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if some post - inflationary physics involves the spontaneous breaking of an exact @xmath3 symmetry with @xmath201 , then the ordering of these scalar fields may provide a secondary contribution to primordial perturbations . current constraints allow up to @xmath5 of the power in primordial perturbations to be due to sosfs . sosf models are appealing from the theoretical perspective because they are simple , well - defined , and parametrized only by the symmetry - breaking scale @xmath7 and number @xmath6 of fields . in this paper we have calculated the matter and curvature bispectra induced by the ordering of such scalar fields . given that the density perturbation is quadratic in the scalar - field perturbation , sosf density perturbations are expected to be highly non - gaussian , and if so , measurements of non - gaussianity may provide the means to test these models . here we have calculated analytically the bispectrum due to sosfs and presented results in a way that should be easily accessible to those doing measurements with the cmb and large - scale structure . we find that the triangle - shape dependence of the bispectrum peaks for aligned triangles , unlike the local - model bispectrum , which is largest for squeezed triangles , and the equilateral bispectrum , which is largest for equilateral triangles . we have estimated a current upper limit to the non - gaussianity parameter @xmath9 for the model and find that the implied constraints to the @xmath7-@xmath6 sosf parameter space are competitive with those from the upper limit to cmb temperature fluctuations . finally , we have already argued above , in section [ sec : currentconstraints ] , that the correlation of modes will be similar for the large - scale modes as they enter the horizon , those relevant for large - angle cmb fluctuations . we therefore believe that rough constraints to the model can be derived from cmb measurements by assuming that the curvature bispectrum we calculate is the primordial one . clearly , there is room for further numerical work to test our assumptions and to make our predictions more precise . in the meantime , though , we believe that our analytic approximation captures the essential physics and that our bispectrum can be used in the meantime as a `` working - horse '' model to derive constraints , from non - gaussianity measurements , to this interesting class of models for secondary contributions to primordial perturbations . finally , we note that the model makes a number of other predictions . given that density perturbations are actively generated as new modes come within the horizon , vector and tensor modes will be excited , and these may give rise to interesting polarization signals @xcite in the cmb and perhaps excite b modes @xcite in the cmb that might be distinguished from those due to inflation @xcite . there will also be a scale - invariant spectrum of primordial gravitational waves produced @xcite that can be sought in gravitational - wave observatories . dgf thanks caltech and cern for hospitality during the completion of this work . dgf acknowledges support from an fpu fellowship from the spanish ministry of science , with ref . ap-2005 - 1092 . this work was supported at caltech by doe de - fg03 - 92-er40701 and the gordon and betty moore foundation and at dartmouth by nsf ast-0349213 .

we calculate the bispectrum that arises in models of self - ordered scalar fields . the bispectrum is largest for triangles that are aligned ( have edges ) as opposed to the local - model bispectrum , which peaks for squeezed triangles ( ) , and the equilateral bispectrum , which peaks at .

the universe may harbor relics of the post - inflationary epoch in the form of a network of self - ordered scalar fields . such fossils , while consistent with current cosmological data at trace levels , may leave too weak an imprint on the cosmic microwave background and the large - scale distribution of matter to allow for direct detection . the non - gaussian statistics of the density perturbations induced by these fields , however , permit a direct means to probe for these relics . here we calculate the bispectrum that arises in models of self - ordered scalar fields . we find a compact analytic expression for the bispectrum , evaluate it numerically , and provide a simple approximation that may be useful for data analysis . the bispectrum is largest for triangles that are aligned ( have edges ) as opposed to the local - model bispectrum , which peaks for squeezed triangles ( ) , and the equilateral bispectrum , which peaks at . we estimate that this non - gaussianity should be detectable by the planck satellite if the contribution from self - ordering scalar fields to primordial perturbations is near the current upper limit .

