + m1 - 13 & 20.3 & 160 & 1.6 & -154 @xmath88 & & part of of1 & lv + m1 - 14 & 21.2 & 100 & 0.4 & -41 @xmath92 & & part of of1 & lv + m1 - 15 & 23.7 & 160 & 4.1 & -325 @xmath88 & 280 & part of of2 & ne - hv + m1 - 16 & 23.9 & 150 & 3.3 & -323 @xmath93 & & part of of2 & ne - hv + m1 - 17 - 1 & 27.2 & 80 & 0.6 & -145 @xmath94 & & part of of2 & lv + m1 - 17 - 2 & 27.4 & 100 & 0.8 & -438 @xmath95 & & part of of2 & ne - hv + m1 - 19 & 29.0 & 100 & 1.0 & -311 @xmath88 & & part of of4 & ne - hv + m1 - 20 & 30.1 & 80 & 0.3 & -217 @xmath96 & & part of of4 & ne - hv + m1 - 21 & 30.9 & 160 & 1.3 & -318 @xmath97 & & part of of4 & ne - hv + & & & & & + m2 - 1 - 1 & 2.9 & 150 & 21.0 & -215 @xmath86 & & part of ne plume & nep + m2 - 1 - 2 & 3.2 & 180 & 31.7 & -124 @xmath86 & 30 & part of ne plume & nep + m2 - 2 & 4.2 & 440 & 15.8 & -219 @xmath87 & 40 & part of ne plume & nep + m2 - 3 - 1 & 4.5 & 180 & 8.0 & -126 @xmath89 & 140 & part of ne plume & nep + m2 - 3 - 2 & 4.9 & 80 & 2.5 & -152 @xmath89 & & part of ne plume & nep + m2 - 4 & 6.1 & 130 & 1.4 & + 72 @xmath94 & & disk region & disk + m2 - 5 & 9.4 & 340 & 11.5 & -357 @xmath89 & & c26 & w - hv + m2 - 6 & 8.5 & 320 & 14.7 & -206 @xmath87 & 350 & c2+c3 & n - hv + m2 - 7 & 9.7 & 190 & 4.9 & -542 @xmath87 & & c8 & vhv + m2 - 8 - 1 & 10.6 & 100 & 1.3 & -765 @xmath98 & & c12 & vhv + m2 - 8 - 2 & 10.8 & 100 & 2.5 & -492 @xmath93 & 140 & c12 & vhv + m2 - 9 & 12.3 & 60 & 0.9 & -322 @xmath99 & 460 & c25 & w - hv + m2 - 10 & 14.0 & 80 & 0.6 & -62 @xmath96 & & part of of1 & lv + m2 - 11 & 15.9 & 230 & 4.3 & -322 @xmath97 & 230 & c22 & n - hv + m2 - 12 & 18.6 & 230 & 2.0 & -72 @xmath98 & 70 & part of of1 & lv + m2 - 13 & 20.3 & 80 & 0.7 & -134 @xmath100 & & part of of1 & lv + m2 - 14 - 1 & 22.0 & 130 & 1.1 & -276 @xmath101 & 250 & part of of2 & ne - hv + m2 - 14 - 2 & 22.7 & 340 & 2.7 & -493 @xmath91 & & part of of2 & ne - hv + m2 - 15 & 23.7 & 160 & 4.4 & -337 @xmath87 & 200 & part of of2 & ne - hv + m2 - 16 & 24.2 & 160 & 3.4 & -177 @xmath89 & 290 & part of of2 & lv + m2 - 17 & 25.9 & 360 & 9.2 & -179 @xmath89 & 280 & part of of2 & lv + m2 - 18 & 27.3 & 190 & 1.2 & -403 @xmath96 & & part of of2 & ne - hv + lccrrrrc m1 - 1 & -0.01 @xmath102 & -0.44 @xmath103 & -0.15 @xmath103 & -0.70 @xmath104 + m1 - 2 & 0.09 @xmath104 & -0.42 @xmath103 & -0.12 @xmath103 & -0.73 @xmath104 + m1 - 4 & 0.75 @xmath105 & -0.27 @xmath103 & -0.24 @xmath103 & + m1 - 5 & 0.78 @xmath105 & -0.42 @xmath103 & -0.33 @xmath103 & -0.90 @xmath104 + m1 - 6 & 0.67 @xmath105 & -0.05 @xmath103 & -0.05 @xmath103 & -0.58 @xmath104 + m1 - 7 & 0.81 @xmath106 & -0.03 @xmath103 & -0.02 @xmath103 & -0.75 @xmath102 + m1 - 8 & 0.58 @xmath105 & -0.04 @xmath103 & 0.00 @xmath103 & + m1 - 9 - 1 & & 0.01 @xmath107 & -0.14 @xmath105 & + m1 - 9 - 2 & 0.93 @xmath106 & 0.01 @xmath103 & -0.12 @xmath103 & -0.90 @xmath102 + m1 - 10 & 0.38 @xmath106 & -0.12 @xmath103 & -0.12 @xmath103 & + m1 - 11 & 0.69 @xmath106 & -0.53 @xmath103 & -0.36 @xmath103 & + m1 - 12 & & -0.61 @xmath105 & & + m1 - 13 & & -0.47 @xmath103 & -0.25 @xmath103 & + m1 - 14 & & & & + m1 - 15 & & -0.66 @xmath103 & -0.42 @xmath103 & + m1 - 16 & & -0.51 @xmath103 & -0.26 @xmath103 & + m1 - 17 - 1 & & -0.62 @xmath107 & -0.09 @xmath103 & + m1 - 17 - 2 & & & -0.37 @xmath107 & + m1 - 19 & & -0.57 @xmath103 & -0.30 @xmath103 & + m1 - 20 & & -0.56 @xmath105 & & + m1 - 21 & 0.68 @xmath102 & -0.30 @xmath103 & -0.28 @xmath103 & + & & & & + m2 - 1 - 1 & 0.84 @xmath105 & -0.25 @xmath103 & -0.12 @xmath103 & -1.16 @xmath102 + m2 - 1 - 2 & 0.91 @xmath105 & -0.31 @xmath103 & -0.23 @xmath103 & -0.95 @xmath104 + m2 - 2 & 0.97 @xmath105 & -0.42 @xmath103 & -0.39 @xmath103 & + m2 - 3 - 1 & 1.30 @xmath106 & -0.10 @xmath103 & -0.18 @xmath103 & + m2 - 3 - 2 & 0.90 @xmath105 & -0.16 @xmath103 & -0.24 @xmath103 & + m2 - 4 & & & -0.55 @xmath105 & + m2 - 5 & & -0.36 @xmath103 & -0.23 @xmath103 & + m2 - 6 & 0.71 @xmath105 & -0.39 @xmath103 & -0.27 @xmath103 & + m2 - 7 & 0.59 @xmath105 & 0.00 @xmath103 & 0.04 @xmath103 & + m2 - 8 - 1 & & -0.28 @xmath103 & -0.14 @xmath103 & + m2 - 8 - 2 & 0.65 @xmath106 & -0.11 @xmath103 & -0.10 @xmath103 & + m2 - 9 & & -0.15 @xmath107 & & + m2 - 10 & & & & + m2 - 11 & 0.98 @xmath108 & -0.33 @xmath103 & -0.17 @xmath103 & + m2 - 12 & & -0.74 @xmath106 & -0.25 @xmath103 & + m2 - 13 & & -0.96 @xmath104 & -0.24 @xmath103 & + m2 - 14 - 1 & & -0.48 @xmath107 & -0.37 @xmath107 & + m2 - 14 - 2 & & -0.63 @xmath105 & -0.35 @xmath103 & + m2 - 15 & -0.28 @xmath109 & -0.56 @xmath103 & -0.38 @xmath103 & -0.82 @xmath102 + m2 - 16 & & -0.56 @xmath103 & -0.29 @xmath103 & + m2 - 17 & -0.45 @xmath110 & -0.51 @xmath103 & -0.30 @xmath103 & -0.85 @xmath102 + m2 - 18 & & & 0.02 @xmath103 & +

we report here the results of deep optical spectroscopy of the very extended emission - line region ( veelr ) found serendipitously around the seyfert 2 galaxy ngc 4388 in the virgo cluster using the subaru telescope . the h recession velocities of most of the filaments of the region observed are highly blue - shifted with respect to the systemic velocity of the galaxy . the emission - line ratios of the veelr filaments are well explained by power - law photoionization models with solar abundances , suggesting that the seyfert nucleus of ngc 4388 is the dominant ionization source of the veelr and that the veelr gas has moderate metallicity . we conclude that the veelr was formerly the disk gas of ngc 4388 , which has been stripped by ram pressure due to the interaction between the hot intra - cluster medium ( icm ) and the galaxy . the velocity field and the morphology of the veelr closely resemble snapshots from some numerical simulations of this process . in the case of ngc 4388 , the ram pressure - stripped gas , which is normally seen as extended filaments , happens to be exposed and ionized by the radiation from the agn , and so can be seen as optical emission - line gas .

we report here the results of deep optical spectroscopy of the very extended emission - line region ( veelr ) found serendipitously around the seyfert 2 galaxy ngc 4388 in the virgo cluster using the subaru telescope . the h recession velocities of most of the filaments of the region observed are highly blue - shifted with respect to the systemic velocity of the galaxy . the velocity field is complicated , and from the kinematic and morphological points of view , there seem to be several streams of filaments : low velocity filaments , with radial velocities with respect to the systemic velocity of ngc 4388 km s , high velocity ( km s ) filaments , and a very high velocity ( km s ) cloud complex . the emission - line ratios of the veelr filaments are well explained by power - law photoionization models with solar abundances , suggesting that the seyfert nucleus of ngc 4388 is the dominant ionization source of the veelr and that the veelr gas has moderate metallicity . in addition to photoionization , shock heating probably contributes to the ionization of the gas . in particular , the filaments outside the ionization cone of the seyfert nucleus are mainly excited by shocks . the predicted shock velocity is 300 km s , which is comparable to the velocities of the filaments . we conclude that the veelr was formerly the disk gas of ngc 4388 , which has been stripped by ram pressure due to the interaction between the hot intra - cluster medium ( icm ) and the galaxy . the velocity field and the morphology of the veelr closely resemble snapshots from some numerical simulations of this process . in the case of ngc 4388 , the ram pressure - stripped gas , which is normally seen as extended filaments , happens to be exposed and ionized by the radiation from the agn , and so can be seen as optical emission - line gas .

1103.4370

c

magnetically regulated models predict that a yso will be surrounded by a pseudo - disk a few thousand au in size , and that the pseudo - disk symmetry axis will be aligned or nearly so with that of the yso bipolar outflow . in this sub - section we will explore the extent to which this is the case for our three sources . in the case of l1527 , hogerheijde & sandell ( 2000 ) used a two gaussian model to separate the 450 and 850 @xmath0 m emission of an inner compact core immediately surrounding the embedded yso from the more extended emission . their table 3 shows a deconvolved fwhm compact core size of 10@xmath8 @xmath7 5@xmath8 ( 1400 au @xmath7 700 au ) with a position angle of the major axis @xmath4 30@xmath5 east of north . however , the interferometric c@xmath34o map of this core by ohashi et al . ( 1997 ; see figure 5a ) , made with slightly higher spatial resolution and with the advantage that the extended emission is automatically removed , implies the major axis of the core is oriented north - south , but that the outer regions of the flattened core are distorted possibly by the bipolar outflow thus giving an impression of a tilt away from the north - south orientation when mapped with slightly poorer resolution and extended emission confusion . the bipolar outflow measured by hogerheijde et al . ( 1998 ) in @xmath35co and by zhou , evans & wang ( 1996 ) in @xmath36co has a position angle of 90@xmath5 east of north . thus l1527 is observed to have a flattened core on the scale of a few thousand au , consistent with an edge - on pseudo - disk with its symmetry axis aligned with the outflow axis . in the case of b335 , chandler & sargent ( 1993 ) observed a highly flattened core at 2.7 mm that is resolved only along the major axis , which has a size of @xmath37 ( 2000 au ) with a position angle of 20@xmath5 east of north ( see figure 7a ) . the bipolar outflow measured in @xmath35co by ourselves in this paper , hirano et al . ( 1988 ) and others has a position angle of 90@xmath5 east of north . thus b335 is observed to have a flattened core on the scale of a few thousand au , consistent with an edge - on pseudo - disk with its symmetry axis slightly tilted relative to the outflow axis by about 20@xmath5 . the core emission from ic 348-smm2 has not previously been observed in detail . we use our data to study the morphology of the core surrounding this source . figure 3a shows the underlying 350 @xmath0 m continuum emission intensity from ic348-smm2 which we measured with sharp . the 50% 350 @xmath0 m contour of this source has a major axis with a position angle of 60@xmath5 east of north . the diameter of this major axis is 27@xmath8 , compared to the perpendicular minor axis diameter of 20@xmath8 . however , the 50% contour probably does not represent the fwhm of the core surrounding ic348-smm2 . a more realistic estimation of the fwhm of the core would be the 65% contour , which represents the 50% contour level of the core after the subtraction of a more extended cloud background set at about the 30% contour level in figure 3a . the 65% contour major axis has a position angle of 56@xmath5 east of north , and the diameters of the major and minor 65% contours are 21@xmath8 and 15@xmath8 , respectively . if we assume an elliptical gaussian core , we can deconvolve these fwhm estimates with a 10@xmath8 fwhm gaussian beam to get a core size of 18@xmath8 @xmath7 11@xmath8 ( 5500 au @xmath7 3300 au ) at a position angle of 56@xmath5 . the size measured here is larger than for a typical pseudo - disk quoted in the literature by about a factor of two , but at our spatial resolution we are probably not resolving the true fwhm of the pseudo - disk , we are more likely measuring the outer extended region . the bipolar outflow measured by tafalla , kumar & bachiller ( 2006 ) in @xmath35co has a position angle of 17@xmath5 west of north . thus ic348-smm2 is observed to have a flattened core on the scale of several thousand au , consistent with the outer regions of an edge - on pseudo - disk with its symmetry axis tilted within 20@xmath5 relative to the outflow . in summary , we do see evidence for pseudo - disks and a tendency for alignment , within 20@xmath5 , of the pseudo - disk symmetry axis and the outflow axis for each of the ysos in our sample . our submillimeter polarization measurements displayed in figures 2a , 3a , and 4a do not give a measure of the strength of the magnetic field , but they do give an indication of the net magnetic field direction ( lazarian 2007 ) and the level of uniformity ( hildebrand et al . 2009 ) along a given line - of - sight . the net magnetic field direction along a given line - of - sight is perpendicular to the submillimeter polarization vector measured for that line - of - sight ( lazarian 2007 ) . figures 2b , 3b , and 4b display the direction of the magnetic fields surrounding l1527 , ic348-smm2 and b335 , respectively , as determined by the polarimetry @xmath38-vectors rotated by 90 degrees . we compare these field directions with our observations of the cores density structure ( i.e. , pseudo - disk ) and velocity structure ( i.e. , outflows , infall radii ) . we note , however , that our polarization data for the three cores likely contain contributions from both the magnetic field associated with the core under study as well as that associated with the larger surrounding cloud . to see this , recall ( section 1 ) that the maps shown by kirk et al . ( 2006 ) reveal large changes in field direction as one moves away from the center of a core into the surrounding cloud material ; and note that these changes occur at positions located about one arcminute ( @xmath48000 au ) from the centers of the kirk et al . ( 2006 ) cores , while our own maps extend out to distances of 7000 - 15,000 au from the central yso . thus a significant fraction of the emission we have observed may originate from the cloud at large , not the core under study . one way to account for such contamination is to flag polarization measurements made at positions having lower flux density . such measurements could be contaminated to a large degree by line - of - sight emission associated with the larger parent cloud . the fluxes we measure at the edges of our three maps range from @xmath45% to @xmath440% of the respective peak flux ( see contours in figures 2a , 3a , and 4a ) . we have chosen to set a `` contamination threshold '' at 25% of peak flux ; we will consider polarization measurements obtained at positions having flux below this threshold to be at risk of large amounts of contamination by polarized signals originating in the larger cloud . this choice is somewhat arbitrary , but it has the benefit of flagging polarization measurements coming from regions of very low flux while preserving most of our measurements ; we flag as unreliable just four measurements out of 22 . all of our @xmath39-vectors shown in figures 2b , 3b , and 4b are drawn with the same length and thickness , and those associated with total intensity levels below our contamination threshold are shown using dashed lines . figures 2b and 4b each contain one such suspect @xmath39-vector , and figure 3b contains two . also shown in figures 2b , 3b , and 4b are the bipolar outflow morphologies in these sources ( see the figure captions for references ) . in addition , these figures show circles depicting the measured outer limits of the infall regions in l1527 and b335 based on inverse p - cygni line profiles ( see captions for references ) . no measurement of the infall radius for ic348-smm2 has been made to date , but such an infall region is likely to have a radius range of 20@xmath8 to 30@xmath8 for an infall age similar to the ages of l1527 and b335 ( see table 2 ) . below we will assume an infall radius of 25@xmath8 when we compare our observational results to models . the models we will compare our data to are those of asl03a and als03b . these models consist of self - similar , self - gravitating , singular , isothermal toroids with various amounts of rotation and magnetization . the rotation speeds of the cores range from 0 to 0.5 times their thermal sound speeds and the magnetic - flux - to - mass - ratios of the cores range from from 0 to 0.5 . all models are supercritical in order for collapse to occur without external pressure . presumably the collapse phase occurs after ambipolar diffusion has occurred , producing the supercritical state in the core . als03b note , however , that even in the relatively weakened state of the fields , these fields are responsible for the formation of pseudo - disks , considerable transport of angular momentum , and the resulting size of the centrifugally supported keplerian disk during the collapse phase , and so can not be ignored . in figures 5 , 6 , and 7 we compare our data on l1527 , ic348-smm2 , and b335 , respectively , to the model displayed in figure 8c of als03b , a model with intermediate rotation and magnetic field strengths . it should be noted here that , except for the case where there is no magnetic field to flatten the core and provide polarization , the spatial resolution of our data precludes us from discerning between the various models presented in asl03a and als03b ( see figures 7 and 8 in als03b ) . als03b show ( their figure 7 ) that rotation has only a minor effect on the gas and magnetic field geometry at the spatial scales we are measuring here . however , the aim of our current study is not to test the finer points of magnetic regulated collapse models , but the gross predictions represented in figure 1 and evidence for magnetic field pinches . in addition to our spatial resolution constraints , it is important to bear in mind that our results represent an integration of polarizations along each line of sight , whereas the magnetic field given in figure 8c of als03b represents only the cross - section of the poloidal field on the plane of the sky for an edge - on pseudo - disk . if this cross - section were rotated round the symmetry axis of the pseudo - disk , an integration along a line - of - sight would result in a weakening of the pinch geometry to a more uniform field aligned with the symmetry axis . scrutiny of the results displayed in figures 2 & 3 reveals that the field structures in l1527 and ic348-smm2 are generally consistent with the magnetically regulated dynamical collapse models cited in the introduction in that they show : ( 1 ) pinched field line vectors on the scale of the measured or inferred infall regions for these cores ; and ( 2 ) field line vectors ( with a few exceptions discussed below ) that are basically aligned with the bipolar outflows ( once the distortion of a pinch is subtracted by eye using figures 5 & 6 ) . the exceptions mentioned in ( 2 ) are the three polarization vectors in the low - flux region to the south of ic348-smm2 , which imply an east - west magnetic field , and a vector immediately east of the emission peak of l1527 . a possible explanation for this latter vector is given later in this section . however , the east - west field lines in ic348-smm2 can not be explained in the context of a magnetically regulated model . it is possible these vectors may not be associated with the core of ic348-smm2 , since two of the three reside in a region which has emission less than 25% of the peak emission for the source , and the third resides in a region with emission that is 25.5% of the peak . although in general the polarization results agree with magnetically regulated models , in detail we see significant discrepancies beyond the exceptions mentioned above . the scale of the pinched structure in magnetically regulated models depends on the size ( i.e. , age ) of the infall region . outside the infall region , the magnetic fields should be uniform or nearly uniform , depending on the details of the pre - collapse , quasi - static contraction of the core . only within the infall regions should pinches of the field lines be significant . figure 6 shows how our @xmath39-vectors in ic348-smm2 ( with our assumed infall radius and ignoring the three @xmath39-vector exceptions to the south ) show a remarkable agreement with figure 8c from als03b if the symmetry axis of the pseudo - disk has a 17@xmath40 tilt with respect to the outflow as we measure for this source . the agreement of the predicted field geometry from the als03b model with our measured vector position angles is somewhat surprising since als03b figure 8c gives a cross - section of the poloidal field on the plane of the sky for an edge - on pseudo - disk , while our measurements are an integration along the line of sight . such an integration should smooth out the pinched structure to some degree . the fit by eye between the model and our measurements is not as good if the pseudo - disk symmetry axis in the model is instead aligned with the outflow axis . the fact that the magnetic field fit is better when the model is aligned to the measured pseudo - disk axis , rather than the outflow axis , is consistent with the hypothesis that the pinched magnetic field structure and the pseudo - disk are both products of magnetized contraction and collapse , whereas the outflow is probably a product of rotation . in ic348-smm2 , the rotation axis may not be exactly aligned with the overall magnetic field axis for the core . figure 5 shows that in l1527 our @xmath39-vectors broadly agree with a pinched magnetic field structure aligned with the pseudo - disk axis as shown in figure 8c of als03b , but the figure also shows that there are significant distortions beyond the uncertainties ( @xmath4111@xmath5 ) in the angles of the vectors . we see these distortions close to the edge and in one case beyond the infall boundary . a possible explanation for this additional distortion could be the bipolar outflow in this source which overlaps a significant portion of the region containing our measured vectors ( see figure 2 ) . the effects of bipolar outflows are not included in the models to which we are comparing our results ( asl03a ; als03b ; galli & shu 1993a , b ) . the bipolar outflow in l1527 may also be responsible for the exceptional vector identified previously , which lies immediately east of the l1527 emission peak . this vector implies a magnetic field direction that is almost perpendicular to the outflow . in this scenario , the outflow pushes core material , and therefore also core magnetic field lines , into two polar cones surrounding the bipolar outflow near the emission peak in l1527 , thereby giving rise to both the additional distortions near the edge of the infall boundary as well as the exceptional vector just east of the peak . evidence for conical cavities such as would be required in this scenario has been obtained via mid - ir scattered light observations by tobin et al . ( 2008 ) as well as interferometric measurements of hco@xmath42 by hogerheijde et al . the latter is shown in figure 2b . in addition , the submillimeter maps of hogerheijde & sandell ( 2000 ) and our 350 @xmath0 m map ( figure 2a ) show evidence of an x - like structure in the extended background emission about l1527 that overlaps the observed outflow in that region , implying that significant submillimeter emission ( and any polarization of such emission ) must be coming from the surface of the outflow conical cavities . could the bipolar outflow observed in l1527 have enough energy to distort the magnetic field structure linked to the gas it entrains ? the diagrams in figure 8 in als03b show the pinched magnetic field structures for a number of rotating , dynamically - collapsing toroids of different initial cloud magnetic field strengths . these diagrams also show the contours of @xmath43 ( the ratio of the thermal to magnetic energy density ) . close to the axis of symmetry @xmath43 is much less than one ( @xmath4 0.1 ) , further from the axis of symmetry @xmath43 increases to values above one . these values of @xmath43 can be used together with estimates of the thermal energy within a core to determine the energy density required of an outflow to distort the magnetic field within that core . the core thermal energy density for l1527 can be approximated by @xmath44 , where @xmath45 is given by the mass density of the 10@xmath46 @xmath3 molecular gas measured for the l1527 core about 10@xmath8 away from the center ( hogerheijde & sandell 2000 ) and c@xmath47 is the sound speed which is approximately 0.25kms@xmath32 ( zhou , evans & wang 1996 ) . the lower limit to the outflow energy density in l1527 is expressed as @xmath48 divided by the observed volume of the outflow lobes , where the measured values for @xmath49 ( the mass entrained in the outflows ) and @xmath50 ( the velocity of the entrained gas in the outflows ) are given in table 2 from hogerheijde et al . the volume of both outflow lobes can be approximated by @xmath51 , where @xmath52 , the extent of one lobe in l1527 , is given in table 2 and @xmath53 0.14 sr based on figure 6 in hogerheijde et al . ( 1998 ) showing the extent of the @xmath35co outflow in l1527 . the above imply that the energy density in the outflow is greater than the thermal energy density in the region 10@xmath8 from the peak of l1527 by about a factor of 100 . since in the als03b models the magnetic energy density is less than the thermal energy density away from the axis of symmetry , this implies that the outflow does have the energy required to distort the magnetic field where it disturbs the gas in the core away from the axis of symmetry . indeed , with the energy density of the outflow observed , even the magnetic field very close to the axis of symmetry could be distorted . the ratio of the outflow energy density to core thermal energy density in ic348-smm2 is similar to the ratio in l1527 , if one assumes similar gas densities and sound speeds for ic348-smm2 as measured for l1527 and the outflow parameters in table 2 for ic348-smm2 . but the outflow in ic348-smm2 does not overlap with our measured polarization vectors to a very great degree , so the outflow can not affect the alignment of the magnetic fields which are inferred by these polarization measurements . where there is overlap , the distortion would be minimal for field lines already parallel to the axis of the outflow if the opening angle of the outflow at that location is small as it is for ic348-smm2 ( @xmath4115@xmath5 ; see figure 3 ) . in summary , if one assumes that the low - flux exceptions in ic348-smm2 are not part of the core and one includes the effects of bipolar outflows on field alignment , then our observations of l1527 and ic348-smm2 are consistent with magnetically regulated models . at first glance , our two polarization vectors in b335 imply a magnetic field more perpendicular than parallel to the outflow axis . however , our two inferred @xmath39-vectors are not too different from what would be expected in the region just south - east of the b335 center based on figure 8c of als03b when this figure is aligned with the minor axis of the flattened core as measured by chandler & sargent ( 1993 ) ( i.e. , the symmetry axis of the inferred pseudo - disk ) . in this region of the model , the field lines are pinched towards the axis of symmetry ( see figure 7 ) . figure 7 also shows the @xmath39-vectors inferred from the 850 @xmath0 m polarimetry measurements of wlh03 as well as those inferred from our 350 @xmath0 m polarimetry measurements . our results are broadly consistent with the results of wlh03 , in that they agree with four of the six vectors in the south - east quadrant region of the b335 core , but not , however , with the one vector with which our measurements most nearly overlap . the 20 @xmath39-vectors of wlh03 and our 2 all lie inside the infall region outlined in figures 4 and 7 . the wlh03 results imply on average a more n - s magnetic field structure within b335 , but there is considerable distortion evident in the field lines implied by the 20 vectors , since the standard deviation of the position angles of the @xmath39-vectors is about three times the average measurement error for each vector . wlh03 concluded that the average field they measure in b335 is the direction of the field in the core when it collapsed , and that the flattened core seen in b335 is prolate ( rather than oblate ) with its symmetry axis parallel to the magnetic field . if this is the case , then b335 presents a counter example to the results obtained by tassis et al . ( 2009 ) who concluded the core model that best fits their sample of 24 high - mass cloud cores is an oblate core with the mean magnetic field more aligned with the short axis than the long axis . alternatively , the wlh03 data and ours could imply a more toroidal field in b335 than poloidal . but if this were the case then this is inconsistent with the model of als03b which includes rotation . in this model , only a small volume of a dynamically collapsing core contains twisted ( i.e. , toroidal ) magnetic fields . outside this small region the collapsing flow has yet to be spun up , and inside this region @xmath54 so the field lines are rigid . if b335 does contain a toroidal field configuration , then the als03b model fails to describe it ; there appears to be more twisting of the original poloidal magnetic field lines than can be explained in their model . yet another interpretation of the data , and the one we advocate in this paper , is that b335 is an extreme example of what is happening in l1527 ; the outflow in b335 has distorted the field lines in the core of b335 , either directly or indirectly by exciting more turbulence within the core , so the magnetic field seems to align n - s on average . could the outflow in b335 cause large field distortions in the core ? if we use the same analysis we used for l1527 , but with a core thermal speed of 0.23kms@xmath32 ( zhou et al.1993 ) , a core density at about 10@xmath8 from the center of @xmath4 10@xmath55 @xmath3 ( zhou et al . 1990 ; harvey et al . 2003 ) , the b335 values for the outflow parameters given in table 2 , and @xmath56 0.6 sr ( figure 2 in hirano et al . 1988 ) , then we find that the outflow energy density is about a factor of 6 higher than the core thermal energy density ( 10@xmath8 from the peak ) in b335 . our own outflow data shown in figure 4b give a total kinetic energy for the outflow within the region mapped ( i.e. , @xmath57 , summed over the velocity channels in the ranges 5.4 - 8.0 kms@xmath32 and 8.6 - 11.2 kms@xmath32 ) of 1.8 @xmath7 10@xmath58 erg , once a correction for the 10@xmath5 inclination of the outflow to the plane of the sky has been made . dividing this by the volume of the outflow as defined in figure 4b , we get a kinetic energy density of @xmath4 10@xmath59 erg @xmath3 , which is a factor of 3 higher than the core thermal energy density . this outflow energy density although not enough to distort the magnetic field close to the axis of symmetry of the pseudo - disk in b335 , is enough to distort the field further out . the outflow cavity outlined by the co observations in figure 4b is coincident with the region within the b335 core that most likely would have a magnetic field energy density that is greater than the outflow energy density ; beyond this outflow cavity the reverse is likely to be true . the outflow cavity is a region in which the gas and dust densities are low , and so it is a region of low 350 @xmath0 m emission along our line of sight . our polarization measurements are thus weighted away from the outflow cavity region towards those regions along our line of sight where the energy density of the outflow could distort the magnetic field structure . but why is this distortion observed to be so large in b335 compared to the distortion in l1527 ? the difference between b335 and the other two ysos presented here is that the bipolar outflow in b335 is much larger in length , width and apparent age than the outflows in l1527 and ic348-smm2 ( table 2 ) . therefore , the field lines within the b335 core could be highly distorted because the outflow has had time to plow through a greater portion of the core or excite greater gas turbulence in the core . in order to give some quantitative assessment of the magnetic field scenarios discussed above , and how they compare to other possible configurations , we carried out reduced chi - squared tests of our data using a number of different theoretical magnetic field configurations for each source . for each source we compared the @xmath39-vectors implied by our data to : ( 1 ) a uniform magnetic field model where the angle of the field is aligned with the mean @xmath39-vector angle implied by our data for that source ; ( 2 ) a uniform magnetic field model where the angle of the field is aligned with the outflow ; ( 3 ) a uniform magnetic field model where the angle of the field is aligned with the symmetry axis of the observed pseudo - disk for that source ; ( 4 ) a uniform magnetic field model where the angle of the field is aligned with the major axis of the observed flattened core ( or pseudo - disk ) for that source ; and ( 5 ) a pinched magnetic field aligned with the symmetry axis of the observed pseudo - disk as presented in figure 8c of als03b . note that model ( 4 ) also corresponds to the case where the magnetic field is toroidal . table 3 summarizes our results . each number in the table represents the reduced chi - squared value , @xmath60 , for the data specified for that column against the model for that row . the reduced chi - squared is calculated as @xmath61 where @xmath62 are the data representing the angles of the @xmath39-vector at various locations , i ; @xmath63 is the uncertainty in each data angle ; @xmath64 is the angle of the magnetic field at the location of each data point for a particular model ; and @xmath65 is the number of degrees of freedom for the data set . for these calculations , the values of @xmath66 were constrained to be @xmath6 90@xmath67 since our @xmath39-vectors have been derived from our polarization @xmath38-vectors which are invariant under 180 degree rotations . for cases where @xmath68 , a value of @xmath69| \le 90\arcdeg$ ] was substituted . for b335 , we carried out the same calculations using the data of wlh03 based on their figure 1 . @xmath70 should be close to 1 for a good fit . an inspection of table 3 shows that @xmath60 is close to this value only for the als03b model for ic348-smm2 and b335 when we consider only our data minus the exceptions discussed in section 3.2.1 . however the fits are not good for this model if we include the exceptions for ic348-smm2 , and if we include the wlh03 data for b335 . this is in agreement with our qualitative assessment above . for l1527 , although no model gives a good fit to our data , the two most favored are the als03b model and the uniform field aligned with the mean @xmath39-vector of our data for l1527 ( i.e. , 60@xmath67 east of north ) . our data do not differentiate between these two models , since our vectors lie mostly in two diagonal quadrants . if we had more data in the other two quadrants , a @xmath70 test would be able to differentiate between these two models . as it is , the @xmath70 results re - enforce our qualitative assessment above that although our data agree with the als03b model in a broad sense , there are enough deviations to it to require an explanation ; possibly a disturbance to the magnetic field structure due to the outflow in l1527 . further , based on table 3 , our data for l1527 , ic348-smm2 , and b335 clearly favor the als03b model over the toroidal " models , and the als03b model is slightly more favored than the models with a uniform field aligned with the outflow and a uniform field aligned with the pseudo - disk symmetry axis . this implies there is some evidence for a pinch in the magnetic field configuration for these sources . however , the data of wlh03 for b335 , in contradiction , favor the model with a uniform field aligned with the major axis of the flattened core over all the other models , although the fit is not good for this model , thus implying some other underlying magnetic field configuration must be present - possibly a configuration disrupted by the outflow in b335 . in summary , the chi - squared results in table 3 support the qualitative discussions we presented in sections 3.2.1 and 3.2.2 . we also compared our data to a random magnetic field model for each source . we did this by calculating the root - mean - square ( rms ) of the differences between the directions of the @xmath39-vectors at points lying spatially adjacent to one another in each of our sources . for l1527 we obtained 11 pairs of measurements separated by 10@xmath8 or @xmath71 ( see figure 2 ) and for ic348-smm2 we obtained 10 such pairs ( see figure 3 ) for our rms calculations . points separated by @xmath72 ( i.e. , one beam diameter ) or greater represent independent measurements . for l1527 we calculated an rms value for these differences in adjacent @xmath39-vector directions to be 19@xmath67 , and for ic348-smm2 a value of 15@xmath67 . we then carried out the same calculation on 10 randomly generated numbers ranging between -90 and 90 , and did this 50 times . the resulting rms values formed a peaked gaussian distribution with a mean of 51 and a dispersion @xmath73 . ( this mean is close to the theoretical rms of @xmath4 52 for randomly selected numbers between -90 and 90 . ) thus our rms values for l1527 and ic348-smm2 lie 5.5@xmath33 and 6@xmath33 , respectively , below the expected rms for randomly distributed @xmath39-vectors , implying that the magnetic fields in l1527 and in ic348-smm2 are not random in nature . we carried out the same rms calculation on two different sets of 13 pairs of adjacent @xmath39-vector measurements made by wlh03 in b335 ( see figure 7 ) , resulting in rms values of 42@xmath67 and 34@xmath67 . both values are much larger than the average uncertainties ( @xmath74 ) for the measurements reported in wlh03 . these rms values imply that the magnetic field is possibly more randomized in b335 than in the other sources . this latter point is consistent with our suggestion that the magnetic field in b335 is more distorted by its outflow than are the magnetic fields in l1527 and ic348-smm2 .

the models also predict a magnetic field pinch structure on a scale less than or comparable to the infall radii for these sources . in addition , if the core magnetic field aligns ( or nearly aligns ) the core rotation axis with the magnetic field before core collapse , then the models predict the alignment ( or near alignment ) of the overall pinch field structure with the bipolar outflows in these sources . we show that if one includes the distorting effects of bipolar outflows on magnetic fields , then in general the observational results for l1527 and ic348-smm2 are consistent with these magnetically regulated models . we can say the same for b335 only if we assume the distorting effects of the bipolar outflow on the magnetic fields within the b335 core are much greater than for l1527 and ic348-smm2 . we show that the energy densities of the outflows in all three sources are large enough to distort the magnetic fields predicted by magnetically regulated models .

we report new 350 m polarization observations of the thermal dust emission from the cores surrounding the low - mass , class 0 ysos l1527 , ic348-smm2 and b335 . we have inferred magnetic field directions from these observations , and have used them together with results in the literature to determine whether magnetically regulated core - collapse and star - formation models are consistent with the observations . these models predict a pseudo - disk with its symmetry axis aligned with the core magnetic field . the models also predict a magnetic field pinch structure on a scale less than or comparable to the infall radii for these sources . in addition , if the core magnetic field aligns ( or nearly aligns ) the core rotation axis with the magnetic field before core collapse , then the models predict the alignment ( or near alignment ) of the overall pinch field structure with the bipolar outflows in these sources . we show that if one includes the distorting effects of bipolar outflows on magnetic fields , then in general the observational results for l1527 and ic348-smm2 are consistent with these magnetically regulated models . we can say the same for b335 only if we assume the distorting effects of the bipolar outflow on the magnetic fields within the b335 core are much greater than for l1527 and ic348-smm2 . we show that the energy densities of the outflows in all three sources are large enough to distort the magnetic fields predicted by magnetically regulated models .

1004.1064

i

spherically symmetric potentials have become a well - established paradigm of colloidal science in past decades . @xcite this is because , at a sufficiently coarse - grained level , colloidal surface composition can be regarded as uniform with a good degree of confidence , so that relevant interactions depend only on relative distances among the particles . recent advances in chemical particle synthesis @xcite have however challenged this view by emphasizing the fundamental role of surface colloidal heterogeneities and their detailed chemical compositions . this is particularly true for an important subclass of colloidal systems , namely proteins , where the presence of anisotropic interactions can not be neglected , even at the minimal level . @xcite directional interactions introduce novel properties in such systems . these properties depend both on the number of contacts ( _ i.e. _ , the valency ) and the amplitude of these interactions ( _ i.e. _ , flexibility of the bonds ) , a notable example of this class being hydrogen - bond interactions , ubiquitous in biological , chemical , and physical processes . @xcite as a reasonable compromise between the high complexity of interactions governing the above systems and the necessary simplicity required for a minimal model , patchy - sphere models stand out for their remarkable success in this rapidly evolving field . @xcite see ref . for a recent review on the subject . within this class of models , interactions are spread over a limited part of the surface , either concentrated over a number of pointlike spots @xcite or distributed over one or more extended regions . @xcite while the former have the considerable advantage of a simple theoretical scheme @xcite which allows a first semi - quantitative description , the latter can easily account for both the effect of the number of contacts and their amplitude , unlike `` spotty '' interactions which are always limited by the one - bond - per - site constraint . in this paper we consider a particular model due to kern and frenkel @xcite of this patchy - spheres class wherein short - range attractive interactions of the square - well ( sw ) form are distributed over circular patches on otherwise hard spheres ( hs ) . interactions between particles ( spheres ) are then attractive in the sw - sw interfacial geometry or purely hard - sphere repulsive under the hs - sw or hs - hs interfacial geometries , and can sustain more than one bond in fact , as many as the geometry allows even in the case of a single patch assigned to each sphere . a number of real systems ranging from surfactants to globular proteins can be described with simplified interactions of these particular forms , with well - defined solvophilic and solvophobic regions , and despite their simplicity patchy hard spheres have already shown a remarkable richness of theoretical predictions . @xcite notwithstanding the discontinous nature of the angular interactions , highly simplified integral equation approaches are possible , @xcite but only very recently has a complete well - defined scheme , within the framework of the reference hypernetted - chain ( rhnc ) integral equation , been proposed and solved for patchy spheres . @xcite this integral equation belongs to a class of approximate closures which have been extensively exploited in the field of molecular associating fluids . @xcite its main advantage over other available approximations ( other than its less - accurate parent hnc closure ) lies in the fact that it relies on a single approximation , for the bridge function appearing in the exact relation between pair potential and pair distribution function @xmath4 , @xcite to directly yield structural and thermodynamic properties that include the helmholtz free energy and the chemical potential with no further approximations . @xcite in addition , it can be made to display enhanced consistency among different thermodynamic routes . @xcite this is an important point when analyzing fluid - fluid phase diagrams such as we propose to do here . we thus build upon our previous work with the one - patch potential @xcite to study the two - patch case and its relationship with its one - patch counterpart . in addition to rhnc integral equation results , we provide dedicated monte carlo simulations which can assess the performance of rhnc . we find that rhnc provides a robust representation of both structural and thermophysical properties of the two - patch kern - frenkel model for a wide range of coverage @xmath0 ( the ratio between attractive and total hard - sphere surface ) , extending from an isotropic sw to a bare hs potential . the competition arising between phase separation and polymerisation is discussed in terms of the angular dependence of the pair correlation function and the structure factor . finally , a comparison between the one - patch and two - patch phase diagrams shows a strong impact on the different morphology and stable structures obtained in the two cases . we also report numerical simulation results of the model in the region where the rhnc integral equations do not numerically converge , to explore the low temperature , small @xmath0 limit . we find that for @xmath5 it becomes impossible to investigate the low - temperature disordered phases , since the system quickly transforms into an ordered structure , which itself depends on the coverage value . indeed , on decreasing @xmath0 one progressively enters the region where the maximum number of contacts per patch evolves from four to two and eventually reaches the one - bond - per - patch condition . when three or four bonds per patch are possible , the observed ordered structure is a crystal of interconnected planes , while when only two contacts are possible , particles order themselves into a set of disconnected planes . the patchy interaction model examined here can be regarded as a prototype of a special colloidal architecture where there exist competitive interactions on the colloidal surface that drive , by free energy minimization , the different colloidal particles through a spontaneous self - assembly process into complex superstructures whose final target can be experimentally probed and properly tuned . @xcite the possibility , discussed in the present study , of identifying the position of the gas - liquid coexisting lines and its relative interplay with different structures , opens up fascinating scenarios in material science , on the possibility of novel material design exploiting a bottom - up process not requiring human intervention .

we report on a computer simulation and integral equation study of a simple model of patchy spheres , each of whose surfaces is decorated with two opposite attractive caps , as a function of the fraction of covered attractive surface . finally , we show that the stable ordered phase evolves on decreasing from a three - dimensional crystal of interconnected planes to a two - dimensional independent - planes structure to a one - dimensional fluid of chains when the one - bond - per - patch limit is eventually reached .

we report on a computer simulation and integral equation study of a simple model of patchy spheres , each of whose surfaces is decorated with two opposite attractive caps , as a function of the fraction of covered attractive surface . the simple model explored the two - patch kern - frenkel model interpolates between a square - well and a hard - sphere potential on changing the coverage . we show that integral equation theory provides quantitative predictions in the entire explored region of temperatures and densities from the square - well limit down to . for smaller , good numerical convergence of the equations is achieved only at temperatures larger than the gas - liquid critical point , where however integral equation theory provides a complete description of the angular dependence . these results are contrasted with those for the one - patch case . we investigate the remaining region of coverage via numerical simulation and show how the gas - liquid critical point moves to smaller densities and temperatures on decreasing . below , crystallization prevents the possibility of observing the evolution of the line of critical points , providing the angular analog of the disappearance of the liquid as an equilibrium phase on decreasing the range for spherical potentials . finally , we show that the stable ordered phase evolves on decreasing from a three - dimensional crystal of interconnected planes to a two - dimensional independent - planes structure to a one - dimensional fluid of chains when the one - bond - per - patch limit is eventually reached .