hep-ph0104049

i

after many years of fruitful operation , the lep experiments have been closed down and the lep2 data analysis is approaching its final stage . in the area of @xmath2-pair physics the experimental precision is very high : in order to match it , theoretical calculations must include not only tree - level four - fermion born contributions , with the numerically leading higher - order effects ( mostly qed ) , but also the complete @xmath1 electroweak ( ew ) corrections to @xmath2-pair production @xcite . this applies not only to inclusive quantities such as the total cross section but also to various differential distributions , such as the angular or invariant mass ones . to date there is , however , no single monte carlo ( mc ) event generator that would include simultaneously the complete four - fermion background for massive fermions and the @xmath1 ew corrections to @xmath2-pair mediated processes in _ all _ possible @xmath2-pair decay channels . for example koralw @xcite can generate _ all _ four - fermion final states with the fully massive phase space and the complete born - level four - fermion massive matrix element generated by the grace2 package @xcite . apart from koralw there exists a number of other mc programs for all four - fermion processes at the born level @xcite . the complete @xmath1 corrections to the signal @xmath18 process are implemented only in two mc programs : yfsww3 @xcite and racoonww @xcite . yfsww3 includes the library of electroweak corrections from refs . @xcite . the racoonww program , in addition to @xmath1 corrections to the @xmath3 process , can also calculate the four - fermion corrections in the massless fermion approximation and single , hard , non - collinear , real photon radiation in all four - fermion processes . the massless fermion approximation prevents racoonww from being fully exclusive . also , racoonww seems to still have some problem with providing constant - weight events in the full operational mode . concerning the efficient use of the koralw and yfsww3 mc event generators , the critical open question is : how is it possible to combine their results , so that for every interesting physical observable we get a prediction that includes the complete @xmath1 standard model ( sm ) corrections for the @xmath2-pair production and decay process , keeping sufficient control on the smaller contributions from the `` background diagrams '' ? before we answer this question , let us mention important practical limitations and requirements . for the purpose of the lep2 data analysis it is of paramount importance that the results of yfsww3 and koralw are combined for the _ fully exclusive _ distributions , in other words on an _ event - per - event _ basis . it is not sufficient to combine the predictions of two separate mc runs of yfsww3 and koralw programs for _ inclusive _ observables such as an integrated cross section , asymmetries , single - dimensional angular or @xmath2-mass distributions . such a procedure is not sufficient for full detector simulations and for data analysis , in which the important sm parameter , the mass of the @xmath2 , is fitted to experimental data using a series of the ( fully exclusive ) mc events ! apparently , we are asking whether the koralw and yfsww3 mc programs could be merged into a single new mc event generator , that is a single mc program with a single source code and a single executable object in the machine processor . in principle , this could be done , but not within the time left for the lep2 data analysis . nevertheless , the situation is not completely hopeless and there seem to be some sensible ways out . one possible solution is to combine koralw and yfsww3 into a single tool using events stored on the mass data storage , which we shall call a `` disk file '' or simply a `` disk '' . storing events is done routinely for the purpose of the data analysis anyway . in this scenario , constant - weight events generated with koralw are stored on the disk and later on read by yfsww3 and finally corrected for the missing @xmath1 terms with the help of a special correction weight . the resulting events would be variable - weight ( weighted ) events . this kind of organization is not completely trivial and requires certain `` tuning '' of both programs ; see below for the details . note also that ; for the purpose of fitting the @xmath2 mass , the events generated by koralw and stored on the disk can be corrected in a similar way by koralw , with the weight corresponding to a change of the mass of @xmath2 , or due to any change of the other sm parameters ( any change of the input data of koralw ) . coming back to the above procedure of combining koralw and yfsww3 , we see two important disadvantages : ( i ) running two separate mc programs that communicate through a disk file is inconvenient and ( ii ) the correction weight of yfsww3 may have a long tail , so that it would be difficult or impossible to produce constant - weight ( unweighted ) events through a rejection technique . in this article we present another solution to the above problems and the corresponding mc tool , based on the koralw and yfsww3 mc programs , which is able to provide constant - weight events , implements the @xmath1 corrections for @xmath2-pair production process and includes all of the background diagrams . the present new version 1.51 of the koralw program provides a programming framework for this new solution . contrary to the previous solution where koralw and yfsww3 were communicating through a disk file , here , variable - weight events from koralw are sent immediately , in real time , as an input to yfsww3 , using the `` named pipe '' of the fifo mechanism in the unix / linux operating system . yfsww3 calculates the @xmath1 correction weight and sends it back to koralw with the help of another `` named pipe '' of the fifo . afterward , koralw performs the final rejection according to the total mc weight and invokes hadronization , etc . the important advantage of the above method is that it provides the constant - weight events with the @xmath1 corrected @xmath2-pair process quite efficiently , including all the background diagrams , the higher - order isr corrections , the hadronization , etc . for the fifo - based solution , as compared with the disk - mediated solution mentioned earlier , _ no _ additional modifications of the fortran source codes of both programs are necessary . since koralw and yfsww3 run as two separate , concurrent processes , which communicate with one another , we call this solution a `` concurrent monte carlo ( cmc ) koralw@xmath4yfsww3 '' . from the user s point of view , it acts like a single mc program . to our knowledge , this could be the first important practical application , albeit rather simple , of the concept of `` concurrency '' in the area of the high energy physics monte carlo event generators . we shall also discuss very briefly possible future extensions / improvements of the above technique . the modifications of the yfsww3 program necessary for this technique are discussed in detail in @xcite and in this paper we shall describe them only to a minimum necessary extent . the second group of modifications included in koralw version 1.51 is motivated by the use of koralw to study the background to two - fermion processes due to the emission of a second fermion pair . in short , the modifications provide a number of approximate matrix elements , denoted according to ref . @xcite as isns , fsns , etc . , and a new `` extrapolation procedure '' better suited for the @xmath19-channel - dominated photonic radiation . the layout of the paper is as follows . in section 2 , we discuss various ways of merging koralw with yfsww3 . in particular we show how to do it by means of the fifo ( `` named pipes '' ) mechanism and discuss how to reweight previously generated events from tapes . in the section 3 , we provide some numerical tests of the cmc koralw@xmath4yfsww3 . in section 4 , we describe in detail all modifications of koralw version 1.51 related to the @xmath3 physics and the reweighting procedures , the two - fermion physics and miscellaneous topics , respectively . in section 5 , we explain how to install the version 1.51 of koralw and in section 6 we describe briefly the organization of the source code . in section 7 , we describe in detail various demo programs included in the package , with special emphasis on the practical use of the fifo ( `` named pipes '' ) mechanism and the construction of the concurrent monte carlo . we summarize the paper in section 8 . in an appendix , we describe new and modified program parameters .

the version 1.51 of the monte carlo ( mc ) program koralw for all processes is presented . may be modified in order to fit them to experimental data . another important new feature is the possibility of including complete corrections to double - resonant-pair component - processes in addition to all background ( non- ) graphs . the inclusion is done with the help of the yfsww3 mc event generator for fully exclusive differential distributions ( event per event ) . technically , it is done in such a way that yfsww3 runs concurrently with koralw as a separate slave process , reading momenta of the mc event generated by koralw and returning the correction weight to koralw . the latter introduces the correction using this weight , and finishes processing the event ( rejection due to total mc weight , hadronization , etc . ) . the communication between koralw and yfsww3 is done with the help of the fifo facility of the unix / linux operating system . * cern - th/2001 - 040 + uthep-01 - 0102 * the monte carlo program koralw version 1.51 and + the concurrent monte carlo koralwyfsww3 + with all background graphs and + first - order corrections to-pair production * s. jadach , * * w. paczek , * * m. skrzypek , * * b.f.l . ward * _ and _ * z. was * _cern , theory division , ch-1211 geneva 23 , switzerland , _ + _institute of nuclear physics , ul . kawiory 26a , 30 - 055 cracow , poland , _ + _department of physics and astronomy , + the university of tennessee , knoxville , tn 37996 - 1200 , usa _ + _ _ to be submitted to computer physics communications _ april 2001 * * new version summary * _ title of the program : _ koralw , version 1.51 . commun . * 94 * ( 1996 ) 215 ; * 119 * ( 1999 ) 272 0.2 cm _ computer : _ any computer with the fortran 77 compiler under unix or linux operating system 0.2 cm _ operating system : _ unix , linux version 6.x and 7.x 0.2 cm _ programming language used : _ fortran 77 0.2 cm _ high - speed storage required : _ 25 mb 0.2 cm _ keywords : _ + radiative corrections , initial - state radiation ( isr ) , electroweak ( ew ) corrections , leading - logarithmic ( ll ) approximation , heavy boson , four - fermion processes , monte carlo ( mc ) simulation / generation , quantum electrodynamics ( qed ) , quantum chromodynamics ( qcd ) , yennie frautschi suura ( yfs ) exponentiation , standard model ( sm ) , lep2 , next - generation linear colliders ( lc ) . 0.2 cm _ nature of the physical problem : _ + the precise study of-pair production and decay at lep2 requires both non - double - resonant and corrections . so far each of these corrections is available as a separate monte carlo program and there is no monte carlo that could simulate in a complete way both effects at the same time . such a mc event generator would be of importance for example for apparatus simulations or monte carlo based fits . the previous version of koralw included _ all _ non - double - resonant corrections to _ all _ double - resonant four - fermion processes in annihilation .