1004.1064

r

figure [ fig : fig9 ] shows the critical parameters for the case of particles with one and two patches , both reported as a function of the total coverage . here only mc results are reported in view of their precision and reliability . the @xmath29 limit corresponds to the sw case and coincides for both models . an analogous figure , for the case of adhesive patchy spheres ( the limit of the present model for vanishing ranges ) , has been reported in ref . within a simplified integral equation scheme . with respect to the adhesive limit , the range of coverages which can be explored numerically is significantly wider ( for both one - patch and two - patch cases ) . in the case of two patches , crystallization pre - empts the possibility of exploring the smaller values . in the one - patch case , the process of micelle formation , also observed experimentally , @xcite suppresses the phase - separation process @xcite at small @xmath0 values . the critical parameters decrease on decreasing @xmath0 for both one - patch and two - patch models . the behavior of @xmath161 can be explained on the basis of a progressive reduction of the attractive surface . the decrease in the critical density becomes significantly pronounced only for the smallest @xmath0 values and can be attributed to the lower local density requested for extensive bonding . such behavior is analogous to the suppression of the critical density observed when the particle valence decreases . @xcite in the @xmath0 region where it is possible to evaluate the critical parameters , @xmath161 and @xmath162 for the two - patch case are always larger than the corresponding one - patch values , a trend which can be tentatively rationalized on the basis of the ability to form a larger number of contacts and higher local bonded densities for the case in which both poles of the particles can interact attractively with their neighbors . no evidence of a crossing between the two geometries is observed . such a crossing has been predicted by a theoretical approach based on a virial expansion up to third order in density and appropriate closures of the direct correlation function . @xcite it is worth emphasizing that the above dependence on the number of patches , at a given coverage , provides clear evidence of the impossibility of rationalizing the change of the critical line on the basis of a trivial decrease of the attractive strength of interactions due to the reduction in coverage , as alluded to in section [ subsec : coex ] . for the sake of completness , we also report rhnc integral equation results for the most relevant thermodynamic quantities , as a function of the coverage @xmath0 . these are shown in table [ tab : tab2 ] for the same high - density state , @xmath108 at @xmath109 , considered above for structural information . here we present the reduced internal energy per particle and the reduced excess free energy per particle , @xmath163 and @xmath164 , respectively , the reduced chemical potential @xmath165 , the compressibility factor @xmath166 , and the inverse compressibility @xmath167 . these results may be compared with those of table iv in ref . listing the same quantities for the one - patch counterpart . ( we ignore the tiny difference in densities between the two calculated states . ) the last two columns give the reference hs diameter @xmath43 stemming from the variational rhnc scheme ( see ref . for details ) and the average coordination number within the wells @xmath168 , whose one - patch counterparts are included in tables iv and v of ref . , respectively . note that @xmath168 here is systematically larger than in the one - patch case , in qualitative agreement with the mc results of fig . [ fig : fig9 ] . within the rhnc integral approach , the analysis of the angular distribution of patches within the first shell given in section [ subsec : angular_dist2p ] revealed that the cylindrical symmetry of a pair of patches ( 2p case ) on each particle was very effective in driving the system to morphologically different configurations in the low ( @xmath169 ) and high ( @xmath170 ) coverage limits , as illustrated in fig . [ fig : fig7 ] . it is natural to expect a very different situation in the single - patch case ( 1p case ) . this is indeed the case as further elaborated below . for the single patch with @xmath130 coverage ( fig . [ fig : fig10 ] , bottom panels ( c ) and ( d ) ) parallel patches ( @xmath171 ) are more likely in the perpendicular direction ( @xmath172 or @xmath173 ) , whereas antiparallel patches ( @xmath174 ) are more likely in the forward direction ( @xmath175 ) . the case of perpendicular patches ( @xmath176 ) are conversely more or less equally distributed along the whole angular region @xmath177 . there is no qualitative difference between the situation of high ( @xmath108 ) and low ( @xmath132 ) densities as shown by the contrast between the bottom left ( c ) and right ( d ) panels . note that the result significantly contrasts with the corresponding results of the two - patches case depicted in fig . [ fig : fig7 ] . consider now the opposite situation of very large coverage ( @xmath129 ) ( fig . [ fig : fig10 ] , ( a ) ) where there is a single well - defined peak for antiparallel orientations ( @xmath174 ) in the backward direction ( @xmath178 ) . again , this markedly differs from the two - patch case ( fig . [ fig : fig7 ] , top left panel ( a ) ) , where there is a triple peak for aligned patches ( @xmath179 ) in the forward ( @xmath180 ) , perpendicular ( @xmath173 ) , and backward ( @xmath178 ) orientations . this is a dense state point . under diluted conditions , @xmath132 , we find a qualitatively similar behavior as in the dense case , with antiparallel alignment in the forward direction ( which can not be physically distingushed from the backward one ) . clearly the predominant antiparallel alignment is reflecting the tendency to micellization rather than polymerization which is built into the single patch symmetry . it is also interesting to contrast the coefficients of rotational invariants for the one - patch case with those obtained in the two - patch counterpart in fig . [ fig : fig7 ] . at variance with the two - patch case , here all coefficients are nonvanishing so that we consider the first nonvanishing instances , that is @xmath181 , @xmath182 , and @xmath155 , which are particularly useful as giving the projections over the important invariants . @xcite we have evaluated these coefficients for the same state points considered in the two - patch case in fig . [ fig : fig11 ] for both dense or diluted conditions and small or large coverages . in contrast with the two - patch case , here the effect of coverage appears to be less significant , as can be inferred by inspection of the dense case @xmath108 ( left panels ( a ) and ( c ) ) . for the @xmath181 case the projection coefficient along the ferroelectic invariant @xmath183 in appendix [ app : appb ] we find a negative correlation within the well both for @xmath129 ( top left panel ( a ) ) and @xmath129 ( bottom left panel ( c ) ) , as expected from the tendency to form antiparallel alignments . likewise , the projection @xmath182 along the dipolar invariant @xmath184 is found to be negative and numerically similar to @xmath181 at both coverages , again indicating negative correlation to dipolar alignment . the only positive correlation is found for the @xmath155 component , which does not distinguish between up and down symmetry , in qualitative agreement with the two - patch analogue . this situation is replicated in the diluted case ( right two panels ( b ) and ( d ) ) with different numerical values , thus indicating that these correlations are signatures of robust orientational trends induced by the the particular one - side symmetry of the single - patch potential

the simple model explored the two - patch kern - frenkel model interpolates between a square - well and a hard - sphere potential on changing the coverage . we show that integral equation theory provides quantitative predictions in the entire explored region of temperatures and densities from the square - well limit down to . for smaller , good numerical convergence of the equations these results are contrasted with those for the one - patch case . below , crystallization prevents the possibility of observing the evolution of the line of critical points , providing the angular analog of the disappearance of the liquid as an equilibrium phase on decreasing the range for spherical potentials .

we report on a computer simulation and integral equation study of a simple model of patchy spheres , each of whose surfaces is decorated with two opposite attractive caps , as a function of the fraction of covered attractive surface . the simple model explored the two - patch kern - frenkel model interpolates between a square - well and a hard - sphere potential on changing the coverage . we show that integral equation theory provides quantitative predictions in the entire explored region of temperatures and densities from the square - well limit down to . for smaller , good numerical convergence of the equations is achieved only at temperatures larger than the gas - liquid critical point , where however integral equation theory provides a complete description of the angular dependence . these results are contrasted with those for the one - patch case . we investigate the remaining region of coverage via numerical simulation and show how the gas - liquid critical point moves to smaller densities and temperatures on decreasing . below , crystallization prevents the possibility of observing the evolution of the line of critical points , providing the angular analog of the disappearance of the liquid as an equilibrium phase on decreasing the range for spherical potentials . finally , we show that the stable ordered phase evolves on decreasing from a three - dimensional crystal of interconnected planes to a two - dimensional independent - planes structure to a one - dimensional fluid of chains when the one - bond - per - patch limit is eventually reached .

hep-lat0110159

r

we have tested the lanl method using the ukqcd quenched data set . the simulation details are given in table [ sim ] and discussed in the appendix . the best analysis was possible at @xmath63 . to implement the lanl method we first fix @xmath46 . figure [ fexp1 ] shows the fractional contribution of the ground state to the correlators which appear in @xmath44 and @xmath62 with @xmath64 for the two types of correlators , @xmath65 and @xmath66 , that are available for this data set ( see appendix [ multifits ] ) . the ground state dominates by approximately timeslice 12 for all correlators . we use @xmath67 and as a check also @xmath68 . @xmath45 is allowed to vary in the region @xmath69 while being careful to avoid any overlap with the origin . we present the details of the calculation of @xmath1 for the heaviest @xmath70 using standard , @xmath12 , derivatives in table [ tone ] . the differences , @xmath71 and @xmath72 , are well determined for @xmath45 close to the origin , but rapidly decrease and become dominated by noise as @xmath45 increases to around timeslice 8 . the ratio of equation [ calanl ] agrees with the results obtained using a fit apart from @xmath73 . however , the lanl fit does not give a reasonable @xmath74 ( defined as @xmath75 ) until timeslice @xmath76 for @xmath66 correlators and @xmath77 for @xmath65 correlators . the lanl method is expected to achieve good fits in a region where the @xmath12 errors in @xmath35 ( equation [ pcacimp ] ) are not rapidly changing . in this region , the time dependence of @xmath78 can compensate for any corresponding variation in @xmath79 . this is likely to occur when there are only a few states contributing to @xmath44 and @xmath62 increases and the @xmath12 errors decrease one expects a reasonable fit to be possible including more excited states than on coarser lattices ] . ideally , in this region , the estimates of @xmath1 are stable with a variation of @xmath45 . any dependence on @xmath45 , or any difference between the results from the @xmath65 or @xmath66 correlators means that @xmath12 contributions to @xmath44 and @xmath62 are appearing in @xmath1 . the results from the lanl fits , with reasonable @xmath74s , are shown in figure [ figt ] . @xmath1 is stable with @xmath45 ( possibly excluding @xmath80 for @xmath66 correlators ) , although noise rapidly dominates as the fitting range becomes smaller . there is agreement between the values obtained using @xmath66 and @xmath65 correlators , and @xmath67 and @xmath81 . we can compare the range over which a good fit is found with the fractional contribution of the sum of the ground and first excited state to the correlators which make up @xmath44 and @xmath62 , shown in figure [ fexp1 ] . roughly , the earliest @xmath45 with @xmath75 corresponds to the timeslice when all but the first excited state and the ground state dominate the correlators ; since the @xmath66 correlators have a lower contribution from excited states , the ground state plus first excited state dominate at an earlier timeslice compared to the @xmath65 correlators and a smaller @xmath45 can be used . the results change quite significantly when we switch to improved derivatives . figure [ fig1 ] shows the effects of changing the derivatives on @xmath82 and @xmath83 for @xmath65 correlators . clearly , the time dependence of @xmath24 is much reduced in the range @xmath84 when improved lattice derivatives are used , indicating that most of the discretisation effects seen when using the standard derivatives are due to the @xmath12 error in @xmath79 associated with this derivative and not the @xmath0 errors which we are trying to cancel with @xmath78 . a similar but much less dramatic effect is seen for @xmath83 . this translates into much smaller values for @xmath72 , @xmath71 and @xmath1 , as seen in table [ ttwo ] and figure [ figt ] . for both @xmath65 and @xmath66 correlators , reasonable fits can be obtained with slightly smaller @xmath45 than with standard derivatives , suggesting @xmath85 $ ] in this region is not large . as figure [ figt ] shows , there is agreement to within @xmath86 between the @xmath65 and @xmath66 results , with the exception of the fit to @xmath65 correlators with @xmath87 , which disagrees significantly with the @xmath66 result over the same fitting range . this is presumably due to a larger @xmath0 in @xmath1 for the @xmath65 result , since these correlators have a larger contribution from first excited ( and higher ) states . this fit is on the borderline of being considered reasonable ; changing @xmath46 to @xmath81 , the @xmath74 drops further . we demonstrate the effect of @xmath0 improvement on @xmath88 , for various values of @xmath1 for @xmath65 correlators in figure [ fig1 ] . the discretisation errors in @xmath24 can be reduced using either standard or improved lattice derivatives , however , the latter requires a smaller value of @xmath1 . as expected @xmath35 is constant over the time range used in our fit , with the plateau being one timeslice longer in the case of improved derivatives . our improvement condition is defined in the chiral limit and the results for @xmath1 must be extrapolated to zero quark mass . details of this procedure are given in appendix [ secchiralca ] and the results are presented in figure [ figc ] and in table [ chiralttwo ] . in general , @xmath1 from using standard derivatives has a bigger statistical error than that obtained using improved derivatives since @xmath45 is larger and the chiral extrapolation is usually more severe . the latter point is illustrated in figure [ figd ] . from the discussion above , the large value of @xmath1 from standard derivatives is due to a large contribution to @xmath35 from the @xmath12 errors associated with these derivatives . these errors are @xmath53 dependent and should disappear in the chiral limit . the figure shows that @xmath1 drops significantly with quark mass , agreeing with the result from the improved derivatives in the chiral limit . in contrast @xmath1 from improved derivatives is much less dependent on the quark mass . comparing all results in figure [ figc ] we find @xmath89 from different derivatives , smearing and from different @xmath45 and @xmath46 are consistent in the chiral limit ( with the exception of @xmath80 for @xmath66 correlators ) . we also implemented the lanl lattice derivatives @xcite and found consistent results in the chiral limit . @xmath90 from @xmath65 correlators , fitting @xmath91 , using improved derivatives is taken as the final value for @xmath1 at this @xmath2 . the error reflects the spread in values for @xmath1 and indicates the uncertainty from some of the associated @xmath0 effects . we now consider applying the @xmath92 method at different @xmath2s . in principle , one should ensure , as accurately as possible , that the same improvement conditions are applied to determine @xmath1 as @xmath2 is changed . this ensures the systematic errors are correlated between different determinations and @xmath1 smoothly extrapolates to zero in the continuum limit . for example , we need to keep the proportion of the excited states to ground state contributing to @xmath93 fixed . this requires a tuning of the smearing function changes . ] , which was not possible in this study ( and was not attempted in reference @xcite ) . thus , we have chosen a fairly conservative error for @xmath1 to take into account the difficulty in applying the same improvement conditions for the other simulations . in principle any value of @xmath1 in figure [ figc ] is a valid estimate of the coefficient for a particular simulation . a more aggressive choice for @xmath1 would be , for example @xmath94 from @xmath66 correlators with @xmath95 . in the following , to keep the systematic errors as correlated as possible we extract final numbers for @xmath1 from @xmath65 correlators and improved lattice derivatives ( as used for our choice of @xmath1 above ) . in addition , the physical volume of the simulation should also be kept fixed when determining @xmath1 . we comment on this in the next section . considering the analysis at @xmath4 first , we present the results for @xmath1 in figure [ fig2 ] and table [ chiraltthree ] . in addition to the simulations on the @xmath97 volume with @xmath66 and @xmath65 correlators , @xmath1 was also calculated on a small ensemble of large volume ( @xmath98 ) configurations with @xmath99 smearing ( unfortunately no @xmath65 correlators were available ) . as discussed in appendix [ multifits ] , the fuzzed smearing was optimised for the ground state and hence the first excited state amplitude for the @xmath66 correlators is very small ; an estimate for @xmath1 could only be extracted for one value of @xmath45 . nevertheless , the @xmath66 and @xmath65 results are consistent and there is no significant variation with @xmath46 . a discrepancy was found , however , when comparing to the @xmath99 results on the larger volume . this can be seen in figure [ fig2 ] for @xmath1 at finite @xmath53 around the strange quark mass . there is a @xmath100 disagreement between the @xmath66 value for @xmath101 and the @xmath99 value at @xmath95 ( @xmath102 ) . the discrepancy between the results could be due to @xmath0 terms arising from the use of different smearings or it may indicate a finite volume effect . the @xmath97 lattice corresponds to a physical volume of approximately @xmath103 , which is probably too small to accommodate excited pseudoscalar states . @xmath1 itself is an ultra - violet quantity but may be affected by finite volume effects because of the matrix elements being used to determine it . we attempted to investigate finite volume effects by comparing masses and decay constants ( the matrix element @xmath104 , in @xmath79 , is related to @xmath105 ) on the two volumes . unfortunately , we were only able to extract these quantities for the ground state on the large volume . we found an @xmath106 or @xmath107 decrease in @xmath108 changing from the small to large volume and no significant change in @xmath105 ( this is in agreement with the results in reference @xcite ) . a more thorough investigation of finite volume effects is needed . if the physical volume was the same as at @xmath63 , it would not matter how dependent @xmath1 is on the size of the lattice , since it is a higher order effect . however , the finer lattice is @xmath109 smaller than that at @xmath63 . this must be considered when quoting an error on @xmath1 . the chiral extrapolations of at @xmath4 proved difficult for @xmath1 from the @xmath65 and @xmath66 correlators . apart from the @xmath65 result for @xmath110 , the errors on the extrapolated values are very large due to having to use a fit function quadratic in @xmath111 and/or only being able to fit to the lightest data points . the discrepancy of the @xmath112 result with the @xmath113 @xmath99 value is approximately @xmath107 . as noted in the previous section , to keep the same improvement conditions @xmath1 should be extracted using a @xmath45 with the same relative proportion of ground state to excited states as that used at @xmath63 . one possibility , concentrating on @xmath65 correlators , is to fix @xmath45 to correspond to the same physical time ; @xmath101 chosen at @xmath63 corresponds to approximately timeslice @xmath77 for @xmath4 . the statistical errors of @xmath89 for this @xmath45 are too large for the estimate to be useful in our later analysis . if we choose @xmath101 then the errors do not reflect the unresolved @xmath0 or finite volume effects mentioned above . these problems motivate us to discard the results for @xmath1 at this @xmath2 . at @xmath96 the situation is more straightforward as displayed in figure [ fig2b ] and table [ chiraltfour ] . there is consistency between the results from different smearings , where the fuzzed smearing is optimised in a similar way to that at @xmath4 , and also as @xmath45 is varied . we also found no change in the results if @xmath46 is increased and there was no difficulty with chiral extrapolation . keeping the same physical @xmath45 as at @xmath63 corresponds to using timeslice @xmath114 . unfortunately , the estimates of @xmath1 have fallen into noise at this point . however , given the stability of the results with @xmath45 we are unlikely to introduce significant systematic errors if we choose a fitting range of @xmath115 . thus , our final result at this @xmath2 is @xmath116 . the lattice volumes at @xmath63 and @xmath8 are fairly close in physical size , and we assume that the error on @xmath1 is sufficient to compensate for the small discrepancy . figure [ falpha ] compares our results with those of the alpha collaboration @xcite and the lanl group @xcite in the range of @xmath2s we have simulated . unfortunately , our errors on @xmath1 are quite large after chiral extrapolation . nevertheless , we obtained consistency with the lanl results , in particular at coarser lattice spacings . the lanl results are split up into those extracted using standard @xmath12 derivatives and those obtained using modified @xmath117 derivatives , mentioned in section [ capcac ] . the latter is closer to the choice of derivatives employed here and we find greater consistency with our results , at @xmath96 , in this case . the lanl results have smaller errors compared to our values even though our study has much higher statistics . we believe this is due in part to our more conservative error estimates to take into account the difficulty in applying the improvement conditions consistently as @xmath2 changes . in addition , the lanl group employed much heavier light quark masses , over a wider range , than in our analysis , and this led to lower statistical errors after chiral extrapolation . the results from the lanl method are very slowly varying with @xmath2 and do not change significantly from @xmath118 to @xmath8 . this is in agreement with the 1-loop perturbative results , also shown in the figure for @xmath9 @xcite , where @xmath119 @xcite . our results , with large errors , are consistent with the perturbative result , however the lanl values are somewhat higher . the uncertainty in the perturbative value , from higher order terms , is difficult to estimate . one could take anything between the square of the 1-loop term , @xmath120 to @xmath121 in the range of @xmath96 to @xmath122 . the 2-loop contribution would have to be quite large to obtain consistency with the lanl results @xcite . however , the calculation of this contribution would significantly reduce the uncertainty on @xmath1 ; the perturbative result is valid in the infinite volume limit and there is no @xmath0 ambiguity in @xmath1 terms remain in the axial - vector current . ] which is present in the nonperturbative determination and can be large , in particular at coarser lattice spacings . this can be seen when comparing our results ( and those of the lanl group ) with those of the alpha collaboration . at @xmath96 , all results are consistent , however , at coarser lattice spacings a large discrepancy appears as the alpha @xmath1 rapidly increases , @xmath123 from the pade expansion of the alpha results @xcite . however , it is more likely to be around @xmath124 @xcite . ] . this discrepancy indicates how large the @xmath0 ambiguity in @xmath1 can be . in addition , the lanl group using new results at @xmath125 have found that the difference between their results and that of the alpha collaboration requires @xmath12 terms as well as @xmath0 @xcite . we believe that by extracting @xmath1 in a region where only the first excited state and ground state contributes , looking for consistency between results from different smearings and using improved derivatives we have minimized the @xmath0 artifacts in @xmath1 within the lanl method . nonetheless , if the improvement conditions are kept fixed accurately as @xmath2 is changed , large variations in the estimates of @xmath1 are not important . however , practical difficulties arise if the choice taken leads to significantly worse scaling violations for physical predictions , namely , @xmath5 and the renormalised quark mass .

we find we are able to extract reliable estimates for the coefficient using this method . however , our study of systematic errors shows that for very accurate determinations of , the smearing function must be tuned and the volume fixed to keep the ambiguity in fixed as varies . consistency was found with previous results from the lanl group and ( within fairly large errors ) 1-loop perturbation theory ; does not change significantly over the range .

we report on an investigation of the lanl method for determining the improvement coefficient nonperturbatively . we find we are able to extract reliable estimates for the coefficient using this method . however , our study of systematic errors shows that for very accurate determinations of , the smearing function must be tuned and the volume fixed to keep the ambiguity in fixed as varies . consistency was found with previous results from the lanl group and ( within fairly large errors ) 1-loop perturbation theory ; does not change significantly over the range . the big difference between our results and those of the alpha collaboration , around , show that the differences in between the different methods can be large . we find that the lattice spacing dependence of and the renormalised quark mass is much smaller using our values of the coefficient compared to those of the alpha collaboration .

1609.08620

i

metallic spin - density wave ( sdw ) transitions are ubiquitous to strongly correlated materials such as the electron - doped cuprates @xcite , the fe - based superconductors @xcite , heavy fermion systems @xcite , and organic superconductors @xcite . in all these materials , unconventional superconductivity is found to emerge near the onset of sdw order , with the maximum of the superconducting t@xmath2 occuring either at or near the underlying sdw quantum phase transition ( qpt ) . in addition , the vicinity of the sdw transition is often characterized by strong deviations from fermi liquid theory - both in thermodynamic and in single electron properties . more broadly , understanding the properties of quantum critical points ( qcps ) in itinerant fermion systems has attracted much interest over the past several decades @xcite . unlike thermal critical phenomena and qcps in insulating systems , here the critical order parameter fluctuations are strongly interacting with low - energy fermionic quasiparticles near the fermi surface . in the traditional approach to this problem due to hertz @xcite , later refined by millis @xcite , the fermions are integrated out from the outset , leading to an effective _ bosonic _ action for the order parameter fluctuations . the dynamics of the order parameter is found to be overdamped due to the coupling to the fermions , that act as a bath . the effective bosonic action is then treated using conventional renormalization group ( rg ) techniques . while physically appealing , this approach has the drawback that integrating out low - energy modes is dangerous , since it generates non - analytic terms in momentum and frequency that are difficult to treat within the rg scheme . an alternative popular approach has been to use a @xmath3 expansion @xcite , where @xmath4 is the number of fermion flavors . however , in the important case of two spatial dimensions , this approach turns out to be uncontrolled , as well @xcite . alternative expansion parameters have been proposed @xcite , but a fully controlled analytical treatment of qcps in itinerant electron systems has remained one of the grand challenges in strongly correlated electron physics . in addition to the bosonic critical fluctuation dynamics , an important open question regards the behavior of the _ fermionic _ quasiparticles in the vicinity of the transition . the exchange of sdw critical fluctuations can mediate a superconducting instability ; however , the same fluctuations also strongly scatter the quasiparticles , causing them to lose their coherence and leading to the formation of a non - fermi liquid metal . it is not clear which of these effects dominates ; i.e. , is there a well - defined non - fermi liquid regime that precedes superconductivity , or does pairing always preempt the formation of a non - fermi liquid @xcite ? in this work , we perform extensive numerically exact determinantal quantum monte carlo ( qmc ) simulations @xcite of a metallic system in the vicinity of an sdw transition . we use the approach of refs . @xcite , that introduced a two - dimensional multi - band lattice model that captures the generic structure of the `` hot spots '' - points on the fermi surface where quasiparticles can scatter off critical sdw fluctuations resonantly . the universal properties of metallic sdw transitions are believed to depend only on the vicinity of the hot spots . at the same time , the model is amenable to qmc simulations without a sign problem @xcite . our goal here is both to understand the generic properties of the transition , and to provide a controlled benchmark to analytic theories . we present detailed information about the bosonic and fermionic correlations and the interplay with unconventional superconductivity in the vicinity of the qcp . previously , the finite - temperature phase diagram of the model has been characterized , and a dome - shaped superconducting phase peaked near the sdw transition was found @xcite . here , we measure the sdw correlations in the vicinity of the transition , above the superconducting @xmath1 . we find that , over a broad range of parameters , the sdw susceptibility is well described by the following form : @xmath5 here @xmath6 is the ordering wavevector [ chosen to be @xmath7 in our model ] , @xmath8 is a matsubara frequency , and @xmath9 is a parameter used for tuning through the sdw qcp , while @xmath10 , @xmath11 , @xmath12 , and @xmath13 are nonuniversal constants . the function @xmath14 extrapolates to @xmath15 as @xmath16 . importantly , eq . ( [ eq : hertz ] ) captures the behavior of both the bosonic sdw correlations and the susceptibility of a fermion bilinear operator with the same symmetry , establishing the consistency of our analysis . interestingly , @xmath17 has precisely the form predicted by hertz and millis ; in particular , the bosonic critical dynamics are characterized by a dynamic critical exponent @xmath0 . the function @xmath14 does not follow the predicted behavior , however . in a window of temperatures above t@xmath2 , we find a power - law dependence @xmath18 with @xmath19 , in contrast to the linear behavior predicted by millis @xcite . the single - fermion properties above @xmath1 are found to depend strongly on the distance from the hot spots . away from the hot spots , a behavior consistent with fermi liquid theory is observed . at the hot spots , a substantial loss of spectral weight is seen upon approaching the qcp . in a temperature window above t@xmath2 , the fermionic self energy is only weakly frequency and temperature dependent , corresponding to a nearly - constant lifetime of quasiparticles at the hot spots . this behavior indicates a strong breakdown of fermi liquid theory at these points . it is not clear , however , whether it represents the asymptotic behavior at the putative underlying sdw qcp , since superconductivity intervenes before the qcp is reached . finally , in order to probe the interplay between magnetic quantum criticality and superconductivity , we measure the superconducting gap , @xmath20 , and the momentum - resolved superconducting susceptibility , @xmath21 , across the phase diagram . no strong feature is found in @xmath20 at the hot spots . rather , @xmath20 and @xmath21 vary smoothly on the fermi surface . while the pairing interaction may be strongly peaked at wavevector @xmath22 , the resulting gap function does not reflect such a strong momentum dependence . this paper is organized as follows . in sec . [ sec : model ] we describe the model and review its phase diagram . [ sec : sdw_corr ] presents a detailed analysis of the sdw susceptibility across the phase diagram . in sec . [ sec : fermion_corr ] we study the single - fermion properties , providing evidence for the breakdown of fermi liquid theory in the vicinity of the hot spots . [ sec : sc ] analyzes the gap structure in the superconducting state . the cumulative results are put into perspective in sec . [ sec : discussion ] . supplementary data sets and some technical details are presented in the appendices .

we report on numerically exact determinantal quantum monte carlo simulations of the onset of spin - density wave ( sdw ) order in itinerant electron systems captured by a sign - problem - free two - dimensional lattice model . this indicates a clear breakdown of fermi liquid theory around these points .

we report on numerically exact determinantal quantum monte carlo simulations of the onset of spin - density wave ( sdw ) order in itinerant electron systems captured by a sign - problem - free two - dimensional lattice model . extensive measurements of the sdw correlations in the vicinity of the phase transition reveal that the critical dynamics of the bosonic order parameter are well described by a dynamical critical exponent , consistent with hertz - millis theory , but are found to follow a finite - temperature dependence that does not fit the predicted behavior of the same theory . the presence of critical sdw fluctuations is found to have a strong impact on the fermionic quasiparticles , giving rise to a dome - shaped superconducting phase near the quantum critical point . in the superconducting state we find a gap function that has an opposite sign between the two bands of the model and is nearly constant along the fermi surface of each band . above the superconducting our numerical simulations reveal a nearly temperature and frequency independent self energy causing a strong suppression of the low - energy quasiparticle spectral weight in the vicinity of the hot spots on the fermi surface . this indicates a clear breakdown of fermi liquid theory around these points .

0710.5087

i

we have carried out a spectroscopic study of the central 2 arcminutes of centaurus a using short low and long high spectral modules of the infrared spectrograph on board the _ spitzer space telescope_. most of the emission lines detected in the spectral cubes ( e.g. , [ siii](33.5@xmath0 m ) , [ siii](34.8 ) , [ feii](26.0 ) , [ feiii](23.9 ) , [ arii](6.98 ) and h@xmath25s(0)(28.2 ) ) and dust emission features primarily trace regions of star formation in the warped disk . our previous study based on irac and mips imaging suggested that centaurus a hosts an oval or bipolar dustshell at a distance approximately 500 pc from the nucleus seen above and below the warped disk . this dust shell , if confirmed , would be the first extragalactic shell to be discovered in the infrared . here we see the dust shell even more clearly and prominently in the 11.3@xmath0 m dust emission feature than we saw previously in the broad band irac images . we have found variations in the dust emission feature 7.7@xmath0m/11.3@xmath0 m ratio and dust 11.3@xmath0m/[neii](12.8@xmath0 ) ratio , with the oval dust shell having the lowest ratios compared to the star forming disk . the clearer shell morphology at 11.3@xmath0 m than previously seen in broad band images , the association of the molecular hydrogen emission in the shell , and the variation in line ratios in the shell compared to those in the disk , confirm spectroscopically that the shell discovered previously @xcite is a separate coherent entity and is unlikely to be a chance superposition of dust filaments . we find evidence for higher ionization species line emission in [ nev](@xmath30 m ) and [ oiv](@xmath29 m ) near the jet axis . emission in these two lines is seen both north - east and south - west of the nucleus along position angles @xmath31 and @xmath102 . these angles are similar to but not exactly the same as the jet axis at 55@xmath33 as seen at 5ghz . outside the nucleus , the peak surface brightness in these lines is 25or 400 pc south - west of the nucleus . emission line ratios and limits at the location of the [ oiv ] peak suggest that the emitting region is at low ionization parameter , @xmath84 , and has low electron density , @xmath86@xmath87 . we crudely estimate that the agn can provide sufficient uv photons to account for the [ oiv ] luminosity 400 pc from the nucleus , as long as uv photons are not absorbed by intervening material as they travel from the agn to the dust shell . a much more detailed photo - ionization study is required to understand the excitation of the [ oiv ] and [ nev ] emission . previous reports of an ionization cone in cen a were based on near - infrared imaging of the central few arcseconds @xcite . subsequent studies interpreted line emission in terms of a disk rather than ionization cone @xcite . unfortunately the morphology of the near - infrared images is strongly affected by extinction and the warp disk models have not been good enough to accurately predict the extinction in the central few arcsecond of the nucleus . cen a might be the only active galaxy in which mid - infrared spectroscopy has found evidence for high ionization species such as nev at hundred pc distances from the nucleus . as far as we know cen a hosts the only ionization cone that has been resolved with observations from the spitzer space telescope . we see evidence for warm molecular hydrogen coincident with the peak in [ oiv ] in the odd pure rotational odd transitions s(3 ) and s(5 ) . the s(7 ) and s(2 ) transitions are also detected but at weaker levels . the s(3 ) and s(5 ) emission also lies in the vicinity of the dust shell that is most prominent in the 11.3@xmath0 m dust ( pah ) emission feature . a two temperature component model can fit the rotational line ratios and implies that there is warm molecular hydrogen with temperatures in the range 250720k . the temperatures are warmer than seen in nucleus of non - active nearby galaxies , similar to those of liners and seyferts but lower than exhibited by supernova remnants ulirgs ( as compared to studies by @xcite , @xcite and @xcite ) . near the jet axis , the column depth of warm molecular hydrogen is @xmath1@xmath2 similar to that estimated from the infrared continuum emission of the dust shell by @xcite . this suggests that gas associated with the dust shell has been heated near the jet axis . there is probably more than one excitation process as [ oiv ] and [ nev ] emission are detected primarily along the jet axis whereas the higher s pure rotational molecular hydrogen lines are detected there and in the vicinity of the dust shell . previous studies of the pure - rotational molecular hydrogen lines in extra - galactic objects ( e.g. , @xcite ) have not well resolved the emission . the association of the warm molecular hydrogen gas with a shell is most similar to phenomena exhibited by galactic supernova remnants where the blast wave encounters molecular clouds @xcite . the physical conditions estimated from the molecular hydrogen observations are similar in properties ( column depth , temperatures and fraction of gas in the two temperature components ) to the parameters estimated by @xcite in 4 galactic supernova remnants . this suggests that theory of interstellar shock waves be applied to interpreting observations of the shell . @xcite associates the warmer molecular hydrogen component responsible for the higher s pure rotational transitions with dissociative shocks . these require shock velocities @xmath103km / s ( e.g. , @xcite ) . a physical scenario and model accounting for the shell s structure and energetics is currently lacking . deep optical spectroscopic and radio studies are particularly needed to better constrain gas motions and physical conditions in this shell . 1.0truein we thank dan watson , paul van der werf , ralph kraft , jacqueline van gorkom , martin hardcastle , and christine jones - forman for helpful discussions and correspondence . we thank martin hardcastle for providing us with images of centaurus a in the radio . support for this work was in part provided by by nasa through an award issued by jpl / caltech , national science foundation grants ast-0406823 @xmath104 phy-0552695 , the national aeronautics and space administration under grant no.@xmath46nng04gm12 g issued through the origins of solar systems program , and hst - ar-10972 to the space telescope science institute . jbh is funded by a federation fellowship from the australian research council . continuum emission from the lh spectral cube from @xmath13 m wide bands . contours are evenly spaced with the lowest contour and spacing at 0.01 mjy / sr . a ) continuum centered at @xmath20 m . b ) continuum centered at @xmath105 m . , title="fig:",width=336 ] continuum emission from the lh spectral cube from @xmath13 m wide bands . contours are evenly spaced with the lowest contour and spacing at 0.01 mjy / sr . a ) continuum centered at @xmath20 m . b ) continuum centered at @xmath105 m . , title="fig:",width=336 ] dust emission feature at 11.3@xmath0 m . no continuum has been subtracted as the emission feature dominates the spectrum by a factor of 38 . the minimum contour and spacing is approximately 10 mjy / sr in the peak of the line . the black contours show the oval dust shell previously described by @xcite . , width=336 ] continuum subtracted line emission images in the lh spectral cube , showing emission in the folded star forming disk . contours are evenly spaced . the lowest contours and spacing for the [ siii](@xmath106 m ) and [ siii](@xmath107 m ) images are 1.0 and 1.5 @xmath108erg @xmath2 s@xmath6 sr@xmath6 , respectively . a ) for [ siii](@xmath106 m ) . b ) for [ siii](@xmath109 m ) . , title="fig:",width=336 ] continuum subtracted line emission images in the lh spectral cube , showing emission in the folded star forming disk . contours are evenly spaced . the lowest contours and spacing for the [ siii](@xmath106 m ) and [ siii](@xmath107 m ) images are 1.0 and 1.5 @xmath108erg @xmath2 s@xmath6 sr@xmath6 , respectively . a ) for [ siii](@xmath106 m ) . b ) for [ siii](@xmath109 m ) . , title="fig:",width=336 ] continuum subtracted line emission images in the lh spectral cube , showing emission in the folded star forming disk . contours are evenly spaced . the lowest contours and spacings for [ feii](25.988@xmath0 m ) and [ feiii](22.925@xmath0 m ) images with lowest contour are 0.05 and 0.025 @xmath108erg @xmath2 s@xmath6 sr@xmath6 , respectively . a ) for [ feii](@xmath110 m ) . b ) for [ feiii](22.925@xmath0 m ) . , title="fig:",width=336 ] continuum subtracted line emission images in the lh spectral cube , showing emission in the folded star forming disk . contours are evenly spaced . the lowest contours and spacings for [ feii](25.988@xmath0 m ) and [ feiii](22.925@xmath0 m ) images with lowest contour are 0.05 and 0.025 @xmath108erg @xmath2 s@xmath6 sr@xmath6 , respectively . a ) for [ feii](@xmath110 m ) . b ) for [ feiii](22.925@xmath0 m ) . , title="fig:",width=336 ] continuum subtracted line emission images in the lh spectral cube , showing emission in the folded star forming disk . for the h@xmath25s(0)(@xmath111 m ) line with lowest contour at and spacing at 0.01 @xmath108erg @xmath2 s@xmath6 sr@xmath6 . , width=336 ] continuum subtracted line emission images in the lh spectral cube , showing emission near the jet axis . contours are evenly spaced . the lowest contours and spacing for the [ oiv](@xmath4 m ) and [ nev](@xmath3 m ) images are 0.5 and 0.1 @xmath108erg @xmath2 s@xmath6 sr@xmath6 , respectively . a ) for [ oiv](@xmath4 m ) . b ) for [ nev](@xmath3 m ) . , title="fig:",width=336 ] continuum subtracted line emission images in the lh spectral cube , showing emission near the jet axis . contours are evenly spaced . the lowest contours and spacing for the [ oiv](@xmath4 m ) and [ nev](@xmath3 m ) images are 0.5 and 0.1 @xmath108erg @xmath2 s@xmath6 sr@xmath6 , respectively . a ) for [ oiv](@xmath4 m ) . b ) for [ nev](@xmath3 m ) . , title="fig:",width=336 ] ( @xmath29 m ) contours . the radio map is a 6resolution map of the inner radio lobes by @xcite . the [ oiv]@xmath29 and [ nev]@xmath30 m line emission are oriented approximately but not exactly along the jet axis . [ radioo4 ] , width=336 ] continuum subtracted line emission images from the sl spectral cube , showing the h@xmath25s(3)(9.665@xmath0 m ) and h@xmath25s(5)(6.909@xmath0 m ) lines with lowest contours at 1 @xmath112erg @xmath2 s@xmath6 sr@xmath6 . the higher s rotational lines from h@xmath25 exhibit different morphology than the h@xmath25s(0)28@xmath0 m line that was seen primarily in the folded star forming disk . emission in the higher s lines is seen above the disk . contours are evenly spaced . lowest contour and spacing is @xmath112erg @xmath2 s@xmath6 sr@xmath6 for both lines . for a ) h@xmath25s(3)(9.665@xmath0 m ) . for b ) h@xmath25s(5)(6.909@xmath0 m ) . , title="fig:",width=336 ] continuum subtracted line emission images from the sl spectral cube , showing the h@xmath25s(3)(9.665@xmath0 m ) and h@xmath25s(5)(6.909@xmath0 m ) lines with lowest contours at 1 @xmath112erg @xmath2 s@xmath6 sr@xmath6 . the higher s rotational lines from h@xmath25 exhibit different morphology than the h@xmath25s(0)28@xmath0 m line that was seen primarily in the folded star forming disk . emission in the higher s lines is seen above the disk . contours are evenly spaced . lowest contour and spacing is @xmath112erg @xmath2 s@xmath6 sr@xmath6 for both lines . for a ) h@xmath25s(3)(9.665@xmath0 m ) . for b ) h@xmath25s(5)(6.909@xmath0 m ) . , title="fig:",width=336 ] a ) emission in h@xmath25s(3)(9.665@xmath0 m ) shown as gray scale overlayed with [ oiv](@xmath4 ) contours . contours are evenly spaced with lowest contours at are 0.5 @xmath108erg @xmath2 s@xmath6 sr@xmath6 and a spacing 4 times this . the gray scale range for the h@xmath25s(3 ) image is 0(white ) to 7(black ) @xmath112erg @xmath2 s@xmath6 sr@xmath6 . b ) same as a ) except the h@xmath25s(3 ) emission is overlayed with contours of the 11.3@xmath0 m pah dust emission feature ( as shown in figure [ fig : pah11 ] ) . contour spacing and lowest level is 20 mjy / sr . , title="fig:",width=336 ] a ) emission in h@xmath25s(3)(9.665@xmath0 m ) shown as gray scale overlayed with [ oiv](@xmath4 ) contours . contours are evenly spaced with lowest contours at are 0.5 @xmath108erg @xmath2 s@xmath6 sr@xmath6 and a spacing 4 times this . the gray scale range for the h@xmath25s(3 ) image is 0(white ) to 7(black ) @xmath112erg @xmath2 s@xmath6 sr@xmath6 . b ) same as a ) except the h@xmath25s(3 ) emission is overlayed with contours of the 11.3@xmath0 m pah dust emission feature ( as shown in figure [ fig : pah11 ] ) . contour spacing and lowest level is 20 mjy / sr . , title="fig:",width=336 ] flux at 7.7 and 8.6@xmath0 m showing dust emission features . contours are evenly spaced . no continuum subtraction has been done . the star forming disk is evident as the parallelogram shaped feature corresponding to the folded disk . the dust shell is seen above and below the parallelogram feature . the minimum contour and spacing is approximately 10 mjy / sr in the peak of the line . a ) the 7.7@xmath0 m dust emission feature . b ) the 8.6@xmath0 m dust emission feature . , title="fig:",width=336 ] flux at 7.7 and 8.6@xmath0 m showing dust emission features . contours are evenly spaced . no continuum subtraction has been done . the star forming disk is evident as the parallelogram shaped feature corresponding to the folded disk . the dust shell is seen above and below the parallelogram feature . the minimum contour and spacing is approximately 10 mjy / sr in the peak of the line . a ) the 7.7@xmath0 m dust emission feature . b ) the 8.6@xmath0 m dust emission feature . , title="fig:",width=336 ] line emission in [ neii](@xmath113 m ) . no continuum has been subtracted as the [ neii ] line dominates the continuum by a factor greater than 2 everywhere . contours are evenly spaced with lowest contour at 4 @xmath112erg @xmath2 s@xmath6 sr@xmath6 . , width=336 ] a ) the dust emission feature at 7.7@xmath0 m divided by that at 11.3@xmath0 m . the lowest and highest contours are shown at a ratios of 0.5 ( in shell ) and 1.0 ( in parallelogram ) , with spacing of 0.1 . black is 1.0 , white is 0.5 . the 7.7 to 11.0@xmath0 m dust feature ratio varies with the dust shell having the lowest ratio . b ) the [ neii](12.8@xmath0 m ) line divided by the @xmath114 m dust emission feature . the lowest and highest contours are shown at ratios of 1.9 ( in shell ) and 3.0 ( in parallelogram ) , with spacing of 0.1 . black is 3.0 , white is 1.9 . the strength of the neii](12.8@xmath0 m ) compared to the 11.3@xmath0 m dust feature also varies with the dust shell having the lowest ratios . , title="fig:",width=336 ] a ) the dust emission feature at 7.7@xmath0 m divided by that at 11.3@xmath0 m . the lowest and highest contours are shown at a ratios of 0.5 ( in shell ) and 1.0 ( in parallelogram ) , with spacing of 0.1 . black is 1.0 , white is 0.5 . the 7.7 to 11.0@xmath0 m dust feature ratio varies with the dust shell having the lowest ratio . b ) the [ neii](12.8@xmath0 m ) line divided by the @xmath114 m dust emission feature . the lowest and highest contours are shown at ratios of 1.9 ( in shell ) and 3.0 ( in parallelogram ) , with spacing of 0.1 . black is 3.0 , white is 1.9 . the strength of the neii](12.8@xmath0 m ) compared to the 11.3@xmath0 m dust feature also varies with the dust shell having the lowest ratios . , title="fig:",width=336 ] a ) spectrum from the star forming parallelogram . d refers to a dust emission feature . b ) spectrum from the jet region . the pure rotational molecular hydrogen lines s(2)s(7 ) are labeled as s2-s7 . molecular hydrogen lines are more prominent in the jet region than in the star forming parallelogram . in the star forming disk the [ arii](6.985@xmath0 m ) line is brighter than the nearby pure rotational molecular hydrogen s(2 ) line at @xmath115 m whereas the opposite is true in the jet region . there is a change in the ratio of the dust emission features in these two spectra and in the ratio of the [ neii]/11.3 dust emission feature . , title="fig:",width=336 ] a ) spectrum from the star forming parallelogram . d refers to a dust emission feature . b ) spectrum from the jet region . the pure rotational molecular hydrogen lines s(2)s(7 ) are labeled as s2-s7 . molecular hydrogen lines are more prominent in the jet region than in the star forming parallelogram . in the star forming disk the [ arii](6.985@xmath0 m ) line is brighter than the nearby pure rotational molecular hydrogen s(2 ) line at @xmath115 m whereas the opposite is true in the jet region . there is a change in the ratio of the dust emission features in these two spectra and in the ratio of the [ neii]/11.3 dust emission feature . , title="fig:",width=336 ] a ) spectra from the star forming warped disk ( seen as a parallelogram in continuum ) are shown at the 4 peaks in the parallelogram and at one additional point also in the parallelogram . each spectrum is offset by @xmath1160.1 mjy / sr from the other . from bottom to top : the northern peak west of the nucleus , the southern peak west of the nucleus , the southern peak east of the nucleus , the northern peak east of the nucleus , a point between the southern and eastern peak and the nucleus . positions are given in the text . in the star forming disk or parallelogram [ nev](@xmath3 m ) is not detected and [ oiv](@xmath4 ) is weaker than [ feii](@xmath110 m ) . b ) spectrum from a region near the jet axis south - west of nucleus . near the jet axis [ nev](@xmath3 m ) is detected and [ oiv](@xmath4 ) is 3 - 5 times brighter than [ feii](@xmath110 m ) . the presence of [ nev ] implies suggests that the radiation field is hard near the jet axis . , title="fig:",width=336 ] a ) spectra from the star forming warped disk ( seen as a parallelogram in continuum ) are shown at the 4 peaks in the parallelogram and at one additional point also in the parallelogram . each spectrum is offset by @xmath1160.1 mjy / sr from the other . from bottom to top : the northern peak west of the nucleus , the southern peak west of the nucleus , the southern peak east of the nucleus , the northern peak east of the nucleus , a point between the southern and eastern peak and the nucleus . positions are given in the text . in the star forming disk or parallelogram [ nev](@xmath3 m ) is not detected and [ oiv](@xmath4 ) is weaker than [ feii](@xmath110 m ) . b ) spectrum from a region near the jet axis south - west of nucleus . near the jet axis [ nev](@xmath3 m ) is detected and [ oiv](@xmath4 ) is 3 - 5 times brighter than [ feii](@xmath110 m ) . the presence of [ nev ] implies suggests that the radiation field is hard near the jet axis . , title="fig:",width=336 ] excitation diagram of the h@xmath25 pure rotational lines . points are based on those measured in the jet region with fluxes listed in table [ tab : hjet ] . solid squares refer to measurements and open triangles to upper limits . the solid line is for a temperature of @xmath71 whereas the dotted one is @xmath117 . , width=336 ] + fluxes were measured in the same region as listed in table [ tab : emjet ] and in the spectra shown in figures [ fig : lhspec]b and [ fig : slspec]b . fluxes are given in units of @xmath118 . for the s(4 ) and s(6 ) lines we estimate upper limits . the upper limits are high because of dust emission features .