the version 1.51 of the monte carlo ( mc ) program koralw for all processes is presented . the most important change from the previous version 1.42 is the facility for writing mc events on the mass storage device and reprocessing them later on . in the reprocessing parameters of the standard model may be modified in order to fit them to experimental data . another important new feature is the possibility of including complete corrections to double - resonant-pair component - processes in addition to all background ( non- ) graphs . the inclusion is done with the help of the yfsww3 mc event generator for fully exclusive differential distributions ( event per event ) . technically , it is done in such a way that yfsww3 runs concurrently with koralw as a separate slave process , reading momenta of the mc event generated by koralw and returning the correction weight to koralw . the latter introduces the correction using this weight , and finishes processing the event ( rejection due to total mc weight , hadronization , etc . ) . the communication between koralw and yfsww3 is done with the help of the fifo facility of the unix / linux operating system . this does not require any modifications of the fortran source codes . from the user s point of view , the resulting concurrent mc event generator koralwyfsww3 looks as a regular single mc event generator with all the standard features . * cern - th/2001 - 040 + uthep-01 - 0102 * the monte carlo program koralw version 1.51 and + the concurrent monte carlo koralwyfsww3 + with all background graphs and + first - order corrections to-pair production * s. jadach , * * w. paczek , * * m. skrzypek , * * b.f.l . ward * _ and _ * z. was * _cern , theory division , ch-1211 geneva 23 , switzerland , _ + _institute of nuclear physics , ul . kawiory 26a , 30 - 055 cracow , poland , _ + _department of physics and astronomy , + the university of tennessee , knoxville , tn 37996 - 1200 , usa _ + _ slac , stanford university , stanford , ca 94309 , usa _ + _ institute of computer science , jagellonian university , + ul . nawojki 11 , cracow , poland _ _ to be submitted to computer physics communications _ * work supported in part by the polish government grant kbn 5p03b09320 , the us doe contracts de - fg05 - 91er40627 and de - ac03 - 76sf00515 , the european commission 5-th framework contract hprn - ct-2000 - 00149 , nato grant st.clg.977761 and the polish - french collaboration within in2p3 through lapp annecy . * cern - th/2001 - 040 + april 2001 * * new version summary * _ title of the program : _ koralw , version 1.51 . 0.2 cm _ reference to original program : _ comput . . commun . * 94 * ( 1996 ) 215 ; * 119 * ( 1999 ) 272 0.2 cm _ computer : _ any computer with the fortran 77 compiler under unix or linux operating system 0.2 cm _ operating system : _ unix , linux version 6.x and 7.x 0.2 cm _ programming language used : _ fortran 77 0.2 cm _ high - speed storage required : _ 25 mb 0.2 cm _ keywords : _ + radiative corrections , initial - state radiation ( isr ) , electroweak ( ew ) corrections , leading - logarithmic ( ll ) approximation , heavy boson , four - fermion processes , monte carlo ( mc ) simulation / generation , quantum electrodynamics ( qed ) , quantum chromodynamics ( qcd ) , yennie frautschi suura ( yfs ) exponentiation , standard model ( sm ) , lep2 , next - generation linear colliders ( lc ) . 0.2 cm _ nature of the physical problem : _ + the precise study of-pair production and decay at lep2 requires both non - double - resonant and corrections . so far each of these corrections is available as a separate monte carlo program and there is no monte carlo that could simulate in a complete way both effects at the same time . such a mc event generator would be of importance for example for apparatus simulations or monte carlo based fits . the previous version of koralw included _ all _ non - double - resonant corrections to _ all _ double - resonant four - fermion processes in annihilation . the present version 1.51 allows , for the first time ever , the inclusion on an _ event - per - event basis _ of the respective corrections generated at the same time by the independently running monte carlo program yfsww3 , as well as a reweighting of any earlier generated events with modified parameter sets . 0.2 cm _ method of solution : _ + the monte carlo method used to simulate the all four - fermion final - state processes in the collisions in the presence of multiphoton initial - state radiation has not changed since version 1.42 . adding the corrections generated by yfsww3 is done at the level of the unix / linux operating system with the help of the fifo mechanism ( `` named pipes '' ) . 0.2 cm _ restrictions on the complexity of the problem : _ + for koralw as in version 1.42 ; for koralwyfsww3 as in and . 0.2 cm _ typical running time : _ + approximate times on a pc pentium iii @ 800 mhz for cuts as described in this article : + 5 minutes per 1000 constant - weight ccall events ( koralw stand - alone ) + 50 minutes per 1000 constant - weight ccall events with the correction ( the cmc koralwyfsww3 , max . weight for rejection increased by a factor 2 ) .

1410.3422

i

the wiretap channel model @xmath0 was introduced by wyner in 1975 @xcite . in this model , there are two receivers @xmath1 and a single transmitter @xmath2 . the transmitter aims at sending messages to receiver 1 through a communication channel @xmath3 . the information sent from @xmath2 to @xmath4 is also received by receiver 2 through another channel @xmath5 . the transmission problem in the system @xmath6 calls for designing a coding system that supports communication between @xmath2 and @xmath4 in a way that is both reliable and secure . the reliability requirement is the usual one for communication systems , namely , that the error probability of decoding the information by @xmath4 be made arbitrarily low by increasing the block length of the encoding . at the same time , the transmission needs to be made secure in the sense that the information extracted by receiver 2 about the message of @xmath2 approaches zero as a function of the block length . to describe the problem in formal terms , denote the input alphabet of the transmitter by @xmath7 , and the output alphabets of the channels @xmath3 and @xmath5 by @xmath8 and @xmath9 , respectively . the messages that the transmitter can convey to receiver 1 form a finite set denoted below by @xmath10 for transmission over the channel the message is encoded using a mapping @xmath11 where @xmath12 is an @xmath13-fold repetition of the input alphabet . we say that @xmath14 is a length-@xmath13 block encoder of the transmitter . capacity - attaining schemes for the wiretap channel rely on randomized encoding , i.e. , a mapping that sends @xmath15 to a probability distribution on @xmath16 in other words , the message @xmath17 is encoded as a sequence @xmath18 with probability @xmath19 and the encoder is defined as a matrix of conditional probabilities @xmath20 the decoder of receiver 1 is a mapping @xmath21 . we also denote by @xmath22 and @xmath23 the conditional distributions induced by the channels @xmath3 and @xmath5 , respectively , and define the induced distributions @xmath24 where , for instance , @xmath25 , where @xmath26 and @xmath27 refer to the @xmath28-th symbol of the vectors @xmath29 and @xmath30 , respectively . [ def:1.1 ] we say that the encoder - decoder pair @xmath31 _ gives rise to @xmath32-transmission _ over the wiretap channel @xmath0 if [ wiretap_definition ] @xmath33 where @xmath34 is the message random variable ( rv ) and @xmath35 is the rv that corresponds to the observations of receiver 2 . in definition [ wiretap_definition ] , eq . represents the reliability of communication condition while answers the security of transmission requirement . we note that in many works on transmission with a secrecy constraint the security condition was formulated in a more relaxed way , namely as the inequality @xmath36 this is particularly true about pre-1990s works in information theory , but also applies to some very recent works on the wiretap channel , e.g. , @xcite . however , as shown by maurer in @xcite , this constraint does not fulfill the intuitive security requirements in the system . more specifically , it is possible to construct examples in which inequality is satisfied and at the same time receiver 2 is capable of learning @xmath37 out of @xmath13 bits of the encoding @xmath38 in view of this , maurer suggested as a better alternative to condition . as a result , currently is called the `` weak security constraint '' as opposed to the stronger constraint . in this paper we design coding schemes that provide strong secrecy , so below we work only with condition . the secrecy capacity of the wiretap channel is defined as follows . [ def:1.2 ] the value @xmath39 is called an achievable rate for the wiretap channel @xmath0 if there exists a sequence of message sets @xmath40 and encoder - decoder pairs @xmath41 giving rise to @xmath42 transmission with @xmath43 and @xmath44 as @xmath45 . the secrecy capacity @xmath46 is the supremum of achievable rates for the wiretap channel . the following theorem provides an expression for @xmath46 . [ thm : dg ] ( @xcite ; see also @xcite ) the secrecy capacity of the wiretap channel @xmath0 equals @xmath47 , \label{eq : cs}\ ] ] where the maximum is computed over all rvs @xmath48 such that the markov condition @xmath49 holds true , and such that @xmath50 , @xmath51 . while most general constructive coding schemes for the wiretap channels rely on polar codes , there were some constructive solutions even before the publication of arikan s seminal work @xcite . at the same time , these schemes applied only to some special cases of the channels @xmath52 for instance the case when @xmath3 is noiseless and @xmath5 is a binary erasure channel was addressed in @xcite which show that in this case the capacity @xmath46 can be achieved using low - density parity - check codes . the results in @xcite are based on the weak security assumption while strong security is considered in @xcite . moreover , @xcite extends the construction to the cases when both @xmath3 and @xmath5 are erasure channels , and when @xmath3 is noiseless and @xmath5 is a binary symmetric channel . as usual with the application of low - density codes , the constructions are based on code ensembles and strictly speaking are not explicit . another special case of the wiretap channel relates to the combinatorial version of the erasure channel ( the so - called wiretap channel of type ii ) in which receiver 2 can choose to observe any @xmath53 symbols out of @xmath13 transmitted symbols . constructive capacity - achieving solutions for this case are based on mds codes @xcite or extractors @xcite . in @xcite , it is shown that @xmath46 is achievable with strong security using invertible extractors , if both @xmath3 and @xmath5 are binary symmetric channels . both encoding and decoding algorithms in @xcite have polynomial complexity . moreover , @xcite also claims that its proof method can be easily extended to other wiretap channels as long as both @xmath3 and @xmath5 are symmetric . after the introduction of polar codes by arikan , achieving @xmath46 via polar coding has been considered by different works , mostly under the degradedness assumption . recall that a channel @xmath54 is called _ degraded _ with respect to a channel @xmath55 if there exists a stochastic @xmath56 matrix @xmath57 such that for all @xmath58 @xmath59 the wiretap channel @xmath60 is called degraded if the channel to the eavesdropper is degraded with respect to the main channel . in this case theorem [ thm : dg ] affords a simpler formulation because there is no need in the auxiliary rv @xmath61 . namely , in the degraded case the secrecy capacity equals ( * ? ? ? * probl . 17.8 ) @xmath62 ( this specialization is true under slightly more general assumptions , but we will not need them below ) . communication over degraded wiretap channels using polar codes was considered in a number of papers , notably , @xcite . the main result of these works is that secrecy capacity can be attained under the weak security constraint . we note that the degraded case is easier to handle with polar codes because of the specific nature of the polar codes construction ( more on this below in sect . [ sect : closer ] ) . another step was made by @xcite which suggested a polar coding scheme that attains the rate @xmath46 of a symmetric degraded wiretap channel @xmath0 under the strong security requirement . more details about the results of @xcite are given in sect . [ sect : closer ] below . the problem of attaining secrecy capacity of the general wiretap channel under the strong secrecy condition and without the degradedness assumption was further studied in @xcite . a polar coding scheme suggested in this work attains a transmission rate of @xmath63.$ ] clearly @xmath64 for all @xmath2 since one can take @xmath65 in the markov chain @xmath66 which appears in theorem [ thm : dg ] . it is not immediately clear for which channels the result of @xcite actually attains the secrecy capacity of @xmath67 at the same time , the coding scheme employed in @xcite relies on two nested layers of the polarizing transform . the decoder for the second ( outer ) layer works with the probability distribution generated by the first decoder , which is not easily computable . thus , the low complexity decoding claim of the construction made in @xcite is not supported by the known decoding procedures for polar codes . for these reasons the construction in @xcite does not resolve the question of constructing an explicit capacity - achieving scheme for the nondegraded case of wiretap channels . in related works @xcite the problem of constructing capacity achieving schemes for wiretap channels was addressed for the case of quantum channels . the constructions suggested in these works attain symmetric secrecy capacity of quantum wiretap channels . these constructions require a shared secret key between the transmitter and receiver 1 . this requirement seems to be intrinsic to polar code constructions for this problem including our work . however the constructions in @xcite require a positive - rate shared key , which results in a communication scheme that transmits at rates separated from capacity . to summarize , to the best of our knowledge the question of constructing explicit capacity - achieving transmission schemes for the non - degraded wiretap channel with strong secrecy is an open problem . it is this problem that we aim to solve in this paper by removing the degradedness assumption . we also do not assume that either of the channels @xmath68 is symmetric . the main idea of our work is to exploit the markov chain conditions intrinsic to secure communication problems using polar codes . in section [ sect : wt ] we propose a polar coding scheme that attains the secrecy capacity under the strong security assumption . both the encoding and decoding complexity estimates of our construction are @xmath69 , where @xmath13 is the length of the encoding . in section [ csiszar - korner ] we generalize our construction to cover the case when a part of transmitter s message is public , i.e. , is designed to be conveyed both to receivers 1 and 2 . this model , called a broadcast channel with confidential messages , is in fact the principal model in the founding work of csiszr and krner @xcite on this topic . apart from the basic polar coding results @xcite , our solution of the described problems relies on the previous work on the wiretap channel @xcite , the polar coding scheme for the broadcast channel of @xcite , and the construction of polar codes for general memoryless channels in @xcite . a new idea introduced in our solution is related to a stochastic encoding scheme that emulates the random coding proof of the capacity theorem in @xcite , whereby polarization is used for the values of the auxiliary random variable @xmath61 in theorem [ thm : dg ] , followed by a stochastic encoding into a channel codeword . another insight , which is particularly useful for the broadcast channel result in sect . [ sect : bcc ] , is related to a partition of the coordinates of the transmitted block that enables simultaneous decoding of different parts of the transmitted message by both receivers , whereby the decoder of polar codes is used by the receivers according to their high- and low - entropy bits . it becomes possible to show that the receivers recover the bits designed to communicate with each of them with high probability , and that the secret part of the message is not accessible to the unintended recipient .