we report on the results of spectroscopic mapping observations carried out in the nuclear region of centaurus a ( ngc5128 ) over the 5.2 - 15 and 20 - 36 m spectral regions using the infrared spectrograph on the _ spitzer space telescope_. we have detected and mapped s(0 ) , s(2 ) , s(3 ) , and s(5 ) pure rotational transition lines of molecular hydrogen and emissions in the fine - structure transitions of [ siii ] , [ siii ] , [ feii ] , [ feiii ] , [ arii ] , [ siv ] , [ neii ] , [ nev ] and [ oiv ] . the 500 pc bipolar dust shell discovered by quillen et al.(2006 ) is even more clearly seen in the 11.3 m dust emission feature than previous broad band imaging . the clearer shell morphology at 11.3 m , warm molecular hydrogen emission in the shell , and variation in line ratios in the shell compared to those in the disk , confirm spectroscopically that this shell is a separate coherent entity and is unlikely to be a chance superposition of dust filaments . the physical conditions in the shell are most similar to galactic supernova remnants where blast waves encounter molecular clouds . fine structure line ratios and limits from this region suggest that the medium is low density and illuminated by a hard radiation field at low ionization parameter .

we report on the results of spectroscopic mapping observations carried out in the nuclear region of centaurus a ( ngc5128 ) over the 5.2 - 15 and 20 - 36 m spectral regions using the infrared spectrograph on the _ spitzer space telescope_. we have detected and mapped s(0 ) , s(2 ) , s(3 ) , and s(5 ) pure rotational transition lines of molecular hydrogen and emissions in the fine - structure transitions of [ siii ] , [ siii ] , [ feii ] , [ feiii ] , [ arii ] , [ siv ] , [ neii ] , [ nev ] and [ oiv ] . the 500 pc bipolar dust shell discovered by quillen et al.(2006 ) is even more clearly seen in the 11.3 m dust emission feature than previous broad band imaging . the pure rotational lines of molecular hydrogen other than the s(0 ) line are detected above the dusty disk and associated with the oval dust shell . the molecular hydrogen transitions indicate the presence of warm gas at temperatures 250720k . the column density of the warm molecular hydrogen in the shell is and similar to that estimated from the continuum dust shell surface brightness . the ratio of the dust emission features at 7.7 m and 11.3 m and the ratio of the [ neii](12.8 m ) and 11.3 m dust emission feature are lower in the 500 pc dust shell than in the star forming disk . the clearer shell morphology at 11.3 m , warm molecular hydrogen emission in the shell , and variation in line ratios in the shell compared to those in the disk , confirm spectroscopically that this shell is a separate coherent entity and is unlikely to be a chance superposition of dust filaments . the physical conditions in the shell are most similar to galactic supernova remnants where blast waves encounter molecular clouds . the lines requiring the highest level of ionization , [ nev]( m ) and [ oiv]( m ) , are detected 2025north - east and south - west of the nucleus and at position angles near the radio jet axis . fine structure line ratios and limits from this region suggest that the medium is low density and illuminated by a hard radiation field at low ionization parameter . these higher s molecular hydrogen pure rotational transitions are also particularly bright in the same region as the [ oiv ] and [ nev ] emission . this suggests that the gas associated with the dust shell has been excited near the jet axis and is part of an ionization cone . [ firstpage ]

1010.1008

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transiting exoplanets ( teps ) are tremendously useful objects for studying the properties of planets outside of the solar system because their photometric transits , combined with precise measurements of the radial velocity variations of their host stars , enable determinations of their masses and radii . of the @xmath17 confirmed teps discovered to date , all but five are saturn or jupiter - size gas giant planets with masses above @xmath18@xmath9 . the five teps below this limit , including the super - earths corot-7b ( @xmath19@xmath9 , @xmath20@xmath11 ; * ? ? ? * ; * ? ? ? * ) , and gj 1214b ( @xmath21@xmath9 , @xmath22@xmath11 ; * ? ? ? * ) , and the super - neptunes gj 436b ( @xmath23@xmath9 , @xmath24@xmath11 ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , hat - p-11b ( @xmath25@xmath9 , @xmath26@xmath11 ; * ? ? ? * ) , and kepler-4b ( @xmath27@xmath9 , @xmath28@xmath11 ; * ? ? ? * ; * ? ? ? * ) are likely composed primarily of elements heavier than hydrogren and helium , and are therefore assumed to be qualitatively different from the more massive gas giants . in addition to these five teps , the candidate tep kepler-9d has an estimated radius of @xmath29@xmath30 @xcite , and is most likely a low - mass planet @xcite , but currently lacks a mass determination . while the gas giant planets exhibit a wide range of radii at fixed mass ( and hence a great diversity in their physical structure at fixed mass ) , the low mass teps , together with the six solar system planets smaller than saturn , appear to follow a nearly monotonic relation between mass and radius . the two super - neptunes with precise radius measurements ( gj 436b and hat - p-11b ) have radii that are similar to one another ( to within 15% ) as well as to uranus ( @xmath31@xmath9 , @xmath32@xmath11 ) and neptune ( @xmath33@xmath9 , @xmath34@xmath11 ) . while the mass and radius of kepler-4b given in the discovery paper @xcite are similar to those of gj 436b and hat - p-11b , a reanalysis by @xcite finds that the radius may be @xmath35% larger , though with a @xmath36 uncertainty , it may still be similar to the other super - neptunes . the lack of significant scatter in the radii among uranus , neptune , and the super - neptunes is perhaps surprising given the vast range of radii permitted by theoretical structure models for planets in this mass range . for example , the theoretical models by @xcite predict that a @xmath37 nonirradiated neptune - mass planet may have a radius that ranges from 0.14@xmath11 ( pure iron composition ) to 0.29@xmath11 ( pure water ice composition ) or 0.86@xmath11 ( pure gas composition ) . these same models also predict that the radii of gas - dominated neptune - mass planets should be far more sensitive to stellar irradiation than those of jupiter - mass planets . for example , a @xmath38 pure hydrogen - helium neptune - mass planet at @xmath39au has a radius of @xmath40@xmath11 compared to @xmath41@xmath11 for a similarly irradiated jupiter - mass planet . in this paper we present the discovery of hat - p-26b , a tep orbiting the relatively bright star gsc 0320 - 01027 with a mass similar to that of neptune , but with a radius of @xmath42@xmath11 or 65% larger than that of neptune . this is the 26th tep discovered by the hungarian - made automated telescope network ( hatnet ; * ? ? ? * ) survey . in operation since 2003 , hatnet has now covered approximately 14% of the sky , searching for teps around bright stars ( @xmath43 ) . hatnet operates six wide - field instruments : four at the fred lawrence whipple observatory ( flwo ) in arizona , and two on the roof of the hangar servicing the smithsonian astrophysical observatory s submillimeter array , in hawaii . the layout of the paper is as follows . in we report the detection of the photometric signal and the follow - up spectroscopic and photometric observations of hat - p-26 . in we describe the analysis of the data , beginning with the determination of the stellar parameters , continuing with a discussion of the methods used to rule out nonplanetary , false positive scenarios which could mimic the photometric and spectroscopic observations , and finishing with a description of our global modeling of the photometry and radial velocities . our findings are discussed in .

we report the discovery of hat - p-26b , a transiting extrasolar planet orbiting the moderately bright v=11.744 k1 dwarf star gsc 0320 - 01027 , with a periodd , transit epoch ( bjd ) , and transit durationd . it has a mass that is comparable to those of neptune and uranus , and slightly smaller than those of the other transiting super - neptunes , but a radius that is% larger than those of neptune and uranus , and also larger than those of the other transiting super - neptunes .

we report the discovery of hat - p-26b , a transiting extrasolar planet orbiting the moderately bright v=11.744 k1 dwarf star gsc 0320 - 01027 , with a periodd , transit epoch ( bjd ) , and transit durationd . the host star has a mass of , radius of , effective temperature k , and metallicity}}= { \ifthenelse{\equal{{i}}{i}}{{\ensuremath{-0.04\pm0.08}}}{{\ensuremath{-0.04\pm0.08}}}}$ ] . the planetary companion has a mass of , and radius of yielding a mean density of . hat - p-26b is the fourth neptune - mass transiting planet discovered to date . it has a mass that is comparable to those of neptune and uranus , and slightly smaller than those of the other transiting super - neptunes , but a radius that is% larger than those of neptune and uranus , and also larger than those of the other transiting super - neptunes . hat - p-26b is consistent with theoretical models of an irradiated neptune - mass planet with a 10 heavy element core that comprises of its mass with the remainder contained in a significant hydrogen - helium envelope , though the exact composition is uncertain as there are significant differences between various theoretical models at the neptune - mass regime . the equatorial declination of the star makes it easily accessible to both northern and southern ground - based facilities for follow - up observations .

1010.1008

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we have presented the discovery of hat - p-26b , a transiting neptune - mass planet . below we discuss the physical properties of this planet , and compare them to the properties of similar planets ; we comment on the possibility that the planet has undergone significant evaporation , on the significance of its orbital eccentricity , and on the possible presence of additional bodies in the system ; and we discuss the prospects for detailed follow - up studies . figure [ fig : exomr ] compares hat - p-26b to the other known teps on a mass - radius diagram . with a density of @xmath12@xmath13 , hat - p-26b is significantly less dense than the four other neptune - size planets with well measured masses and radii ( uranus , neptune , gj 436b , hat - p-11b ) . for kepler-4b , @xcite find a large uncertainty on the radius which results from significant uncertainties on the eccentricity and the transit impact parameter . kepler-4b may be comparable in size to gj 436b and hat - p-11b , or it could be even less dense than hat - p-26b . from the theoretical models of @xcite , hat - p-26b has a radius that is well above the maximum radius of @xmath473@xmath11 for a @xmath474@xmath9 planet lacking a hydrogen - helium envelope ( i.e. a planet with a 100% water - ice composition ) . the best - fit mass and radius for hat - p-26b falls just below the 4gyr model with a 10@xmath15 rocky core and 8@xmath15 gas envelope , implying that a 4gyr model with a slightly higher core mass would provide a better match to the mass and radius . we note that the isochrone - based age ( @xmath277gyr ) and the activity - based age ( @xmath475gyr ) for the hat - p-26 system are somewhat older than 4gyr , so the inferred core - mass would therefore be somewhat smaller . we also compare hat - p-26b to the theoretical models of @xcite which predict more significant inflation due to irradiation for low mass planets than do the @xcite models . in this case the radius of hat - p-26b is intermediate between the @xmath476 and @xmath477 heavy - element enrichment models . observations of the transiting hot jupiters hd 209458b and hd 189733b in the lyman-@xmath478 line have indicated that both planets are evaporating at a rate of up to @xmath479gs@xmath413 ( e.g , * ? ? ? * ; * ? ? ? prompted by the observations for hd 209458b , several theoretical studies have indicated that atmospheric evaporation is likely to be important for close - in planets , particularly those with low surface gravities , such as hot neptunes ( see for example @xcite and the review by @xcite ) . it has even been suggested that some close - in neptune - mass and smaller planets may be the evaporated cores of planets which initially had masses comparable to saturn or jupiter ( e.g. * ? ? ? * ) . in the case of energy - limited escape , the evaporative mass - loss is given by ( see @xcite , and @xcite ; see also @xcite and @xcite for applications to corot-7b ) : @xmath480 where @xmath481 is the incident flux of extreme ultraviolet ( xuv ) stellar radiation , @xmath482 is the heating efficiency and is estimated to be @xmath483 for the case of hd 209458b @xcite , and @xmath484 is a factor that accounts for an enhancement of the evaporation rate in the presence of tides , and is given by : @xmath485 where @xmath486 is the ratio of the roche radius to the planet radius . @xcite find that for solar type stars the xuv flux at 1 au integrated over the wavelength range @xmath487 to @xmath488 is given by : @xmath489 where @xmath490 is the age in gyr . to our knowledge , a similar study has not been completed for k dwarfs , however long term x - ray observations of the 5 - 6gyr @xmath478 cen ab system reveal that on average the k1 dwarf star @xmath478 cen b has an x - ray luminosity in the 6 - 60 band that is approximately twice that of the sun , while the g2 dwarf @xmath478 cen a has a luminosity that is approximately half that of the sun @xcite . for simplicity we therefore assume that the total xuv luminosity of hat - p-26 is comparable to that of the sun ( 4.64ergss@xmath413@xmath491 at 1 au ; * ? ? ? * ) , which is likely correct to within an order of magnitude . assuming @xmath492 , we estimate that the expected present - day mass - loss rate for hat - p-26b is @xmath493 . to determine the total mass lost by hat - p-26b over its lifetime , we integrate equation [ eqn : mdotevap ] assuming an age of @xmath494gyr , @xmath495 for @xmath496gyr and @xmath497 for @xmath498gyr , neglecting tidal evolution of the orbit , and assuming that the radius is constant . we find that hat - p-26b may have lost a significant fraction its mass ( @xmath14 30% ) ; the exact value depends strongly on several poorly constrained parameters including @xmath481 and its dependence on age for a k1 dwarf , @xmath482 , and the age of the system . using the relation given by @xcite , the expected tidal circularization time - scale for hat - p-26b is @xmath499gyr which is much less than the age of the system . this time - scale is estimated assuming a large tidal quality factor of @xmath500 , and that there are no additional bodies in the system exciting the eccentricity . however , because at least two of the three hot neptunes have significant eccentricities ( gj 436b has @xmath501 , @xcite ; and hat - p-11b has @xmath502 , @xcite ; the eccentricity for kepler-4b is poorly constrained , @xcite ) , we can not conclude that the eccentricity must be zero on physical grounds , and therefore do not adopt a zero - eccentricity model for the parameter determination . as discussed in the eccentricity of hat - p-26b is poorly constrained by the rv observations , and is instead constrained by requiring that the star be younger than the age of the universe ( without the age constraint we get @xmath503 , whereas including the age constraint gives @xmath216 ) . to establish the significance of the eccentricity measurement , we also fit a model with the eccentricity fixed to zero . an f - test ( e.g. * ? ? ? * ) allows us to reject the null hypothesis of zero eccentricity with only 79% confidence . alternatively , the @xcite test for the significance of an eccentricity measurement gives a false alarm probability of @xmath504% for detecting @xmath505 with an error of @xmath506 , or 88% confidence that the orbit is eccentric . if the eccentricity is fixed to zero , the required jitter to achieve @xmath507 is 2.4@xmath244 , which is closer to the typical keck / hires jitter of other chromospherically quiet early k dwarfs than the jitter of @xmath243@xmath244 that is obtained with an eccentric orbit fit . we therefore are not able to claim a significant eccentricity for hat - p-26b , and instead may only place a @xmath508 confidence upper limit of @xmath509 . for the @xmath352 model discussed at the end of , the @xmath508 confidence upper limit is @xmath510 . further rv observations , or a photometric detection of the occultation of the planet by its host star , are needed to determine if the eccentricity is nonzero . the @xmath352 model discussed in with parameters given in table [ tab : planetparam ] includes a linear drift in the radial velocities , @xmath349 , as a free parameter . we find @xmath511ms@xmath413d@xmath413 . conducting an odds ratio test ( see * ? ? ? * ) , we conclude that the drift is real with 96.6% confidence , making this a @xmath512 detection . while the detection is not significant enough for us to be highly confident that there is at least one additional body in the system , this suggestive result implies that hat - p-26 warrants long - term rv monitoring . we also searched for a linear time - shift in the rvs due to potential trojans . we do not detect a significant shift , and may exclude @xmath513d with 95% confidence . this translates to an upper limit of @xmath514@xmath15 on the mass of a trojan companion , which is greater than the mass of the planet . with the present data we are thus not able to place a meaningful limit on the presence of trojan companions . hat - p-26 has a number of features that make it an attractive target for potential follow - up studies . at @xmath515 , it is bright enough that precision spectroscopic and photometric observations are feasible with moderate integration times . the equatorial declination of @xmath46 also means that hat - p-26 is accessible to both northern and southern ground - based facilities . the exceptionally low jitter will facilitate further rv observations , which might be used to confirm and refine the eccentricity determination , to measure the rossiter - mclaughlin effect ( r - m ; discussed in more detail below ) and to search for additional planets in the system . a detection of the occultation of hat - p-26b by hat - p-26 with irac/ _ spitzer _ would provide a strong constraint on @xmath516 , while the duration of the occultation would provide a constraint on @xmath322 . we note that the median value of the _ a posteriori _ distribution for the time of occultation that results from our global fit when the eccentricity is allowed to vary ( ) is @xmath517h after the expected time of occultation assuming a circular orbit . the expected depth of the occultation event is a challenging @xmath518 and @xmath519 at 3.6 and 4.5 respectively . scaling from tres-4 , a somewhat fainter star at these wavelengths , for which @xcite measured occultations at 3.6 and 4.5 using irac/_spitzer _ with precisions of @xmath520 and @xmath521 respectively , one may hope to achieve a @xmath522 and @xmath523 detection for hat - p-26b for one event at each bandpass . one would need to observe 5 and 4 occultations respectively to achieve a @xmath304 detection . recent measurements of the r - m effect for teps have revealed a substantial population of planets on orbits that are significantly misaligned with the spin axes of their host stars ( e.g. * ? ? ? @xcite note that misalignment appears to be more prevalent for planets orbiting stars with @xmath524k , and suggest that most close - in planets migrate by planet - planet or planet - star scattering mechanisms , or by the kozai effect , rather than disk migration , and that tidal dissipation in the convective surfaces of cooler stars realigns the stellar spin axis to the orbital axis of the close - in massive planet . @xcite also finds evidence that planets orbiting stars with @xmath525@xmath4 are more likely to be misaligned than planets orbiting cooler stars using a method that is independent of the r - m measurements . one prediction of the @xcite hypothesis is that lower mass planets orbiting cool stars should show a greater degree of misalignment than higher mass planets due to their reduced tidal influence . the detection of misalignment for hat - p-11b @xcite is consistent with this hypothesis . measuring the r - m effect for hat - p-26b would provide an additional test . using equation ( 40 ) from @xcite , the expected maximum amplitude of the r - m effect for hat - p-26b is @xmath526@xmath244 , which given the low jitter of hat - p-26 , should be detectable at @xmath527 . by measuring the primary transit depth as a function of wavelength it is possible to obtain a transmission spectrum of an exoplanet s atmosphere . such observations have been made for a handful of planets ( e.g. @xcite ; see also the review by @xcite ) . following @xcite , the expected difference in transit depth between two wavelengths is given approximately by : @xmath528 where @xmath529 is the scale height of the atmosphere , @xmath530 is the planet surface gravity , @xmath531 is the mean molecular weight of the atmosphere , and @xmath532 where @xmath533 and @xmath534 are the opacities per gram of material at wavelengths in a strong atomic or molecular line and in the nearby continuum respectively . assuming a pure h@xmath535 atmosphere , @xmath536 kg , we find for hat - p-26b @xmath537 km , and @xmath538 . if instead we assume that the atmosphere has the same composition as neptune ( e.g. * ? ? ? * ) , we have @xmath539 kg , @xmath540 km , and @xmath541 . for comparison , assuming a pure h@xmath535 atmosphere , the planet hd 209458b has @xmath542 , while gj 436b has @xmath543 , hat - p-11b has @xmath544 and kepler-4b has @xmath545 . due to its low surface gravity , hat - p-26b easily has the highest expected transmission spectrum signal among the known transiting neptune - mass planets . while it is relatively faint compared to the well studied planets hd 209458b and hd 189733b , we note that @xcite used the gran telescopio canarias ( gtc ) to detect a @xmath546 absorption level at 7582 due to potassium in the atmosphere of xo-2b , which orbits a @xmath547 early k star . scaling from this observation , it should be possible to detect components in the atmosphere of hat - p-26b with @xmath548 at the @xmath549 level using the gtc . in summary , hat - p-26b is a low - density neptune - mass planet . its low - density relative to the other known neptune - mass planets means that hat - p-26b likely has a more significant hydrogen - helium gas envelope than its counterparts . the existence of hat - p-26b provides empirical evidence that , like hot jupiters , hot neptunes also exhibit a wide range of densities . comparing to the @xcite models , we find that hat - p-26b is likely composed of a gas envelope and a heavy - element core that are approximately equal in mass , while the @xcite models prefer a higher heavy - element fraction . it is also likely that irradiation - driven mass - loss has played a significant role in the evolution of hat - p-26b we find that the planet may have lost @xmath550 of its present - day mass over the course of its history , though this conclusion depends strongly on a number of very poorly constrained parameters , particularly the xuv flux of hat - p-26 and its evolution in time . we place a 95% confidence upper limit on the eccentricity of @xmath509 . if further observations detect a nonzero eccentricity , it would mean that at least three of the four known neptune - mass teps have nonzero eccentricities , which may imply that the tidal quality factor is higher than expected for these planets . observations of the planetary occultation event for hat - p-26b with irac/_spitzer _ would greatly constrain the eccentricity , however the low expected depth is likely to make this a challenging observation . we find suggestive evidence for a linear drift in the rvs which is significant at the @xmath512 level . if confirmed , this would imply the existence of at least one additional body in the hat - p-26 system . with an expected r - m amplitude of @xmath551@xmath244 and a low stellar rv jitter , hat - p-26b is a good target to measure the r - m effect and thereby test the hypothesis that low - mass planets are more likely to be misaligned than high - mass planets . the low surface gravity also makes hat - p-26b a good target for transmission spectroscopy . hatnet operations have been funded by nasa grants nng04gn74 g , nnx08af23 g and sao ir&d grants . work of g..b . and j. johnson were supported by the postdoctoral fellowship of the nsf astronomy and astrophysics program ( ast-0702843 and ast-0702821 , respectively ) . gt acknowledges partial support from nasa grant nnx09af59 g . we acknowledge partial support also from the kepler mission under nasa cooperative agreement ncc2 - 1390 ( d.w.l . thanks the hungarian scientific research foundation ( otka ) for support through grant k-81373 . this research has made use of keck telescope time granted through nasa ( n018hr and n167hr ) .

hat - p-26b is the fourth neptune - mass transiting planet discovered to date . hat - p-26b is consistent with theoretical models of an irradiated neptune - mass planet with a 10 heavy element core that comprises of its mass with the remainder contained in a significant hydrogen - helium envelope , though the exact composition is uncertain as there are significant differences between various theoretical models at the neptune - mass regime . the equatorial declination of the star makes it easily accessible to both northern and southern ground - based facilities for follow - up observations .

we report the discovery of hat - p-26b , a transiting extrasolar planet orbiting the moderately bright v=11.744 k1 dwarf star gsc 0320 - 01027 , with a periodd , transit epoch ( bjd ) , and transit durationd . the host star has a mass of , radius of , effective temperature k , and metallicity}}= { \ifthenelse{\equal{{i}}{i}}{{\ensuremath{-0.04\pm0.08}}}{{\ensuremath{-0.04\pm0.08}}}}$ ] . the planetary companion has a mass of , and radius of yielding a mean density of . hat - p-26b is the fourth neptune - mass transiting planet discovered to date . it has a mass that is comparable to those of neptune and uranus , and slightly smaller than those of the other transiting super - neptunes , but a radius that is% larger than those of neptune and uranus , and also larger than those of the other transiting super - neptunes . hat - p-26b is consistent with theoretical models of an irradiated neptune - mass planet with a 10 heavy element core that comprises of its mass with the remainder contained in a significant hydrogen - helium envelope , though the exact composition is uncertain as there are significant differences between various theoretical models at the neptune - mass regime . the equatorial declination of the star makes it easily accessible to both northern and southern ground - based facilities for follow - up observations .

1008.3985

r

the spectroscopic properties of sn 2005hk have already been described in some detail in other works @xcite . here the prominent spectroscopic features , which characterise sn 2005hk at the epochs at which spectropolarimetry was acquired , will be briefly reviewed to orient the reader . the flux spectra from our two spectropolarimetric observations are presented as fig . [ fig : obs : spec ] . + our data from 2005 november 9 are interleaved with the coverage presented by @xcite who give spectra from 7 and 14 november that they assign to -3 and + 4 days with respect to b maximum which they determine to be jd2,453,685.1 . this means our data are from very near b maximum , perhaps a day earlier . we confirm that the spectral features are very similar to those of sn 2002cx at the same epoch @xcite . furthermore , @xcite acquired a flux spectrum of sn 2005hk in the course of acquiring spectropolarimetry at november 5.4 , 4 days prior to our first observation . @xcite performed line identifications using the synow code for their spectrum . they found that the strongest lines were from with other lines of intermediate mass elements being present , but relatively weaker . they obtained a better fit in the blue by adding lines of , , and . they used an excitation temperature of 10,000 k for the low - ionization stage elements and 15,000 k for the higher ionization stages , and . our flux spectrum from the 2005 november 09 observation , despite being acquired 4 days later , requires similar identifications to those made by @xcite . in the red portion of the spectrum , we identify the ir triplet , although the synthetic spectra of @xcite suggested that at the epoch of their observations this was mostly due to and . the feature at @xmath19 is identified by @xcite as , while @xcite suggested it was a mixture of and . @xcite observed the appearance of @xmath20 after maximum in spectra of sn 2002cx , which suggests that at 0 days for sn 2005hk this feature could be at least partially due to . + our spectrum from 2005 november 23 corresponds to an epoch two weeks after b maximum . our data are very similar to spectra of that date presented by @xcite , but our data have higher signal to noise and broader wavelength coverage . the spectrum of @xcite from november 25 ( + 15 days ) has similar wavelength coverage to ours of november 23 and remains very similar to our flux spectrum . at this epoch , the underlying continuum is cooler with a relative paucity of flux in the blue compared to the spectrum of 9 november . the spectrum is characterized by the growth in amplitude of small scale features . synow was used by us , in conjunction with previously published line identifications , to determine line identifications specific to the spectrum at this epoch . the degree of blending of multiple lines is lower at the second epoch , due to the relative decrease in the expansion velocity . the truncation of the red - side of the @xmath20 emission line profile at @xmath21 may be evidence for , but it is located close to strong telluric absorption features . the identification of @xmath22 at + 14 days is debatable , and is likely to be due to an increase in @xmath23 @xcite . @xcite similarly found that was no longer required to fit spectra of sn 2002cx at a similar epoch . the photospheric velocity was estimated , using lines of ( 42 ) , to be @xmath24@xmath0 . + at the second epoch , there are also two distinct absorption features that are likely to be caused by the ir triplet . the ir triplet was identified at 12 days after maximum in the spectrum of sn 2002cx @xcite . the two features might be due to partially resolving the triplet in this low velocity photosphere ( @xmath25 @xmath0 ) , or there could be two kinematically separate components such as those observed in normal type ia sne @xcite . if the latter , the absorption minima correspond to velocities of @xmath26 and @xmath27 @xmath0 , respectively , taking the mean wavelength of the blend to be 8579 . the bluer of these two components is moving somewhat more rapidly than the typical range identified for photospheric features for type ia sne at similar epochs @xcite . comparison with sn 2002cx at 12 days @xcite leads to the identification of the strong absorption observed at 5730 as intrinsic to the sn , corresponding to a velocity of @xmath28@xmath0(which is similar to the high velocity feature ) . + at the first epoch , there is a feature at @xmath29 . @xcite argue it is unlikely to be due to due to absence of other stronger lines that should occur in the wavelength range of these observations ( e.g. @xmath30 ) . rather @xcite suggests the @xmath31 may arise from @xmath32 . @xcite could not identify features in spectra of sn 2002cx . at the second epoch , however , there is a suggestion of an absorption ( blended with an line giving rise to a flat topped emission line profile for that line ) which is consistent with the expected position of @xmath30 with a velocity of @xmath27 @xmath0 ( similar to the low velocity component of ) . spectropolarimetry of sn 2005hk at the two epochs is presented in figs . [ fig : obs : panela ] and [ fig : obs : panelb ] . + the correct measurement of the intrinsic polarization of sne requires the subtraction of the polarization contribution of the interstellar medium , both in the galaxy and in the host . in the first instance , a general limit can be placed on the degree of the interstellar polarization ( isp ) by the amount of reddening measured towards sn 2005hk . for galactic - type dust the maximum degree of the isp is related to the reddening by the limit @xmath33 @xcite . the degree of galactic foreground reddening in the direction of sn 2005hk has been reported to be @xmath34 @xcite . the limit on isp arising in the foreground is @xmath35 . + the reddening towards sn 2005hk can be estimated , if we assume that the narrow d absorption component arises in the interstellar medium ( ism ) of the host . the equivalent width of the d absorption feature at the first epoch was measured to be @xmath36 . this value is smaller than the value reported by @xcite , for observations 4 days prior to our first observations , although the difference between the two measured values is @xmath37 . we note @xcite do not quote errors on their determined equivalent width . it is not clear if this difference is within the measurement errors or if it reflects evolution triggered by the sn @xcite . we follow @xcite , who adopt the results of for evaluating the relationship between d absorption and the reddening . this relationship is based on galactic - type extinction laws ( e.g. * ? ? ? it is , therefore , implicitly assumed that the reddening component , measured from the narrow absorption component in the host galaxy , follows a similar law . as the d component lines are not resolved in our data , we also adopt a range of flux ratios between d1 and d2 of 1.1 to 2 @xcite . this limits the reddening of the host to @xmath38 . the total reddening , for galactic type reddening and isp law , yields a constraint on the total isp of @xmath39 . + @xcite present a technique for the determination of the isp for specific wavelength ranges which have null intrinsic polarization . this assumes that , for these specific wavelength ranges , there is sufficient overlap between groups of lines such that there is complete intrinsic depolarization over these wavelengths . @xcite suggest that the wavelength region of 4800 - 5600 is intrinsically depolarized , where line blanketing opacity dominates over electron scattering opacity . any polarization , observed over this wavelength range , is expected to be due to the isp alone . for sn 2005hk , at both epochs , the lack of significant overlap and blending of lines leads to the complex behaviour of the stokes parameters . @xcite find that the wavelength range of 4000 - 4200 satisfies the criteria for intrinsic depolarization , namely significant line blanketing . the observation of @xcite at november 5.4 is sufficiently close to our observation at the first epoch that we observed similar features in the polarization spectrum and the stokes parameter spectra . importantly , we too determine that this wavelength range provides the best approximation to a line blanketed regime . the measured stokes parameters across this range at the first epoch are @xmath40 and @xmath41 . the uncertainties on these quantities are the combined systematic and statistical uncertainties . + the spectral evolution of sn 2005hk by the second epoch , with the increase in the strengths of individual and lines in the range of 4000 - 4200 , leads to the presence of intrinsic polarization ( @xmath42 and @xmath43 ) . instead , we identify the region of 4250 - 4450 as being spectroscopically similar to a line blanketed regime with no unblended line structure . over this wavelength range the average values of the stokes parameters are measured as @xmath44 and @xmath45 . the measured stokes parameters , over the depolarized wavelength range , agree with those determined at the first epoch . + we adopt values of the isp stokes parameters of @xmath46 and @xmath47 , for both the galactic and host isp components , which are approximately consistent with the values measured by @xcite ( who calculate separate galactic and host components ) . the value of the isp relative to the observed stokes parameters is shown on figs . [ fig : obs : panela ] and [ fig : obs : panelb ] . these values correspond to a polarization of @xmath48 with an angle of @xmath49 . the orientation of the isp component is shown on fig . [ fig : obs : hostimage ] . as previously observed for other sne , the isp component is aligned with the spiral arm pattern at the sn location , due to alignment of magnetic field lines and , hence , dust grains along spiral arms @xcite . + given the limited wavelength range over which it can be determined , it is not clear if and how the isp component varies with wavelength . although a standard serkowski - type law could be applied , it is unclear what the appropriate values of @xmath50 and @xmath51 would be . furthermore , it has been observed for a number of sne with significant isps that the isp does not necessarily even follow a galactic - serkowski type law of wavelength dependence . given the small value of the isp , we subtract , therefore , a constant isp component from the observed data , to recover the intrinsic polarization of the sn ( as shown by @xmath52 in figs . [ fig : obs : panela ] and [ fig : obs : panelb ] ) , under the assumption that any wavelength dependence of the isp is smaller than the uncertainties derived above . + on the stokes @xmath53 plane ( see figs . [ fig : obs : qupanela ] and [ fig : obs : qupanelb ] ) , the isp component is located close to the centroid of the sn 2005hk data . the calculated weighted centroids for the isp - corrected data @xmath54 are listed in table [ tab : obs : domaxis ] . + after correction for the isp , the intrinsic polarization of sn 2005hk is observed to be extremely low across the observed wavelength range . the degree of polarization of a number of features observed to be relatively strongly polarized in the uncorrected polarization spectrum , are no longer as polarized once the data have been corrected for the isp . utilising the data across the range @xmath55 as representative of a region of pure continuum emission , the level of the continuum polarization is measured as @xmath56 and @xmath57 at the first and second epochs , respectively . at the second epoch the assumption that this wavelength range represents a true continuum region is most likely invalid , due to the presence of a number of minor , broad undulations which are most likely due to the lines ( rather than incorrect flatfielding of the flux spectrum ) . this wavelength range avoids any polarization associated with the feature at @xmath31 , and is less than the continuum polarization measured by @xcite at 2005 nov 5.4 of @xmath58 . this level of polarization is consistent with a spheroidal configuration with axial ratio @xmath59 . + the significance of the polarization signal is given by @xmath60 @xcite . at both epochs there are no features , at either @xmath61 or @xmath62 binning , which are detected in the intrinsic polarization spectrum @xmath52 at @xmath63 and only a small number of bins detected at @xmath64 . @xcite argue that in their data from 5 november , only the line of @xmath65 is polarized and at a rather small level . on inspection , their data suggest that @xmath66 is also somewhat polarized . there is another feature of similar amplitude showing a minimum at @xmath67 in the polarized flux that has no strong component in the total flux spectrum , but is likely to correspond to @xmath68 . + our data at the first epoch also show possible modulation in the polarization spectrum associated with @xmath65 , as well as @xmath22 and the @xmath31 feature . at redder wavelengths there are a number of peaks which are associated with telluric features , suggesting that these were variable over the course of the observations . the apparent significance of these features is therefore overestimated , as the possible variability of telluric features was not considered in the reduction process and not accounted for in the final error analysis . + by the second epoch , there are possible peaks in the intrinsic polarization associated with the absorptions of the multiplet 42 , the intrinsic feature and the absorption of @xmath69 . + the absence of a significant signal in the polarization spectrum does not necessarily imply that the intrinsic polarization of spectral features is also not significant . @xcite and @xcite studied the change in polarization @xmath70 across particular spectral features , by comparing the modulation in the stokes @xmath10 and @xmath11 parameters from the approximate `` continuum '' level and at the wavelength of absorption minimum , where : @xmath71 @xmath72 is independent of the choice of the isp component . the values of @xmath72 for particular spectral features , at both epochs , are presented in table [ tab : res : delp ] . + even when assessed by modulation of the stokes parameters , the data at both epochs show few significant features . at the first epoch , h&k , and , importantly , @xmath73 show significant modulation , whereas at the second epoch the significant modulation is associated with the , now stronger , lines . the interpretation of the data presented in table [ tab : res : delp ] requires some caution , however , as the selection of @xmath74 and @xmath75 , by eye , can lead to a bias in favour of selecting those wavelengths that yield the maximum change in the stokes parameters . the principal differences between the data presented by @xcite at -4 days , compared to our data at 0 days , is due to much larger s / n achieved in their observation . we estimate that at @xmath31 , at 50 binning , @xcite achieved a final @xmath76 , whereas our observation reached @xmath77 . + at the first epoch , two sets of two contiguous bins ( at 30 ) are observed at both the 7200 feature and immediately redward at 7315 . an obvious line feature is associated with the former spectral line in the flux spectrum . the latter feature corresponds to a telluric feature that , although it should be equally cancelled between the two beams at each retarder plate position , may appear polarized due to variability in the telluric line between the pair of observations used to derive each stokes parameter . + on the stokes @xmath53 plane ( see figs . [ fig : obs : qupanela ] and [ fig : obs : qupanelb ] ) , the data at both epochs assume an approximate elliptical distribution , with no major structure deviating from the main concentration of points . at the first epoch , the data have no obvious preferred direction . by the second epoch the data are more extended across the @xmath53 plane , although again with no major deviations from the main concentration of data points . from fig . [ fig : obs : qupanelb ] it is also evident that , by the second epoch , the degree of polarization has become more wavelength dependent , with data at bluer wavelengths being concentrated at lower values of @xmath10 and @xmath11 than the data at the red extreme of the observed wavelength range . our lower @xmath78 data does not show the wavelength dependent elongation to the same degree as observed at -4 days , for which a dominant axis is clear to the eye . the behaviour of the data on the stokes @xmath53 plane , at both epochs , is quantified and discussed in section [ sec : res : decomp ] . the determination of the dominant axis , and the decomposition of the stokes vector , permits a correction for the random position angle at which target sne have been observed , as well as determination of the principal axis of symmetry of the data , the relative orientations of the different line forming species and , ultimately , the underlying geometry . the dominant axis forms a line across the stokes @xmath53 plane , and the decomposition process involves rotating the data so that the principal rotated stokes axis is aligned with the axis of greatest variance for the data on the stokes plane . the polarization signal is measured in the two orthogonal directions , which are effectively the `` rotated stokes parameters '' , along the dominant axis ( @xmath79 ) and along the orthogonal axis ( @xmath80 ) . a polarization component in the orthogonal direction permits the identification of deviations from the single axial symmetry represented by the dominant axis . + here we explore two complementary techniques for determining the dominant axis : least - squares fitting of a straight line and a principal components analysis of the data on the stokes @xmath53 plane . importantly , these two different analyses _ should _ give identical measures of the dominant axis , but provide different parametrisation of the data on the stokes @xmath53 plane . this latter point is particularly crucial for applying the sn spectropolarimetric classification scheme of . + straight lines , of the form @xmath81 , were fit to the data of both epochs , using a weighted least - squares fitting technique , where the data were weighted according to the errors in both @xmath10 and @xmath11 @xcite . in order to confirm the validity of this technique , the form of the straight line was reversed and the best fit was calculated for @xmath82 , giving identical results . the value of @xmath83 yields the angle of the dominant axis with respect to the stokes @xmath10-axis , through which the data are to be rotated to decompose the stokes vector onto the dominant and orthogonal axes . for a single axial symmetry , the dominant axis will pass through the origin of the stokes @xmath53 plane . in instances where the data are offset from the origin ( e.g. by a wavelength - independent continuum polarization component ) the offset will be _ partially _ manifested in the measured @xmath84 parameter . + dominant axes were calculated for the data at both epochs over two different wavelength ranges : 3700 to 8600 and 4000 - 7000 . the former range wavelength encompasses the entire wavelength range of the observed data , whereas the latter excludes regimes with poor levels of signal - to - noise ( @xmath85 ) . the regions of low signal - to - noise arise at the blue and red extremes of the data , due to line - blanketing and the blue spectral energy distribution significantly reducing the observed flux in the blue and red , respectively , and the declining detector response ( in the red ) . + the results of the least - squares analysis and the properties of the determined dominant axes are presented in table [ tab : obs : domaxis ] . the values of @xmath84 , @xmath83 , and the polarization angle of the dominant axis ( @xmath86 ) were found to be relatively insensitive , within the uncertainties , to the choice of the wavelength range over which the dominant axis was calculated . the dominant axes are shown on the stokes @xmath53 plane on figs . [ fig : obs : qupanela ] and [ fig : obs : qupanelb ] . the large values of @xmath87 for the straight line fit , at both epochs , indicate that the data are poorly described by a straight line , with a significant polarization component in the orthogonal direction . at the first epoch , simple inspection of the data on the stokes @xmath53 plane would suggest that the data are evenly distributed in angle about the centroid ( as is illustrated in section [ sec : res : pca ] ) . at the second epoch , a dominant axis is more clearly observed . + in order to better understand and quantify the distribution of the data on the @xmath53 stokes plane and , in particular , the degree of the orthogonal polarization component , a principal component analysis of the data was conducted . + the elements of the @xmath88 @xmath89 covariance matrix take the form : @xmath90 where @xmath91 , @xmath92 , @xmath93 ( see * ? ? ? * ) , @xmath94 and the weighted average of the stokes parameters are @xmath95 , as shown in table [ tab : obs : domaxis ] , over the @xmath96 wavelength bins . the eigenvectors and eigenvalues of the covariance matrix provide an alternative measure of the angles of the dominant and orthogonal axes ( @xmath97 ) and the ratio of the degrees of polarization in the dominant and orthogonal directions ( an axial ratio for the resulting ellipse @xmath98 ) , respectively . this latter quantity can be used to describe an ellipse on the stokes @xmath53 plane which contains the data . the results of the principal component analysis are presented in table [ tab : obs : domaxis ] , and corresponding ellipses are presented on figs . [ fig : obs : qupanela ] and [ fig : obs : qupanelb ] . as expected , the polarization angle of the dominant axis determined using this analysis agrees , within the uncertainties , with the result from the least - squares fit . + the non - zero values of @xmath98 determined from the principal components analysis show that the data at the two epochs are inconsistent with both straight lines and null polarization . this suggests that , although the polarization measured at both epochs is low , we have measured a real polarization signal for sn 2005hk . the ratio of the dominant and orthogonal components measured at the second epoch is smaller than that measured at the first , implying that at the first epoch the ejecta were approximately round and , with time , departed more significantly from the spherical symmetry . + this interpretation requires some caution , however , as @xcite observed data that corresponded to a dominant axis four days prior to our first observation , which we do not see in our data at the first epoch . this may reflect the low @xmath78 of our first observation , rather than an `` oscillating '' evolution in shape of the structure of the ejecta ; with the ejecta appearing approximately spherical at maximum but departing from a spherical symmetry both before and after maximum light . the data were rotated onto the dominant and orthogonal axes , using the angles determined from the least - squares fit analysis ( for the limited wavelength range of 4000 - 7000 ) . the rotated data are presented as figs . [ fig : obs : doma ] and [ fig : obs : domb ] . despite the apparent increase in the polarization angle from the first to second epochs , the determined polarization angles for the dominant axes are different from the angle measured at -4 days , for which @xcite determined @xmath99 . + at the first epoch , the dominant and orthogonal polarization components are similar to stokes @xmath10 and @xmath11 , due to the small angle through which the data were rotated . the polarization modulations associated with , , are predominantly observed in the dominant polarization component , and over the range 4000 - 7000 the deviations observed in the orthogonal polarization spectrum are consistent with the expected noise level . similar to the @xcite observations at -4 days , an important exception is the 7200 absorption feature ( and possibly @xmath65 ) which has both dominant and orthogonal polarization components ( although @xcite refer to the rotated stokes parameters @xmath100 and @xmath101 , these are equivalent to our dominant and orthogonal axes ) . at our second epoch , the majority of features , associated with , and , particularly , the @xmath31 feature show some modulation in both the dominant and orthogonal polarization components . while @xcite observed an obvious wavelength dependence in the dominant polarization component , with increasing @xmath79 at redder wavelengths ( which we estimate to be @xmath102 ) , 4 days later we found the wavelength dependence to be shallower @xmath103 . at @xmath104 days we measure a similar wavelength dependence @xmath105 . this wavelength dependence is clearly seen on fig . [ fig : obs : qupanelb ] . the change may not be evidence for evolution in the wavelength dependence of the dominant polarization component , in itself , as the observations of @xcite were acquired with higher @xmath78 . such wavelength dependence of the polarization , increasing at redder wavelengths was observed for sn 1999by @xcite . at the temperatures determined for sn 2005hk , and for fe - rich matter , the opacity at the photosphere is dominated by blends of line transitions for @xmath106 . at redder wavelengths , the opacity is primarily due to electron scattering . the continuum polarization may indicate an aspherical thomson scattering region , e.g. by a global asymmetry induced by the rotation of the white dwarf progenitor @xcite or off - center delayed detonations @xcite . because multiple line scatterings are effectively depolarizing , the observation of increasing polarization with wavelength may be understood in terms of the decrease of the role of line opacity at redder wavelengths . if the dominant axis corresponds to a principal axial symmetry , then the line forming regions of the species observed in the flux spectrum follow the same axial symmetry as that of the continuum at the first epoch , but not at the second epoch . on the basis of the continuum polarizations measured at 0 and 14 days , any asymmetry in the shape of the photosphere ( assuming a spheroidal configuration ) requires an axial ratio @xmath59 . a similar limit on the asphericity of the photosphere is achieved if one uses the higher value of continuum polarization ( @xmath58 ) determined by @xcite + the general level of line polarization is low , suggesting that the line forming regions cover an approximately spherically symmetric photosphere homogeneously . limits on the amount of polarization expected to be observed can be calculated , given a level of continuum polarization and line depth , under the assumption that the line forming region blocks only _ unpolarized light _ from the photosphere , while not blocking polarized light arising from the limb ( i.e. that the photosphere can be separated into discrete polarized and unpolarized zones ) : @xmath107 where @xmath108 and @xmath109 are the observed fluxes in the continuum and in the absorption line minimum , respectively ( i.e. such that the line depth is @xmath110 - this convention is chosen as the observed polarization arises from the light that is not absorbed ) . as @xcite calculated for their observation of sn 2005hk , we also calculate the theoretical limits on the line polarization for measured absorption line depths in our observations . + at the first epoch , the maximum polarization for the @xmath22 line is only 0.14% . as @xcite suggest , that the lines are not strongly polarized is commensurate with their apparent weakness . this is true at the first epoch , where line strengths of only @xmath111 are observed . at the second epoch , however , absorption line depths of @xmath112 are observed , and with the increase in depth of these lines it might be expected that , should the line forming regions be asymmetric , that there would also be a commensurate increase in the polarization observed across these lines ( see fig . [ fig : obs : monte ] ) [ eqn : res : linepollim ] assumes that all of the polarization is due to the continuum , which implicitly assumes that the photosphere itself is asymmetric . in a number of cases , in particular for core - collapse sne , the classical limit for line polarization is exceeded ( see e.g. * ? ? ? * ; * ? ? ? * ) , for low values of continuum polarization which suggest approximately spherical photospheres . violations of this criterion can be explained by large scale structure , with a dissimilar geometry to that of the photosphere , or clumping , which may produce polarization irrespective of the shape of the photosphere or the degree of continuum polarization . the degree of observed polarization , for a clumpy line forming region , should depend on the size of the clumps : for a given line absorption depth , fewer larger clumps block larger areas with contiguous polarization vectors , whereas more smaller clumps can be distributed more evenly across the photosphere . + in order to explore the possible role of clumping , and the expectation for the production of polarization across shallow lines , a monte - carlo toy model of a simple photosphere and obscuring clumped line forming region was constructed following the scheme of @xcite . a circular continuum emitting photosphere was adopted , with the luminosity as a function of projected radius @xmath113 across a photosphere of radius @xmath114 set to : @xmath115 with limb darkening modelled using the coefficient @xmath116 , which for @xmath117 yields no limb darkening . for a three - dimensional spherical photosphere , this would correspond to to a limb darkening law of @xmath118 . the radial dependence of the polarization was assumed to follow a quadratic form @xmath119 , with the constant of proportionality chosen to yield 15% polarization for light emitted at the limb of the photosphere @xcite . opaque circular clumps were assumed , with @xmath120 , such that all photospheric flux from the region underlying the clump was blocked . for each iteration of the model , @xmath96 clumps of size @xmath121 were randomly positioned across the photosphere and the corresponding flux of the uncovered regions , and their polarization components , were summed . clumps were permitted to overlap and only partially cover the photosphere . for each size of clumps , 3000 simulations were conducted . this permits a comparison of the expected polarization for a given absorption line depth , assuming a particular clump size in the line forming region . the results of this model ( for @xmath122 , @xmath123 , @xmath124 and @xmath125 ) are shown as fig . [ fig : obs : monte ] . + for some of the models , zero polarization was achieved for uniform coverage of the photosphere by the clumps , however the difference between the average polarizations expected ( as shown in fig . [ fig : obs : monte ] ) and null polarization was @xmath126 for all the calculated models . these models suggest that , for a clumpy line forming region , the clump scale for sn 2005hk is very small ( @xmath127 ) to produce lines of the depths observed , in the flux spectra at both epochs , with low polarization . the uniformly low polarization observed for lines arising from different species suggest that the ejecta are generally mixed , with no separate structures _ on the plane of the sky _ for different elements or ionization stages(e.g and ) . the element responsible for the absorption at 7200 may be an exception , with a line forming region that is more aspherical than other species . the data for sn 2005hk , at the two epochs presented here and those presented by @xcite , are consistent with an approximately spherical symmetric photosphere surrounded by similar line forming regions for all species . + the principal assumption of the model presented above is that the line forming region and the photosphere are separate . as discussed in [ sec : res : domort ] , the opacity at the photosphere ( where the quasi - continuum forms ) is not due to electron scattering alone , but rather includes a significant wavelength dependent contribution from atomic transitions ; this implies that line forming regions are not , in reality , separate entities except in the most high - velocity regions such as those discussed by @xcite . + the size of the clumps and their relation to `` large - scale '' structure within the ejecta , leads to an interesting problem of semantics : since very large clumps ( @xmath128 ) may be considered large scale structure and very small clumps ( @xmath129 ) tend towards constituting an effectively homogeneous medium . large opacities require that a large fraction of the photosphere , the last thomson scattering distance , are reprocessed by lines , mostly due to iron - group elements ( which will result in a significantly altered spectrum ) .

epochs the data corresponds to the spectropolarimetric type d1 . the general low level of line polarization suggests that the line forming regions for most species observed in the spectrum have a similar shape to that of the photosphere , which deviates from a spherical symmetry by . in comparison with spectropolarimetry of type ia and core - collapse sne at similar epochs , we find that the properties of sn 2005hk are most similar to those of type ia sne . in particular , we find the low levels of continuum and line polarization to indicate that the explosion mechanism is approximately spherical , with homogeneous ejecta ( unlike the chemically segregated ejecta of ccsne ) .

we report two spectropolarimetric observations of sn 2005hk , which is a close copy of the very peculiar " sn 2002cx , showing low peak luminosity , slow decline , high ionization near peak and an unusually low expansion velocity of only about 7,000 . further to the data presented by chornock et al . , ( 2006 ) , at -4 days before maximum , we present data of this object taken on 9 november 2005 ( near maximum ) and 23 november ( + two weeks ) that show the continuum and most of the spectral lines to be polarized at levels of about 0.2 - 0.3% . at both epochs the data corresponds to the spectropolarimetric type d1 . the general low level of line polarization suggests that the line forming regions for most species observed in the spectrum have a similar shape to that of the photosphere , which deviates from a spherical symmetry by . in comparison with spectropolarimetry of type ia and core - collapse sne at similar epochs , we find that the properties of sn 2005hk are most similar to those of type ia sne . in particular , we find the low levels of continuum and line polarization to indicate that the explosion mechanism is approximately spherical , with homogeneous ejecta ( unlike the chemically segregated ejecta of ccsne ) . we discuss the possibility that sn 2005hk was the result of the pure deflagration of a white dwarf and note the issues concerning this interpretation .

1008.3985

c

the class of sne similar to sn 2002cx currently has 15 members , including 2005hk and 2008 ha @xcite . as discussed in detail by @xcite and @xcite , both sn 2002cx and sn 2005hk were of especially low velocity at the photosphere near maximum light , @xmath130 @xmath0 , had early relatively high ionization , and low peak luminosity . neither showed the typical secondary maxima in r and i of normal sn ia , but were also dissimilar to previously studied under - luminous sn ia that do not show the secondary maxima ( e.g. * ? ? ? there is also extreme diversity within the class , with sn 2008 ha being @xmath131 magnitudes fainter than sn 2002cx @xcite . the light curve decline is rather slow , unlike previous under - luminous sn ia that serve to define the light curve brightness / decline relation prominently used in cosmology studies . + @xcite pointed out that no published model of a sn ia corresponds to all the behavior of sn 2002cx , but suggested that a pulsating delayed detonation model might be worth considering further . @xcite suggested that the nebular spectral characteristics that they determined might be consistent with a pure deflagration model since the models in the literature have insufficient energy to correspond to normal sne ia and hence tend to have smaller expansion velocities and produce less @xmath132ni and hence tend to be dim . @xcite suggest that the low expansion velocities , low peak luminosity , and the absence of secondary maxima in the nir light curves may be reproduced by a 3d pure - deflagration model that produces 0.25@xmath133 of @xmath132ni . + a key issue with the hypothesis that this class of explosions represents pure deflagrations of white dwarfs is that the pure deflagration models leave a substantial amount of unburned c and o in the outer layers . this c and o should show up in the early phases and while @xmath20 is clearly present at the second epoch ( and possibly the first ) , the case for @xmath30 ( and possibly for a contribution to the @xmath31 feature ) is less clear but it is not conclusively absent . in addition , suggest that the late - time spectra of pure deflagration models show no similarity to that of sn 2002cx either , in particular the absence of strong features due to c and o. @xcite claim a marginal detection of in late - time nebular spectra of sn 2002cx , with the suggestion that more unburned c and o may be contained inside the dense , still optically thick core at late times . @xcite claim that at early times @xmath20 is suppressed by high temperatures and , at late times , nebular lines are also suppressed by high temperatures . the lack of observation of @xmath20 for sn 2005hk at very early times ( before our observations ) is uncertain , due to poor spectral coverage at early times @xcite and low s / n @xcite . @xcite are able to approximately model the photospheric spectrum of sn 2005hk , based on the w7 deflagration explosion model @xcite . importantly , @xcite find that , given the conditions of the sn , their spectral synthesis suggests large amounts of unburned o. their model also assumes spherical symmetry , for which they achieve a reasonable approximation to the line profiles ( which are somewhat sensitive to any departures from spherical symmetry ; see e.g. @xcite for a counter example ) . the features remain too broad , are forbidden rather than permitted , and show prominent emission of [ ] @xmath134 . high densities , as evidenced by the low expansion velocities and p cygni profiles observed at late nebular epochs , might suppress the [ ] feature , but it is predicted in the models and so its absence is a definite constraint on the nature of sn 2005hk . + @xcite consider the possibility that these events may be related to normal sne ia , but viewed along the hole " left by having the binary companion nearly directly along the line of sight @xcite . such an aspect might increase the prominence of high - ionization species , weaken absorption lines , reduce the photospheric velocity and induce some polarization due to the non - spherical geometry of the ejecta . one issue with this model for sn 2002cx and related explosions is that it would result in higher luminosities than when viewed from other aspect angles . even if the underlying explosion were a subluminous event such as sn 1991bg , if the view were down the hole , " the result would be brighter than sn 1991bg . both sn 2002cx and sn 2005hk were subluminous by about 1 magnitude in all bands ( except h ; * ? ? ? it is certainly not clear that this is consistent with a hole " model . @xcite comment that their measurement of a small but appreciable continuum polarization and weak line features was inconsistent with the prediction of @xcite of a continuum polarization of @xmath2 0.1 percent and strong line polarization peaks for an explosion viewed slightly off the axis of the hole . as the sn evolves , the relative size of the hole and the photosphere will change ( in particular if the hole closes , which @xcite expect to be a slow process if it occurs ) , which should lead to a commensurate change in the polarization properties . importantly , we see only moderate change in the polarization , despite the significant changes in the flux spectrum , between the epochs at which sn 2005hk was observed . in addition , it is not at all clear how such a model would account for the late - time permitted line spectrum delineated by @xcite . our observations do suggest some line polarization . this demands some asymmetry in the ejecta , consistent with a single axial symmetry , but does not spell out quantitative agreement with the hole " model . + an alternative model might be a plume " model @xcite in which a single plume ( or very few plumes ) reach the surface , spreading fresh @xmath132ni . if the plume burned little , the expansion might be slow and leave high densities at late times . our spectropolarimetry suggests that the outer layers of the ejecta are approximately homogeneously mixed , although stratified , which suggests mixing in a large number of smaller plumes ( with size @xmath135 at the first epoch ) . + this class of objects thus presents many conundra . they show high excitation early on but otherwise have none of the properties of sne ia like sn 1991 t that show early . their light curves are dim but broad , violating the `` phillips relation '' . they have very slow expansion velocities and may remain partially optically thick at nearly 300 days after the explosion . they are mildly asymmetric in the continuum , in the early on and in near maximum . the polarization of sn 2005hk is completely compatible with the observed range of polarization properties for type ia sne ( see table [ tab : disc : comp ] ) . the level of polarization of sn 2005hk is not the lowest _ detected _ for a sn , with sn 1996x ( a normal type ia sn ; @xcite ) showing polarization just above statistical significance and with no apparent dominant axis . the observations of sn 2005hk show it to have a spectropolarimetric type of d1 , similar to most type ia sne , indicating that there is a principal axis of symmetry to the ejecta . importantly , there are no apparent loop like features , even for the strongest lines ( which is particularly pertinent for the observations at the second epoch ) which would indicate a significant departure from this main axial symmetry . normal type ia sne , such as sn 2001el @xcite and sn 2004s @xcite , show some structure in their ejecta principally in the , as well as the high velocity component of the ir3 . conversely , there are type ia sne , such as sn 2004dt @xcite , whose line polarization is principally in the dominant polarization component which is consistent with a single axial symmetry . in the case of sn 2004dt , however , the observed line polarization was @xmath136 . in summary , the similarity between the spectropolarimetry of sn 2005hk and type ia sne indicates that their respective explosion mechanisms are both approximately spherical ( see table [ tab : disc : comp ] ) . + @xcite identified a correlation between the degree of polarization of , at -5 days , with the decline rate ( @xmath137 ) of the light curve . at some wavelengths sn 2005hk is an outlier from the phillips brightness - decline relationship , although it is consistent with the relationship in the @xmath138 and @xmath139 bands @xcite . while the polarization measurements of sn 2005hk is offset from the measured relation derived for normal type ia sne by @xcite , it is not as significant an outlier as the subluminous type ia sne 1999by and 2005ke ( see fig . [ fig : disc : wang ] ) . + @xcite , @xcite and @xcite consider the possibility that events such as sn 2002cx and 2005hk are not related to type ia sne , but may instead be a type of ccsn . based on the photometric and spectroscopic similarity between sn 2008 ha and sn 2005hk with low - luminosity type iip and type ic sne ( 2005cs and 2007gr , respectively ) and the occurrence of these events in late - type galaxies , @xcite suggest 2002cx - like sne are low - luminosity type ic sne , potentially associated with gamma ray bursts ( grbs ) . @xcite present additional events in this class , which are claimed to have taken place in lenticular s0 galaxies , which may argue against massive stars as the universal progenitors for this type of event . spectropolarimetry provides additional parameter space in which to examine the similarities between different types of sne . + @xcite and @xcite note the spectroscopic similarity between sn 2005hk and sn 2008 ha at + 15 and + 8 days ( after optical maximum ) , respectively , as well as their similarity with the subluminous type iip sn 2005cs at + 44 days , whilst it was still on the photometric plateau @xcite . at such times type iip sne have generally low polarizations @xcite , seemingly similar to that observed by us for sn 2005hk . from a spectropolarimetric perspective , however , comparison of sn 2005hk with sn 2005cs whilst on the plateau is inappropriate . during the plateau phase , in type iip sne , the photosphere is located in the hydrogen envelope . due to the low ionization energy of h , the shape of the photosphere is approximately spherical . once the photosphere has descended below the h envelope , into the he layer ( he being harder to ionize and excite ) , the shape of the photosphere more closely follows the shape of the underlying exciting material . despite an asymmetric explosion , @xcite observed that during the plateau sn 2004dj had a low polarization , which increased significantly once the plateau phase had ended . given the h - deficient nature of sn 2002cx - like sne , a more appropriate comparison is with the h - deficient ccsne , which have been observed ( as listed in table [ tab : disc : comp ] ) to have significant continuum and line polarization for different species indicating the role of highly asymmetric explosion mechanisms . highly asymmetric interiors have also been observed for the type iip sne 2001dh and 2003gd ( maund et al . , 2010 , in prep . ) , which suggest that an asymmetric explosion mechanism is common to all these ccsn events . + it is interesting to note another ongoing controversy involving sne ia and sne ic . sn 2002ic was revealed by @xcite to resemble a sn ia embedded in a hydrogen - rich medium . @xcite interpreted this as a sn ia exploding with an evolved binary companion . @xcite showed that the hydrogen component was strongly polarized and argued that the geometry was consistent with an extended , clumpy , disk - like structure such as observed in proto - planetary nebula stars . @xcite and @xcite identified other events of this category that were originally identified as type iin events , but which , on closer inspection and comparison with sn 2002ic , revealed an underlying type i spectrum . more recently , @xcite have challenged this interpretation , arguing that the underlying supernova in sn 2002ic more closely matched a sn ic than a sn ia . + in summary , the nature of the polarization of sn 2005hk is inconsistent with the polarization measured for ccsne , in particular those of type ibc which have been generally observed to have very large polarization ( especially line polarization ) that increases with time .

we report two spectropolarimetric observations of sn 2005hk , which is a close copy of the very peculiar " sn 2002cx , showing low peak luminosity , slow decline , high ionization near peak and an unusually low expansion velocity of only about 7,000 . we discuss the possibility that sn 2005hk was the result of the pure deflagration of a white dwarf and note the issues concerning this interpretation .

we report two spectropolarimetric observations of sn 2005hk , which is a close copy of the very peculiar " sn 2002cx , showing low peak luminosity , slow decline , high ionization near peak and an unusually low expansion velocity of only about 7,000 . further to the data presented by chornock et al . , ( 2006 ) , at -4 days before maximum , we present data of this object taken on 9 november 2005 ( near maximum ) and 23 november ( + two weeks ) that show the continuum and most of the spectral lines to be polarized at levels of about 0.2 - 0.3% . at both epochs the data corresponds to the spectropolarimetric type d1 . the general low level of line polarization suggests that the line forming regions for most species observed in the spectrum have a similar shape to that of the photosphere , which deviates from a spherical symmetry by . in comparison with spectropolarimetry of type ia and core - collapse sne at similar epochs , we find that the properties of sn 2005hk are most similar to those of type ia sne . in particular , we find the low levels of continuum and line polarization to indicate that the explosion mechanism is approximately spherical , with homogeneous ejecta ( unlike the chemically segregated ejecta of ccsne ) . we discuss the possibility that sn 2005hk was the result of the pure deflagration of a white dwarf and note the issues concerning this interpretation .

1008.3985

c

sn 2005hk has been observed at two epochs , corresponding to maximum light and two weeks after maximum . after subtraction of the isp component , the sn is observed to have a very low to null intrinsic polarization . a modulation in the stokes parameters is observed across the @xmath22 line being the most significant feature , at the first epoch , with @xmath140 . + at both epochs , a dominant axis can be fit to the data , although the data are poorly described by simple straight line fits on the stokes @xmath53 plane . while there is modulation in the dominant polarization component , at the first epoch , that is associated with line features in the flux spectrum , the absence of similar modulations in the orthogonal polarization component implies that the line forming regions of the species in the flux spectrum share the same axial symmetry as that of the photosphere . the data at both epochs is classified as being of spectropolarimetric type d1 . + in comparison with previously published high s / n observations of sn 2005hk at -4 days @xcite , we observe a possible rotation of the polarization angle of the dominant axis , but it is unclear ( due to the differences in s / n ) if this represents a real rotation of the principal axis of symmetry with depth into the ejecta . + the low level of continuum polarization limits the asymmetry of the photosphere , at both epochs , to @xmath1 . the low line polarization is suggestive that the line forming regions are mixed , that different species occupy similar locations within the ejecta , and that they have a similar geometry to that of the photosphere . this is similar to the general behaviour of type ia sne , and different from the chemically segregated ejecta observed for ccsne . + we conclude that the spectropolarimetry of sn 2005hk is not inconsistent with some of the expectations of the deflagration explosion model . we find that , in order to preserve the approximate spherical symmetry of the photosphere and the line forming regions , any plume - like structures would be required to have a scale , in the plane of the sky , of @xmath135 at both epochs . this would give the overall appearance of homogeneously mixed ejecta containing both the products of nucleosynthesis ( fe , ni , co ) and unburned o at all depths . + spectral similarities between sn 2002cx - like events and low - luminosity type iip sne are likely to be merely superficial . the differences in the observed spectropolarimetry of sn 2005hk with ccsne suggests , from a geometry perspective , that these events have different underlying explosion mechanisms . unfortunately , with spectropolarimetry of only one sn from the 2002cx - like class it is not possible to determine if these results are applicable to the entire class , in particular to the most peculiar member of this class , sn 2008 ha .

, ( 2006 ) , at -4 days before maximum , we present data of this object taken on 9 november 2005 ( near maximum ) and 23 november ( + two weeks ) that show the continuum and most of the spectral lines to be polarized at levels of about 0.2 - 0.3% . at both

we report two spectropolarimetric observations of sn 2005hk , which is a close copy of the very peculiar " sn 2002cx , showing low peak luminosity , slow decline , high ionization near peak and an unusually low expansion velocity of only about 7,000 . further to the data presented by chornock et al . , ( 2006 ) , at -4 days before maximum , we present data of this object taken on 9 november 2005 ( near maximum ) and 23 november ( + two weeks ) that show the continuum and most of the spectral lines to be polarized at levels of about 0.2 - 0.3% . at both epochs the data corresponds to the spectropolarimetric type d1 . the general low level of line polarization suggests that the line forming regions for most species observed in the spectrum have a similar shape to that of the photosphere , which deviates from a spherical symmetry by . in comparison with spectropolarimetry of type ia and core - collapse sne at similar epochs , we find that the properties of sn 2005hk are most similar to those of type ia sne . in particular , we find the low levels of continuum and line polarization to indicate that the explosion mechanism is approximately spherical , with homogeneous ejecta ( unlike the chemically segregated ejecta of ccsne ) . we discuss the possibility that sn 2005hk was the result of the pure deflagration of a white dwarf and note the issues concerning this interpretation .

quant-ph0501056

i

many problems of interest in quantum computing can be reduced to an instance of the _ hidden subgroup problem _ ( hsp ) . we are given a group @xmath0 and a function @xmath1 with the promise that , for some subgroup @xmath2 , @xmath1 is invariant precisely under translation by @xmath3 : that is , @xmath1 is constant on the cosets of @xmath3 and takes distinct values on distinct cosets . we then wish to determine the subgroup @xmath3 by querying @xmath1 . for example , in simon s problem @xcite , @xmath4 and @xmath1 is an oracle such that , for some @xmath5 , @xmath6 for all @xmath7 ; in this case @xmath8 and we wish to identify @xmath5 . in shor s factoring algorithm @xcite @xmath0 is the group @xmath9 where @xmath10 is the number we wish to factor , @xmath11 for a random @xmath12 , and @xmath3 is the subgroup of @xmath9 whose index is the multiplicative order of @xmath13 . both simon s and shor s algorithms use the following approach , referred to as the _ standard method _ or _ fourier sampling _ @xcite . : : prepare two registers , the first in a uniform superposition over the elements of @xmath0 and the second with the value zero , yielding the state @xmath14 step 2 . : : query ( or calculate ) the function @xmath1 defined on @xmath0 and xor it with the second register . this entangles the two registers and results in the state @xmath15 step 3 . : : measure the second register . this puts the first register in a uniform superposition over one of @xmath1 s level sets , i.e. , one of the cosets of @xmath3 , and disentangles it from the second register . if we observe the value @xmath16 , we have the state @xmath17 where @xmath18 alternately , we can view the first register as being in a mixed state with density matrix @xmath19 where the sum includes one representative @xmath20 for each of @xmath3 s cosets . : : carry out the quantum fourier transform on @xmath21 and measure the result . ( note that in shor s algorithm , since @xmath22 is unknown , the fourier transform is performed over @xmath23 for some @xmath24 ; see @xcite or @xcite . ) in both simon s and shor s algorithms , the group @xmath0 is abelian ; it is not hard to see that , in this abelian case , a polynomial number ( i.e. , polynomial in @xmath25 ) of experiments of this type determine @xmath3 . in essence , each experiment yields a random element of the dual space @xmath26 perpendicular to @xmath3 s characteristic function , and as soon as these elements span @xmath26 we are done . while the _ nonabelian _ hidden subgroup problem appears to be much more difficult , it has very attractive applications . in particular , solving the hsp for the symmetric group @xmath27 would provide an efficient quantum algorithm for the graph automorphism and graph isomorphism problems ( see e.g. jozsa @xcite for a review ) . another important motivation is the relationship between the hsp over the dihedral group with hidden shift problems @xcite and cryptographically important cases of the shortest lattice vector problem @xcite . so far , algorithms for the hsp are only known for a few families of nonabelian groups , including wreath products @xmath28 @xcite ; more generally , semidirect products @xmath29 where @xmath30 is of polynomial size , and groups whose commutator subgroup is of polynomial size @xcite ; `` smoothly solvable '' groups @xcite ; and some semidirect products of cyclic groups @xcite . ettinger and hyer @xcite provided another type of result , by showing that fourier sampling can solve the hsp for the dihedral groups @xmath31 in an _ information - theoretic _ sense . that is , a polynomial number of experiments gives enough information to reconstruct the subgroup , though it is unfortunately unknown how to determine @xmath3 from this information in polynomial time . to discuss fourier sampling for a nonabelian group @xmath0 , one needs to develop the fourier transform over @xmath0 which relies on the group s _ linear representations_. for abelian groups , the fourier basis functions are homomorphisms @xmath32 such as the familiar exponential function @xmath33 for the cyclic group @xmath34 . in the nonabelian case , there are not enough such homomorphisms to span the space of all @xmath35-valued functions on @xmath0 ; to complete the picture , one introduces _ representations _ of the group , namely homomorphisms @xmath36 where @xmath37 is the group of unitary matrices acting on some @xmath35-vector space @xmath38 of dimension @xmath39 . it suffices to consider _ irreducible _ representations , namely those for which no nontrivial subspace of @xmath38 is fixed by the various operators @xmath40 . once a basis for each irreducible @xmath41 is chosen , the matrix elements @xmath42 provide an orthogonal basis for the vector space of all @xmath35-valued functions on @xmath0 . the quantum fourier transform then consists of transforming ( unit - length ) vectors in @xmath43}= \ { \sum_{g \in g } \alpha_g { \left| g \right\rangle } \mid \alpha_g \in { \mathbb{c}}\}$ ] from the basis @xmath44 to the basis @xmath45 where @xmath41 is the name of an irreducible representation and @xmath46 index a row and column ( in a chosen basis for @xmath38 ) . indeed , this transformation can be carried out efficiently for a wide variety of groups @xcite . note , however , that a nonabelian group @xmath0 does not distinguish any specific basis for its irreducible representations which necessitates a rather dramatic choice on the part of the transform designer . indeed , careful basis selection appears to be critical for obtaining efficient fourier transforms for the groups mentioned above . perhaps the most fundamental question concerning the hidden subgroup problem is whether there is always a basis for the representations of @xmath0 such that measuring in this basis ( in step 4 , above ) provides enough information to determine the subgroup @xmath3 . this framework is known as _ strong fourier sampling_. in this article , we answer this question in the negative , showing that natural subgroups of @xmath27 can not be determined by this process ; in fact , we show this for an even more general model , where we perform an arbitrary positive operator - valued measurement ( povm ) on coset states @xmath47 . we emphasize that the subgroups on which we focus are among the most important special cases of the hsp , as they are those to which graph isomorphism naturally reduces . [ [ related - work . ] ] related work . + + + + + + + + + + + + + the terminology `` strong fourier sampling '' @xcite was invented to distinguish this approach from the natural variant , called _ weak fourier sampling _ , where one only measures the name of the representation @xmath41 , and ignores the row and column information . weak fourier sampling is basis - independent , making it attractive from the standpoint of analysis ; however , it can not distinguish conjugate subgroups from each other , and hallgren , russell and ta - shma @xcite showed that it can not distinguish the trivial subgroup from an order-2 subgroup consisting of @xmath48 disjoint transpositions . specifically , they used character bounds to show that the probability distribution obtained on representation names for the trivial and order-2 subgroups are exponentially close in total variation distance : it requires an exponential number of such experiments to distinguish them . kempe and shalev @xcite have generalized this result to other conjugacy classes , and conjecture that one can do no better than classical computation with this approach . in an effort to shed light on the power of strong fourier sampling , grigni , schulman , vazirani and vazirani @xcite showed that , for groups such as @xmath27 , measuring in a _ random _ basis yields an exponentially small amount of information . this can be explained , roughly , by the fact that projecting a vector into a sufficiently high - dimensional random subspace results in tightly concentrated length . on the other hand , moore , rockmore , russell and schulman @xcite showed that for the affine and @xmath49-hedral groups , measuring in a well - chosen basis can solve the hsp ( at least information - theoretically ) in cases where random bases can not . [ [ our - contribution . ] ] our contribution . + + + + + + + + + + + + + + + + + in this paper we show that strong fourier sampling , in an arbitrary basis of the algorithm designer s choice , can not solve the hsp for @xmath27 . as in @xcite we focus on order-2 subgroups of the form @xmath50 where @xmath51 is an involution consisting of @xmath48 disjoint transpositions ; we remark that if we fix two rigid connected graphs of size @xmath48 and consider permutations of their disjoint union , then the hidden subgroup is of this form if the graphs are isomorphic and trivial if they are not . then we show that strong fourier sampling and more generally , arbitrary measurements of coset states cannot distinguish these subgroups from each other , or from the trivial subgroup , without an exponential number of experiments . we remark that our results do not preclude the existence of an efficient quantum algorithm for the hsp on @xmath27 . rather , they force us to consider _ multi - register _ algorithms , in which we prepare multiple coset states and subject them to entangled measurements . ettinger , hyer and knill @xcite showed that the hsp on arbitrary groups can be solved information - theoretically with a polynomial number of registers , and the authors have shown how to carry out such a measurement in the fourier basis @xcite . kuperberg @xcite devised a subexponential ( @xmath52 ) algorithm for the hsp on the dihedral group @xmath31 that works by performing entangled measurements on two registers at a time , bacon , childs , and van dam @xcite have determined the optimal multiregister measurement for the dihedral group , and the present authors have generalized this to all cases where the @xmath3 and @xmath0 form a gelfand pair @xcite . whether a similar approach can be taken to the symmetric group is a major open question . in a companion paper @xcite , the first two authors take a step towards answering this question by showing that if we perform arbitrary entangled measurements over pairs of registers , distinguishing @xmath53 from the trivial group in @xmath27 requires a superpolynomial number ( specifically , @xmath54 ) of experiments .

we resolve the question of whether fourier sampling can efficiently solve the hidden subgroup problem . specifically , we show that the hidden subgroup problem over the symmetric group can not be efficiently solved by strong fourier sampling , even if one may perform an arbitrary povm on the coset state . these results apply to the special case relevant to the graph isomorphism problem .

we resolve the question of whether fourier sampling can efficiently solve the hidden subgroup problem . specifically , we show that the hidden subgroup problem over the symmetric group can not be efficiently solved by strong fourier sampling , even if one may perform an arbitrary povm on the coset state . these results apply to the special case relevant to the graph isomorphism problem .

astro-ph0302434

i

knowledge of physical conditions ( @xmath1 and @xmath2 ) is an essential ingredient in the understanding of planetary nebulae . information on the structure , chemistry and kinematics of these objects comes from individual diagnostics and from the cross - comparison of different diagnostics . in this work , two different diagnostics will be used to investigate the physical conditions in the planetary nebula ngc 6543 : the temperature - sensitive [ o iii ] ratio @xmath11 , and the ( @xmath1 , @xmath2 ) diagnostic diagram based on the [ o iii ] optical and infrared lines , which was first proposed by @xcite ( henceforth dlw ; see also * ? ? ? the first method , the one based on the @xmath11 ratio , is one of the most popular ones . advantages of this method are that the lines involved are bright , and close enough to be easily observed with the same instrumental setup ; a caution to be taken is that this ratio selectively samples the hottest zones , so that in presence of strong temperature fluctuations the derived temperature , @xmath8o@xmath9 , is biased towards the highest values ( see , e.g. , * ? ? ? furthermore , this ratio measures the temperature of the o@xmath0 region , which is not necessarily representative of the whole observed volume . the second method , the diagnostic diagram by dlw , allows the simultaneous determination of the electron density and temperature by combining the optical and the fir fine - structure [ o iii ] lines . the two infrared lines [ o iii ] 52@xmath12 and 88@xmath12 arise from low - energy levels of the ground term , so their ratio 52@xmath12/88@xmath12 is almost insensitive to the temperature , while the critical densities of their upper levels are different , so the ratio is strongly sensitive to density . on the other hand , a ratio like @xmath3/52@xmath12 is strongly dependent on temperature , due to the very different excitation energies of the upper levels of the two lines , and it has a weak dependence on density too , due to the difference in the critical densities . by combining the two line ratios , one can obtain a simultaneous measurement of the electron temperature , @xmath8o@xmath10 , and density , @xmath13o@xmath10 ( we will use throughout the text the subindex _ ir _ when referring to these @xmath1 and @xmath2 determinations , though an optical line is involved also ; this choice responds to simplicity criteria , and highlights the fact that the density is , to a good approximation , a function of the ratio of the two infrared lines alone ) . one of the main advantages of this method is its internal consistency , since all the lines involved belong to the same ion , so that the same volume is mapped to derive both temperature and density ( although the optical and infrared emissivities might follow different distributions within the o@xmath0 zone if temperature or density fluctuations are present ) . two major disadvantages are consequences of the lines involved lying far apart in the spectrum : first , the lines must be observed with different instruments , a procedure implying the risk of systematic offsets in the calibration ; and second , any uncertainty in the reddening correction is amplified by the large wavelength baseline . by means of these methods , we want to reassess the physical conditions in the bright core of ngc 6543 . a similar analysis was performed on a small sample of pne , including ngc 6543 itself , by dlw . these authors used infrared data obtained with the kuiper airborne observatory ( kao ) , and complemented them with optical spectra from the lick observatory crossley reflector ; the analysis was later repeated by @xcite ( henceforth dhew ) , with quite different results . in the work we present here , the intensity of the infrared lines is obtained from iso archive spectra , and the intensity of [ o iii ] @xmath3 and [ o iii ] @xmath4 from hst archive images . additionally , h@xmath7 and h@xmath14 hst images were used to determine the reddening correction to be applied to the other images , and narrow band hst images around @xmath15 were used to correct the h@xmath7 images for the [ n ii ] contribution . finally , long - slit , ground - based data obtained with the isaac newton telescope at the observatorio del roque de los muchachos were used to correct the hst images for the contribution of other lines and the continuum . these data will be described in sections [ sec : isodata ] , [ sec : intdata ] and [ sec : hstdata ] . ngc 6543 ( the ` cat s eye ' ) is a very well known , low - excitation planetary nebula . many studies have been devoted to understand its complex structure ; an incomplete list of the most recent ones includes @xcite . the bright core of the nebula can be roughly described as the superposition of two ellipses , equal in shape but perpendicular to each other @xcite . this region is about @xmath16 in diameter , and can be seen in direct images in the balmer and [ o iii ] lines . other structures form part of the nebula : surrounding the bright core , a series of dim concentric rings is visible in [ o iii ] , extending at least out to @xmath17 @xcite ; in turn , the rings are surrounded by a giant filamentary halo of about @xmath18 in diameter @xcite ; x - ray emission coming from the bubble surrounding the central star has been recently reported by @xcite ; the variability of the central star has been investigated by @xcite .

we revise the physical conditions in the o zone of the planetary nebula ngc 6543 , obtaining two different estimates of the electron temperature ( ) and one estimate of the electron density ( ) . the electron temperature is computed by means of two independent methods , the nebular - to - auroral ratio [ o iii ]/ , and the diagnostic diagram that combines to the [ o iii ] infrared lines and . alternative possibilities , outside the framework of recombination theory , have also been considered : e.g. , the optical tail in the x - ray emission of a very hot plasma , and dust scattering of stellar radiation , but these hypotheses are not supported by quantitative estimates . while the electron temperature and density derived from the diagnostic diagram

we revise the physical conditions in the o zone of the planetary nebula ngc 6543 , obtaining two different estimates of the electron temperature ( ) and one estimate of the electron density ( ) . the electron temperature is computed by means of two independent methods , the nebular - to - auroral ratio [ o iii ]/ , and the diagnostic diagram that combines to the [ o iii ] infrared lines and . the optical and infrared fluxes have been obtained from archive hst / wfpc2 images and iso lws spectra respectively , and the continuum intensity in the optical has been measured from narrow - slit spectra obtained with the isaac newton telescope at la palma . the measured continuum intensity is higher than predicted by recombination theory under the hypothesis that all the ly photons either escape or are destroyed . this fact can be explained in terms of an enhancement of the 2-photon continuum due to ly- conversion , a process that depends strongly on the local structure of the nebula . alternative possibilities , outside the framework of recombination theory , have also been considered : e.g. , the optical tail in the x - ray emission of a very hot plasma , and dust scattering of stellar radiation , but these hypotheses are not supported by quantitative estimates . while the electron temperature and density derived from the diagnostic diagram agree with the most recent determination , the temperature derived from/ ,o , is somewhat smaller than previously published values . we discuss several technical issues that contribute to the overall uncertainty in our results , focusing on the instrumental effects that might bias the [ o iii ] intensity . we also discuss the effects of the collisional de - excitation of the o ground terms on the relation betweeno ando .

1106.5548

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ever since acoustic peaks were detected in the cosmic microwave background @xcite and galaxy surveys @xcite , much effort has been devoted to use baryon acoustic oscillations ( bao ) as standard rulers to estimate cosmological distances with precision @xcite . bao signals are manifested as a wiggly feature in the matter power spectrum , and precise measurements could shed light on the dynamics of dark energy . the accuracy and precision of such measurement depends directly on the covariance matrix of the matter power spectrum , which is straightforward to compute for a gaussian density field using wick s theorem . however , it is known that non - gaussianities are significant in that covariance matrix @xcite and may have an impact on cosmological distance measurements . a non - linear model is needed for a non - gaussian calculation , hence some criterion for the accuracy of such effects is needed to quantify the precision of the measurement . in particular , an optimal bao measurement should in general incorporate a proper error weighting of the data , which involves the inversion of the full covariance matrix . the accuracy criterion must therefore be based on the confidence we have on the inverted matrix . the estimator constructed in most forecasts and data analyses follow the prescription of @xcite , which is a procedure that constructs both the estimator of the bao scale and the estimator of its uncertainty under the gaussian assumption . the method was originally cross - checked with a @xmath2 analysis of @xmath3 simulations , including a jackknife sub - sampling of the n - body data , and showed good agreement . the actual deviation between this proposed estimator and the optimal estimator constructed in this paper is indeed small , therefore consistent with the work of @xcite . in this paper , we aim at improving on the accuracy of that method , and present a first significant detection of the effect of non - gaussian errors on the measurement of the bao scale ( the effect of non - linear evolution , in the form of erasure of the wiggle signal , has been well - studied of course @xcite ) . some data analyses @xcite also improved on the original method by constructing a non - gaussian estimator for the bao dilation scale uncertainty . this is typically done by modeling the non - linearities in the density fields with mock catalogs , which are produced from log - normal densities @xcite , @xmath4 order perturbation theory @xcite , halo models @xcite , etc . such techniques all attempt to increase the robustness of the analysis by taking into account the coupling between the fourier modes . as mentioned above , an optimal analysis must be based on a reliable inverted covariance matrix , and the accuracy of the inverse matrix constructed from mock catalogs is yet to be demonstrated . the covariance matrix in power spectrum is a four point function that relates pairs of wave numbers . the error on this covariance consists of pairs of these pairs , and is indeed difficult to quantify . without this metric , however , one does not know the significance of a non - gaussian computation . in addition , @xcite have found significant departures between the covariance matrix constructed from lagrangian perturbation theory and that obtained from their @xmath5 simulations . also unknown is the accuracy of log - normal densities at modeling the true covariance matrix and its inverse . other analyses @xcite treat the mode coupling as coming exclusively from the survey selection function , following the widely used fkp @xcite prescription . this specific coupling effect can be reduced with other choices of power spectrum estimators , like that presented in @xcite . in both cases , however , the non - linear mode coupling is not modeled . when it comes to the impact on the bao dilation scale , a gaussian treatment of the data yields a sub - optimal estimation of the mean , and the error bars obtained that way are systematically biased , usually on the low side . in the limit where the sample is large enough , the value of the mean estimated in that fashion does converge to the `` true '' mean , but the estimated error bars never capture the correlation that occurs in the non - linear regime . many analyses attempt to correct for this bias with monte carlo simulations , however this effect is very small and takes a high accuracy and precision to observe . in the non - gaussian case , however , an inversion of the covariance matrix is required , hence it can not be singular . consequently , the convergence of our measured matrix depends on the binning , and the inversion increases the noise even more . for an adequate resolution on all the scales relevant for bao analyses , the number of simulations required to obtain statistically significant conclusions can be large . in the past , different groups used drastically different numbers of simulations : @xcite used 51 , @xcite used 400 , and @xcite used 5000 ; we use 1000 n - body simulations in this work . in order to invert a @xmath6 covariance matrix , one needs _ at least _ @xmath7 simulations to make the matrix non - singular . it is also generally thought that to achieve convergence on each element , we need of the order @xmath8 simulations . even then , the level of accuracy is not clear , and to make a significant claim about non - gaussian effects , one needs to know the uncertainty on the inverted matrix , which we measure from a bootstrap re - sampling , and to propagate the error onto the bao scale . to address this convergence issue , we also apply a noise reduction technique before the inversion : we factorize the covariance matrix with an eigenvector decomposition , and keep only the principal component . this factorization is repeated at each of the bootstrap samplings , which allows us to draw robust conclusions on the convergence of our results . given the fact that the precision of the inverse covariance matrices used in analyses has never been demonstrated , the measurement of the mean and of the error on the mean found on the literature are most likely not optimal . measuring an optimal bao scale in actual data is complicated in many aspects , such as the fact that the universe is not periodic , and that surveys have selection functions . it would nevertheless involve a covariance weighted measurement , which is not included in the prescription given by @xcite . if one could improve the measurement of the power spectrum covariance , however i.e. from n - body simulations , it would be possible to measure a more robust and more accurate _ uncertainty _ on the sub - optimal mean , compared to the original claim . the difference in performance between these two bao dilation scale estimator is still an unmeasured quantity . in this paper , we first attempt to address this question by comparing three different analysis scenarios : 1 . the first case we consider is an attempt at measuring a correct error bar on a sub - optimal mean of the bao dilation scale . even if we know that the universe is non - gaussian , it is still possible to treat it as gaussian , i.e. not use an optimally weighted sum when estimating the mean , even though the power spectrum itself is non - linear . doing so , we must keep in mind that the measurements are non - optimal , and that the naive gaussian error bars are most likely too small compared to the true " error . however , given the fact that we can measure a full covariance matrix from n - body simulations , we can get a better estimate of the error bars on that sub - optimal mean by treating the original covariance matrix as noisy and by performing an appropriate inverse covariance weighting . from now on , we refer to this case as the `` sub - optimal '' estimator of the bao error . this approach is commonly used to obtain `` monte - carlo '' error bars , and exactly what is measured by the forecasting prescriptions mentioned above . we call this approach `` sub - optimal '' because the errors bars could still be further reduced by improving the estimator of the mean bao scale using the non - gaussian model . it provides a quick estimate of the magnitude of non - gaussianity , and a simple way of scaling errors bars obtained from gaussian analysis , which is often used in surveys . the second case , dubbed `` optimal estimator '' , is the best quadratic analysis one can possibly do knowing that the universe is non - gaussian , we treat it as is , measuring a fully non - linear power spectrum covariance matrix and performing an optimally weighted sum to estimate both the means and the uncertainties on the parameters . given the fact that we rely on a large number of n - body simulations , that our volume is periodic , and that we have a high signal to noise , then both our estimators are truly optimal in the least squares sense . is six - dimensional , and non - isotropic in the sense that pairs of mode separated by smaller angles are more correlated . on top of that , the observed quantity is convoluted in six - dimensional with pairs of survey selection function @xcite . for these reasons , we find solutions that apply to periodic volumes , and we leave it for future work the extraction of optimal estimator in more complex data . ] 3 . many times in the literature @xcite , the above case is modified by replacing the non - linear covariance matrix by a gaussian one . this effectively treats the power spectrum measurements as gaussian , even though the data are correlated . under the widely used fkp @xcite approximation , for example , the only source of mode coupling comes from the convolution with the survey selection function ; it thus considers the underlying covariance matrix to be diagonal . for reasons mentioned above , the error bars obtained this way could be systematically underestimated . we did not address the question of shot noise , however , which is also non - gaussian in nature . in the case of surveys that address some of the non - gaussianities with mock catalogs , the error correct bars should lie somewhere between case ( i ) and case ( ii ) ( while some approach case ( iii ) ) , depending on how close to optimal the measured power spectrum is , and how well the catalogs model the non - linear dynamics . @xcite showed that the difference in estimator between cases ( ii ) and ( iii ) is very small ( i.e. , with optimal weighting , errors near the pure - gaussian errors are achieved ) , but this is not the complete story , especially when dealing with current gaussian or sub - optimal data analyses . the question we address is the following by how much does the error bars on the _ least robust _ bao dilation scale ( case ( iii ) ) differ from a correct calculation based on an optimal covariance matrix and properly inverse covariance weighted ( case ( i ) ) ? finally , we go one step further and repeat the measurements of non - gaussian effects on reconstructed density fields . we apply a density reconstruction algorithm @xcite that was developed to improve the bao signal at late times , which is partially lost due to non - linear coupling between fourier modes @xcite . other approaches have been explored to recover some of the fisher information lost in gravitational collapse @xcite , but it was not verified how these methods propagate to constraints on cosmological parameters . the full bao analysis is indeed sensitive to this intermediate stage , but in a non - gaussian treatment , the interplay between the off - diagonal elements of the covariance matrix and the derivatives is quite subtle . we thus set forth to test quantitatively how this reconstruction algorithm affects the bao dilation error , for the three analysis cases mentioned above . the paper is organized as follows . in section [ sec : background ] we briefly review how bao dilation measurements can constrain dark energy . in section [ sec : nbodysimulations ] we describe our set of n - body simulations and the reconstruction algorithm . in section [ sec : powerspectrumanalysis ] we discuss how to extract both the gaussian and the non - gaussian covariance matrices . in section [ sec : eigen ] we describe the eigenvector decomposition , while in section [ sec : parameterestimation ] we present the fisher matrix formalism and the estimators of the bao dilation uncertainty for the three analysis cases . finally , in section [ sec : resultsanddiscussion ] we present and discuss our results .