explicit capacity - achieving schemes for various models of the wiretap channel have received considerable attention in recent literature . in this paper research supported in part by nsf grant ccf1217245 ] department of ece and institute for systems research , university of maryland , college park , md 20742 , and iitp , russian academy of sciences , moscow , russia . email : [email protected] . + the results of this paper were presented in part at the ieee information theory workshop , jerusalem , israel , april 27-may 1 , 2015 . ] * _ _ * index terms : polar codes , chaining construction , strong secrecy , coordinate partition .

the wiretap channel model of wyner is one of the first communication models with both reliability and security constraints . explicit capacity - achieving schemes for various models of the wiretap channel have received considerable attention in recent literature . in this paper , we address the original version of this problem , showing that capacity of the general ( not necessarily degraded or symmetric ) wiretap channel under a `` strong secrecy constraint '' can be achieved using a transmission scheme based on polar codes . we also extend our construction to the case of broadcast channels with confidential messages defined by csiszr and krner , achieving the entire capacity region of this communication model . department of ece and institute for systems research , university of maryland , college park , md 20742 , email : [email protected] . research supported in part by nsf grant ccf1217245 ] department of ece and institute for systems research , university of maryland , college park , md 20742 , and iitp , russian academy of sciences , moscow , russia . email : [email protected] . research supported in part by nsf grants ccf1217245 , ccf1217894 , and ccf1422955 . + the results of this paper were presented in part at the ieee information theory workshop , jerusalem , israel , april 27-may 1 , 2015 . ] * _ _ * index terms : polar codes , chaining construction , strong secrecy , coordinate partition .