we revisit the uncertainty in baryon acoustic oscillation ( bao ) forecasts and data analyses . in particular , we study how much the uncertainties on both the measured mean dilation scale and the associated error bar are affected by the non - gaussianity of the non - linear density field . we examine two possible impacts of non - gaussian analysis : ( 1 ) we derive the distance estimators from gaussian theory , but use 1000 n - body simulations to measure the actual errors , and compare this to the gaussian prediction , and ( 2 ) we compute new optimal estimators , which requires the inverse of the non - gaussian covariance matrix of the matter power spectrum . obtaining an accurate and precise inversion is challenging , and we opted for a noise reduction technique applied on the covariance matrices . by measuring the bootstrap error on the inverted matrix , this work quantifies for the first time the significance of the non - gaussian error corrections on the bao dilation scale . we finally discuss the impact of this work on current data analyses .

we revisit the uncertainty in baryon acoustic oscillation ( bao ) forecasts and data analyses . in particular , we study how much the uncertainties on both the measured mean dilation scale and the associated error bar are affected by the non - gaussianity of the non - linear density field . we examine two possible impacts of non - gaussian analysis : ( 1 ) we derive the distance estimators from gaussian theory , but use 1000 n - body simulations to measure the actual errors , and compare this to the gaussian prediction , and ( 2 ) we compute new optimal estimators , which requires the inverse of the non - gaussian covariance matrix of the matter power spectrum . obtaining an accurate and precise inversion is challenging , and we opted for a noise reduction technique applied on the covariance matrices . by measuring the bootstrap error on the inverted matrix , this work quantifies for the first time the significance of the non - gaussian error corrections on the bao dilation scale . we find that the variance ( error squared ) on distance measurements can deviate by up to 12% between both estimators , an effect that requires a large number of simulations to be resolved . we next apply a reconstruction algorithm to recover some of the bao signal that had been smeared by non - linear evolution , and we rerun the analysis . we find that after reconstruction , the rms error on the distance measurement improves by a factor of at low redshift ( consistent with previous results ) , and the variance ( ) shows a change of up to 18% between optimal and sub - optimal cases ( note , however , that these discrepancies may depend in detail on the procedure used to isolate the bao signal ) . we finally discuss the impact of this work on current data analyses . [ firstpage ] cosmology : observations dark energy large - scale structure of the universe distance scale methods : statistical

1106.5548

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we have addressed some aspects of the problem of measuring non - gaussian error bars in a bao analysis . we have investigated the full optimal quadratic non - gaussian estimator on reconstructed density field , and quantified the significance of the non - gaussianities on the bao dilation scale error . a major subtlety is that the optimal estimator requires an accurate measurement of the inverse of the covariance matrix of power spectrum , and the actual uncertainty on that inverse had never been measured . the accuracy of the inverse is generally bin dependent , and convergence requires a large number of n - body simulations . we have overcome this problem with a factorization technique that involves an iterative eigenvalue decomposition of the covariance matrix , which we measured from 1000 n - body simulations . we further measured the uncertainty of the inverse of the matrix with bootstrap re - sampling , and were able to achieve convergence at the percent level . having confidence in the inverse matrix , we quantitatively compared the measurement of the error on the bao dilation factor obtained with different estimators . we construct an _ optimal estimator _ , which gives the most accurate measurement of the error achievable on the bao dilation scale . it is derived from a covariance weighted fisher matrix , which is constructed out of the inverse of the non - linear power spectrum covariance matrix . we compared our results with those obtained from the purely gaussian forecast , and we measure significant discrepancies of up to ten percent in the error on the dilation scale . we also measured non - gaussian error bars on the mean bao dilation scale that has been obtained with a gaussian estimator , as is usually encountered in the literature . because we have confidence in the accuracy of our covariance matrix , this _ sub - optimal estimator _ provides a robust estimate of the error bars on the bao dilation scale . to illustrate our point , we considered the case where the original dilation scale was measured under standard gaussian statistics . we found that the variances of those measurements can differ by up to 15% , compared to our optimal estimator . many data analyses did include non - gaussianities in their bao error estimator , hence the discrepancy between these and our optimal estimator is likely to be more modest than that obtained in this work . we note in passing that these results were entirely obtained from n - body simulations , hence the effect of the survey selection function has been factored out of our problem . constructing optimal estimators with actual data will however be more challenging , since it has to include such an effect , which effectively couple fourier modes from different bins , in addition to account for the effect of bias between the sampled tracers ( i.e. galaxies or 21 cm structure ) and the underlying matter density . we have also implemented a density reconstruction algorithm , which recovers some of the lost bao information due to non - linear gravitational collapse at late times . in that case , the error on the dilation scale is reduced by a factor of about 70% at low redshift , but the discrepancy between the sub - optimal and optimal estimates remains similar to the case without reconstruction ( 20% and 15% , with and without reconstruction ) . we mention in conclusion that in a survey , the increase in variance we observed when using a sub - optimal estimator is equivalent to losing about the same percentage of survey volume , because the variance of measurements is inversely proportional to volume . these discrepancies should be taken seriously into account especially when forecasting performances of future telescopes , where the objective is to reach percent level precision on cosmological parameters .

we find that the variance ( error squared ) on distance measurements can deviate by up to 12% between both estimators , an effect that requires a large number of simulations to be resolved . we next apply a reconstruction algorithm to recover some of the bao signal that had been smeared by non - linear evolution , and we rerun the analysis . we find that after reconstruction , the rms error on the distance measurement improves by a factor of at low redshift ( consistent with previous results ) , and the variance ( ) shows a change of up to 18% between optimal and sub - optimal cases ( note , however , that these discrepancies may depend in detail on the procedure used to isolate the bao signal ) .

we revisit the uncertainty in baryon acoustic oscillation ( bao ) forecasts and data analyses . in particular , we study how much the uncertainties on both the measured mean dilation scale and the associated error bar are affected by the non - gaussianity of the non - linear density field . we examine two possible impacts of non - gaussian analysis : ( 1 ) we derive the distance estimators from gaussian theory , but use 1000 n - body simulations to measure the actual errors , and compare this to the gaussian prediction , and ( 2 ) we compute new optimal estimators , which requires the inverse of the non - gaussian covariance matrix of the matter power spectrum . obtaining an accurate and precise inversion is challenging , and we opted for a noise reduction technique applied on the covariance matrices . by measuring the bootstrap error on the inverted matrix , this work quantifies for the first time the significance of the non - gaussian error corrections on the bao dilation scale . we find that the variance ( error squared ) on distance measurements can deviate by up to 12% between both estimators , an effect that requires a large number of simulations to be resolved . we next apply a reconstruction algorithm to recover some of the bao signal that had been smeared by non - linear evolution , and we rerun the analysis . we find that after reconstruction , the rms error on the distance measurement improves by a factor of at low redshift ( consistent with previous results ) , and the variance ( ) shows a change of up to 18% between optimal and sub - optimal cases ( note , however , that these discrepancies may depend in detail on the procedure used to isolate the bao signal ) . we finally discuss the impact of this work on current data analyses . [ firstpage ] cosmology : observations dark energy large - scale structure of the universe distance scale methods : statistical

math0210397

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one of the main mechanisms of integrability of evolution equations is the presence of two compatible hamiltonian structures . in this paper we compare hamiltonian properties of three extensively studied nonlinear equations of mathematical physics , related to various hydrodynamical approximations : the korteweg - de vries equation @xmath0 the camassa - holm equation @xmath1 derived as a shallow water equation in @xcite ( see also the paper @xcite ) , and the hunter saxon equation @xcite @xmath2 describing weakly nonlinear unidirectional waves . all three equations are known to be bihamiltonian and to possess infinitely many conserved quantities , as well as remarkable soliton or soliton like solutions . a motivation for our paper was the paper @xcite , which described scattering theory for all three equations in a unified way . as we show in this paper , the main reason why such a common treatment is possible is that all these equations have the same symmetry group . it turns out to be the virasoro group , a one - dimensional extension of the group of smooth transformations of the circle . more precisely , the virasoro group serves as the configuration space , and all three equations can be regarded as equations of the geodesic flow related to different right - invariant metrics on this group ( in the case of kdv and ch ) or on an associated homogeneous space ( in the case of hs ) . ( here we will be mostly concerned with the periodic case , though many statements can be extended to the case of rapidly decaying potentials on the real line . ) the main goal of this paper is to give a description of the three equations as _ bihamiltonian _ systems on the dual to the virasoro algebra , and to relate them to the geometry of the virasoro coadjoint orbits . one of the corresponding hamiltonian ( or poisson ) structures is provided by the linear lie - poisson bracket , and it is the same for all three equations . the other poisson structure is constant and can be viewed as a `` linear structure frozen at a point . '' the corresponding `` freezing points '' are different for each equation . we will also see that , in a sense , equations ( [ eq : kdv ] ) , ( [ eq : ch ] ) , and ( [ eq : hs ] ) exhaust all generic possibilities , and among them the camassa - holm equation ( [ eq : ch ] ) is the `` most general '' equation that can be obtained by the `` freezing argument '' method on the dual virasoro space . we tried to make the paper self - contained , including in it necessary background on the euler equations and the classification of virasoro orbits . for additional information we refer the interested reader to the expositions in @xcite or @xcite , as well as to the original papers listed in the bibliography . in @xcite v. arnold suggested a general framework for the euler equations on an arbitrary ( possibly infinite - dimensional ) group , which we recall below . in this framework the euler equation describes a geodesic flow with respect to a suitable one - sided invariant riemannian metric on the given group . in section 2 we show how arnold s approach to the euler equation works for the virasoro group and provides a natural geometric setting for the korteweg de vries and camassa holm equations . in section 3 we give a hamiltonian reformulation of the euler equation . in section 4 we extend this approach to include geodesic flows on homogeneous spaces and then use it to describe the hunter saxton equation and its relatives . this extension might be thought of as a version of the hamiltonian formalism for homogeneous spaces developed in @xcite , @xcite , which is applied to the case of a degenerate metric and in our infinite - dimensional situation . in sections 56 we develop the bihamiltonian formalism for the euler systems . we show why the three equations above represent three main classes ( and exhaust the rotation - invariant ) bihamiltonian systems on the virasoro algebra that can be integrated by means of the `` freezing '' ( called also , the translation of ) argument method . it turns out that the above three equations correspond to three different types of virasoro coadjoint orbits of low codimensions . in our classification of poisson pairs and the corresponding equations we rely heavily on the classical classification of the virasoro orbits , and we recall it in the appendix . an interesting open question is to extend the classification of the equations to orbits of higher codimension , as well as to show how the discrete invariant of virasoro orbits manifests itself in the related bihamiltonian systems .

we show that the following three systems related to various hydrodynamical approximations : the korteweg de vries equation , the camassa holm equation , and the hunter saxton equation , have the same symmetry group and similar bihamiltonian structures . it turns out that their configuration space is the virasoro group and all three dynamical systems can be regarded as equations of the geodesic flow associated to different right - invariant metrics on this group or on appropriate homogeneous spaces . in particular , we describe how arnold s approach to the euler equations as geodesic flows of one - sided invariant metrics extends from lie groups to homogeneous spaces . we also show that the above three cases describe all generic bihamiltonian systems which are related to the virasoro group and can be integrated by the translation argument principle : they correspond precisely to the three different types of generic virasoro orbits . finally , we discuss interrelation between the above metrics and kahler structures on virasoro orbits as well as open questions regarding integrable systems corresponding to a finer classification of the orbits .

we show that the following three systems related to various hydrodynamical approximations : the korteweg de vries equation , the camassa holm equation , and the hunter saxton equation , have the same symmetry group and similar bihamiltonian structures . it turns out that their configuration space is the virasoro group and all three dynamical systems can be regarded as equations of the geodesic flow associated to different right - invariant metrics on this group or on appropriate homogeneous spaces . in particular , we describe how arnold s approach to the euler equations as geodesic flows of one - sided invariant metrics extends from lie groups to homogeneous spaces . we also show that the above three cases describe all generic bihamiltonian systems which are related to the virasoro group and can be integrated by the translation argument principle : they correspond precisely to the three different types of generic virasoro orbits . finally , we discuss interrelation between the above metrics and kahler structures on virasoro orbits as well as open questions regarding integrable systems corresponding to a finer classification of the orbits .

1603.08455

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riemannian manifolds all of whose geodesics are closed have been studied since the beginning of the @xmath0th century , when the first nontrivial examples were constructed by tannery and zoll . the famous book of besse @xcite still describes the state of knowledge of the subject to a large extent . some notable exceptions are concerned with relations between the geodesic period spectrum of a riemannian manifold all of whose geodesics are closed , henceforth called besse manifold , and its topology . for instance a conjecture of berger , stating that on a simply connected besse manifold all prime geodesics have the same length , was proved by gromoll and grove for @xmath1-spheres @xcite and recently by radeschi and wilking for all topological spheres of dimension at least @xmath2 @xcite . apart from spheres , which admit many besse metrics , i.e. riemannian metrics all of whose geodesics are closed , the only known besse manifolds are the other compact rank one symmetric spaces . moreover , it was shown by pries that the conclusion of berger s conjecture also holds for the real projective plane @xcite , i.e. that all prime geodesics of a besse metric have the same length . only little is known in the more general setting of riemannian orbifolds . we define a _ besse metric _ on an orbifold as a riemannian orbifold metric all of whose orbifold geodesics are closed and a _ besse orbifold _ as an orbifold endowed with a besse metric ( cf . section [ sub : riem_orb ] ) . on besse orbifolds new phenomena occur that are not present in the manifold case . for instance , berger s conjecture does not hold for spindle orbifolds @xcite , which admit many besse metrics ( cf . section [ sub : p - metrics_on_spindle ] ) . however , it turns out that there is still a relation between the geodesic period spectrum of a besse @xmath1-orbifold and its topology . in fact , we generalize the results of gromoll , grove and pries mentioned above in a unifying approach to the setting of riemannian @xmath1-orbifolds . we prove the following result . the geodesic period spectrum of a besse @xmath1-orbifold is determined up to a constant by its orbifold topology . in the manifold case all prime geodesics have the same length . the geodesic period spectrum of a besse 2-orbifold is by definition the set of lengths of all unoriented prime geodesics counted with multiplicity . in the manifold case the proofs by gromoll , grove and pries hinge on the existence of at least three simple closed geodesics , i.e. closed geodesics without self - intersections . using a connectedness argument they moreover show that all prime geodesics are simple . this observation combined with the blaschke conjecture for @xmath3 proved by green @xcite shows that a besse metric on the real projective plane has constant curvature @xcite . our proof is independent of the existence of simple closed geodesics . in the appendix we show how rigidity on the real projective plane can be deduced from our result based on a systolic inequality due to pu @xcite . the latter observation was explained to us by a. abbondandolo . in the appendix we moreover partially strengthen our result by showing that the geodesic flow on the unit tangent bundle of a besse @xmath1-orbifold with isolated singularities can be conjugated by a contactomorphism to a standard geodesic flow . the paper is structured as follows . after reviewing some preliminaries and examples , we will see in section [ prp : admit_besse ] that a @xmath1-orbifold admits a besse metric if and only if its orbifold euler characteristic is positive ( cf . proposition [ prp : admit_besse ] ) . this is the case if and only if it is either a quotient of @xmath3 or bad , i.e. not covered by a manifold . quotients of @xmath3 by finite subgroups of @xmath4 inherit canonical besse metrics from @xmath3 . besse metrics on bad @xmath1-orbifolds , can be constructed as quotients of @xmath5 by almost - free isometric @xmath6-actions @xcite and @xmath7-quotients thereof . other constructions via metrics of revolution are given in @xcite and will be discussed in section [ sub : p - metrics_on_spindle ] . the space of oriented prime geodesics on a besse @xmath1-orbifold has a natural orbifold structure ( cf . section [ sub : orb_of_geo ] ) . we show that its orbifold topology only depends on the orbifold topology of the given besse orbifold in the following way . let @xmath8 be a besse @xmath1-orbifold and let @xmath9 be the corresponding orbifold of oriented geodesics . the following cases can occur . 1 . @xmath10 and @xmath11 as orbifolds where @xmath12 is a finite subgroup and @xmath13 . 2 . @xmath14 and @xmath15 with @xmath16 being @xmath17 or @xmath1 depending on whether @xmath18 is odd or even . 3 . @xmath19 and @xmath20 with @xmath16 being @xmath17 or @xmath1 depending on whether @xmath18 is odd or even . for explanations on the notations we refer to section [ sec : pre ] . based on the above list we will be able to show that the geodesic period spectrum also only depends on the orbifold topology of a given besse 2-orbifold . the proof of the above list relies on the following ideas . the unit tangent bundle @xmath21 of a besse @xmath1-orbifold @xmath8 with isolated singularities is a manifold and the geodesic flow on it is periodic due to a result of epstein @xcite . we obtain two transversal seifert fiberings on @xmath22 , one from the geodesic flow and another one from the projection @xmath23 . properties of these seifert fiberings and their interplay imply the claim in many cases . for besse @xmath1-orbifolds with codimension one singularities the result is obtained by considering the orientable double cover . in this case geometric arguments come into play . an explicit list of all @xmath1-orbifolds admitting a besse metric together with their orbifolds of prime geodesics and their geodesic period spectra can be found in the appendix , table [ tab : gls ] independently frauenfelder and suhr used similar methods to show a hamiltonian version of the result of gromoll and grove on an assumption analogous to the existence of three simple closed geodesics @xcite . as in the riemannian case our proof shows that this assumption can be avoided ( cf . @xcite ) . note that in general our result is a riemannian phenomenon that can not be seen from the hamiltonian point of view . for instance , the real projective plane and the teardrop @xmath24 have the same unit tangent bundle ( cf . lemma [ lem : gluing ] and section [ sub : pro_plane ] ) , but the period stectra of besse metrics on them differ ( cf . appendix , table [ tab : gls ] ) . _ acknowledgements . _ the author would like to thank alexander lytchak for drawing his attention to the subject . he is grateful to alberto abbondandolo for explaining to him how this paper s result combined with work by pu implies rigidity on the real projective plane ( cf . appendix ) .

we show that the geodesic period spectrum of a riemannian 2-orbifold all of whose geodesics are closed depends , up to a constant , only on its orbifold topology and compute it . in the manifold case we recover the fact proved by gromoll , grove and pries that all prime geodesics have the same length . in the appendix we partly strengthen our result in terms of conjugacy of contact forms and explain how to deduce rigidity on the real projective plane based on a systolic inequality due to pu .

we show that the geodesic period spectrum of a riemannian 2-orbifold all of whose geodesics are closed depends , up to a constant , only on its orbifold topology and compute it . in the manifold case we recover the fact proved by gromoll , grove and pries that all prime geodesics have the same length . in the appendix we partly strengthen our result in terms of conjugacy of contact forms and explain how to deduce rigidity on the real projective plane based on a systolic inequality due to pu .

1403.7469

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the study of out - of - equilibrium dynamics of isolated many - body quantum systems has seen great progress during the last decade . in particular , much theoretical progress was made in the field of one - dimensional quantum integrable models . out - of - equilibrium realizations of these models , despite being strongly - correlated @xcite and having a complete set of algebraically independent conserved quantities , are believed to exhibit relaxation behaviour . this relaxation can be described , in principle , by a generalized gibbs ensemble ( gge ) @xcite . an alternative way was recently proposed in the context of a quantum quench , the so - called `` quench action approach '' @xcite . this first - principles - based analysis of time - evolved expectation values of physical observables uses as input the overlaps of the initial state with energy eigenstates . after a saddle - point approximation that is exact in the thermodynamic limit , it predicts both the time evolution of expectation values of physical observables and their long - time stationary values . to obtain the latter , one in particular needs the leading order term of the overlaps in the thermodynamic limit . despite the fact that slavnov s theorem @xcite gives overlaps between eigenstates of a bethe ansatz - solvable @xcite hamiltonian with ( in principle ) generic states , until recently very little was known about overlaps between eigenstates of two hamiltonians of the same family but at different values of interaction ( here , we primarily focus on two xxz chains with different anisotropies , one of which is in the ising limit ) . it is these overlaps that are required for the application of the quench action approach to interaction quenches . for the lieb - liniger model , exact overlaps of the ground state for an even number of free bosons ( bose - einstein condensate ( bec ) state ) and energy eigenstates at generic finite interaction parameter were conjectured in @xcite and thereafter proven in @xcite . their form resembled the gaudin determinant form for norms of bethe states @xcite , and was suitable for analysis in the thermodynamic limit @xcite . this made an application of the quench action approach possible , leading to a description of the stationary state at late times after the quench . surprisingly , and in contrast to thermal properties of the lieb - liniger gas , this description turned out to yield a closed - form solution in the thermodyamic limit , for any ( repulsive ) value of the final interaction strength . of particular interest was the conclusion that these results remain inaccessible to gge - based calculations @xcite . in the context of spin chains , in @xcite overlaps between the nel state and parity - invariant xxz bethe states with an even number of down spins were derived from an earlier form of the overlaps @xcite . this new form has the same gaudin - like structure as the lieb - liniger overlaps and therefore can be treated in the thermodynamic limit as done in @xcite . note that this result is still restricted to an even number of down spins . in this paper we present a derivation of the overlaps of the zero - momentum nel state and parity - invariant bethe states , but now in the sectors of odd numbers of down spins . we also take the scaling limit to the lieb - liniger model and present the overlaps between the bec state and bose gas bethe states with an odd number of bosons . the calculations are not trivial and the results show a slightly different structure of the determinant as compared to the even particle case @xcite . these new overlap formulas may be specifically useful in broader contexts , such as in their relation to exact solutions of the 1d kardar - parisi - zhang equation @xcite . furthermore , unlike the lieb - liniger case , up to now a proof that non - parity - invariant xxz bethe states have vanishing overlaps with the initial nel state was lacking . in this paper we present this proof , both for an even and odd number of down spins . the relevance for the quench action approach is clear , as the time evolution of expectation values is governed by a double sum over the complete hilbert space , including non - parity - invariant states . the paper is organized as follows . in section [ sec : xxzchain ] we review the bethe ansatz solution of the xxz chain and recall the gaudin norm formula of bethe states @xcite , which will be used in subsequent sections . in section [ sec : oddandnpi ] we present the derivation of the overlap formula with parity - invariant bethe states with an odd number of down spins , and we prove that non - parity - invariant states have zero overlap with the nel state . in section [ sec : scaling_ll ] we perform the scaling limit to the lieb - liniger bose gas and present the bec overlap formula for an odd number of bosons .

we specialize a recently - proposed determinant formula for the overlap of the zero - momentum nel state with bethe states of the spin-1/2 xxz chain to the case of an odd number of downturned spins , showing that it is still of `` gaudin - like '' form , similar to the case of an even number of down spins . the generalized determinant expression can then be used to derive the corresponding determinants and their prefactors in the scaling limit to the lieb - liniger ( ll ) bose gas . the odd number of down spins directly translates to an odd number of bosons . this is based on a determinant expression for overlaps with general bethe states that was obtained in the context of the xxz chain with open boundary conditions .

we specialize a recently - proposed determinant formula for the overlap of the zero - momentum nel state with bethe states of the spin-1/2 xxz chain to the case of an odd number of downturned spins , showing that it is still of `` gaudin - like '' form , similar to the case of an even number of down spins . we generalize this result to the overlap of-raised nel states with parity - invariant bethe states lying in a nonzero magnetization sector . the generalized determinant expression can then be used to derive the corresponding determinants and their prefactors in the scaling limit to the lieb - liniger ( ll ) bose gas . the odd number of down spins directly translates to an odd number of bosons . we furthermore give a proof that the nel state has no overlap with non - parity - invariant bethe states . this is based on a determinant expression for overlaps with general bethe states that was obtained in the context of the xxz chain with open boundary conditions . the statement that overlaps with non - parity - invariant bethe states vanish is still valid in the scaling limit to ll which means that the bec state has zero overlap with non - parity - invariant ll bethe states .

1411.2948

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in this paper we have analysed the evolution of a quantum field in @xmath224 dimensions under time - dependent robin boundary conditions that occur in superconducting microwave circuit experiments in the high plasma frequency limit . we solved the evolution explicitly to linear order in the time variation of the robin boundary condition , in a formalism that allowed us to handle both a semiopen waveguide and a closed waveguide , and for the latter allowing the boundary conditions at the two ends to be varied independently . for frequencies that are much smaller than the effective inverse length associated with the squid(s ) at the end(s ) of the waveguide , we verified that a suitable modulation of the squid(s ) allows the waveguide to simulate a dirichlet boundary condition at a mechanically moving boundary of the dce , even in the regime where the mechanical motion is relativistic ; both the experiment reported in @xcite and the experimental proposals of @xcite appear to operate within in this domain by a margin of approximately one order of magnitude . for higher frequencies the waveguide still exhibits particle creation and mode mixing , but these can no longer be quantitatively matched to those of the dce , and in particular the large frequency falloff properties in the evolution are qualitatively different . these features in the large frequency bogoliubov coefficients result in differing particle emission spectrum for the moving and non - moving systems when the effective length is larger than the inverse driving frequency @xmath225 . in this limit , mechanically moving boundary radiation can be characterised as having a larger total flux and a less steep falloff at high frequencies compared to radiation from the static waveguide with time - varying robin boundary conditions . while the analogy between a moving dirichlet boundary and a time - varying robin boundary condition is useful for simulation purposes it is important to keep in mind that the physical systems corresponding to these two situations are different and therefore can lead to different outcomes . on the one hand , our results support proposals to simulate in a mechanically static waveguide quantum phenomena due to motion , including entanglement generation and degradation , even in a regime where the mechanically moving system experiences significant relativistic effects @xcite . on the other hand , our results demonstrate that the interpretation of a waveguide experiment in terms of the simulation of the dce is possible only in certain parameter ranges . within the robin boundary condition approximation that we have analysed , the range of dce interpretation is determined just by the effective inverse length scale set by the squid(s ) at the end(s ) of the waveguide . it remains a subject to future work to establish the range of dce interpretation when all relevant effects beyond the robin boundary condition approximation are considered @xcite , including the effects due to a large but finite squid plasma frequency analysed in @xcite .

we study analytically the time - dependent boundary conditions of superconducting microwave circuit experiments in the high plasma frequency limit , in which the conditions are robin - type and relate the value of the field to the spatial derivative of the field . the correspondence between the microwave robin boundary conditions and the mechanically - moving dirichlet boundary conditions of the dynamical casimir effect is shown to break down at high field frequencies , approximately one order of magnitude above the frequencies probed in the 2011 experiment of wilson et al .

we study analytically the time - dependent boundary conditions of superconducting microwave circuit experiments in the high plasma frequency limit , in which the conditions are robin - type and relate the value of the field to the spatial derivative of the field . we give an explicit solution to the field evolution for boundary condition modulations that are small in magnitude but may have arbitrary time dependence , in a formalism that applies both to a semiopen waveguide and to a closed waveguide with two independently adjustable boundaries . the correspondence between the microwave robin boundary conditions and the mechanically - moving dirichlet boundary conditions of the dynamical casimir effect is shown to break down at high field frequencies , approximately one order of magnitude above the frequencies probed in the 2011 experiment of wilson et al . our results bound the parameter regime in which a microwave circuit can be used to model relativistic effects in a mechanically - moving cavity , and they show that beyond this parameter regime moving mirrors produce more particles and generate more entanglement than their non - moving microwave waveguide simulations .

quant-ph0306078

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entanglement and secret correlation share an `` exclusiveness '' in the one case towards the total outside world , in the other towards an entity `` eve '' that has led quantum information scientists to speculate on a systematic relation between their theories : the works in this direction range from building analogies @xcite to using entanglement to prove information theoretic security of quantum key distribution @xcite , to attempts to prove the equivalence of the distillability of secret key and of entanglement @xcite . of course there are also conceptual differences : while the task of distilling secret perfect correlation derives from potential cryptographic applications ( and requires a third , malicious , party to formulate the operational problem ) , entanglement is useful for simple transmission tasks between two perfectly cooperating parties , as exemplified by dense coding @xcite and teleportation @xcite . the present paper falls into the third of the above categories , for we address the two questions , of distilling secret key from many copies of a quantum state ( itself a generalisation of classical information theoretic work begun by maurer @xcite and ahlswede and csiszr @xcite ) by public discussion and of distilling epr pairs by local operations and classical communication ( locc ) , in a unified way . to be more precise , after describing a protocol for secret key distillation from a state by one way public discussion , we show how secrecy codes of a particular structure can be converted into one way locc entanglement distillation protocols achieving the _ coherent information _ , as was conjectured for some time under the name of the `` hashing inequality '' ( after the hashing protocol in @xcite which attains the bound for bell diagonal two qubit states ) . it is well known from @xcite that this inequality yields information theoretic characterisations of distillable entanglement under general locc , as well as the quantum transmission capacity , without , with forward and with bidirectional classical side channel ( the first of these capacity theorems proved recently by shor @xcite , following a heuristic argument of lloyd @xcite , and subseqently in @xcite ) . our approach is very close to that of @xcite , and as far as secret key distillation is concerned the work @xcite : while here our resource is a three party quantum state ( `` static '' model ) , these papers deal with the `` dynamic '' analogue , where the resource is a quantum / wiretap channel . as for the structure of the paper : the main result of the cryptographic part is theorem [ thm : cqq:1way : coding ] in section [ sec : oneway - secret : cqq ] ; the form of the optimal rates is then not hard to obtain , as we shall show in the detailed discussion . it is theorem [ thm : cqq:1way : coding ] which we return to in the entanglement distillation part : a very general modification of the coding procedure will give us theorem [ thm : hashing ] , the hashing inequality ; and as before , the form of the optimal rates is not hard to get from there . a reader only interested in entanglement distillation can thus skip the second part of section [ sec : oneway - secret : cqq ] : there the general form of optimal one way distillable secret key is derived . in section [ sec : oneway - ent ] we turn to one way entanglement distillation , proving the hashing inequality and exhibiting the general form of optimal one way distillation ; then in section [ sec : cap - and - ent ] the consequences of the hashing inequality are detailed . appendices collect the necessary facts about typical subspaces ( [ app : types ] ) , some miscellaneous lemmas ( [ app : facts ] ) and miscellaneous proofs ( [ app : proofs ] ) .

we study and solve the problem of distilling secret key from quantum states representing correlation between two parties ( alice and bob ) and an eavesdropper ( eve ) via one way public discussion : we prove a coding theorem to achieve the `` wire tapper '' bound , the difference of the mutual information alice bob and that of alice eve , for so called cqq correlations , via one way public communication . this result is well known to imply a whole set of distillation and capacity formulas which we briefly review .

we study and solve the problem of distilling secret key from quantum states representing correlation between two parties ( alice and bob ) and an eavesdropper ( eve ) via one way public discussion : we prove a coding theorem to achieve the `` wire tapper '' bound , the difference of the mutual information alice bob and that of alice eve , for so called cqq correlations , via one way public communication . this result yields information theoretic formulas for the distillable secret key , giving `` ultimate '' key rate bounds if eve is assumed to possess a purification of alice and bob s joint state . specialising our protocol somewhat and making it coherent leads us to a protocol of entanglement distillation via one way locc ( local operations and classical communication ) which is asymptotically optimal : in fact we prove the so called `` hashing inequality '' which says that the coherent information ( i.e. , the negative conditional von neumann entropy ) is an achievable epr rate . this result is well known to imply a whole set of distillation and capacity formulas which we briefly review .

1203.2010

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ballistic electron transport @xcite in two - terminal graphene systems is in the focus of intensive studies ever since the pioneering experiments on single - layer carbon . @xcite the dirac hamiltonian @xcite describes charge transport close to the charge - neutrality point and leads to a linear dispersion relation @xmath0 . this allows to observe several relativistic phenomena in solid - state system , such as klein tunneling @xcite or the zitterbewegung . @xcite in the very early works on graphene the minimal conductivity @xcite @xmath1 per valley and pseudo - spin at the charge - neutrality point has been found and stimulated the research on current and noise properties . the current - current correlations around the minimal conductivity lead to a zero frequency sub - poissonion fano factor with a maximal value of @xmath2 , @xcite remarkably similar to diffusive systems as disordered metals . @xcite the suppression of the fano factor below the poissonian value originates from noiseless , open quantum channels that are found at all conductance minima in graphene - based two - terminal structures @xcite , and can be explained as an interplay between klein tunneling , resonant tunneling and pseudo - spin matching . this pseudo - diffusive behavior @xcite is due to the special band - structure of graphene . without impurity scattering , coherent transport through such a graphene sheet @xcite gives rise to the same shot noise as in classical diffusive systems . the opening of a gap @xcite in the quasiparticle spectrum leads to an enhanced fano factor . @xcite such a gap can be opened for example by photon - assisted tunneling , as shown recently for the case of a graphene p - n junction @xcite with a linear potential drop across the interface . @xcite there , landau - zener like transitions stimulated by photon emission or absorption via resonant interaction of propagating quasiparticles in graphene with an irradiating electric field lead to hopping between different trajectories . + ) sandwiched between two heavily - doped , metallic graphene leads . the fermi - level of the sheet can be tuned by a center gate voltage @xmath3 . electron- and hole states are injected via the time - dependent bias - voltages in left- and right leads @xmath4.,title="fig : " ] + the scattering approach as put forward by landauer and bttiker @xcite has been applied to ac - driven charge transport @xcite through a metal - graphene interface with an abrupt potential change . @xcite the metal can be formed by a graphene lead strongly electrostatically doped by a gate potential , thus shifting the dirac point far away from the fermi energy . in this work we adopt the formalism and parameterization introduced in refs . @xcite and calculate the finite - frequency current - current correlations at finite dc- and ac - bias voltages in the system depicted in fig . we complement recent results on ac - transport in fabry - prot graphene devices of ref . @xcite , in which the influence of different boundary conditions , i.e. zigzag or armchair configurations , on the fabry - prot patterns in a combined tien - gordon / tight - binding approach has been investigated . the influence on transmission properties of a time - dependent potential barrier in a graphene monolayer has been investigated . @xcite in our work the transverse boundary effects are central and we assume so - called infinite mass boundaries @xcite describing a short but wide ( @xmath5 ) graphene strip . we focus on the interplay between the dirac - spectrum with the fabry - perot interferences . interestingly , the well - known oscillations as function of gate voltage on a scale of the return frequency @xmath6 , related to the length @xmath7 of the graphene sheet , can be seen as a reminiscence of zitterbewegung . @xcite the role of the complex reflection amplitude and the onset of contributions of scattering states coming from terminal @xmath8 and being scattered into terminal @xmath9 will be the key characteristics in our discussion of the results for the noise as function of bias voltage and frequency . as a consequence of these onsets the oscillations add up de- or constructively depending on the precise values of voltage and frequency . in our setup , the separation of oscillations caused by the fabry - prot reflections and effects caused by the band - structure of the dirac hamiltonian is a priori not obvious . in both cases phase - coherent transport is essential . however , for charge injection either into the conduction or the valence band only , effects like zitterbewegung should not be present and all oscillating features of the noise spectra have to be of fabry - prot nature .

we study finite - frequency quantum noise and photon - assisted electron transport through a wide and ballistic graphene sheet sandwiched between two metallic leads . we identify different features in the current - current auto- and cross - correlation spectra and trace them back to the interference patterns of the product of transmission- and reflection amplitudes which define the integrands of the involved correlators . at positive frequencies

we study finite - frequency quantum noise and photon - assisted electron transport through a wide and ballistic graphene sheet sandwiched between two metallic leads . the elementary excitations allow as to examine the differences between effects related to fabry - prot like interferences and signatures caused by correlations of coherently scattered particles in electron- and hole - like parts of the dirac spectrum . we identify different features in the current - current auto- and cross - correlation spectra and trace them back to the interference patterns of the product of transmission- and reflection amplitudes which define the integrands of the involved correlators . at positive frequencies the correlator of the auto - terminal noise spectrum with final- and initial state associated to the measurement terminal is dominant . phase jumps occur within the interference patterns of corresponding integrands , which also reveal the intrinsic energy scale of the two - terminal graphene setup . the excess noise spectra , as well as the cross - correlation ones , show large fluctuations between positive and negative values . oscillatory signatures of the cross - correlation noise are due to an alternating behavior of the integrands .

hep-th0206206

i

let @xmath1 be a surface obtained by blowing up nine base points of two generic cubics in @xmath2 . @xmath1 has an elliptic fibration @xmath3 and , in this note , we call it rational elliptic surface or @xmath4k3 . ( the latter name comes from the fact that @xmath1 has 12 singular fibers of kodaira @xmath5 type while a generic elliptic k3 surface has 24 . ) the surface @xmath1 is of considerable interest in the study of gromov - witten invariants and , in fact , has been providing a testing ground for ( local ) mirror symmetry [ kmv ] of calabi - yau threefolds and its applications to enumerative geometry . for example , in [ hss ] the celebrated modell - weil group of @xmath1 has been connected to certain genus zero gromov - witten invariants of @xmath1 . in [ hst1 ] , a certain recursion relation ( _ holomorphic anomaly equation _ ) was found , which determines the generating function of gromov - witten invariants of @xmath1 for all genera . the main purpose of this note is to present a detailed study of the solutions of the holomorphic anomaly equation . also we study gromov - witten invariants using similar but more general holomorphic anomaly equation valid for all calabi - yau threefolds due to [ bcov1,2 ] , and remark a nontrivial relation between two equations . main results in this paper are * proposition 2.4 * , * tables 25 * , and * conjecture 4.3*. to describe the setting in more detail , let us consider a calabi - yau threefold @xmath6 which contain a rational elliptic surface @xmath1 . consider the moduli space of stable maps from genus @xmath7 curves with @xmath8 point on it to @xmath1 . then genus @xmath7 gromov - witten invariant @xmath9 with @xmath10 is defined by @xmath11^{vert } } c(r^1\pi_*\mu^ * n_{s / x})\;\ ; , \mylabel{eqn : gwdef}\ ] ] where @xmath12 is the normal sheaf and @xmath13 is the evaluation map and @xmath14 is the forgetful map . for some special @xmath15 , using localization method of torus actions , we may calculate @xmath9 directly based on the definition , see e.g. [ ko][kz ] for details . another way to determine @xmath9 is to use the calculational technique based on mirror symmetry conjecture in [ cdogp ] and [ bcov1 ] . although the latter way has great advantage in calculating gromov - witten invariants , its equivalence to the abstract definition ( [ eqn : gwdef ] ) has been established in [ g ] and [ lly1 ] only for some restricted calabi - yau hypersurfaces , see also [ ck ] for more backgrounds . our holomorphic anomaly equation for @xmath1 came from the calculational technique based on the mirror symmetry[hst1 ] . 0.3 cm \(1 ) to reproduce the holomorphic anomaly equation more specifically , let @xmath16 and @xmath17 in @xmath18 , respectively , be the fiber class and the class of a section of the elliptic fibration . then consider the following summation over @xmath15 ; @xmath19 and define the corresponding generating function with formal variable @xmath20 ; @xmath21 in [ hst1 ] , generalizing the result in [ mnw ] for @xmath22 , it was found that : _ ( holomorphic anomaly equation ) : the generating function @xmath23 has the form @xmath24 with some quasi - modular form @xmath25 $ ] of weight @xmath26 , where @xmath27 are eisenstein series of weight two , four and six , respectively , and @xmath28 . moreover @xmath23 satisfies @xmath29 with the initial data @xmath30 . _ one of the interesting features of this equation is that , under certain additional vanishing conditions ( gap condition ) on @xmath31 , we can determine @xmath32 for all @xmath33 and @xmath34 . some explicit formulas are presented in the end of this section . in this paper , using the affine @xmath0 weyl symmetry which arises as isomorphisms of rational elliptic surfaces [ lo][do ] , we will determine @xmath9 for @xmath10 with @xmath35 and @xmath36 . ( proposition 2.4 and tables 25 . ) 0.3 cm \(2 ) another important aspect of gromov - witten invariants is that the invariants take values in @xmath37 , however these can be related to _ integer _ `` invariants '' which , for example , may be identified with the number of ( rational ) curves in calabi - yau manifold . the relation to the integer `` invariants '' has appeared as multiple cover formula in [ cdogp ] and [ am ] for genus @xmath22 , and its most general form has been proposed by gopakumar and vafa giving physical meanings for the integer `` invariants '' , i.e. the number of _ bps states _ : _ ( gopakumar - vafa conjecture ) : gromov - witten invariants @xmath9 are related to integer invariants @xmath38 ( the number of bps states of charge @xmath15 ) by @xmath39 where @xmath40 means the summation over positive integer @xmath41 which divide the integral class @xmath15 , and @xmath42 is the rational number defined by @xmath43 _ our result in this respect is that we verify the integrality of @xmath38 up to @xmath44 and @xmath45 for rational elliptic surface @xmath1 . ( tables 25 . ) gopakumar and vafa have also proposed that the integer `` invariants '' @xmath38 should be geometric invariants on the moduli space of d2 branes of charge @xmath15 , i.e. suitable moduli space of curves of a fixed homology class @xmath15 and with local system on it . precise mathematical definition of the moduli space of d2 branes @xmath46 has been proposed in [ hst2 ] for calabi - yau threefold @xmath6 with an ample class @xmath47 . there the moduli space @xmath46 is defined as the normalization of the moduli space of semistable sheaves of pure dimension one with its support having homology class @xmath15 , and also with a fixed hilbert polynomial @xmath48 @xmath49 . some numbers @xmath38 have been explained from this definition[hst2 ] . we will provide a brief scketch in sect.3.3 about the expected geometrical interpretation about the numbers @xmath38 , although its detailed study is beyond the scope of our note . here we remark that in case of elliptic surfaces , like @xmath4k3 , the moduli spaces of d2 branes may be mapped to the moduli space of stable sheaves on the surface under fiberwise fourier - mukai transformations , see for example [ mnvw ] , [ yo],[hst3 ] . 0.3 cm ( 3 ) the most general form of the holomorphic anomaly equation which is applicable , in principle , to arbitrary calabi - yau threefold is known in [ bcov1,2 ] . we will connect our holomorphic anomaly equation ( [ eqn : haea ] ) to a certain limit ( local mirror symmetry limit ) of the equations in [ bcov1,2 ] . we will make explicit comparisons of these two equations for @xmath50 , and conjecture their equivalence . ( conjecture 4.3 ) . also we will find a nontrivial relation in the holomorphic ambiguities of these equations . 0.5 cm finally , for reader s convenience , we present here some explicit forms of solutions of the holomorphic anomaly equation ( [ eqn : haea ] ) : @xmath51 @xmath52 @xmath53 for @xmath54 a closed formula valid for all genus is known in [ hst1 ] . 0.3 cm * acknowledgements : * the author would like to thank department of mathematics , harvard university for the hospitality and support during his visit in the summer 1999 and 2001 - 2002 . most of this work has been done during his visit in the summer , 1999 . he would like to thank b. andreas , r. donagi , a. klemm , b. lian , c - h liu , k.oguiso , m .- h.saito , a.takahashi , c. vafa , and s .- t . yau for their valuable discussions and comments . especially he would like to thank m .- h.saito , a.takahashi and r. donagi for their collaboration at early stage of this work . this research is also supported in part by education ministry of japan .

we study gromov - witten invariants of a rational elliptic surface using holomorphic anomaly equation in [ hst1 ] . formulating invariance under the affine weyl group symmetry , we determine conjectured invariants , the number of bps states , from gromov - witten invariants . we also connect our holomorphic anomaly equation to that found by bershadsky , cecotti , ooguri and vafa [ bcov1 ] .

we study gromov - witten invariants of a rational elliptic surface using holomorphic anomaly equation in [ hst1 ] . formulating invariance under the affine weyl group symmetry , we determine conjectured invariants , the number of bps states , from gromov - witten invariants . we also connect our holomorphic anomaly equation to that found by bershadsky , cecotti , ooguri and vafa [ bcov1 ] .

0910.2348

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the fact that compact conformations of polymers are principal configurations of the native states of globular proteins makes them an important subset of all the physically accessible conformations . since compact conformations occupy space as densely as possible , one of the simplest ways to model them is to use hamiltonian walks ( hws ) on a lattice , which are , by definition , self - avoiding walks ( saws ) that visit all the lattice sites exactly once @xcite . in order to make this model more capable for capturing different features of various physical phenomena ( such as protein melting @xcite or protein folding @xcite ) local interactions can be introduced , but even in its simplest form , with no interactions taken into account , the problem of enumeration and classification of hamiltonian walks proved to be extremely difficult . studies of hamiltonian walks are primarily focused on finding the overall numbers @xmath2 of open and closed hws on lattice with @xmath3 sites . it is expected that limiting value of @xmath14 exists when @xmath15 , and its particular value @xmath16 corresponds to the configurational entropy per monomer ( site ) . this means that to the lowest approximation , @xmath2 behaves as @xmath6 and , therefore , the so - called connectivity constant @xmath7 can be interpreted as average number of steps available to the walker having already completed a large number of steps . the leading corrections to the exponential term are expected to have the power - law form @xmath17 ( as in the case of ordinary self - avoiding walks ) , and the stretched exponential form @xmath9 , with @xmath10 , so that @xmath2 should scale as @xmath18 expectations of such forms are based on the exact studies of hws on the manhattan @xcite and some fractal lattices @xcite , as well as on results obtained for closely related models of collapsed interacting self - avoiding walks on square @xcite and cubic lattice @xcite . in the case of collapsed saws appearance of the stretched exponential term , which is not present in the scaling form for non - interacting saws , was explained as a consequence of surface effects . namely , a collapsed saw forms a compact globule , with a sharp boundary separating it from the surrounding solvent , so that monomers on the boundary have smaller number of contacts with other monomers than those in the bulk of the globule , and therefore surface tension should arise . for homogeneous lattices one can assume that the boundary itself is homogeneous surface , and then straightforward arguments @xcite lead to the conclusion that term @xmath9 , with @xmath19 ( @xmath20 being the dimensionality of the lattice ) , should appear . exact studies @xcite , series analysis of data obtained via exact enumeration @xcite , as well as monte - carlo simulations @xcite of collapsed saws on homogeneous lattices , certainly confirm existence of the stretched exponential term with the proposed formula for @xmath11 . although it is believed that hw model corresponds to the interacting saw model at temperature @xmath21 , in spite of the continuous improvements of exact @xcite and monte carlo @xcite enumeration techniques , direct confirmation of scaling relation for hws on non - oriented homogeneous lattices has not been achieved yet . apart from manhattan lattice , scaling forms for hamiltonian walks were obtained only for some fractal lattices , where stretched exponential corrections for both open and closed hws were found only for @xmath22-simplex fractals with even @xmath22 @xcite . even in that cases , its presence can not be explained using a simple generalization of the argument used for collapsed self - avoiding walks on homogeneous lattices . however , results of the studies on fractals suggest that stretched exponential term can be expected on lattices where larger number of entangled conformations is possible . in order to get a deeper insight into this issue , here we apply an exact recursive method for enumeration and classification of hws on modified three - dimensional sierpinski gasket family of fractals . in contrast to most of the previously in this context studied fractals , which were embedded either in two - dimensional spaces or spaces with dimensionality higher than 3 , each member of the family studied in the present paper is embedded in three - dimensional space . therefore , hws on these fractals can be understood as a toy model for compact polymers critical behaviour in realistic nonhomogeneous 3d media , which , to the best of our knowledge , has not been studied so far . the paper is organized as follows . modified 3d sierpinski gasket fractals , as well as the method itself , are described in the next section . explicit forms of the recursion relations , obtained for the types of hamiltonian walks which are needed for generation and enumeration of all closed conformations are presented for the first three members of the fractal family . numerically analyzing these relations we find scaling form @xmath23 . using some general features of these relations ( obtained in [ ap : kb ] and [ app : xasimptotika ] ) , we argue that such form should be correct for the whole fractal family , and derive the closed - form formula for the exponent @xmath11 . in section 3 we extend the method to open hws , explicitly apply it again on the first three fractals , and then generalize it . it turns out that the number of open hws scales as @xmath24 , with the same values of the connectivity constant @xmath25 and the exponent @xmath11 as for the closed hws , but with @xmath26 . general features of the recursion relations for open hws are derived in [ app : ac ] and [ app : dh ] . all the obtained results are summarized and discussed in the section 4 , and some auxiliary considerations , needed for the discussion , are given in appendix e.

each member of this fractal family is labeled with an integer . in contrast to that , the stretched exponential term depends on the type of hw through constant , whereas exponent is determined by alone . for larger values , using some general features of the applied recursive relations , without explicit enumeration of hws , we argue that asymptotical behavior of should be the same , with $ ] , valid for all . this differs from the formulae obtained recently for hamiltonian walks on other fractal lattices , as well as from the formula expected for homogeneous lattices . we discuss the possible origin and implications of such result .

we study hamiltonian walks ( hws ) on the family of three dimensional modified sierpinski gasket fractals , as a model for compact polymers in nonhomogeneous media in three dimensions . each member of this fractal family is labeled with an integer . we apply an exact recursive method which allows for explicit enumeration of extremely long hamiltonian walks of different types : closed and open , with end - points anywhere in the lattice , or with one or both ends fixed at the corner sites , as well as some hamiltonian conformations consisting of two or three strands . analyzing large sets of data obtained for and 4 , we find that numbers of hamiltonian walks , on fractal lattice with sites , for behave as . the leading term is characterized by the value of the connectivity constant , which depends on , but not on the type of hw . in contrast to that , the stretched exponential term depends on the type of hw through constant , whereas exponent is determined by alone . for larger values , using some general features of the applied recursive relations , without explicit enumeration of hws , we argue that asymptotical behavior of should be the same , with $ ] , valid for all . this differs from the formulae obtained recently for hamiltonian walks on other fractal lattices , as well as from the formula expected for homogeneous lattices . we discuss the possible origin and implications of such result . _ keywords _ : solvable lattice models ; polymers , copolymers , polyelectrolytes and biomolecular solutions ; structures and conformations ( theory )

0910.2348

i

in this paper we have analyzed asymptotic behavior of the numbers of open and closed hamiltonian walks on three - dimensional modified sierpinski gasket family of fractals . numbers of extremely long hws on these lattices can be generated by applying an exact recursive enumeration scheme , based on the fact that any hw on the @xmath178th step of the construction of the 3d msg fractal , @xmath31 , consists of @xmath179 hws within its @xmath43 constitutive @xmath37 structures , which can be of one of six possible types : @xmath180 , and @xmath109 ( and ) . numbers of these hws , @xmath119 , @xmath45 , @xmath120 , @xmath121 , @xmath46 , and @xmath122 , fulfil closed set of recursive relations , , and , which , due to the self - similarity of the lattices under study , do not depend on @xmath30 , and therefore can be obtained by explicit enumeration and classification of hw conformations on the first step of the fractal construction , @xmath27 . as @xmath8 grows , number of hw conformations rapidly increases already on @xmath27 , so that we have managed to find explicit form of the recursive relations only up to @xmath68 . however , we have shown that for any @xmath13 these recursive relations have some features that enable general analysis , leading to conclusion that overall numbers @xmath181 and @xmath175 of closed and open hws , respectively , on any 3d msg fractal , scale with the number @xmath89 of the lattice sites as @xmath182^{n_l^\sigma}\ , , \quad z_l^o\sim \omega^{n_l}\left[\lambda^{\frac{k_c+3}{n_g-3}\,4^{-\sigma}}\right]^{n_l^\sigma}\ , , \ ] ] with @xmath11 given by formula : @xmath183 constants @xmath25 and @xmath72 can be obtained numerically , using relations @xmath184 and their particular values for @xmath1 , and 4 are given in . number @xmath185 represents the maximal number of @xmath37 generators within the @xmath31 they belong to , which are traversed by two - stranded @xmath40-type hw conformation ( @xmath40-step ) within any closed @xmath186 on @xmath31 ( see equation and [ ap : kb ] ) . as one can see , hw conformations that traverse @xmath37 , and recursion relations for the corresponding numbers @xmath45 and @xmath46 , are sufficient for obtaining connectivity constant @xmath25 that governs the leading exponential term in the scaling forms for @xmath181 and @xmath175 , as well as constant @xmath72 which appears in their correction terms . whereas the leading term @xmath187 is the same for both closed and open hws , correction term in both cases has the same stretched exponential form @xmath188 , but with different values for @xmath189 and @xmath190 , indicating that number of open hws is larger than the number of closed hws . one should notice here that the fact that scaling form obtained for open hws is determined by the behavior of the numbers @xmath45 and @xmath46 only , means that contribution of one and two leg hw conformations ( @xmath106 , @xmath107 , @xmath108 and @xmath109type walks ) , _ i.e. _ hws with their ends in the interior of @xmath37 fractal structures , is not significant . furthermore , in sections 2 and 3 it was elaborated that the main mathematical reason for obtaining scaling forms with the stretched exponential correction term is the fact that @xmath191 , meaning that entangled conformations ( with large number of two - stranded parts ) dominate over those in which hws rarely return to already visited fractal generators . results of the study of hws on 3d msg fractals , presented in this paper , should be compared with the results recently obtained for other fractal lattices @xcite . for @xmath22-simplex fractal lattices with even values of @xmath22 the same asymptotic behavior of the hw numbers was found , @xmath192 , but with @xmath193 , which differs from the formula derived here for @xmath11 . the existence of the term @xmath9 was also related with the facts that : ( 1 ) entangled hws prevail , and ( 2 ) hws with `` interior '' terminating points do not contribute to the asymptotic behavior of hw numbers , as in the 3d msg fractals case . for odd @xmath22 , stretched exponential terms in the scaling forms for hws on @xmath22-simplex fractals do not exist , hws with `` interior '' terminating points do affect the scaling forms for the numbers of open hws , and entangled conformations do not dominate in this case . for given - mandelbrot and 2d modified sierpinski gasket fractals ( which are two - dimensional generalizations of the sierpinski gasket and 3-simplex fractal , respectively ) stretched exponential terms are also absent , whereas again , one and two leg conformations are necessary for obtaining the scaling forms for open hws , and , due to the specific topology of these lattices , only one - stranded hw conformations are possible . therefore , results of the present study confirm the assumption that existence of the stretched exponential term is related with the issue of hw entanglement . however , the discrepancy between the formulas obtained for the exponent @xmath11 for different fractal families , and , more generally , the question which properties of the underlying lattice and in what way determine @xmath11 , deserves further consideration . to this end we recall that stretched exponential terms were obtained for hws on manhattan @xcite , as well as for low - temperature saws on square @xcite and cubic @xcite lattice . in this context , one should also mention the spiral saws on 2d regular lattices @xcite and lattice animals on some hierarchical lattices . whereas , to the best of our knowledge , physical interpretation of the stretched exponential term for the 2d spiral saw models has never been proposed , its presence in the scaling forms obtained for lattice animals on hierarchical lattices was directly connected with the existence of the sets of sites with different coordination numbers @xcite . utilizing similar idea , in the case of low - temperature ( collapsed ) saws it was explicitly explained in @xcite why term of the form @xmath9 , with @xmath19 for regular lattices , should arise . however , as was elaborated in @xcite , direct application of such approach on hws on fractal lattices does not give satisfactory result . yet , the scaling forms obtained in this paper can be expound in the spirit of the physical reasoning given in @xcite , as will be explained in the following paragraph . we shall first focus on closed hws on @xmath37 with the maximal number of two - stranded @xmath40 conformations within the unit tetrahedrons . such hws represent maximally entangled closed ( mec ) compact conformations and they accomplish the maximal possible connectedness between the generators @xmath37 of all orders @xmath30 . now , from all the @xmath38 sites visited by such maximally entangled hw , observe those which belong to one - stranded conformations ( @xmath39-steps ) within the unit tetrahedrons , and which are directly connected only with the sites belonging to the same unit tetrahedron . for instance , vertices 9 and 10 , or 15 and 16 in represent examples of such sites . since these sites are not directly connected with the other tetrahedrons of the lattice ( via hw ) , they are the maximally isolated sites within the maximally entangled closed hw conformation . it is shown in [ app : diskusija ] that number @xmath194 of such sites is equal to @xmath195 and one can easily see that , using this expression , scaling relation for the numbers od closed hws can be transformed into the following form @xmath196 in a similar way ( see [ app : diskusija ] ) , one can show that scaling relation for open hws can be expressed as @xmath197 where @xmath198 is the number of maximally isolated sites on @xmath37 visited by maximally entangled open hw ( which is an open hw with the maximal number of @xmath40-steps on unit tetrahedrons and with both loose ends being of type @xmath107 , on all levels @xmath30 ) . comparing forms and with the scaling relations expected for hws on homogeneous lattices , one can say that in this case terms @xmath199 and @xmath200 play the role of the stretched exponential correction term @xmath9 in the case of homogeneous lattices . indeed , for homogeneous lattices @xmath201 , with @xmath19 , is proportional to the number of sites on the lattice boundary , which have smaller number of neighbors than the bulk sites , and in that sense they are similar to the maximally isolated sites within the maximally entangled hws on 3d msg lattices . therefore , one might generally expect that scaling relation for the number of hws on nonhomogeneous lattices instead of stretched exponential correction term has a term @xmath202 , where @xmath203 is the number of conveniently defined `` maximally isolated sites '' . relation between @xmath203 and the overall number of lattice sites @xmath3 depends on the particular topology of the lattice under study , which is the reason why different scaling forms , as functions of @xmath3 , are obtained . conclusion of the previous paragraph can be supported by performing a similar analysis in the case of hws on previously studied fractal families @xcite . for instance , for @xmath22-simplex fractals maximally isolated sites can be defined in a similar way as for 3d msg fractals , _ i.e. _ these are the sites which are directly connected by maximally entangled hw only with the sites within the same fractal generator they belong to . here , maximally entangled hws are those that contain maximal number of maximally - stranded hw parts . then , it can be shown @xcite that @xmath204 and @xmath205 , where @xmath206 . since overall numbers of closed and open hws on @xmath22-simplex fractal with even @xmath22 asymptotically behave as @xmath207 ( see ( 5.8 ) in @xcite ) and @xmath208 ( formula ( 5.14 ) in @xcite ) , respectively , they immediately fit into the scaling relation @xmath209 , where @xmath210 and @xmath211 for both types of hws . for odd values of @xmath22 , however , it can be shown @xcite that number @xmath203 of maximally isolated sites , for both open and closed hws , is proportional to @xmath38 , so that any term of the form @xmath202 can only contribute to the leading term @xmath6 . this certainly is in accord with the scaling forms found in @xcite for odd @xmath22 , which do not have stretched exponential corrections . to conclude , we may say that presented exact study of hamiltonian walks on modified three - dimensional sierpinski gasket fractals supports the idea that entangled conformations are of the most physical importance for the behavior of compact polymers in inhomogeneous media . the introduced concept of `` maximally isolated sites '' proved to be useful in physical interpretation of different scaling forms obtained for hamiltonian walks on all so far studied fractals . whether such concept can be applied on homogeneous and other nonhomogeneous lattices will be the matter of our further investigations . this paper has been done within the project no oi 141020b , funded by the serbian ministry of science and environmental protection .

we study hamiltonian walks ( hws ) on the family of three dimensional modified sierpinski gasket fractals , as a model for compact polymers in nonhomogeneous media in three dimensions . _ keywords _ : solvable lattice models ; polymers , copolymers , polyelectrolytes and biomolecular solutions ; structures and conformations ( theory )

we study hamiltonian walks ( hws ) on the family of three dimensional modified sierpinski gasket fractals , as a model for compact polymers in nonhomogeneous media in three dimensions . each member of this fractal family is labeled with an integer . we apply an exact recursive method which allows for explicit enumeration of extremely long hamiltonian walks of different types : closed and open , with end - points anywhere in the lattice , or with one or both ends fixed at the corner sites , as well as some hamiltonian conformations consisting of two or three strands . analyzing large sets of data obtained for and 4 , we find that numbers of hamiltonian walks , on fractal lattice with sites , for behave as . the leading term is characterized by the value of the connectivity constant , which depends on , but not on the type of hw . in contrast to that , the stretched exponential term depends on the type of hw through constant , whereas exponent is determined by alone . for larger values , using some general features of the applied recursive relations , without explicit enumeration of hws , we argue that asymptotical behavior of should be the same , with $ ] , valid for all . this differs from the formulae obtained recently for hamiltonian walks on other fractal lattices , as well as from the formula expected for homogeneous lattices . we discuss the possible origin and implications of such result . _ keywords _ : solvable lattice models ; polymers , copolymers , polyelectrolytes and biomolecular solutions ; structures and conformations ( theory )

nucl-th9408009

i

the electromagnetic production of electron - positron pairs in relativistic heavy ion collisions has gained some interest recently due to the observation that the total probability violates unitarity if calculated in lowest order even for realistic energies and impact parameters as large as the compton wavelength @xcite . it can be expected therefore that higher - order effects especially the multiple - pair production are of importance . several models have been used in order to cure the unitarity violation and predict multiple - pair probabilities , based on the summation of some subclasses of diagrams@xcite . all authors find that the pair multiplicity can be approximated by a poisson distribution and that the lowest - order results should be interpreted as the pair multiplicity . unitarity is no longer violated due to the inclusion of the vacuum amplitude , which reduces all @xmath0-pair probabilities by the same factor . recently ionescu @xcite has proposed a model , which differs from the previous ones , but which is not applicable for multiple - pair production . we are going to extend these existing models into two directions : first we address the question how the @xmath0-pair creation amplitude is exactly reducible to one - pair creation amplitudes and what approximations are necessary in order to get the poisson distribution . we then compare with earlier results . secondly we study higher - order processes contributing to the lowest - order one - pair creation amplitude . we concentrate on multiple - particle effects , which have not been included in previous models . this paper is arranged as follows : in sec . [ feynman ] we show that the @xmath0-pair creation amplitude can be written as an antisymmetrised product of reduced one - pair creation amplitudes and the vacuum amplitude . for this we use feynman boundary conditions for the fermion field . neglecting contributions from exchange terms in the calculation of the total probability we get a poisson distribution for the total @xmath0-pair probability quite easily . in sec . [ sec : pertubation ] the same result is derived using the perturbation expansion of the @xmath2-matrix , which gives us some insight into the processes contributing to the reduced pair creation amplitude and the vacuum amplitude . finally we compare in sec . [ sec : comparision ] our results with other existing ones . in sec . [ sec : magnus ] we derive the general form of the @xmath2-operator in second - order magnus theory and use it in sec . [ sec : highercorr ] in order to extract from this the lowest - order multiple - particle correction to the one - pair creation probability . this correction is then calculated in sec . [ bornzero ] based on our analytic form of the differential pair creation amplitude in second - order born approximation for impact parameter @xmath1 zero@xcite . the same calculation is used also to study the deviation of the total two - pair creation probability from the poisson distribution , which is found to be rather small . results of these calculations together with conclusions are then summarized in sec . [ results ] . in the appendix , we show a way to calculate the coefficients appearing in the magnus theory expansion , which can therefore be calculated to arbitrary order . throughout this paper , we treat the fields of the heavy ions as external fields . we neglect the electromagnetic interaction between electrons and positrons . this seems to be justified for almost all fermions , apart from electrons and positrons , which are produced with very low relative velocitiy , and even in a bound @xmath3@xmath4 state , due to the smallness of the coupling constant @xmath5 between the fermions compared to the effective coupling constant @xmath6 for the interaction with the external field . due to these assumptions , our many particle system is essentially a system of independent fermions in an external field . for such a system the @xmath2 operator is known to be of the form of a time - ordered exponential @xmath7 \psi(x ) : \right\ } \label{intro : smatrix } , \end{aligned}\ ] ] where @xmath8 is the hamiltonian in the interaction picture . this form of the @xmath2 operator is the starting point for our calculations . the general theory of a fermion interacting with an external electromagnetic field is rather old and has been developed already from the beginning of qed . it has been developed especially by feynman @xcite and schwinger @xcite . an overview can also be found in @xcite . although we discuss only the electromagnetic pair production by heavy ion collisions , the general theory can also be applied to other pair production processes in external fields , for example , pair creation due to bremsstrahlung@xcite .

we study higher - order effects in the electromagnetic production of electron - positron pairs in relativistic heavy ion collisions . treating the field of the heavy ions as an external field and neglecting the interaction among electrons and positrons , we show that the-pair creation amplitude is the antisymmetrised product of one - pair creation amplitudes and the vacuum amplitude . neglecting contributions coming from exchange terms , we show that the total probability for pairs is approximately a poisson distribution . we calculate the first of these corrections in second order magnus theory based on our previous result in second - order born approximation for impact parameter zero . explicit calculations show that the total probability is increased up to 10 % by this correction for realistic collider parameters .

we study higher - order effects in the electromagnetic production of electron - positron pairs in relativistic heavy ion collisions . treating the field of the heavy ions as an external field and neglecting the interaction among electrons and positrons , we show that the-pair creation amplitude is the antisymmetrised product of one - pair creation amplitudes and the vacuum amplitude . neglecting contributions coming from exchange terms , we show that the total probability for pairs is approximately a poisson distribution . we investigate further the structure of the reduced one - pair amplitude , concentrating especially on multiple - particle corrections . we calculate the first of these corrections in second order magnus theory based on our previous result in second - order born approximation for impact parameter zero . explicit calculations show that the total probability is increased up to 10 % by this correction for realistic collider parameters . the calculations can also be used to confirm the use of the poisson distribution for the total probability .

1109.1389

i

in a previous paper @xcite we studied moduli spaces of holomorphic discs in certain @xmath0-dimensional symplectic cobordisms . as in the classical work of hofer @xcite on the weinstein conjecture in dimension @xmath1 , the non - compactness of these moduli spaces was used to detect periodic reeb orbits . moreover , this approach enabled us to give a unified view of many results in @xmath1-dimensional contact topology and @xmath0-dimensional symplectic topology . in the present paper we extend this work to higher dimensions . using an idea that can be traced back to mcduff @xcite , we modify our set - up by constructing a symplectic cap on the convex end of the symplectic cobordism . we can then work with moduli spaces of holomorphic spheres rather than discs , which allows us to invoke a compactness theorem from symplectic field theory @xcite . our main technical result ( theorem [ thm : main ] ) makes quantitative predictions about periodic reeb orbits in the concave end of the symplectic cobordisms under consideration . in corollary [ cor : main ] we rephrase this as a statement about the weinstein conjecture @xcite in the strong version proposed by abbas et al . @xcite , which will be recalled in section [ section : weinstein ] . we also recover a result of mcduff about a class of symplectic fillings whose boundary is necessarily connected ( theorem [ thm : mcduff ] ) . in section [ section : applications ] we explore various applications of these results . our main focus is on specific instances of the strong weinstein conjecture and on quantitative reeb dynamics . these examples include contact type hypersurfaces in subcritical stein manifolds ( corollary [ cor : stein ] ) and in cotangent bundles over split manifolds @xmath2 ( corollary [ cor : cotangent ] ) . as in our previous paper , the quantitative results give rise to the definition of a symplectic capacity via the periods of reeb orbits on contact type hypersurfaces . a typical application is the weinstein conjecture for subcritically stein fillable contact manifolds ( corollary [ cor : filling ] ) . this result is complementary to that of albers hofer @xcite on the weinstein conjecture for higher - dimensional contact manifolds that are overtwisted in the sense of niederkrger @xcite and hence , as shown there , do not admit semipositive strong symplectic fillings . hofer study holomorphic discs in trivial symplectic cobordisms only , but it seems likely that this can be extended to the more general cobordisms considered here . for other recent work on the higher - dimensional weinstein conjecture see @xcite . the final two sections contain the proof of the main technical result . in section [ section : completing ] we describe a completion of the symplectic cobordism . in section [ section : moduli ] we introduce certain moduli spaces of holomorphic spheres in this completed cobordism ; the non - compactness of these moduli spaces implies the main result . part of the motivation for this paper comes from the recent article by oancea viterbo @xcite on the topology of symplectic fillings . at the end of the present paper we briefly indicate the relation of our results with their work .

we study holomorphic spheres in certain symplectic cobordisms and derive information about periodic reeb orbits in the concave end of these cobordisms from the non - compactness of the relevant moduli spaces . we use this to confirm the strong weinstein conjecture ( predicting the existence of null - homologous reeb links ) for various higher - dimensional contact manifolds , including contact type hypersurfaces in subcritical stein manifolds and in some cotangent bundles . the quantitative character of this result leads to the definition of a symplectic capacity .

we study holomorphic spheres in certain symplectic cobordisms and derive information about periodic reeb orbits in the concave end of these cobordisms from the non - compactness of the relevant moduli spaces . we use this to confirm the strong weinstein conjecture ( predicting the existence of null - homologous reeb links ) for various higher - dimensional contact manifolds , including contact type hypersurfaces in subcritical stein manifolds and in some cotangent bundles . the quantitative character of this result leads to the definition of a symplectic capacity .

1602.08544

i

the classical gauss problem of minimizing the coulomb energy to solve the problem of thomson and its generalization to riesz potentials together with the discretization is the basic problem of many applications ( in @xcite are listed coding theory , cubature formulas , tight frames and packing problems ) . in the works @xcite , @xcite , @xcite , @xcite , and @xcite , the discretization is obtained by approximating the minimizing charges by a distribution of finitely many dirac measures on the given manifold . if the number of dirac points tends to infinity , then the minimizing densities approach distributions in the form of sobolev space elements . therefore , in @xcite , @xcite , @xcite , the minimizing measures are considered as distributions in hilbert spaces of finite riesz energy . this continuous setting is simpler and more efficient from the numerical point compared to the discrete approach in @xcite , @xcite , @xcite , @xcite . for potentials with riesz kernel @xmath11 , where @xmath12 , and borel measures supported on a given @xmath3-dimensional manifold @xmath5 immersed into @xmath6 , a surface potential is generated , which on @xmath5 defines a boundary integral operator with weakly singular kernel . this boundary integral operator is a pseudodifferential operator of _ negative _ order @xmath13 if @xmath14 . the energy space of this pseudodifferential operator on @xmath5 is thus the sobolev space @xmath15 of distributions and the minimizing measure of finite energy is an element of this sobolev space . hence , the determination of the minimizer is reduced to an optimization problem with a quadratic functional which is defined in terms of the single layer riesz potential on @xmath5 . the strong ellipticity of the corresponding pseudodifferential operator in @xmath16 and its trace on @xmath5 then provides the coerciveness of the associated quadratic functional . for @xmath17 , which corresponds to the newtonian kernel , the riesz energy of the single layer potential is just its dirichlet integral over @xmath18 . in this paper , however , we consider the riesz kernels with @xmath19 . for @xmath20 , in classical potential theory , the energy of the harmonic double layer potential in @xmath18 now equals the riesz energy if we define the latter as to be hadamard s partie finie integral of the hypersingular potential which is the natural distributional regularization ( see section [ s : double ] where @xmath5 is a @xmath3-dimensional planar bounded domain in @xmath6 ) . let @xmath21 where @xmath22 , @xmath23 , are finitely many compact , connected @xmath3-dimensional @xmath4-manifolds immersed into @xmath6 . in section [ s : manifold ] , we then consider the riesz potential as a pseudodifferential operator just on @xmath8 since we can not use its extension to @xmath24 ( for @xmath25 , the transmission conditions ( * ? ? ? * theorem 8.3.11 ) are not satisfied ) . we call the bilinear form with the strongly singular partie finie integral of the riesz kernel the _ energy of the riesz potential_. the partie finie integral operator with the hypersingular riesz kernel defines now a strongly elliptic pseudodifferential operator @xmath26 of _ positive _ order @xmath27 on @xmath5 . in contrast to the analysis of weakly singular riesz kernels provided earlier by the authors in @xcite , @xcite , in the case under consideration , the trace theorem in @xmath28 is not valid anymore , because of the negativity of the order @xmath29 , cf . nevertheless , we have succeeded in overcoming this difficulty , and we have shown that all the borel measures on @xmath8 with finite riesz energy whose restriction on any @xmath22 takes sign either @xmath30 or @xmath31 form a certain cone in the sobolev space @xmath32 , @xmath33 . _ this is our main result in section [ s : manifold ] , theorems [ th:3.3 ] and [ th:3.4]_. in this framework , the corresponding gauss variational problem admits a unique solution which belongs to @xmath32 , which is a compact subspace of @xmath34 . these results have again a potential theoretic meaning in the particular situation @xmath35 in relation to the harmonic double layer potential as explained in section [ s : null ] . in the fundamental work @xcite by d.p . hardin and e.b . saff , discrete minimal energy problems have been investigated . there , the discrete riesz energies are obtained by distributing a finite number ( @xmath36 ) of evenly weighted dirac measures on a compact @xmath3-dimensional manifold @xmath37 where the set @xmath38 is excluded . then , the discrete minimal riesz energy determines an optimal geometric arrangement of the @xmath36 distinct dirac points on @xmath37 . in @xcite , three cases are distinguished : ( i ) the riesz kernel is weakly singular , ( ii ) the case @xmath39 ( see @xcite ) , and ( iii ) the hypersingular case @xmath40 . for all these three cases , the behavior of the discrete minimal energies for @xmath36 tending to infinity is explicitly determined ( see section [ s : mini ] below for details ) . in the works @xcite , @xcite , and @xcite , these results are generalized to more general riesz kernels with weights . during a miniworkshop in august 2012 in stuttgart with e.b . saff , d.p . hardin , and p.d . dragnev , we have learned from them that in the hypersingular case the discretized minimal energies tend to infinity if the number of dirac basic points approaches infinity and at the same time those minimizing charges tend to a charge with a constant density . this discussion inspired us to pick up this topic gratefully in our paper and to analyze also this approach by cutting out the set @xmath41 of @xmath42 where @xmath43 . we first figure out the idea in section [ s : mini ] by studying a perturbed riesz energy problem . then , in section [ s : comp ] , we perform the computations in detail for the punched riesz energy problem and give an asymptotic expansion of the solution in the corresponding family of finite energy spaces for @xmath44 . in particular cases ( see corollary [ c:4.6 ] for details ) , the minimizers tend to a constant distribution on @xmath5 while the corresponding minimal energies tend to infinity .

, we are motivated to formulate the natural regularization of such minimization problems by switching to hadamard s partie finie integral operator which defines a strongly elliptic pseudodifferential operator of order on . the measures with finite energy are shown to be elements from the sobolev space , , and the corresponding minimal energy problem admits a unique solution . we relate our continuous approach also to the discrete one , which has been worked out earlier by d.p . hardin and e.b . saff .

we study minimal energy problems for strongly singular riesz kernels , where and , considered for compact-dimensional-manifolds immersed into . based on the spatial energy of harmonic double layer potentials , we are motivated to formulate the natural regularization of such minimization problems by switching to hadamard s partie finie integral operator which defines a strongly elliptic pseudodifferential operator of order on . the measures with finite energy are shown to be elements from the sobolev space , , and the corresponding minimal energy problem admits a unique solution . we relate our continuous approach also to the discrete one , which has been worked out earlier by d.p . hardin and e.b . saff .

1701.05714

i

a homogeneous magnetic field acting on charged particles has a localizing effect , both classically and quantum mechanically . since numerous physical effects are based on moving electrons between different places , mechanism that can produce transport in the presence of a magnetic field are of great interest . they typically require presence of an infinitely extended perturbation , a standard example being a barrier or a potential wall producing edges states , cf . @xcite and references therein . this is not the only possibility , though . in his classical paper @xcite iwatsuka demonstrated that a transport can be induced be a modification of the magnetic field itself under the assumption of a translational invariance , see also @xcite . the aim of the present paper is to show still another mechanism which can produce transport in a homogeneous field for particles confined to a layer with hard walls . as in the case of the iwatsuka model we will express the effect in spectral terms seeking perturbations that change the hamiltonian spectrum to absolutely continuous . our departing point is a flat layer of width @xmath0 to which a charged particle is confined and which is exposed to the homogeneous magnetic field perpendicular to the layer plane . the spectrum of such a system is easily found by separation of variables . it combines the landau levels with the dirichlet laplacian eigenvalues in the perpendicular direction , and needless to say that all the resulting eigenvalues are infinitely degenerate , see sec . [ sss : flatlayer ] below for more details . we are going to discuss _ geometric perturbations _ of such a system , in particular , deformations of the layer which are invariant with respect to translation in a fixed direction . such layers can be described , e.g. , as a set of points satisfying @xmath1 where @xmath2 is a surface obtained by shifting a smooth curve which can be parametrized by relation below . we are going to derive several conditions which ensure that the unperturbed pure point spectrum will change into an absolutely continuous one . more specifically , our main results can be summarized in the following assertion . let @xmath3 be the hamiltonian of a charged quantum particle confined to a layer @xmath4 of a constant width @xmath0 in @xmath5 built over a @xmath6-smooth , translationally invariant surface and exposed to a nonzero homogeneous magnetic field pointing in the @xmath7-direction . the spectrum of @xmath3 is purely absolutely continuous if together with technical assumptions [ eq : curv_bound ] and [ eq : diff_cond ] any of the following conditions is satisfied : a. @xmath4 is a one - sided - fold layer , @xmath8 or @xmath9 . furthermore , we suppose that the second part of [ eq : v_bound ] is fulfilled . b. @xmath4 is bent and asymptotically flat , @xmath10 for all large enough positive and negative @xmath11 , respectively , where @xmath12 $ ] . furthermore , one requires that @xmath13 and the halfwidth @xmath14 satisfies the bound described in lemma [ lem : ev_diff ] and remark [ rem : a_crit_bound ] below . moreover , for a fixed @xmath15 , the spectrum of @xmath3 below @xmath16 is absolutely continuous if @xmath4 is thin , i.e. the halfwidth @xmath14 is sufficiently small , and the generating surface satisfies one of the conditions specified in proposition [ prop : thin ] . the proof of the theorem will be given in sec . [ s : classes ] , before coming to it we will describe the geometry of the layer and explain the main steps of the argument . let us add a few remarks . first of all , in sec . [ sss : flatlayer ] we demonstrate that the perturbation must be geometrically nontrivial , because a mere tilt of the layer with respect to the field direction is not enough , with one notable exception . furthermore , except the claim ( i ) our condition impose restrictions on the layer thickness . on the other hand , the thinner the layer , the more general deformations we can treat . in particular , the last claim covers perturbations which are compact with respect to the @xmath17 variable , cf . proposition [ prop : thin ] . note also that the shift by @xmath18 in the last claim is needed ; without it the claim would be trivial because in a thin layer the spectral threshold is pushed up due to the dirichlet boundaries . the method used to treat thin layers is also useful with respect to the original iwatsuka model and its generalization including addition of a potential perturbation . recall , in particular , the conjecture stated in @xcite according to which _ any _ nontrivial translationally invariant magnetic perturbation gives rise to the purely absolutely continuous spectrum . despite a number of sufficient conditions derived after the original iwatsuka paper @xcite to which we add a new one in theorem [ theo : iwatsuka ] , the question in its generality remains open . in a similar vein , we are convinced that the sufficient conditions we find in this paper are by far not necessary .

we study motion of a charged particle confined to dirichlet layer of a fixed width placed into a homogeneous magnetic field . if the layer is planar and the field is perpendicular to it the spectrum consists of infinitely degenerate eigenvalues . we consider translationally invariant geometric perturbations and derive several sufficient conditions under which a magnetic transport is possible , that is , the spectrum , in its entirety or a part of it , becomes absolutely continuous .

we study motion of a charged particle confined to dirichlet layer of a fixed width placed into a homogeneous magnetic field . if the layer is planar and the field is perpendicular to it the spectrum consists of infinitely degenerate eigenvalues . we consider translationally invariant geometric perturbations and derive several sufficient conditions under which a magnetic transport is possible , that is , the spectrum , in its entirety or a part of it , becomes absolutely continuous .

0901.2506

i

a ternary algebra or triple system is a vector space @xmath1 endowed with a ternary law of composition @xmath2 which is a linear mapping with respect to each its argument , and we will call this mapping a ternary multiplication or triple product of a ternary algebra @xmath1 . hence a ternary algebra is an algebra which closes under a suitable triple product . obviously any binary algebra which closes under double product can be considered as a ternary algebra if one defines the ternary multiplication as twice successively applied binary one , and in this case the ternary multiplication is generated by a binary one . however there are ternary multiplications which can not be obtained as twice successively applied binary multiplication . for instance , pure imaginary numbers or elements of grading one of a superalgebra closes under triple product . a well known example of a ternary matrix algebra is the vector space @xmath3 of @xmath4 matrices endowed with the ternary multiplication @xmath5 , where @xmath6 and @xmath7 is transpose of the matrix @xmath8 . since lie algebras play a fundamental role in physics , particular attention was given to ternary algebras when they were shown to be building blocks of ordinary lie algebras . given ternary algebra one can construct a lie algebra by using the method proposed by kantor in @xcite . this method was extended to super lie algebras in @xcite and later was applied by the same authors in @xcite to construct a gauge field theory by introducing fundamental fields associated with the elements of a ternary algebra . a skew - symmetric bilinear form is an important component in the large class of algebraic structures such as lie algebras , grassmann algebras and clifford algebras . for example , the lie brackets @xmath9:{\frak l}\times{\frak l}\to { \frak l}$ ] of a lie algebra @xmath10 is the skew - symmetric bilinear form , and the multiplication @xmath11 of a grassmann algebra @xmath12 restricted to the subspace of odd elements is the skew - symmetric bilinear form . a skew - symmetry of a bilinear form can be interpreted by means of the faithful representation of the symmetric group @xmath13 , where @xmath14 is the identity permutation , as follows : a bilinear form @xmath15 is skew - symmetric if @xmath16 . making use of this interpretation we can construct a ternary analog of a skew - symmetric bilinear form replacing @xmath17 by @xmath18 with its faithful representation by cubic roots of unity @xmath19 , i.e. @xmath20 , where @xmath14 is the identity permutation and @xmath21 are the cyclic permutations , as follows : a trilinear form @xmath22 is called @xmath0-skew - symmetric if for any elements @xmath23 of a vector space @xmath1 it satisfies @xmath24 the notion of a @xmath0-skew - symmetric form can be assumed as a basis for a ternary analog of grassmann , clifford and lie algebras . these ternary structures were developed in @xcite and applied to construct a ternary analog of supersymmetry algebra in @xcite . in this paper we study algebras with ternary law of composition . in section 2 we consider partially and totally associative ternary algebras of first and second kind . we show that a triple product of a ternary algebra induces three binary multiplications and find the sufficient and necessary condition a triple product of a ternary algebra must satisfy in order to induce the associative binary algebra . assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle . the sufficient and necessary condition a ternary multiplication must satisfy in order to induce a structure of associative binary algebra in each fiber is given in terms of the vector bundle over a ternary algebra . the relations for different kinds of partial and total associativity of a ternary algebra and induced by it binary algebras are found in the terms of the structure constants of a ternary algebra . it should be pointed out that the cohomologies of a ternary algebra of associative type are studied in @xcite . in section 3 we consider an algebraic structure consisting of two bimodules over unital associative algebras with involution and construct a ternary algebra by means of this algebraic structure . choosing different modules , unital associative algebras and homomorphisms we show that this structure allows to construct a large class of ternary algebras including a ternary algebra of rectangular matrices and ternary algebras of sections of a vector bundle over a smooth finite dimensional manifold . we end the section 3 by constructing the binary lie algebra of matrices whose entries are the elements of bimodules and unital associative algebras . it should be mentioned that there are @xmath25-ary generalizations of lie algebra which include the concepts such as @xmath25-ary algebra of lie type enclosing @xmath25-ary nambu algebra , @xmath25-ary nambu - lie algebra . the concept of @xmath25-ary hom - algebra structure generalizing previously mentioned @xmath25-ary generalizations of lie algebra is introduced and studied in @xcite . a good and detailed survey on the theory of ternary algebras can be found in @xcite . it is well known that a large class of associative algebras can be constructed by means of square matrices and their multiplication . though the rectangular matrices can be successfully used to construct a ternary algebra we think that probably more appropriate objects to construct ternary algebras are the cubic matrices . our aim in section 4 is to construct ternary algebras of cubic matrices and to study their structures . we find four different totally associative ternary multiplications of second kind of cubic matrices and prove that these are the only totally associative ternary multiplications of second kind in the case of cubic matrices . it is worth mentioning that our search for associative ternary multiplications of cubic matrices has shown that there is no totally associative ternary multiplication of first kind in the case of cubic matrices . i section 5 we describe the ternary analog of lie algebra of cubic matrices of second order by finding all commutation relations of generators of this algebra with respect to @xmath0-commutator .

we study partially and totally associative ternary algebras of first and second kind . assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle . we find the sufficient and necessary condition for a ternary multiplication to induce a structure of associative binary algebra in each fiber of this vector bundle . we construct ternary algebras of cubic matrices and find four different totally associative ternary multiplications of second kind of cubic matrices . it is proved that these are the only totally associative ternary multiplications of second kind in the case of cubic matrices . we describe a ternary analog of lie algebra of cubic matrices of second order which is based on a notion of-commutator and find all commutation relations of generators of this algebra . 17a40 , 20n10 . [ firstpage ]

we study partially and totally associative ternary algebras of first and second kind . assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle . we find the sufficient and necessary condition for a ternary multiplication to induce a structure of associative binary algebra in each fiber of this vector bundle . given two modules over the algebras with involutions we construct a ternary algebra which is used as a building block for a lie algebra . we construct ternary algebras of cubic matrices and find four different totally associative ternary multiplications of second kind of cubic matrices . it is proved that these are the only totally associative ternary multiplications of second kind in the case of cubic matrices . we describe a ternary analog of lie algebra of cubic matrices of second order which is based on a notion of-commutator and find all commutation relations of generators of this algebra . 17a40 , 20n10 . [ firstpage ]

math0407521

i

the jones polynomial was discovered by jones in 1984 @xcite and has made a revolution in knot theory . despite many efforts little is known about the relationship between the jones polynomial and classical topology invariants like the fundamental group . the @xmath0-polynomial of a knot , introduced in @xcite , describes more or less the representation space of the knot group into @xmath1 , and has been fundamental in geometric topology . in the present paper we study relationships between the jones polynomial and the a - polynomial . one main goal of the paper is to establish for a large class of two - bridge knots the aj conjecture ( made by garoufalidis ) that relates the colored jones polynomial and the a - polynomial . this class of knots contains for example all twist knots , and much more . another main result is the calculation of the kauffman bracket skein module of all two - bridge knots . this generalizes the work @xcite where the calculations were carried out for @xmath2-torus knots and twists knots , a special class of two - bridge knots . our method is more geometric and we hope that it can be generalized to all knots . in a previous paper @xcite garoufalidis and the author proved that for every knot , the colored jones polynomial satisfies a recurrence relation . the aj conjecture states that when reducing the quantum parameter to 1 , the recurrence polynomial is essentially equal to the @xmath0-polynomial ( for details see below ) . the present paper is independent of @xcite , since we will prove the existence of recurrence relations for two - bridge knots in another way . we also formulate a weaker version of the aj conjecture ( see conjecture [ weakconjecture ] ) that we believe reflects more accurately the algebra / topology relations between the jones polynomial and the a - polynomial . we prove that the weaker conjecture holds true for all two - bridge knots . some properties of the colored jones polynomial are established . we also show that for an arbitrary alternating knot , the degree of the recurrence polynomial must be at least 2 . for a knot @xmath3 in the 3-space @xmath4 the colored jones function ( see for example @xcite ) @xmath5\ ] ] is defined for integers @xmath6 ; its value @xmath7 is known as the colored jones polynomial of the knot @xmath3 with color @xmath8 . we will recall the definition of @xmath7 in section [ jonescolor ] . in our joint work in s. garoufalidis @xcite we showed that the function @xmath9 always satisfies a non - trivial recurrence relation as described in the next subsection . partial results were obtained earlier by frohman , gelca , and lofaro through their theory of non - commutative a - ideal @xcite , which also plays an important role in the present paper . consider a function with domain the set of integers , @xmath11 , and define the linear operators @xmath12 and @xmath13 acting on such functions by : @xmath14 it is easy to see that @xmath15 , and that @xmath16 generate the _ quantum torus _ @xmath17 , a non - commutative ring with presentation @xmath18 we also use the notation @xmath19 for the subring of @xmath17 which consists only of polynomials with non - negative powers of @xmath13 and @xmath12 . traditionally @xmath19 is called the _ quantum plane_. the _ recurrence ideal _ of the discrete function @xmath20 is the left ideal @xmath21 in @xmath17 that annihilates @xmath20 : @xmath22 we say that @xmath20 is @xmath10-_holonomic _ , or @xmath20 satisfies a linear recurrence relation , if @xmath23 . in @xcite we proved that for every knot @xmath3 , the function @xmath9 is @xmath10-holonomic . denote by @xmath24 the recurrence ideal of @xmath9 . for the right - handed trefoil , one has @xmath25 the function @xmath9 satisfies @xmath26 , where @xmath27 together with the initial conditions @xmath28 , this recurrence relation determines @xmath7 uniquely . the quantum torus @xmath17 is not a principal ideal domain , and @xmath24 might not be generated by a single element . garoufalidis @xcite noticed that by adding to @xmath17 all the inverses of polynomials in @xmath13 one gets a principal ideal domain @xmath29 , and hence from the ideal @xmath24 one can define a polynomial invariant . formally one can proceed as follows . let @xmath30 be the fractional field of the polynomial ring @xmath31 $ ] . let @xmath32 be the set of all laurent polynomials in the variable @xmath12 with coefficients in @xmath30 : @xmath33 and define the product in @xmath32 by @xmath34 then it is known that every left ideal in @xmath29 is principal , and @xmath17 embeds as a subring of @xmath32 . the extension @xmath35 of @xmath24 in @xmath32 is then generated by a single polynomial @xmath36 where the degree in @xmath12 is assumed to be minimal and all the coefficients @xmath37 $ ] are assumed to be co - prime . that @xmath38 can be chosen to have integer coefficients follows from the fact that @xmath39 $ ] . it is clear that @xmath40 annihilates @xmath9 , and hence it is in the recurrence ideal @xmath41 . note that @xmath40 is defined up to a factor @xmath42 . we will call @xmath38 the _ recurrence polynomial _ of @xmath3 . for example , the polynomial @xmath43 in the previous subsection is the recurrence polynomial of the right - handed trefoil . if @xmath43 is a polynomial in @xmath44 and @xmath13 ( no @xmath12 ) , and @xmath45 then @xmath46 . hence adding all the inverses of polynomials in @xmath13 does not affect the recurrence relations . let @xmath47 be the map reducing @xmath48 . formally , if @xmath49 is an @xmath50-module , then let @xmath51 , where @xmath52 is considered as an @xmath50-module by setting @xmath48 . also if @xmath53 then @xmath54 is the image of @xmath55 in @xmath56 . thus @xmath57 is the polynomial obtained from @xmath40 by putting @xmath48 . for example , when @xmath3 is the right - handed trefoil , @xmath58 . for non - zero @xmath59 $ ] , we say that @xmath20 is _ @xmath13-essentially equal to _ @xmath60 , and write @xmath61 if the quotient @xmath62 does not depend on @xmath12 . we say that two algebraic subsets of @xmath63 with parameters @xmath64 are _ @xmath13-essentially equal _ if they are the same up to adding some lines parallel to the @xmath12-axis . it s clear that if @xmath20 is @xmath13-essentially equal to @xmath60 , then @xmath65 and @xmath66 are @xmath13-essentially equal . here @xmath65 is the algebraic set of zero points of @xmath20 . let @xmath67 $ ] be the @xmath0-polynomial of @xmath3 ( see @xcite ) ; we will review its definition in section [ apolynomial ] . garoufalidis @xcite made the following conjecture . ( * the aj conjecture * ) the polynomials @xmath57 and @xmath68 are @xmath13-essentially equal . actually , this is the strong version . the weak version of the conjecture says that @xmath69 and @xmath70 are @xmath13-essentially equal . the algebraic set @xmath70 is known as the _ deformation variety _ of the knot group , with the component @xmath71 corresponding to abelian representations of the knot group into @xmath72 , and @xmath73 to non - abelian ones . garoufalidis @xcite verified the conjecture for the trefoil and the figure 8 knot . takata @xcite gave some evidence to support the conjecture for twist knots , but did not prove it . both works are based heavily on the computer programs of wilf and zeilberger . hikami @xcite verifies the conjecture for torus knots . in all these works direct calculations with explicit formulas are used . in the present paper we prove the conjecture for a large class of two - bridge knots , using a more conceptual approach . two - bridge knots @xmath74 are parametrized by a pair of odd positive integers @xmath75 , with @xmath76 if @xmath77 ( see @xcite and section [ twobridge ] below ) . suppose @xmath78 is a two - bridge knot . \a ) the recurrence polynomial @xmath38 has @xmath12-degree less than or equal to @xmath79 . \b ) the algebraic set @xmath69 is @xmath13-essentially equal to an algebraic subset of @xmath80 . \c ) the aj conjecture holds true if ( * ) the @xmath0-polynomial is @xmath81-irreducible and has @xmath12-degree @xmath82 . [ main1 ] here @xmath81-irreducibility means irreducibility in @xmath83 $ ] . there are many two - bridge knots that satisfy condition ( * ) . for example in a recent work @xcite hoste and shanahan proved that all the twist knots satisfy the condition ( * ) . hence we have the following corollary . the aj conjecture holds true for twist knots . in a separate paper @xcite we will prove that if both @xmath84 and @xmath82 are prime , then @xmath74 satisfies the condition ( * ) . also knot tables show that many two - bridge knots with small @xmath85 satisfy the condition ( * ) . our proof of the main theorem is more or less based on the ideology that the kauffman bracket skein module ( kbsm ) is a quantization of the @xmath72-character variety ( see @xcite and section [ peripheral ] below ) , which has been exploited in the work of frohman , gelca , and lofaro @xcite where they defined the non - commutative @xmath0-ideal . the calculation of the kbsm of a knot complement is a difficult task . bullock @xcite and recently bullock and lofaro @xcite calculated the kbsm for the complements of @xmath86 torus knots and twist knots . another main result of this paper is a generalization of these works : we calculate explicitly the kbsm for complements of all two - bridge knots . we will use another , more geometric approach that allows us to get the results for all two - bridge knots . we also prove that the growth of degree ( or breadth ) of the colored jones polynomial of an arbitrary knot is at most quadratic with respect to the color , and if the knot is alternating , then the growth is exactly quadratic , given by explicit formula . this is based on the exact estimate of the crossing number , used in the proof ( of kauffman , murasugi , and thistlethwaite ) of the tait conjecture on the crossing number of alternating knots . as a corollary , we show that the @xmath12-degree of the recurrence polynomial of an alternating knot must be at least 2 . in section 1 we review the theory of skein modules the colored jones polynomial . in section 2 we study the growth of the degree of the colored jones polynomial and the @xmath12-degree of the recurrence polynomial . in section 3 we review the a - polynomial and introduce a closely related polynomial , @xmath87 . section 4 is devoted to the quantum " version of @xmath87 , the peripheral polynomial . we will formulate another weaker version of the aj conjecture and prove it holds true for two - bridge knots ( in section [ proof1 ] ) . in section 5 we calculate the skein module of the complement of two - bridge knots . the last section contains a proof of the theorem [ main1 ] . i would like to thank s. garoufalidis , r. gelca , t. ohtsuki , a. referee , p. shanahan , a. sikora , t. takata , and x. zhang for valuable helps and discussions .

we study relationships between the colored jones polynomial and the a - polynomial of a knot . the aj conjecture ( of garoufalidis ) that relates the colored jones polynomial and the a - polynomial is established for a large class of two - bridge knots , including all twist knots . we formulate a weaker conjecture and prove that it holds for all two - bridge knots . along the way we also calculate the kauffman bracket skein module of the complements of two - bridge knots . some properties of the colored jones polynomial are established .

we study relationships between the colored jones polynomial and the a - polynomial of a knot . the aj conjecture ( of garoufalidis ) that relates the colored jones polynomial and the a - polynomial is established for a large class of two - bridge knots , including all twist knots . we formulate a weaker conjecture and prove that it holds for all two - bridge knots . along the way we also calculate the kauffman bracket skein module of the complements of two - bridge knots . some properties of the colored jones polynomial are established .