astro-ph9512143

i

a few years ago , we started a project to determine ages , metallicities , and reddenings of distinct stellar populations employing a newly developed technique of simultaneous multi - colour isochrone fitting ( roberts 1996 , grebel et al . when applying this technique to the young cluster ngc 330 in the small magellanic cloud ( smc ) , we found a number of stars above the main - sequence turnoff , as indicated by our isochrone fit , but below the location of the blue supergiants ( sect . [ sect_photdata ] ) . when only photometric data are available , these bright blue stars would usually be considered main - sequence stars , which implies that either the cluster is much younger than our simultaneous multi - colour isochrone fit shows or forces the conclusion that there is a considerable age spread in star formation times . spectroscopy is needed in order to investigate the nature of these stars . we therefore obtained spectra to properly classify these stars ( sect . [ n330data ] ) . llllllccclll & & & & above & + arp & rob & fb & cjf & lmpbc & this study & v [ mag ] & b v [ mag ] & ms ? & & & + ii-13 & a1 & & & b0.5 iii / ve & b0 - 1 iii & @xmath0&@xmath1 & y & 145 & & @xmath2 + ii-14 & a2 & b5 i & b6 i & b4 ib & b5 i & @xmath3&@xmath4 & y & @xmath5 & @xmath6 & + ii-31 & a4 & & & & b2 - 3 iie & @xmath7&@xmath8 & y & 144 & & + ii-16 & a16&b9 i & a2 i & & & @xmath9&@xmath10 & y & @xmath11 & @xmath12 & + ii-33 & a25&a1 i & a0 i & & & @xmath13&@xmath14 & y & @xmath15 & @xmath16 & + ii-40 & a29&b9 i & & & & @xmath17&@xmath18 & y & @xmath19 & & + ii-35 & a47&b9 i & & & & @xmath20&@xmath21 & y & @xmath22 & & + i-243 & b2 & & a7 i & & & @xmath23&@xmath24 & y & & @xmath25 & + i-235 & b4 & & & b2 iiie & & @xmath26&@xmath27 & n & & & @xmath28 + i-234 & b5 & & & b2 iiie & & @xmath29&@xmath30 & n & & & + i-233 & b6 & & & b2 iiie & & @xmath31&@xmath32 & n & & & + i-232 & b7 & & & b2 iiie & & @xmath33&@xmath34 & n & & & + i-223 & b11 & & & a0 ii & & @xmath35&@xmath36 & n & & & + i-47 & b12 & & & b2 iiie & & @xmath37&@xmath38 & y & 154 & & + ii-28 & b13 & & & b2 iii / ive & & @xmath39&@xmath40 & n & 138 & & + i-222 & b16 & & a0 i & a0 ii & b9/a0 ib & @xmath41&@xmath42 & y & & & + i-204 & b18 & & & o9 iii / ve & & @xmath43&@xmath44 & n & & & + ii-46 & b21 & & b4e , n & b2.5 iie & & @xmath45&@xmath46 & y & & @xmath47 & + ii-45 & b22 & & & b2 iie & b3 ii & @xmath48&@xmath49 & y & @xmath50 & @xmath51 & + i - f & b24 & & & b2 iiie & b1 i ve & @xmath52&@xmath53 & y & & & + & b28 & & & b0.2 iiie & & @xmath54&@xmath55 & n & & & + ii-1 & b29&a0 i & a1 i & & & @xmath56&@xmath57 & y & @xmath58 & @xmath59 & + ii-3 & b30 & & b6 i & b2 ii & b1 ii & @xmath60&@xmath61 & y & @xmath62 & @xmath63 & + ii-4 & b33 & & & & b2 - 3 ve & @xmath64&@xmath65 & n & & & + & b35 & & & b2 iiie & & @xmath66&@xmath67 & y & & & + ii-8 & b37&b5 i & b5 i & b3 ib & & @xmath68&@xmath69 & y & @xmath70 & @xmath71 & + ii-9 & b38&a1 i & a5 i & & & @xmath72&@xmath73 & y & @xmath74 & @xmath75 & + i - c & & & & & b8 ii & @xmath76&@xmath77 & y & & & + i-201 & & & a1 i & & & @xmath78&@xmath79 & y & & @xmath80 & + i-206 & & & & & b9 ii & @xmath81&@xmath82 & y & & & + i-207 & & & & & b8 iii & @xmath83&@xmath84 & y & & & + i-211 & & & a0 i & & & @xmath85&@xmath86 & y & & @xmath87 & + i-218 & & & & & b1 v & @xmath88&@xmath89 & n & & & + i-219 & & & & & b9/a0 iii & @xmath90&@xmath91 & y & & & + i-220 & & & & & b3 iii - iv & @xmath92&@xmath93 & y & & & + in addition to our own spectral classifications we make use of previously published classifications ( sect . [ sect_specresults ] ) . these classifications and determinations of surface gravities and effective temperatures place these stars where one would not expect to find so many : in the post main - sequence gap of the hertzsprung - russell diagram ( h - r diagram ) . in the following , we define main - sequence stars as stars in the core h burning phase . when talking about `` ordinary '' main - sequence stars we are referring to stars undergoing the usual , undisturbed main - sequence evolution typical for single stars , to which also the geneva evolutionary tracks pertain . according to these models , an ordinary main - sequence star in the turnoff region of a 20-myr isochrone has a @xmath94 value of 3.7 to 3.8 . of course neither of these values nor a mere spectral classification alone can tell whether a star is core h burning or not . we shall refer to the area redward of the main sequence as post main - sequence gap or blue hertzsprung gap . this area lies between the terminal - age main sequence ( tams ) and the area where the blue loops of the supergiants occur . precise size and location of the gap depend on the stellar models used . according to stellar evolution theory , this region is traversed very quickly ( see , e.g. , langer & maeder 1995 for time scales ) making it highly unlikely to find a large number of stars there , or even any stars . in sect . [ sectbg_giants ] and [ sectbg_ms ] we discuss whether the blue stars above the main - sequence turnoff and below the blue supergiant locus are evolved stars or main - sequence stars . in sect . [ sect_exception ] we review indications that ngc 330 is not an exception among young magellanic cloud clusters in containing blue giants . the implications for the upper imf and age determinations are discussed in sect . [ sect_imf ] and [ sect_age ] .