1605.02058

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we have studied the scalar , electromagnetic , axial and polar gravitational perturbations of the reissner - nordstrm black hole ( with tidal charge instead of electric charge ) in the randall - sundrum braneworld . by using the sixth order wkb method , we have calculated the quasinormal frequencies of these perturbations . results have shown that with increasing tidal charge parameter the frequency of the real oscillations decreases while damping rate increases , unlike the case of the standard reissner - nordstrm black hole . the reflection probability of the wave by the scalar potential barrier is larger than for the electromagnetic and gravitational ones ; i.e. , scalar fields are the most favorite in terms of reflection of waves , while the gravitational fields are the most favorite in terms of transmission of waves . with increasing tidal charge parameter reflection abilities of the perturbative fields decrease , as the radii of the horizon and the photon sphere increase with the tidal charge . however , we should note that because of no upper limit on the value of the tidal charge parameter , black holes on the brane always have event horizons and photon spheres which are located further away from the central object in comparison to the schwarzschild ones . we have studied also the absorption cross section of the massless scalar waves by the braneworld black hole in the low- and high - frequency regimes . calculations have shown that the braneworld black holes always have bigger absorption cross sections than the corresponding ones related to the schwarzschild and reissner - nordstrm black holes . one of the main results of this paper is that in the high - frequency regime distinction of the black holes from the particle emission spectrum is almost impossible . from this point of view the low - frequency regime is more significant . authors would like to thank the anonymous referee for his careful reading of our manuscript and many insightful comments and suggestions that have improved the paper . the authors would like to thank naresh dadhich for his useful discussions on the properties of the black hole solution on the brane and luciano rezzolla for noting a problem with our calculations in a previous version of the manuscript . b.t . , z.s . , and j.s . would like to express their acknowledgments for the institutional support of the faculty of philosophy and science of the silesian university in opava , the internal student grant of the silesian university ( grant no . sgs/23/2013 ) and the albert einstein centre for gravitation and astrophysics under the czech science foundation ( grant no . 14 - 37086 g ) . b.a . acknowledges the faculty of philosophy and science , silesian university in opava , czech republic , and the goethe university , frankfurt am main , germany , for their warm hospitality . the research of b.a . is supported in part by projects no . f2-fa - f113 , no . ef2-fa-0 - 12477 , and no . f2-fa - f029 of the uzas , and by the ictp through grants no . oea - prj-29 and no . oea - net-76 and by the volkswagen stiftung , grant no . 86 866 . r. emparan , g. t. horowitz , and r. c. myers , j. high energy phys . * 01 * ( 2000 ) 007 , [ http://arxiv.org/abs/hep-th/9911043 [ hep - th/9911043 ] ] ; 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we study scalar , electromagnetic , axial and polar gravitational perturbations of the four - dimensional reissner - nordstrm - like black holes with a _ tidal charge _ in the randall - sundrum braneworld in the first approximation when the tidal perturbations are not taken into account . calculations have shown that the black holes on the randall - sundrum brane are stable against all kinds of perturbations . moreover , we determine the greybody factor , giving transmission and reflection of the scattered waves through the effective potentials . it has been shown that the scalar perturbative fields are the most favorite to reflect the wave as compared to the other fields . with increasing value of the tidal charge , the ability of the all perturbative potentials to reflect the waves decreases . our calculations in low- and high - frequency regimes have shown that black holes on the braneworld always have a bigger absorption cross section of massless scalar waves than the schwarzschild and standard reissner - nordstrm black holes .

we study scalar , electromagnetic , axial and polar gravitational perturbations of the four - dimensional reissner - nordstrm - like black holes with a _ tidal charge _ in the randall - sundrum braneworld in the first approximation when the tidal perturbations are not taken into account . the quasinormal modes of these perturbations have been studied in both normal and eikonal regimes . calculations have shown that the black holes on the randall - sundrum brane are stable against all kinds of perturbations . moreover , we determine the greybody factor , giving transmission and reflection of the scattered waves through the effective potentials . it has been shown that the scalar perturbative fields are the most favorite to reflect the wave as compared to the other fields . with increasing value of the tidal charge , the ability of the all perturbative potentials to reflect the waves decreases . our calculations in low- and high - frequency regimes have shown that black holes on the braneworld always have a bigger absorption cross section of massless scalar waves than the schwarzschild and standard reissner - nordstrm black holes .

math0010282

i

to understand the structure of @xmath0-manifolds and links inside them , the first author introduced the concept of the skein module @xcite motivated by the conway idea of linear skein " . skein modules are quotients of a free module of formal linear combinations of links in a @xmath0-manifold by properly chosen ( local ) skein relations . in search of appropriate skein relations , we analyze deformations of moves on links previously studied in knot theory . the simplest of such moves are @xmath6 ( twist ) moves ( figure @xmath9 ) . the simplest skein modules are deformations of @xmath9-moves , @xcite ( a linear skein relation ) . the conway type skein modules are deformations of @xmath10-moves ( a quadratic skein relation ) and they are studied extensively ( e.g. @xcite ) . in this paper we start a systematic study of skein modules based on a deformation of @xmath0-moves ( a cubic skein relation ) . since there are four terms involved in the relation , we call such a skein module the fourth skein module and denote it by @xmath11 , following the notation of @xcite . in section [ secmnc ] , we discuss the montesinos - nakanishi conjecture on @xmath0-moves . this conjecture , and its partial solutions , make the study of fourth skein modules feasible . in section [ secfsm ] , we define the fourth skein module and we make the general conjecture about generators of the fourth skein module in @xmath8 and @xmath12 with @xmath6 boundary points ( @xmath6-tangles ) . in section [ seclitl ] , we discuss the necessary conditions for coefficient ring so that trivial links are linearly independent in the fourth skein module . we prove the independence in two , rather degenerated cases . in section [ secgfsm ] , we consider the case in which trivial links differ only by a multiplicative constant . we show that after proper substitution the skein module reduces to the kauffman skein module , at least for links generated by trivial links . generally we have always epimorphism into the kauffman skein module . in section [ sectorusandtwists ] , we give an example of computation , finding eigenvectors of dehn twists on @xmath10-tangles and applying this to describe the effect of @xmath6-moves on elements of the skein module . as a corollary we compute the values for @xmath7-torus links and twist knots . in section [ secmrfsm ] , we use the idea of mutants and rotors to construct different links representing the same element in the fourth skein module . in section [ secnalgtl ] , we introduce a notion of an @xmath6-algebraic tangle and link , generalizing the notion of an algebraic link in the sense of conway . we show that @xmath6-bridge links and closed @xmath6-braids are @xmath6-algebraic . we prove conjectures [ generalconjmn ] and [ conjgenerator ] for @xmath10- and @xmath0-algebraic tangles . in the last section , we speculate on existence of fourth " polynomial link invariants of classical links ( in @xmath8 ) and show connection of our work with investigation of coxeter , assion and wajnryb on finite quotients of braid groups .

we study the concept of the fourth skein module of-manifolds , that is a skein module based on the skein relation and a framing relation ( , , invertible ) . we investigate the behavior of elements of the skein module under the-move and compute the values for-torus links and twist knots as elements of the skein module . using the idea of mutants and rotors , we show that there are different links representing the same element in the skein module . we also show that algebraic links ( in the sense of conway ) and closed-braids are linear combinations of trivial links . we introduce the concept of-algebraic tangles ( and links ) and analyze the skein module for-algebraic links . as a byproduct one of them generalizes the kauffman polynomial of links and another one can be used to analyze amphicheirality of links ( and may work better than the kauffman polynomial ) . in the end , we speculate about the meaning and importance of our new knot invariants . jzef h. przytycki and tatsuya tsukamoto in memory of rodica simion ( january 18 , 1955 - january 7 , 2000 )

we study the concept of the fourth skein module of-manifolds , that is a skein module based on the skein relation and a framing relation ( , , invertible ) . we give necessary conditions for trivial links to be linearly independent in the module . we investigate the behavior of elements of the skein module under the-move and compute the values for-torus links and twist knots as elements of the skein module . using the idea of mutants and rotors , we show that there are different links representing the same element in the skein module . we also show that algebraic links ( in the sense of conway ) and closed-braids are linear combinations of trivial links . we introduce the concept of-algebraic tangles ( and links ) and analyze the skein module for-algebraic links . as a byproduct we prove the montesinos - nakanishi-moves conjecture for-algebraic links ( including-bridge links ) . in the case of classical links ( i.e. links in ) our skein module suggests three polynomial invariants of unoriented framed ( or unframed ) links . one of them generalizes the kauffman polynomial of links and another one can be used to analyze amphicheirality of links ( and may work better than the kauffman polynomial ) . in the end , we speculate about the meaning and importance of our new knot invariants . jzef h. przytycki and tatsuya tsukamoto in memory of rodica simion ( january 18 , 1955 - january 7 , 2000 )

astro-ph9510123

i

it is well known that a superstrong magnetic field of order @xmath5 gauss , typically found on the surfaces of neutron stars , can dramatically change the structure of neutral atoms and other bound states ( see , e.g. , ref.@xcite for an early review and ref.@xcite for a recent text on atoms in strong magnetic fields ) . the atomic unit @xmath6 for the magnetic field strength and a dimensionless parameter @xmath7 are b_o = m_e^2e^3 c^3=2.35 10 ^ 9 g ; b. when @xmath8 , the cyclotron energy of the electron @xmath9 , where @xmath10 is the magnetic field strength in units of @xmath11 , is much larger than the typical coulomb energy , thus the coulomb forces act as a perturbation to the magnetic forces on the electrons , and at most temperatures the electrons settle into the ground landau level . because of the extreme confinement of electrons in the transverse direction , the coulomb force becomes much more effective for binding electrons in the parallel direction . the atom has a cigar - like structure . moreover , it is possible for these elongated atoms to form molecular chains by covalent bonding along the field direction . hydrogen atoms in strong magnetic field have been studied extensively@xcite . we have also recently completed a study of the electronic structure of hydrogen molecules and chains in the strong field regime ( @xmath8)@xcite . however , in many of these studies , the center - of - mass ( cm ) effects of the proton motion have been neglected . in the case of the hydrogen atom , although significant effort has been devoted to calculating the energy levels of an electron in the static coulomb potential of a _ fixed _ proton ( infinite mass ) to a high precision and for arbitrary magnetic field strength@xcite , the two - body problem in strong magnetic field , including the effects of finite proton mass , has been studied in detail only recently ( e.g.,@xcite ) . in this paper we focus on the hydrogen atom , but discuss those aspects which are important for application to molecules in very strong fields ( we shall study molecular excitation levels in a later paper@xcite ) . a free electron confined to the ground landau level , the usual case for @xmath8 , does not move perpendicular to the magnetic field . such motion is necessarily accompanied by landau excitations . when the electron ( still in the landau ground state ) combines with a proton , the mobility of the neutral atom across the field depends on the ratio of the atomic excitation energy and the landau excitation energy @xmath12 for the proton . as the typical coulomb excitation is @xmath13 in atomic units , it is convenient to define a critical field strength @xmath14 via b_critb_crit=1.8010 ^ 4 ; b_crit = b_critb_o=4.2310 ^ 13 g. for @xmath15 ( terrestrial conditions ) the landau energies of both electron and proton are minor perturbations and one can construct wave packets that mimic the classical motion of a neutral atom across the field . in this case the internal structure of the atom or molecule is coupled to the center - of - mass motion only through a `` motional stark effect '' ( see sec . ii ) . in the opposite limit of @xmath16 , the landau energies are larger than the coulomb excitation energy , and both electron and proton ( in the atom ) are in the landau ground state at reasonable temperatures . in this case , quantum mechanics can not mimic classical motion . the canonical field strengths of radio pulsars , with @xmath0 slightly less than @xmath14 , present an intermediate case . however , at all field strengths one can introduce a pseudomomentum @xmath17 perpendicular to the field and , in principle , find the bound - state energy @xmath18 as a function of @xmath17 . one question of interest is the range of @xmath1 for which @xmath18 increases linearly with @xmath19 ( as it does for ordinary kinetic energy ) ; but in any case @xmath20 is needed to evaluate the saha equation for the equilibrium between neutral and ionized hydrogen ( sec . previous treatments@xcite of the ionization equilibrium in strong magnetic fields did not properly take account of the non - trivial effects of atomic motion . states with large @xmath1 , where velocity decreases with increasing @xmath1 ( see ref.@xcite and our eq . [ 3.29 ] ) are of particular interest , especially for @xmath0 larger than @xmath14 . the separation of the center - of - mass ( cm ) motion of a bound state in the presence of a magnetic field has been studied previously based on the conserved pseudomomentum ( e.g.,@xcite ) . we briefly review and clarify this pseudomomentum scheme in sec . ii . when @xmath21 , perturbation calculations for hydrogen atom motion ( e.g.,@xcite ) are valid over a wide range of @xmath1 values and lead to interesting phenomena such as bent trajectories@xcite . model atmospheres can be affected by details of the transverse motion ( e.g.,@xcite ) . some accurate numerical calculations for general @xmath1 and for several values of @xmath0 ( but all below @xmath14 ) are now available @xcite , but we concentrate on the @xmath22 regime in sec . a different approach to the two - body problem ( for positronium atom ) in the superstrong field regime @xmath8 has been developed in@xcite . our purpose in this paper is not to obtain accurate energy spectra of a moving hydrogen atom in certain limited regimes , as have been done in most of the papers mentioned above ; rather , we seek complete ( though approximate ) solutions of the two - body problem for a wide range of parameter space , including @xmath0 just below @xmath14 ( a common case for neutron stars ) , but especially for @xmath23 ( in case @xmath24 g exists in some neutron stars , as has been suggested recently@xcite ) . our emphasis is on finding physically meaningful approximate fitting formulae for the atomic energy of the moving atom over all relevant values of @xmath1 ( sec . iii ) , in order to determine the equilibrium between neutral and ionized hydrogen ( sec . however , in practice we shall be interested mainly in the regimes where the thermal energy @xmath25 is much less than the ground - state binding energy of the atom , while the gas density is much smaller than the internal density of the atom , so that the neutral and ionized fractions are of the same order of magnitude . in such cases , we are most interested in two kinds of excited bound states : ( i ) those with excitation energies up to a few atomic units ( comparable to @xmath25 but a small fraction of the binding energy ) and ( ii ) states that are only barely bound ( e.g. , those with extremely large @xmath1 ) , for which one has to check whether phase - space factors make them unimportant relative to ionized hydrogen . for applications to molecules@xcite and multi - electron atoms@xcite with @xmath4 , a controversy arises regarding the `` coupling '' of the electron s orbital quantum number with the landau level of the proton ( or nuclei ) . this is discussed in sec . our calculations in this paper are based on non - relativistic quantum mechanics . for @xmath26 g ( note that @xmath27 is close to @xmath14 only by coincidence ) , i.e. , @xmath28 , the transverse motion of the electron becomes relativistic . however , the relativistic correction to the atomic binding energy is small as long as the electron remains non - relativistic along field direction@xcite . except as otherwise noted , we shall use atomic units ( a.u . ) throughout the paper , in which mass and length are expressed in units of the electron mass @xmath29 and the bohr radius @xmath30 cm , energy in units of @xmath31 ev ; field strength is in units of @xmath6 ( eq . [ 1.1 ] ) and temperature in units of @xmath32 k.

field strengths of order gauss are typically found on the surfaces of neutron stars , but we also study the regime gauss , where the landau excitation energy of the proton is large . the final results for the excitation energies are given in the form of analytical fitting formulae .

we study the effects of finite proton mass on the energy levels of hydrogen atoms moving transverse to a superstrong magnetic field with generalized pseudomomentum . field strengths of order gauss are typically found on the surfaces of neutron stars , but we also study the regime gauss , where the landau excitation energy of the proton is large . we adopt two different approaches to the two - body problem in strong magnetic field , and obtain an approximate , but complete solution of the atomic energy as a function of and . we show that , for , there is an orthogonal set of bound states , which do not have any landau excitation contribution in their energies . the states with very large have small binding energy and small transverse velocity , but are nevertheless distinct from the fully ionized states . the final results for the excitation energies are given in the form of analytical fitting formulae . the generalized saha equation for the ionization - recombination equilibrium of hydrogen gas in the presence of a superstrong magnetic field is then derived . although the maximum transverse velocity of a bound atom decreases as increases , the statistical weight due to transverse motion is actually increased by the strong magnetic field . for astrophysically interesting case of relatively low density and temperature , we obtain analytic approximations for the partition functions . the highly excited bound states have a smaller statistical weight than the fully ionized component .

astro-ph9510123

i

the effects of center - of - mass motion of neutral hydrogen atom in a strong magnetic field are rather intricate , mainly due to the high degree of degeneracy associated with the quantum states . using the usual pseudomomentum scheme ( sec . ii - iii ) , we have obtained approximate solutions for the energy of the atom as a function of the field strength and conserved pseudomomentum for a wide range of parameter regimes . in particular , we have considered field strengths @xmath380 g , when the landau excitation energy of proton is considerable . states with large transverse pseudomomentum have small binding energy and transverse velocity , but are nevertheless quite distinct from fully ionized states . we have concentrated on convenient analytic fitting formulae which give at least a reasonable approximation over various parameter regimes ( see particularly eq . ( 3.26 ) for the `` transverse kinetic energy '' ) . since there may be neutron star atmospheres with @xmath381 g , we are particularly interested in the cases with @xmath4 , where the proton landau energy @xmath382 is very large . by considering an alternative scheme to the usual pseudomomentum formulation ( sec . iv ) , we have shown that there are atomic states with orbital wavefunctions orthogonal to that of the ground state , but without any landau excitation appearing in their energies . we have also derived the generalized saha equation for the equilibrium between neutral hydrogen atoms and the ionized component . we focused on the cases of astrophysical interest , where the density is relatively low and the thermal energy @xmath25 is small compared to the atom s ground state binding energy . although the maximum transverse velocity of bound atoms is small in strong magnetic fields , the statistical weight due to transverse motion is actually increased by the strong fields , not decreased ( sec . the statistical weight of highly excited bound states is smaller than that of the fully ionized component . our results are important for determining the physical conditions of magnetic neutron star atmospheres as well as the soft x - ray ( or euv ) radiation spectra from them . some of these issues will be studied in a future paper@xcite . we thank lars bildsten , george pavlov and ira wasserman for useful discussions . this work has been supported in part by nsf grants ast 9119475 , ast 9315375 , and nasa grant nagw666 to cornell university , and nagw-2394 to caltech . in this appendix , we derive some mathematical formulae needed for evaluating the function @xmath253 defined by eq . ( here the lengthscale is in units of the cyclotron radius @xmath59 . ) using the identity @xmath383 we write eq . ( 4.8 ) as g_m_1m_1^(m_t)(z)=g_m_1m_1^(m_t)(z)= 12 ^ 2e^iq_zz m_t+m_1|e^i*q*__1|m_t+m_1m_1|e^-i*q*__2|m_1 . using the general result@xcite for the matrix element @xmath384 , and integrating over @xmath385 , we obtian ( assuming @xmath386 without loss of generality ) : g_m_1m_1^(m_t)(z)=_0^ dq e^-q|z|-q^2 ( q^22)^m_1-m_1 l_m_t+m_1^m_1-m_1(q^22 ) l_m_1^m_1-m_1(q^22 ) , where @xmath387 is the laguerre polynomial of order @xmath70@xcite . we now define constant coefficients @xmath388 via ( x2)^m_1-m_1 l_m_t+m_1^m_1-m_1(x2 ) l_m_1^m_1-m_1(x2 ) = _ n=0^m_1+m_1+m_t g_n^(m_t)(m_1,m_1)l_n(x ) . using the relation v_n(z)=_0^dq e^-q^2/2-q|z|l_n(q^22 ) = 1 n!_0^ dx x^n e^-x(x+z^2/2)^1/2 , where the second equality can be used to evaluate the function @xmath389 , we obtain g_m_1m_1^(m_t)(z)=_n=0^m_1+m_1+m_tg_n^(m_t)(m_1,m_1 ) v_n(z ) . we calculate the coefficients @xmath388 using the orthogonal relations of laguerre polynomials . we can identify two special cases : ( i ) when @xmath264 , we have @xmath390 and @xmath391 , where @xmath392 and @xmath393 are given in@xcite ; ( ii ) when @xmath394 , we have @xmath395 and @xmath396 , where @xmath397 and @xmath398 are again given in@xcite . early study of essentially the same problem dealt with excitons in semiconductors , where the strong field condition can be mimicked in virtue of the small effective mass and the presence of a dielectric medium . see r. j. elliot and r. loudon , j. phys . solids * 15 * , 196 ( 1960 ) ; h. hasegawa and r. e. howard , _ ibid . _ * 21 * , 179 ( 1961 ) . for calculations in the superstrong field regime ( @xmath399 g ) , see r. cohen , j. lodenquai , and m. ruderman , phys . lett . * 25 * , 467 ( 1970 ) ; v. canuto and d. c. kelley , astrophys . space sci . * 17 * , 277 ( 1972 ) ; j. simola and j. virtamo , j. phys . b : at . mol . * 11 * , 3309 ( 1978 ) , and references therein .

we study the effects of finite proton mass on the energy levels of hydrogen atoms moving transverse to a superstrong magnetic field with generalized pseudomomentum . we adopt two different approaches to the two - body problem in strong magnetic field , and obtain an approximate , but complete solution of the atomic energy as a function of and . the states with very large have small binding energy and small transverse velocity , but are nevertheless distinct from the fully ionized states . although the maximum transverse velocity of a bound atom decreases as increases , the statistical weight due to transverse motion is actually increased by the strong magnetic field . for astrophysically interesting case of relatively low density and temperature , we obtain analytic approximations for the partition functions . the highly excited bound states have a smaller statistical weight than the fully ionized component .

we study the effects of finite proton mass on the energy levels of hydrogen atoms moving transverse to a superstrong magnetic field with generalized pseudomomentum . field strengths of order gauss are typically found on the surfaces of neutron stars , but we also study the regime gauss , where the landau excitation energy of the proton is large . we adopt two different approaches to the two - body problem in strong magnetic field , and obtain an approximate , but complete solution of the atomic energy as a function of and . we show that , for , there is an orthogonal set of bound states , which do not have any landau excitation contribution in their energies . the states with very large have small binding energy and small transverse velocity , but are nevertheless distinct from the fully ionized states . the final results for the excitation energies are given in the form of analytical fitting formulae . the generalized saha equation for the ionization - recombination equilibrium of hydrogen gas in the presence of a superstrong magnetic field is then derived . although the maximum transverse velocity of a bound atom decreases as increases , the statistical weight due to transverse motion is actually increased by the strong magnetic field . for astrophysically interesting case of relatively low density and temperature , we obtain analytic approximations for the partition functions . the highly excited bound states have a smaller statistical weight than the fully ionized component .

1004.2289

i

a novel quantum gravity model , which claims power - counting renormalizability , has been formulated recently by horava @xcite . this scenario is based on an anisotropy between space and time coordinates , which is expressed via the scalings @xmath11 and @xmath12 , where @xmath13 is a dynamical critical exponent . for @xmath14 the uv behaviour of the model is governed by a non - standard lifshitz fixed point , while for @xmath15 we recover the well - known free gaussian fixed point . in the horava model , for three spatial dimensions , the suitable choice is @xmath16 . it is worth noting that in the horava - lifshitz ( hl ) gravity the four - dimensional diffeomorphism invariance of general relativity is sacrificed in order to achieve power - counting renormalizability . the action of the model can be split into a kinetic plus a potential term , which both respect a restricted @xmath17 diffeomorphism invariance . the interesting feature is that the kinetic term contains only second order time derivatives , while the potential term consists of higher order spatial derivatives of the metric components . this particular structure improves significantly the uv properties of the graviton propagator , and renders the model power - counting renormalizable . moreover , in this way we avoid ghost modes which are usual in conventional higher order gravity models . for the construction of the potential term , there has been proposed @xcite the so called `` detailed balance principle '' , which is inspired by condensed matter physics . the main advantage of this approach is the restriction of the large number of arbitrary couplings that appear in the bare action of the model . however , the physical motivation for a consideration such as the `` detailed balance '' is not clear @xcite . an alternative way for constructing an action is to include all possible operators which are compatible with the renormalizability of the model ; this implies that all operators with dimension less or equal to six are allowed in the action ( for the exact form of the action see @xcite ) . as it has been already mentioned , the hl gravity violates local lorentz invariance in the uv , however it is expected that general relativity is recovered in the ir limit . this implies a very special renormalization group flow for the couplings of the model . in particular , the parameter @xmath18 in the kinetic term of the action ( which measures the departure from the lorentz invariance ) should flow to unity , while the higher order couplings should vanish , or they should become appropriately small , in the ir . note that , even though phenomenology suggests a particular ir limit there is no theoretical study supporting this behaviour . in addition , there are several other possible inconsistencies in hl gravity which have been discussed in several works . in particular , the absence of full diffeomorphism invariance introduces an additional scalar mode which can lead to strong coupling problems or instabilities ( see for example @xcite-@xcite and references therein ) . however , these problems will not be addressed in the present paper . apart from these problems , the hl gravity is an interesting quantum gravity theory , which has stimulated an extended research on cosmology and black hole solutions @xcite , @xcite-@xcite . in addition to general relativity studies , quantum field theory models in flat space - time with anisotropy have also been considered @xcite-@xcite . before proceeding it is important to mention that the hl gravity can be separated into two versions which are known as projectable and non - projectable . in the projectable version the lapse function @xmath19 depends only on the time coordinate , while in the non projectable version @xmath19 is a function of both the space and time coordinates . although in general relativity the projectable and non - projectable ansatz for the metric are equivalent , since they are connected via a diffeomorphism transformation , in the hl gravity the full diffeomorphism invariance is broken and they lead to two distinct theories . issues connected with broken lorentz invariance were studied in the spherically symmetric solutions of 4d hl gravity . in the case of detailed balance , such spherically symmetric solutions were found @xcite , but they exhibited an unconventional large distance asymptotic behaviour . the correct schwarzchild - flat asymptotic behaviour can be recovered if the detailed balance action is modified in the ir by a term proportional to ricci scalar , and the cosmological constant term is considered to be zero @xcite . a similar study , in the case of non - vanishing cosmological constant , has also been carried out @xcite . a generalization to topological black holes was obtained in @xcite . finally , a systematic study of static spherically symmetric solutions of 4d hl gravity was presented in @xcite where the most general spherically symmetric solution for @xmath20 and general coupling parameters was obtained . in this work we present a full study of spherically symmetric solutions in the non - projectable version of the five - dimensional horava - lifshitz gravity , for @xmath21 . for the construction of the 5d action we do not use the `` detailed balance principle '' , but we include all the terms which are compatible with the renormalizability of the model . in particular , we can include all spatial curvature terms with dimension less than or equal to eight . however , the large number of possible terms , which are allowed in the action , leads to equation of motion of great complexity . for this reason we restrict our study only to terms of up to second order in the curvature . also , we suppose that in the ir limit 5d the hl gravity reduces to the 5d general relativity plus a bulk cosmological constant . a class of spherically symmetric solutions of the 5d hl gravity has been considered previously @xcite , but only for a very specific choice of the couplings . our main motivation in considering static solutions in 5d hl gravity is to investigate whether the rich spectrum of black hole solutions found in 4d ( see ref . @xcite ) also persists in 5d . it seems that the known static solutions of the hl gravity in 4d with @xmath22 do not have any obvious relation with the corresponding static solutions of the relativistic 4d gravity . in 5d however we found that there is a class of spherically symmetric solutions which after a proper identification of coupling parameters coincide with the known black hole solutions of conventional relativistic 5d gauss - bonnet gravity . static solutions of 5d gauss - bonnet theory are well known @xcite . among them there is a black hole solution which has two branches ( for a review see @xcite ) . the first branch is referred to as the einstein branch while the second as the gauss - bonnet branch . both branches coincide in the chern - simons limit . as we will discuss in the following , we find both branches of solutions and in addition these solutions can also be obtained for a different combination of coupling parameters of the quadratic curvature terms than the usual combination that appears in the relativistic gauss - bonnet theory . we also find the black hole solution corresponding to the chern - simons limit with a particular choice of coupling parameters . this solution has also been found in @xcite using the `` detailed balance principle '' . the paper is organized as follows . in section 2 we write down the action of 5d hl gravity . in section 3 we derive the equations of motion . in section 4 we analyze the static spherically symmetric solutions for a special choice of coupling parameters . in section 5 we study the most general static spherically symmetric solutions of 5d horava - lifshitz gravity and finally section 6 contains our conclusions .

we study the full spectrum of spherically symmetric solutions in the five dimensional non - projectable horava - lifshitz type gravity theories . in addition we have found solutions with an unconventional short or large distance behaviour , and for a special range of the coupling parameters solutions which coincide with black hole solutions of conventional relativistic five - dimensional gauss - bonnet gravity .

we study the full spectrum of spherically symmetric solutions in the five dimensional non - projectable horava - lifshitz type gravity theories . for appropriate ranges of the coupling parameters , we have found several classes of solutions which are characterized by an , or flat large distance asymptotic behaviour , plus the standard tail of the usual five - dimensional schwarzschild black holes . in addition we have found solutions with an unconventional short or large distance behaviour , and for a special range of the coupling parameters solutions which coincide with black hole solutions of conventional relativistic five - dimensional gauss - bonnet gravity . + * george koutsoumbas * , * eletherios papantonopoulos * , * pavlos pasipoularides * , * minas tsoukalas * + department of physics , national technical university of athens , + zografou campus gr 157 73 , athens , greece + e - mail address : [email protected] + e - mail address : [email protected] + e - mail address : [email protected] + e - mail address : [email protected] +

1004.2289

i

in this section we present same mathematical details for the derivation of formulae of eqs . ( [ gcy1 ] ) and ( [ gcy2 ] ) . in particular we have to integrate eq . ( [ genericeqz ] ) @xmath250 in order to perform the above integral we make the replacement @xmath251 , then we obtain @xmath252 where a=-3 _ 0a + , b=(-4 ) . note that @xmath253 so we have @xmath254 . for @xmath255 , we obtain [ integ1 ] c+(r)&=&-=-dy + & = & -|(^2-b)y^2-a|+dy , where @xmath26 is an integration constant . in order to calculate the second integral in eq . ( [ integ1 ] ) separately , we write the corresponding integrand in the form = ( + ) . for @xmath160 we obtain [ intb1 ] & = & | y+| + & -&|| , while for @xmath154 we get [ intb2 ] dy & = & ^-1 ( ) + & -&|| , where we have taken into account that = - , and the well known relations ( ) = , = || , x= . moreover , we will use the identity [ ln1 ] ( [ intb1 ] ) and ( [ ln1 ] ) , if we take into account that @xmath256 , we obtain c+(r)&= & |(^2-b)y^2-a|+ | y+| + & -&|y+| , or equivalently c+(r)=-|y+|+ | y+| , where @xmath257 is a new constant which is defined appropriately . finally , we obtain |y+| | y+|^-= , where @xmath258 is the final integration constant which is related to the mass of the black hole . for @xmath154 , in a similar way , if we use eq . ( [ intb2 ] ) instead of ( [ intb1 ] ) , we obtain |y+| e^ ^-1 ( ) = . finally , for the computation of @xmath77 we use the following equations - ( y ) ( y)=0 , [ neqzgc1 ] where @xmath152 is given by the equation [ genericeqny1 ] ( y)=- , and we find in a similar way , as it is described above , that [ gcn11 ] ( y)= for @xmath160 , and ( y)=e^ ^-1 ( ) for @xmath154 , where @xmath157 is an integration constant . p. horava , jhep * 0903 * ( 2009 ) 020 [ arxiv:0812.4287 [ hep - th ] ] ; p. horava , phys . rev . d * 79 * , 084008 ( 2009 ) [ arxiv:0901.3775 [ hep - th ] ] . e. kiritsis and g. kofinas , nucl . phys . b * 821 * ( 2009 ) 467 [ arxiv:0904.1334 [ hep - th ] ] . t. p. sotiriou , m. visser and s. weinfurtner , jhep * 0910 * , 033 ( 2009 ) , arxiv:0905.2798 [ hep - th ] ; t. p. sotiriou , m. visser and s. weinfurtner , phys . * 102 * ( 2009 ) 251601 [ arxiv:0904.4464 [ hep - th ] ] . a. kehagias and k. sfetsos , phys . b * 678 * ( 2009 ) 123 [ arxiv:0905.0477 [ hep - th ] ] ; c. germani , a. kehagias and k. sfetsos , jhep * 0909 * , 060 ( 2009 ) , arxiv:0906.1201 [ hep - th ] . m. i. park , jhep * 0909 * ( 2009 ) 123 [ arxiv:0905.4480 [ hep - th ] ] . r. g. cai , l. m. cao and n. ohta , phys . d * 80 * ( 2009 ) 024003 [ arxiv:0904.3670 [ hep - th ] ] . e. kiritsis and g. kofinas , jhep * 1001 * ( 2010 ) 122 [ arxiv:0910.5487 [ hep - th ] ] . e. kiritsis , phys . d * 81 * ( 2010 ) 044009 [ arxiv:0911.3164 [ hep - th ] ] . r. g. cai , y. liu and y. w. sun , jhep * 0906 * , 010 ( 2009 ) [ arxiv:0904.4104 [ hep - th ] ] . e. n. saridakis , arxiv:0905.3532 [ hep - th ] ; m. jamil , e. n. saridakis and m. r. setare , arxiv:1003.0876 [ hep - th ] . y. f. cai and e. n. saridakis , jcap * 0910 * , 020 ( 2009 ) [ arxiv:0906.1789 [ hep - th ] ] ; s. dutta and e. n. saridakis , jcap * 1001 * ( 2010 ) 013 [ arxiv:0911.1435 [ hep - th ] ] . g. leon and e. n. saridakis , jcap * 0911 * , 006 ( 2009 ) [ arxiv:0909.3571 [ hep - th ] ] . a. wang , d. wands and r. maartens , jcap * 1003 * ( 2010 ) 013 [ arxiv:0909.5167 [ hep - th ] ] ; a. wang and r. maartens , phys . d * 81 * , 024009 ( 2010 ) , arxiv:0907.1748 [ hep - th ] ; a. wang and y. wu , jcap * 0907 * ( 2009 ) 012 [ arxiv:0905.4117 [ hep - th ] ] . e. o. colgain and h. yavartanoo , jhep * 0908 * , 021 ( 2009 ) [ arxiv:0904.4357 [ hep - th ] ] . b. r. majhi , phys . b * 686 * ( 2010 ) 49 [ arxiv:0911.3239 [ hep - th ] ] . y. s. myung and y. w. kim , arxiv:0905.0179 [ hep - th ] . s. r. das and g. murthy , arxiv:0909.3064 [ hep - th ] . j. alexandre , k. farakos , p. pasipoularides and a. tsapalis , phys . d * 81 * ( 2010 ) 045002 [ arxiv:0909.3719 [ hep - th ] ] . w. chao , arxiv:0911.4709 [ hep - th ] . t. koslowski and a. schenkel , arxiv:0910.0623 [ gr - qc ] . d. g. boulware and s. deser , phys . * 55 * ( 1985 ) 2656 ; j. t. wheeler , nucl . b * 268 * ( 1986 ) 737 ; d. l. wiltshire , phys . b * 169 * , 36 ( 1986 ) ; r. g. cai , phys . rev . d * 65 * ( 2002 ) 084014 [ arxiv : hep - th/0109133 ] ; c. charmousis and j. f. dufaux , class . * 19 * ( 2002 ) 4671 [ arxiv : hep - th/0202107 ] ; s. deser and j. franklin , class . quant . * 22 * ( 2005 ) l103 [ arxiv : gr - qc/0506014 ] . s. deser and z. yang , class . * 6 * , l83 ( 1989 ) ; s. deser and b. tekin , phys . rev . d * 67 * ( 2003 ) 084009 [ arxiv : hep - th/0212292 ] ; s. deser and b. tekin , phys . rev . d * 75 * ( 2007 ) 084032 [ arxiv : gr - qc/0701140 ] ; g. kofinas and r. olea , jhep * 0711 * ( 2007 ) 069 [ arxiv:0708.0782 [ hep - th ] ] . c. charmousis and a. padilla , jhep * 0812 * , 038 ( 2008 ) [ arxiv:0807.2864 [ hep - th ] ] . l. randall and r. sundrum , phys . * 83 * ( 1999 ) 3370 [ arxiv : hep - ph/9905221 ] ; l. randall and r. sundrum , phys . rev . lett . * 83 * ( 1999 ) 4690 [ arxiv : hep - th/9906064 ] . c. csaki , j. erlich and c. grojean , nucl . b * 604 * ( 2001 ) 312 [ arxiv : hep - th/0012143 ] . k. farakos , n. e. mavromatos and p. pasipoularides , jhep * 0901 * ( 2009 ) 057 [ arxiv:0807.0870 [ hep - th ] ] ; k. farakos , n. e. mavromatos and p. pasipoularides , j. phys . ser . * 189 * ( 2009 ) 012029 [ arxiv:0902.1243 [ hep - th ] ] . k. farakos , jhep * 0908 * ( 2009 ) 031 [ arxiv:0903.3356 [ hep - th ] ] .

+ * george koutsoumbas * , * eletherios papantonopoulos * , * pavlos pasipoularides * , * minas tsoukalas * + department of physics , national technical university of athens , + zografou campus gr 157 73 , athens , greece + e - mail address : [email protected] + e - mail address : [email protected] + e - mail address : [email protected] + e - mail address : [email protected] +

we study the full spectrum of spherically symmetric solutions in the five dimensional non - projectable horava - lifshitz type gravity theories . for appropriate ranges of the coupling parameters , we have found several classes of solutions which are characterized by an , or flat large distance asymptotic behaviour , plus the standard tail of the usual five - dimensional schwarzschild black holes . in addition we have found solutions with an unconventional short or large distance behaviour , and for a special range of the coupling parameters solutions which coincide with black hole solutions of conventional relativistic five - dimensional gauss - bonnet gravity . + * george koutsoumbas * , * eletherios papantonopoulos * , * pavlos pasipoularides * , * minas tsoukalas * + department of physics , national technical university of athens , + zografou campus gr 157 73 , athens , greece + e - mail address : [email protected] + e - mail address : [email protected] + e - mail address : [email protected] + e - mail address : [email protected] +

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a notion at the very core of graph theory , chordality is a statement about the geometry and complexity of cycles in a graph , stating in essence that a cycle is decomposable in the most economic way imaginable . the relation of graph chordality to commutative algebra in particular has motivated many to attempt a generalization of graph chordality to higher dimensions , often using a homological or combinatorial perspective ( we surveyed and summarized this perspective in @xcite ) . however , homological notions , as we shall argue here , are not adequate to capture graph chordality in simplicial complexes , especially not in relation to commutative algebra , and the apparent failure of several important results of graph chordality for homological chordality is a flaw of the approach rather than the problem . as we will see , higher chordality has a better life if we add more information , and let it live in the toric variety ( for simplicial polytopes at least ) , and is a natural symptom of the hard lefschetz theorem , reflecting geometric changes ( as measured by the size of the support ) brought about by multiplication with a lefschetz element . philosophically , we argue that to describe the geometric behavior of simplicial chain complexes , it is better if the boundary map is close to injective . toric geometry allows us to control the boundary map by removing redundant chains in its kernel by factoring out the torus action . to understand this for general simplicial complexes , we use stress spaces @xcite , a construction going back to equilibrium problems in mechanics and elastic introduced by varignon @xcite . it turned out much later that they form a useful model for the intersection theory of a toric variety , in particular the fact that it allows us to describe the support of a chow cohomology class straightforwardly and combinatorially @xcite . the key observation inspiring us was made by kalai @xcite ( compare also ( * ? ? ? * section 2.4.10 ) ) , using a synthetic approach to relate chordality of the graph of a simplicial polytope to minimal rigidity . this beautiful observation deserves a full understanding , especially so because it gives a useful picture of simplicial polytopes with vanishing of primitive second betti numbers ( with respect to the action of a lefschetz element in the cohomology ring of the associated toric variety ) . two natural questions that arise in this context are to extend the observation to all primitive betti numbers and , far more challenging , quantify it beyond the extreme case of vanishing primitive betti numbers . the first problem has been addressed in the celebrated generalized lower bound theorem of murai and nevo @xcite , though without clarifying the beautiful relation to the geometry of homology cycles kalai exhibited . additionally , their proof relies rather heavily on earlier work of green which seems hard , if not impossible , to quantify satisfyingly due to the reliance on generic initial ideals that destroy much of the combinatorial properties of the simplicial complex . the first goal is therefore to understand , reprove and generalize kalai s theorem in a proper context . a secondary objective is to provide a direct and , most importantly , quantifiable proof of the generalized lower bound theorem of murai and nevo @xcite , thereby solving both problems at once , using the newly introduced method of toric chordality . we will also apply our technique to the balanced generalized lower bound conjecture of klee and novik @xcite . more conceptually , this investigation is in line with combinatorial - geometric approaches to intersection theory that has seen remarkable successes disconnecting it from the algebraic varieties it classically lives on ( compare @xcite ) . toric chordality is way to study models of intersection theory in a rather precise geometric way without going to the toric variety . in particular , the present research also has some application to conjectures detailing the interplay between toric algebraic geometry and approximation theory @xcite . * acknowledgements * we thank satoshi murai and eran nevo for extraordinarily useful comments and inspiring conversations concerning their work on the generalized lower bound theorem , and robert macpherson for pointing out some historical facts . we also thank the referee for a thorough read of this paper .

we study the geometric change of chow cohomology classes in projective toric varieties under the weil - mcmullen dual of the intersection product with a lefschetz element . based on this , we introduce toric chordality , a generalization of graph chordality to higher skeleta of simplicial complexes with a coordinatization over characteristic 0 , leading us to a far - reaching generalization of kalai s work on applications of rigidity of frameworks to polytope theory . in contrast to `` homological '' chordality , the notion that is usually studied as a higher - dimensional analogue of graph chordality , we will show that toric chordality has several advantageous properties and applications . most strikingly , we will see that toric chordality allows us to introduce a higher version of dirac s propagation principle . aside from the propagation theorem nevo generalized lower bound theorem . finally , we apply our technique to give a simple proof of the generalized lower bound theorem in polytope theory and prove the balanced generalized lower bound conjecture of klee and novik .

we study the geometric change of chow cohomology classes in projective toric varieties under the weil - mcmullen dual of the intersection product with a lefschetz element . based on this , we introduce toric chordality , a generalization of graph chordality to higher skeleta of simplicial complexes with a coordinatization over characteristic 0 , leading us to a far - reaching generalization of kalai s work on applications of rigidity of frameworks to polytope theory . in contrast to `` homological '' chordality , the notion that is usually studied as a higher - dimensional analogue of graph chordality , we will show that toric chordality has several advantageous properties and applications . most strikingly , we will see that toric chordality allows us to introduce a higher version of dirac s propagation principle . aside from the propagation theorem , we also study the interplay with the geometric properties of the simplicial chain complex of the underlying simplicial complex , culminating in a quantified version of the stanley murai nevo generalized lower bound theorem . finally , we apply our technique to give a simple proof of the generalized lower bound theorem in polytope theory and prove the balanced generalized lower bound conjecture of klee and novik .

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low energy dynamics of field theories can be described by only light fields such as nambu - goldstone modes when one integrates out massive modes . the low - energy effective theories are usually expanded by derivative expansions ; thereby , they inevitably contain higher derivative terms of fields . chiral perturbation theory is such a theory describing low - energy pion dynamics in qcd with a chiral symmetry breaking @xcite . the skyrme model @xcite , which is a non - linear sigma model with fourth order derivative terms , is one of such a class . supergravity as low - energy effective theory of string theory should have higher derivative correction terms @xcite . other examples include world - volume effective actions of solitonic objects such as topological solitons in field theories and d - branes in string theories @xcite . the effective theory of a d - brane is described by the dirac - born - infeld ( dbi ) action @xcite containing an infinite number of derivatives . higher derivative field theories are also useful in other areas of physics . in the cosmological context , higher derivative theories are proposed for inflation models such as the k - inflation @xcite and the galileon inflation @xcite . these higher derivative models are known to admit characteristic soliton solutions such as k - defects @xcite , compactons @xcite and so on . on the other hand , supersymmetry is one of the most important tools in modern high energy physics . it has not only been considered as the most promising candidate to solve the naturalness problem in the standard model in the phenomenological side , but also it plays important roles to control quantum corrections in supersymmetric field theories , leading to determining exact low - energy dynamics @xcite . when one constructs low - energy effective theories in supersymmetric field theories , one is required to consider higher derivative corrections in a supersymmetric manner . it is , however , not so easy to construct supersymmetric completion of general higher derivative theories . off - shell superfield formalisms are useful to write down actions of supersymmetric higher derivative models . in particular , the four - dimensional @xmath4 superfield formalism that incorporates the chiral superfield @xmath5 is a simple starting point . it is , however , known that not all the off - shell supersymmetric higher derivative models exhibit good physical properties . off - shell formulations of higher derivative terms often encounter with an auxiliary field problem ; chiral superfields with space - time derivatives ( e.g. @xmath6 ) sometimes introduce derivative interactions of the auxiliary field @xmath0 . consequently , the auxiliary fields become dynamical . it is hard to eliminate them , and the on - shell structure of the action is not obvious . for instance , the chiral lagrangian of qcd contains the wess - zumino - witten ( wzw ) term to reproduce the quantum anomaly at low energy . however , a supersymmetric completion of the wzw term proposed in ref . @xcite suffers from this auxiliary field problem @xcite . it was proposed in ref . @xcite that a supersymmetric wzw term in superspace can be constructed without the auxiliary field problem if the number of chiral superfields is doubled . the auxiliary field problem would be more problematic if one were to introduce a superpotential , so one could not introduce a potential . nevertheless , supersymmetric higher derivative models of which the building blocks are the chiral superfields are studied in various contexts . among other things , the chiral models studied in refs . @xcite provide a good grounding for studying supersymmetric higher derivative theories . in this model , the auxiliary fields are not accompanied by the space - time derivatives and therefore they can be eliminated by their equations of motion . in principle , it is possible to write down the explicit on - shell actions of the models . in particular , the scalar potential that shows up after eliminating the auxiliary fields looks more apparent @xcite . the coupling of higher derivative chiral models to supergravity was also achieved in this type of model @xcite . a supersymmetric dbi action was constructed in ref . the other examples include a supersymmetric completion of the @xmath7 model @xcite , the supersymmetric galileon inflation models @xcite and models for the ghost condensation @xcite . the same structure appears in quantum effective actions @xcite a higher derivative supersymmetric @xmath8 model free from the auxiliary field problem was also considered previously as a supersymmetric extension @xcite of the faddeev - skyrme model @xcite and a supersymmetric baby skyrme model @xcite . the formalism in refs . @xcite has been also applied to the construction of manifestly supersymmetric higher derivative corrections to supersymmetric nonlinear realizations @xcite . in the former half of this paper , we study higher derivative chiral models developed in refs . @xcite in the superfield formalism , where higher derivative terms can be introduced as a tensor with two holomorphic and symmetric indices and two anti - holomorphic and symmetric indices . we find a surprising fact that has been overlooked in past studies on the supersymmetric completions of various higher derivative models . the model with a single chiral superfield admits a supersymmetric extension of _ arbitrary _ bosonic models that consist of a single complex scalar field . as an example , we present a supersymmetric extension of the faddeev - skyrme model @xcite . the bosonic part of this model does not contain four time derivatives . this is in contrast to the previously proposed supersymmetric extension @xcite of the faddeev - skyrme model that contains an additional four derivative term that includes four time derivatives . moreover , we point out that an arbitrary scalar potential can be introduced even without the superpotential . we further work out the higher derivative chiral models with superpotentials . the resulting on - shell lagrangians are highly non - linear . we study perturbative analysis revealing the possibility of ghost kinetic term and deformations of the scalar potential . meanwhile , bogomolnyi - prasad - sommerfield ( bps ) topological solitons play important roles in the study of non - perturbative dynamics of supersymmetric field theories since they break and preserve a fraction of supersymmetry , belong to short supermultiplets , and consequently are stable against quantum corrections @xcite . when a bps soliton preserves @xmath9 of supersymmetry , it is called a @xmath9 bps soliton . for instance , yang - mills instantons , bps monopoles , vortices , lumps and domain walls @xcite are of @xmath10 bps and composite solitons such as domain wall junctions are of 1/4 bps in theories with four supercharges @xcite and eight supercharges @xcite ( see refs . @xcite as a review for a fraction of supersymmetry for bps states ) . bps solitons remain important in supersymmetric field theories with higher derivative terms . prime examples of such solitons contain 1/2 bps lumps in supersymmetric @xmath8 models with a four - derivative term @xcite , supersymmetric baby skyrmions , which are compactons @xcite ; and bps compactons in k - field theories @xcite . the higher derivative @xmath8 model in ref . @xcite appears as the effective theory of a 1/2 bps non - abelian vortex @xcite in supersymmetric theories with eight supercharges . then , the 1/2 bps lumps in the vortex correspond to yang - mills instantons in the bulk @xcite . while a few examples of bps solitons in higher derivative supersymmetric theories have been studied thus far , a systematic study of bps solitons in such theories is needed . in the latter half of this paper , we give a general framework to examine bps states in supersymmetric higher derivative chiral models . our framework does not only reproduce , in a unified manner , a few remarkable previous studies of the bps bounds in the supersymmetric higher derivative models admitting bps baby skyrmions @xcite , bps compactons @xcite , and bps lumps @xcite , but also includes the more general cases with several new bps states ; 1/2 bps domain walls , 1/4 bps domain wall junctions , 1/2 and 1/4 bps lumps and baby skyrmions . in particular , we find bps baby skyrmions found in ref . @xcite to be 1/4 bps states . we show that 1/2 bps domain walls and 1/2 bps lumps do not receive higher derivative corrections while 1/4 bps domain wall junctions do . the organization of this paper is as follows . in sec . [ sec : hdc ] , we introduce the supersymmetric higher derivative chiral model with four supercharges . we write down the equation of motion for the auxiliary fields and analyze the structure of the on - shell lagrangians . in particular , we introduce the superpotential and the deformation of the scalar potential caused by the higher derivative terms is discussed . we then examine bps states that preserve 1/2 and 1/4 of the original supersymmetry in subsequent sections . the 1/2 bps domain wall and 1/4 bps domain wall junctions are studied in sec . [ sec : wall ] , and 1/2 bps and 1/4 bps lumps are studied in sec . [ sec : lump ] . section [ sec : conc ] is devoted to conclusion and discussions . notations and conventions of superfields are found in the appendix [ sec : notation ] .

we point out that the model admits a supersymmetric completion of arbitrary higher derivative bosonic models of a single complex scalar field and an arbitrary scalar potential can be introduced even without superpotentials . as an example , we present a supersymmetric extension of the faddeev - skyrme model without four time derivatives , in contrast to the previously proposed supersymmetric faddeev - skyrme - like model containing four time derivatives . in general , higher derivative terms together with a superpotential result in deformed scalar potentials . we find that higher derivative corrections to 1/2 bps domain walls and 1/2 bps lumps are exactly canceled out while the 1/4 bps lumps ( as compact baby skyrmions ) depend on a characteristic feature of the higher derivative models . june , 2014 0.5 cm * bps states in supersymmetric chiral models + 0.3 cm with higher derivative terms * 1.1 cm muneto nitta and shin sasaki 0.7 cm _ department of physics , and research and education center for natural sciences , + -0.2 cm keio university , hiyoshi 4 - 1 - 1 , yokohama , kanagawa 223 - 8521 , japan 0.1 cm department of physics , kitasato university + -0.2 cm sagamihara 252 - 0373 , japan _ 0.5 cm

we study the higher derivative chiral models with four supercharges and bogomolnyi - prasad - sommerfield ( bps ) states in these models . the off - shell lagrangian generically includes higher powers of the auxiliary fields which causes distinct on - shell branches associated with the solutions to the auxiliary fields equation . we point out that the model admits a supersymmetric completion of arbitrary higher derivative bosonic models of a single complex scalar field and an arbitrary scalar potential can be introduced even without superpotentials . as an example , we present a supersymmetric extension of the faddeev - skyrme model without four time derivatives , in contrast to the previously proposed supersymmetric faddeev - skyrme - like model containing four time derivatives . in general , higher derivative terms together with a superpotential result in deformed scalar potentials . we find that higher derivative corrections to 1/2 bps domain walls and 1/2 bps lumps are exactly canceled out while the 1/4 bps lumps ( as compact baby skyrmions ) depend on a characteristic feature of the higher derivative models . we also find a new 1/4 bps condition for domain wall junctions which generically receives higher derivative corrections . june , 2014 0.5 cm * bps states in supersymmetric chiral models + 0.3 cm with higher derivative terms * 1.1 cm muneto nitta and shin sasaki 0.7 cm _ department of physics , and research and education center for natural sciences , + -0.2 cm keio university , hiyoshi 4 - 1 - 1 , yokohama , kanagawa 223 - 8521 , japan 0.1 cm department of physics , kitasato university + -0.2 cm sagamihara 252 - 0373 , japan _ 0.5 cm

hep-ph0602140

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some puzzles have been found in @xmath1 meson decaying processes , such as ( a ) the large branching ratios ( brs ) of @xmath12 @xcite , ( b ) the small longitudinal polarizations of @xmath2 decays @xcite and ( c ) the unmatched cp asymmetries ( cpas ) and brs in @xmath6 decays @xcite . the interesting thing is that the mazy problems are all related to the flavor changing neutral current ( fcnc ) @xmath13 decays . the resultants push us not only to consider more precise qcd effects but also to speculate the existence of new physics . it is known that the fcnc processes usually arise from the loop corrections in the standard model ( sm ) like models . the preference of loop corrections originates from the strict constraints of @xmath14 meson oscillation . however , the constraints of @xmath14 system are only on the first two generations , the fcnc at tree level in third generation has no significant limit yet . in especial , the direct constraint from @xmath15 mixing , dictated by @xmath13 interactions , is a lower bound in experiment @xcite . hence , it will be interesting to investigate the models which fcnc occurs at tree level and they could provide the solutions to the puzzles in @xmath13 decays . one of simple extensions of sm for the effects of fcnc is the unconventional @xmath0 model , in which fcnc is arisen from the family nonuniversal couplings @xcite , i.e. the couplings of @xmath0 to different families are not the same . one of possible ways to get the family nonuniversal couplings is to include an additional @xmath16 gauge symmetry ; and then by the requirement of anomaly free , the gauge charges for different families are different @xcite . other models giving the family nonuniversal @xmath0 interactions could be referred to ref . the detailed phenomenological analyses for various low energy physics could be found in ref . especially , the implications on time - dependent cpa of @xmath17 and on the brs of @xmath18 have been studied by ref . moreover , the solution to the @xmath6 puzzle by the nonuniversal @xmath0 couplings is also discussed by the authors of ref . @xcite . to further pursue the effects on @xmath1 decaying processes , in this paper , we will take all the measurements of @xmath19 and @xmath6 into account to constrain the free parameters . by the constrained parameters , we investigate the implications of the @xmath0 model on brs , cpas and polarization fractions ( pfs ) for the decays @xmath20 , @xmath6 and @xmath21 . for two - body color - allowed processes of @xmath1 decays , it is known that the dominant hadronic effects are the factorized parts which could be simply expressed as the multiplication of effective wilson coefficients ( wcs ) , the decay constant , and the transition form factors , _ e.g. _ @xmath22 . furthermore , by the observed cpa of o(10% ) in @xmath23 , we know that the large strong phases have to be introduced . in order to self - consistently calculate the hadronic effects , we employ the perturbative qcd ( pqcd ) approach @xcite to evaluate the hadronic matrix elements , where the large strong phases could be generated by the annihilation effects of the effective operator @xmath24 . it is known that in @xmath1 system which is composed of a heavy quark and a light quark , the residual momentum of the light quark is typically @xmath25 with @xmath26 being the mass of the b - meson ( b - quark ) . in @xmath1 decays , if we regard that the processes are dominated by short - distant interactions , for catching up the energetic quark from the b - quark decay to form a energetic meson with the typical energy being @xmath27 , the light quark inside the @xmath1 meson has to obtain a large momentum from the b - quark via the gluon exchange . hence , the momentum transfer carried by the hard gluon could be estimated to be @xmath28 , where @xmath29 and @xmath30 denote the momenta of spectator quarks inside the @xmath1 meson and produced meson , respectively . in terms of light - cone coordinates , the large components of @xmath31 could be defined by @xmath32 with @xmath33 being the momentum fractions . hence , the squared momentum of the exchanged hard gluon is @xmath34 . as known that the residual momentum of light quark in the @xmath1 meson is @xmath35 , @xmath36 is roughly @xmath37 . since the produced light meson is energetic , the momenta of valence quarks should be @xmath38 , i.e. @xmath39 . by taking @xmath40 , @xmath41 and @xmath42 gev , we get @xmath43 gev . since the value reflects the typical reacting scale of @xmath1 decays in the framework of the pqcd , for the sm contributions , in our calculations the values of weak wcs are estimated at the scale @xmath44 gev . the paper is organized as follows : in sec . [ sec : fcnc ] , we introduce the nonuniversal @xmath0 effects for @xmath13 transition . in sec . [ amplitudes ] , based on the flavor diagrams , we explicitly write out the factorizable amplitudes associated with the new physics for the decays @xmath45 , @xmath6 and @xmath21 . in addition , we also define direct cpa and pfs . then by setting the values of parameters , in sec . [ sec : na ] we give the calculated values for hadronic effects , present various current experimental data for constraining the unknown parameters , display the sm predictions and discuss the results of the @xmath0 model . finally , we give a summary .

we study the impacts of nonuniversal model , providing flavor changing neutral current at tree level , on the branching ratios ( brs ) , cp asymmetries ( cpas ) and polarization fractions of decays . the new introduced effective interactions not only could effectively explain the puzzle of small longitudinal polarization in decays , but also provide a solution to the small cpa of . in addition , by using the values of parameters which are constrained by , we find that the favorable ranges of brs , cpas , longitudinal polarizations , and perpendicular transverse polarizations for are , , and , respectively .

we study the impacts of nonuniversal model , providing flavor changing neutral current at tree level , on the branching ratios ( brs ) , cp asymmetries ( cpas ) and polarization fractions of decays . we find that for satisfying the current data , the new left- and right - handed couplings have to be included at the same time . the new introduced effective interactions not only could effectively explain the puzzle of small longitudinal polarization in decays , but also provide a solution to the small cpa of . we also find that the favorable cpa of is opposite in sign to the standard model ; meanwhile , the cpa of has to be smaller than . in addition , by using the values of parameters which are constrained by , we find that the favorable ranges of brs , cpas , longitudinal polarizations , and perpendicular transverse polarizations for are , , and , respectively .

hep-ph0602140

i

we have studied the effects of nonuniversal @xmath0 model on the processes dictated by the @xmath98 decays with @xmath117 , d , and s. by using the pqcd approach , we calculate the needed hadronic matrix elements . for @xmath19 decays , we find that their brs and the @xmath264 of @xmath371 have provided strict constraints on the new parameters . after marching the currents data , we find the @xmath283 of @xmath372 favors to be larger than @xmath329 . for @xmath6 decays , by requiring that the magnitude of @xmath373 is less than @xmath374 and all brs satisfy the current observations , we find that the magnitude of cpa of @xmath4 should be larger than @xmath375 but sign is the same as sm . meanwhile , the cpa of @xmath3 could be as low as few percent which is indicated by the current experiments . moreover , we also obtain that the cpa of @xmath3 is opposite in sign to the sm . in sum , to satisfy current data , the new left- and right - handed couplings have to be included simultaneously . it is clear that the fc @xmath0 model provides the needed couplings naturally . with more physical observations and accurate data by @xmath1 factories , we could further examine the effects of nonuniversal @xmath0 model . + * acknowledgments * + we thank prof . chao qiang geng and prof . cheng - wei chiang for useful discussions . this work is supported in part by the national science council of r.o.c . under grant # s : nsc-94 - 2112-m-006 - 009 .

we find that for satisfying the current data , the new left- and right - handed couplings have to be included at the same time . we also find that the favorable cpa of is opposite in sign to the standard model ; meanwhile , the cpa of has to be smaller than .

we study the impacts of nonuniversal model , providing flavor changing neutral current at tree level , on the branching ratios ( brs ) , cp asymmetries ( cpas ) and polarization fractions of decays . we find that for satisfying the current data , the new left- and right - handed couplings have to be included at the same time . the new introduced effective interactions not only could effectively explain the puzzle of small longitudinal polarization in decays , but also provide a solution to the small cpa of . we also find that the favorable cpa of is opposite in sign to the standard model ; meanwhile , the cpa of has to be smaller than . in addition , by using the values of parameters which are constrained by , we find that the favorable ranges of brs , cpas , longitudinal polarizations , and perpendicular transverse polarizations for are , , and , respectively .

0710.1363

i

in this paper we present the qualitative and quantitative analysis of the influence of imperfect structure of a crystalline undulator ( in particular , the influence of the variation of the bending amplitude over the crystal thickness due to the stress applied to its surface ) on the spectral distribution of the radiation . the parameters of crystalline undulators ( including the types and lengths of crystals , the periods of bending , the positron energies , and the range of photon energies ) as well as the methods of preparation of periodically bent structures discussed below in the paper correspond to those which are available for the experiments to be carried out within the pecu project@xcite . a periodically bent crystal together with a bunch of ultra - relativistic charged particles which undergo planar channeling constitute a crystalline undulator . in such a system there appears , in addition to the well - known channeling radiation , the undulator type radiation which is due to the periodic motion of channeling particles which follow the bending of the crystallographic planes@xcite . the intensity and characteristic frequencies of this radiation can be varied by changing the beam energy and the parameters of bending . in the cited papers as well as in the subsequent publications ( see the review ref . @xcite and the references therein ) a feasibility was proven to create a short - wave crystalline undulator that will emit intensive monochromatic radiation when a pulse of ultra - relativistic positrons is passed through its channels . more recently , it was demonstrated @xcite that the undulator based on the electron channeling is also feasible . a number of corresponding novel numerical results were presented to illustrate the developed theory , including , in particular , the calculation of the spectral and angular characteristics of the new type of radiation . although the operational principle of a crystalline undulator does not depend on the type of a projectile below in this paper we will consider the case of a positron channeling . under certain conditions @xcite , an ultra - relativistic positron , which enters the crystal at the angle smaller than the lindhard critical angle @xcite , will penetrate through the crystal following the bendings of its planes . provided the bending amplitude @xmath0 greatly exceeds the interplanar distance @xmath1 ( see figure [ figure.1 ] left ) one can disregard the oscillations due to the action of the interplanar force , the channeling oscillations@xcite . in this case the trajectory of the particle can be associated with the periodic profile of channel centerline . the undulator radiation appears as a result of this periodic motion of the particle . thus , the operational principle of a crystalline undulator is the same as for a conventional one@xcite , in which the monochromaticity of the radiation is the result of a constructive interference of the photons emitted from similar parts of trajectory . usually , when discussing the properties of a crystalline undulator and of its radiation , one considers the case of _ a perfect _ crystalline undulator . by this term we will understand the crystal whose planes are bent periodically following a perfect harmonic shape , @xmath2 , see figure [ figure.1 ] ( left ) . for clarity , let us stress that we consider the case when the quantities @xmath1 , @xmath0 and @xmath3 satisfy the double inequality @xmath4 . typically , @xmath5 , @xmath6 and @xmath7 . the spectral - angular distribution from the perfect undulator is characterized by a specific pattern which implies that for each value of the emission angle the spectrum consists of a set of narrow , well - separated and powerful peaks corresponding to different harmonics of radiation . in principle , the perfect crystalline undulators can be produced by using the technologies of growing si@xmath8ge@xmath9 structures @xcite . in this case , by varying the ge content @xmath10 one can obtain periodically bent crystalline structure @xcite . the technological restrictions imposed by this method on the crystalline undulator length is @xmath11 m . the periodic bending can also be achieved by making regularly spaced grooves on the crystal surface either by using a diamond blade @xcite or by means of laser - ablation . the latter method was used @xcite to prepare the si - based crystalline undulators for the pecu experiments . in either case , the regular surface deformation results in the periodic pattern of the crystallographic planes bending in the bulk . the question which appears in connection with these methods of preparation concerns the quality of the periodically bending . indeed , for a crystal of a finite thickness it is natural to expect that the surface deformations , regularly spaced with the period @xmath3 , result in the volume deformations of the same period but of a varied amplitude of bending , @xmath12 ( see figure [ figure.1 ] ( right ) ) . the latter has maximum value in the surface layer but decreases with the penetration distance . therefore , it is important to carry out a quantitative analysis ( a ) of the structure of this _ imperfect _ periodic bending in the bulk , and ( b ) of its influence on the spectrum of undulator radiation . both of these problems constitute the subject of the present paper . the paper is organized as follows . in section [ de ] we briefly outline the basic formulae and definitions which refer to a perfect crystalline undulator . section [ averaging ] describes , in general terms , the modifications to be introduced to the formalism due to the imperfectness of the crystalline undulator . in section [ formalism ] we present the formalism and carry out numerical analysis of the periodic deformations in the bulk caused by a regular stress applied to the crystal surface . finally , in section [ averagedspectra ] we carry out quantitative analysis of the differences in the emission spectra formed in a perfect undulator and in the undulator created by means of periodic surface deformations .

we study the influence of an imperfect structure of a crystalline undulator on the spectrum of the undulator radiation . we demonstrate that this method of preparation of a crystalline undulator inevitably leads to a variation of the bending amplitude over the crystal thickness and to the presence of the subharmonics with smaller bending period .

we study the influence of an imperfect structure of a crystalline undulator on the spectrum of the undulator radiation . the main attention is paid to the undulators in which the periodic bending in the bulk appears as a result of a regular ( periodic ) surface deformations . we demonstrate that this method of preparation of a crystalline undulator inevitably leads to a variation of the bending amplitude over the crystal thickness and to the presence of the subharmonics with smaller bending period . both of these features noticeably influence the monochromatic pattern of the undulator radiation .

cond-mat9811052

i

how a liquid freezes to form a solid is a problem of longstanding interest to physicists . freezing at thermal equilibrium can now be said to be quite well understood in terms of a first - principles order - parameter theory @xcite . the effect of steady nonequilibrium driving on the freezing transition has been studied in the context of _ sheared _ colloids @xcite . a uniformly driven state , with no gradients on the average , as would arise in steady sedimentation @xcite or the fluidized bed @xcite is conceptually simpler : unlike in shear flow , an order - parameter description of the mean state of the driven crystal is straightforward . nonetheless , we know of no studies , experimental or theoretical , of the effect of sedimentation on the liquid - solid phase boundary in a suspension settling uniformly under gravity , or of the freezing of moving flux lattices in the _ absence _ of quenched disorder . a study of freezing in the presence of uniform driving is also of interest as a problem in the general class of driven diffusive systems . most of the investigations in this field @xcite are either away from any equilibrium phase transition or in the neighbourhood of a second order phase transition . the effect of uniform driving on a first order phase transition has received very little attention @xcite ; the freezing transition , in particular holds interesting possibilities since the ordering is at non - zero wavenumber . in this paper we consider a collection of interacting particles in a liquid state , i.e. , with strong short - range translational correlations , and ask what happens to the liquid - solid transition in the presence of an imposed steady mean translational motion of the particles with respect to the ambient medium . our model should apply not only to charge - stabilized colloidal suspensions @xcite , but also to the effect of a steady current on the freezing transition of flux - point liquids @xcite in thin slabs of clean type ii superconductors . the main ingredient in our theory is the concentration dependence of the mobility of particles in a suspension , or of the flux - points in a superconductor . in colloidal suspensions , this dependence arises as a result of the hydrodynamic interactions between particles , while in the flux - liquid , it is the electromagnetic interaction that is primarily responsible for the effect . although our approach is fairly general , we use parameter values appropriate to the specific case of sedimenting colloidal suspensions in the rest of the paper . our main results are as follows : as the mean concentration of the suspension is increased , the hydrodynamic interaction causes it to settle more slowly @xcite . we show that this leads to a nonlinearity in the equations of motion whose effect is to reduce the height of the structure factor relative to its equilibrium value . the suppression is strongly anisotropic , largest for wavevectors along the direction of mean drift , and vanishing for wavevectors normal to it . the reduction is most pronounced at the location of the peak , which means the strong short - range correlations in the liquid , which are the precursor of translational order , are suppressed . this inevitably leads to a shift of the phase boundary towards the crystal side ( i.e. , favours the liquid over the crystalline phase ) , by an amount proportional to the square of the pclet number , in a manner reminiscent of a proposed mechanism @xcite for shear - induced melting . this nonequilibrium phase transition now assumes additional importance in the wake of recent experiments on charged fluidized beds @xcite where it should be possible to test our predictions . constraints on the types of systems to which our theory should apply are discussed at the end of section [ sec : conclude ] . the paper is organised as follows . section [ introfreezing ] gives an overview of equilibrium freezing . the equations describing the motion of a sedimenting suspension are derived in section [ freezingeomsection ] . in section [ freezingphasetrans ] we discuss in a general setting the prescription used in this paper to describe a nonequilibrium phase transition . the perturbative calculation leading to the equal time correlation function in the driven system is the content of section [ freezingperturbation ] , and our numerical results for the structure factor are given in section [ freezingstrucfac ] . in section [ freezingfreezing ] we derive our results for the freezing transition , and conclude in section [ sec : conclude ] .

we study the liquid - solid transition in a collection of interacting particles moving through a dissipative medium under the action of a constant , spatially uniform external force , e.g. a charge - stabilized suspension in a fluidized bed or a flux - point lattice moving through a thin , current - carrying slab of type ii superconductor . we show that the structure factor peak is suppressed in an anisotropic manner as a result of this effect , resulting in a shift of the crystal - liquid phase boundary towards the crystal side . a nonequilibrium phase diagram is presented .

we study the liquid - solid transition in a collection of interacting particles moving through a dissipative medium under the action of a constant , spatially uniform external force , e.g. a charge - stabilized suspension in a fluidized bed or a flux - point lattice moving through a thin , current - carrying slab of type ii superconductor . the mobility of a given region in these systems is in general a function of the local concentration . we show that the structure factor peak is suppressed in an anisotropic manner as a result of this effect , resulting in a shift of the crystal - liquid phase boundary towards the crystal side . a nonequilibrium phase diagram is presented . epsf , 0_0 ( ) _ 0 1 _

1601.06591

i

countable markov maps , that is , interval maps with countably many expanding branches , have received much attention over the past several years . they appear in particular in diophantine approximation in the study of approximation rates of irrationals by rational numbers . the key examples here are the _ gauss map _ @xmath11 , which generates the continued fraction expansion @xcite , and the various _ lroth maps _ , which generate lroth expansions @xcite . moreover , countable markov maps appear naturally in the study of non - uniformly hyperbolic dynamical systems such as the intermittent _ manneville - pomeau maps _ @xcite , where often one considers induced countable markov maps of such systems . various examples are pictured in figure [ fig : countablemarkovmaps ] below . , the lroth map @xmath12 and the alternating lroth map @xmath13 , see @xcite for definitions . ] in this paper , we are interested in the changes to the dynamics of countable markov maps when small pointwise perturbations are applied . a possible way to evaluate the effect of such perturbations on the dynamics of these maps is to investigate the topological conjugacies between the original map and the perturbed map , where we recall that a homeomorphism @xmath14 between two topological dynamical systems is said to be a _ topological conjugacy _ if @xmath15 . in other words , every orbit under @xmath1 corresponds to an orbit under @xmath16 and vice versa . in the case of countable markov maps @xmath1 and @xmath16 the conjugacies will usually be strictly increasing , singular maps , otherwise known as slippery devil s staircases ( a term coined by mandelbrot @xcite ) . singular here means that the derivative is lebesgue - almost everywhere equal to zero : @xmath17 now the _ degree _ of the singularity of the conjugacy @xmath18 gives us a certain sense of how `` close '' the maps @xmath1 and @xmath16 are . natural ways to measure the degree of singularity are for example the hausdorff dimension @xmath19 or the hlder exponent of the conjugacy @xmath18 . perhaps the first well - studied example of a singular function is minkowski s question - mark function @xmath20\to [ 0,1]$ ] , which was constructed by h. minkowski in 1908 ( see @xcite ) . it is illustrated in figure [ fig : minkowskiluroth ] . this function was originally designed precisely to map all rational numbers in @xmath21 $ ] onto the dyadic rationals , and all algebraic numbers of degree two onto the non - dyadic rationals , in an order preserving way . the main idea was to illustrate the lagrange property of the algebraic numbers of degree two ( see theorem 28 in @xcite ) . the function @xmath22 was proved to be singular by denjoy @xcite , and was also studied by salem @xcite . more recently , kessebhmer and stratmann @xcite showed that the minkowski question - mark function can be thought of as the topological conjugacy between the gauss map and the alternating lroth map ( or , equivalently , between the classical farey map from elementary number theory and the tent map ) . moreover , they showed that the derivative can either take the value zero , be infinite , or else it does nt exist . they then applied previous thermodynamical results to compute the hausdorff dimension of the sets where the derivative is infinite and where it does nt exist , and these dimensions turn out to be equal @xcite . and the @xmath23-farey - minkowski function @xmath24 for the classical alternating lroth map @xmath12 , as shown above . ] the hausdorff dimension of the set of non - zero derivative for a variant of the minkowski question - mark function has been studied by li , xiao and dekking in @xcite , and for the case of expanding maps of the interval with finitely many increasing branches by kessebhmer _ _ in @xcite . a similar problem has also been studied in the case of singular functions which are increasing but not strictly increasing , such as for several variants of the cantor ternary function , see @xcite for example . moreover , similar results have been considered for topological conjugacies ( called @xmath9-_farey - minkowski functions _ ) between @xmath9-lroth maps by munday @xcite ( an example is shown in figure [ fig : minkowskiluroth ] ) and later by arroyo @xcite , where he considers the conjugacy maps between the gauss map and any @xmath9-lroth map . there is extensive literature on the perturbations of dynamical systems and their effect on entropy , dimension , and other statistical quantities under both random and deterministic perturbations . in our case we will study the following problem : how do the notions of singularity of the topological conjugacy @xmath18 between countable markov maps @xmath1 and @xmath16 behave when @xmath1 and @xmath16 are sufficiently close ? here by `` closeness '' we mean the relatively weak notion that the inverse branches of @xmath1 and @xmath16 are pointwise close . heuristically here one would expect that the conjugacies @xmath18 would share the properties of the identity mapping as @xmath18 is pointwise close to the identity . we will find out that for the hausdorff dimension of the set of @xmath25 with @xmath26 , we do have some continuity under pointwise perturbations ( see theorem [ mainthm ] below ) , but under other notions of singularity of @xmath18 , such as hlder exponents or hausdorff dimension of the @xmath18 image of the absolutely continuous invariant measure , the continuity fails to occur ( see propositions [ prop : holder ] , [ prop : hausdorff ] , [ prop : lyapunov ] below ) due to the non - compact nature of countable markov maps . to state our main result , let us first fix a little notation ( we refer to section [ sec : prelim ] for a more thorough exposition ) . let @xmath27 \to [ 0,1]$ ] be @xmath28 contractions for each @xmath29 and where either @xmath30 , @xmath31 for all @xmath29 and @xmath32 is a decreasing sequence with @xmath33 or we have that @xmath34 , @xmath35 for all @xmath29 and @xmath36 is a decreasing sequence . these maps are the inverse branches of a piecewise differentiable countable markov map @xmath1 . we assume some regularity on @xmath1 and a standard assumption in this setting is that the geometric potential @xmath37 has _ summable variations _ ( see section [ sec : thermo ] for a definition ) , that is , @xmath38 which is satisfied , for example , for the gauss map , jump transformations of the manneville - pomeau map , and for all @xmath9-lroth maps . we will fix such a system \{@xmath1 , @xmath39 } and consider perturbations of the system , in the following sense . for each @xmath40 we will consider a system with maps @xmath41 and @xmath42 satisfying the variation assumption above and where for each @xmath43 $ ] we have @xmath44 we need that @xmath41 have the same orientation as the maps @xmath45 . this means the dynamical systems @xmath42 and @xmath1 are topologically conjugate and we will denote the conjugacy by @xmath46 , that is the homeomorphism @xmath47\to [ 0,1]$ ] satisfies that @xmath48 . now the pointwise convergence of the inverse branches guarantee that when @xmath2 , we have that the conjugacy @xmath4 will flatten and converge pointwise to the identity mapping , see figure [ fig : limitperturbation ] for example . between two countable markov maps @xmath0 and @xmath1 . the map @xmath1 is the @xmath49-lroth map for the dyadic partition @xmath49 and @xmath0 is the @xmath9-lroth map for a @xmath50-adic partition for @xmath50 attaining the values @xmath51 , @xmath52 , @xmath53 and @xmath54 . the maps @xmath4 approach the identity pointwise when @xmath55 pointwise . ] thus one would expect that @xmath4 should share the properties of the identity in the limit . our main result shows that this happens for the hausdorff dimension of the set @xmath56 under suitable assumptions on the converging family of countable markov maps . [ mainthm ] suppose @xmath1 is a countable markov map with inverse branches @xmath45 such that the potential @xmath57 has summable variations . let @xmath58 be a sequence of countable markov maps with inverse branches @xmath41 . assume the following two assumptions on the tail and variations : * there exists @xmath59 with @xmath60|^t<\infty.\ ] ] * the potentials @xmath61 have summable variations with a uniform bound over @xmath62 : @xmath63 under these assumptions , if for any @xmath64 the inverse branches @xmath55 pointwise as @xmath2 , we have @xmath65 let us make a few remarks on the conditions ( 1 ) and ( 2 ) required in theorem [ mainthm ] . the condition ( 1 ) holds if the countable markov map @xmath1 has at most a polynomially fat tail , in the sense that the lengths @xmath66| = o(i^{-p})$ ] as @xmath67 for some @xmath68 . thus ( 1 ) yields in particular that the absolutely continuous invariant measure for @xmath1 has finite entropy , but it is not an equivalent condition . the condition ( 2 ) on variation in theorem [ mainthm ] is satisfied if the inverse branches of @xmath0 are linear , i.e. , when the maps @xmath0 are @xmath9-lroth maps for certain partitions @xmath9 in the notation of @xcite . thus our result gives rather general conditions to have such a perturbation theorem for @xmath9-lroth maps , provided that the map being perturbed has a thin enough tail . in the non - linear case , the gauss map will satisfy the tail assumption ( 1 ) we impose , so the perturbation theorem is valid provided we have a uniform bound ( 2 ) over the sums of variations on the family of maps converging to the gauss map . furthermore , the conditions in theorem [ mainthm ] are weak enough for us to apply theorem [ mainthm ] to the study of a certain family of intermittent maps in non - uniformly hyperbolic dynamics known as the _ manneville - pomeau maps _ @xmath69 \to [ 0,1]$ ] , @xmath70,\ ] ] for a parameter @xmath71 . the jump transformations ( in other words , `` accelerated dynamics '' or induced maps ) for @xmath72 give us countable markov maps that have polynomial tail and satisfy the assumptions of theorem [ mainthm ] when varying the parameter @xmath9 for the maps @xmath72 , since this means pointwise convergence of the inverse branches . thus we obtain the following corollary to theorem [ mainthm ] : [ cor : mp ] let @xmath73 . then as @xmath74 we have @xmath75 where @xmath76 is the topological conjugacy between the manneville - pomeau maps @xmath77 and @xmath72 . corollary [ cor : mp ] concerns the topological stability for @xmath72 when varying @xmath9 . a related area of study for manneville - pomeau maps is the measure theoretical _ statistical stability _ , where the behaviour of the absolutely continuous invariant measure for @xmath72 is studied when varying @xmath9 , see for example the recent works by freitas and todd @xcite and baladi and todd @xcite . there are also other natural ways to measure the singularity of the conjugacies @xmath4 and the effect of perturbations to them . however , we will see that the continuity as presented in theorem [ mainthm ] fails for these quantities . we will consider three possible examples below . firstly , observe that the topological conjugacies @xmath4 are all hlder continuous . thus one might expect that the hlder exponent @xmath78 of @xmath4 ( see section [ sec : prelim ] for definitions ) would converge to @xmath79 , which is the hlder exponent of the identity . however , this can be made to fail : [ prop : holder ] there exist examples of @xmath0 and @xmath1 satisfying the assumptions of theorem [ mainthm ] such that the hlder exponents @xmath78 of @xmath4 satisfy @xmath80 a similar behaviour can be observed also in the following setting . if @xmath7 is the absolutely continuous @xmath1-invariant measure , then one might also expect that the hausdorff dimensions @xmath6 of the @xmath4-preimages of the measure @xmath7 would converge to @xmath79 . on the other hand , the maps @xmath0 can be chosen such that the the dimensions do not converge to the expected value : [ prop : hausdorff ] there exist examples of @xmath0 and @xmath1 satisfying the assumptions of theorem [ mainthm ] such that the hausdorff dimensions of @xmath81 satisfy @xmath82 moreover , denoting by @xmath83 the absolutely continuous @xmath0-invariant measure , we also consider the entropy ( that is , the lyapunov exponent ) of the absolutely continuous invariant measures for the maps @xmath0 and @xmath1 respectively . if we would have that @xmath84 , instead of pointwise convergence of the inverse branches of @xmath0 , it would be considerably easier to prove the statement of the main result theorem [ mainthm ] . however , @xmath84 is too strong a property to be deduced from pointwise convergence , as the following result shows . [ prop : lyapunov ] there exist examples of @xmath0 and @xmath1 satisfying the assumptions of theorem [ mainthm ] such that the entropy @xmath85 but the limit @xmath86 we remark that in the uniformly hyperbolic compact case , i.e. , in the situation of finitely many branches with uniform expansion rate , all these notions can be shown to be continuous under pointwise perturbations . the heuristic reason for propositions [ prop : holder ] , [ prop : hausdorff ] and [ prop : lyapunov ] is that they represent notions that are very sensitive to the tail behaviour of the countable markov maps @xmath0 . on the other hand , the idea of the proof of theorem [ mainthm ] is that we approximate the infinite systems considered by a finite branch system and in this approximation the precise nature of the tails is not so important , except in terms of the tail of the limiting map @xmath1 ( the tail condition ( 1 ) of theorem [ mainthm ] ) . thus the hausdorff dimension of non - differentiability points will not be as sensitive to the tails as the hlder exponent @xmath78 , hausdorff dimension of @xmath81 or the entropy @xmath87 . the limit obtained in theorem [ mainthm ] does not tell us about the possible rate of the numbers @xmath88 converging to @xmath79 as @xmath89 approaches infinity . if we restrict the class of countable markov maps we consider , then this can be addressed and the hausdorff dimension can be explicitly computed . for this , we will consider a class of countable markov maps similar to those arising from the _ salem family _ considered in @xcite . fix @xmath90 and define the map @xmath91 to be the countable markov map with decreasing linear branches on each interval @xmath92 $ ] , @xmath62 . in the language of @xmath9-lroth maps @xcite , the map @xmath91 is the @xmath9-lroth map for the partition @xmath93 : k \in \n\}$ ] . we obtain the following theorem . [ mainthm2 ] fix @xmath94 and let @xmath95 be the topological conjugacy between @xmath91 and @xmath96 . then @xmath97 where @xmath98 due to the choice of the specific countable markov maps @xmath91 , the proof of theorem [ mainthm2 ] is reduced to the study of conjugacies between tent - like expanding maps with two full branches , one increasing and one decreasing . a similar result was obtained in ( * ? ? ? * theorem 1.1 ) , where the authors consider a family of expanding maps with finitely many increasing full branches . however , as we have one increasing and one decreasing branch , the proof in our situation is rather simpler than in @xcite . the paper is organised as follows . in sections [ sec : prelim ] and [ sec : thermo ] we will give all the necessary background results from dimension theory and thermodynamic formalism . in section [ sec : mainthm ] we will give the proof of theorem [ mainthm ] . in section [ sec : holderentropy ] we present how to achieve propositions [ prop : holder ] , [ prop : hausdorff ] and [ prop : lyapunov ] . in section [ sec : manpom ] we discuss the manneville - pomeau example further and prove corollary [ cor : mp ] , and finally , in section [ sec : geometric ] we prove theorem [ mainthm2 ] .

we study the pointwise perturbations of countable markov maps with infinitely many inverse branches and establish the following continuity theorem : let and be expanding countable markov maps such that the inverse branches of converge pointwise to the inverse branches of as . then under suitable regularity assumptions on the maps and the following limit exists : where is the topological conjugacy between and and stands for the hausdorff dimension . this is in contrast with the fact that other natural quantities measuring the singularity of fail to be continuous in this manner under pointwise convergence such as the hlder exponent of or the hausdorff dimension for the preimage of the absolutely continuous invariant measure for . as an application we obtain a perturbation theorem in non - uniformly hyperbolic dynamics for conjugacies between intermittent manneville - pomeau maps when varying the parameter . 306494 and msca - if grant ) ]

we study the pointwise perturbations of countable markov maps with infinitely many inverse branches and establish the following continuity theorem : let and be expanding countable markov maps such that the inverse branches of converge pointwise to the inverse branches of as . then under suitable regularity assumptions on the maps and the following limit exists : where is the topological conjugacy between and and stands for the hausdorff dimension . this is in contrast with the fact that other natural quantities measuring the singularity of fail to be continuous in this manner under pointwise convergence such as the hlder exponent of or the hausdorff dimension for the preimage of the absolutely continuous invariant measure for . as an application we obtain a perturbation theorem in non - uniformly hyperbolic dynamics for conjugacies between intermittent manneville - pomeau maps when varying the parameter . 306494 and msca - if grant ) ]