the young smc cluster ngc 330 contains a number of blue stars that lie above the main - sequence turnoff found from our isochrone fitting and below the position of the blue supergiants . these stars lie in the rapidly traversed post main - sequence gap , similar to the unexpected concentration found by fitzpatrick & garmany ( 1990 ) in the h - r diagram of the lmc .

the young smc cluster ngc 330 contains a number of blue stars that lie above the main - sequence turnoff found from our isochrone fitting and below the position of the blue supergiants . we used our own , new spectroscopy and published data on these stars to investigate their possible nature . problems in interpreting the evolutionary status of the blue giants have been found in several preceding studies . in theoretical h - r diagrams , these stars lie in the rapidly traversed post main - sequence gap , similar to the unexpected concentration found by fitzpatrick & garmany ( 1990 ) in the h - r diagram of the lmc . we argue that these stars probably are core h burning main - sequence stars that appear as blue stragglers resulting from binary evolution as described in the simulations of pols & marinus ( 1994 ) and effects of rapid rotation . many of the blue stragglers are be stars and likely rapid rotators . we suggest that there is evidence for the presence of blue stragglers also in ngc 1818 , ngc 2004 , and ngc 2100 . we point out that blue stragglers may be a general phenomenon in the cmds of young clusters in the magellanic clouds and discuss the implications for imf and age determinations . = 2.5 cm

1103.4591

i

this article is part of a larger program , which consists in devising and quantitatively analyzing numerical methods to approximate effective coefficients in stochastic homogenization of linear elliptic equations . more precisely we tackle here the case of a discrete elliptic equation with independent and identically distributed coefficients ( see however the end of this introduction for more general statistics ) , and present and fully analyze an approximation procedure based on a monte - carlo method . a first possibility to approximate effective coefficients is to directly solve the so - called corrector equation . in this approach , a first step towards the derivation of error estimates is a quantification of the qualitative results proved by knnemann @xcite ( and inspired by papanicolaou and varadhan s treatment of the continuous case @xcite ) and kozlov @xcite . in the stochastic case , such an equation is posed on the whole @xmath3 , and we need to localize it on a bounded domain , say the hypercube @xmath4 of side @xmath5 . as shown in a series of papers by otto and the first author @xcite , and the first author @xcite , there are three contributions to the @xmath6-error in probability between the true homogenized coefficients and its approximation . the dominant error in small dimensions takes the form of a variance : it measures the fact that the approximation of the homogenized coefficients by the average of the energy density of the corrector on a box @xmath4 fluctuates . this error decays at the rate of the central limit theorem @xmath7 in any dimension ( with a logarithmic correction for @xmath8 ) . the second error is the so - called systematic error : it is due to the fact that we have modified the corrector equation by adding a zero - order term of strength @xmath9 ( as standard in the analysis of the well - posedness of the corrector equation ) . the scaling of this error depends on the dimension and saturates at dimension @xmath10 . it is of higher order than the random error up to dimension @xmath11 . the last error is due to the use of boundary conditions on the bounded domain @xmath4 . provided there is a buffer region , this error is exponentially small in the distance to the buffer zone measured in units of @xmath12 . this approach has two main drawbacks . first the numerical method only converges at the central limit theorem scaling in terms of @xmath13 up to dimension @xmath11 , which is somehow disappointing from a conceptual point of view ( although this is already fine in practice ) . second , although the size of the buffer zone is roughly independent of the dimension , its cost with respect to the central limit theorem scaling dramatically increases with the dimension ( recall that in dimension @xmath14 , the clt scaling is @xmath7 , so that in high dimension , we may consider smaller @xmath13 for a given precision , whereas the use of boundary conditions requires @xmath15 in any dimension ) . based on ideas of the second author in @xcite , we have taken advantage of the spectral representation of the homogenized coefficients ( originally introduced by papanicolaou and varadhan to prove their qualitative homogenization result ) in order to devise and analyze new approximation formulas for the homogenized coefficients in @xcite . in particular , this has allowed us to get rid of the restriction on dimension , and exhibit refinements of the numerical method of @xcite which converge at the central limit theorem scaling in any dimension ( thus avoiding the first mentioned drawback ) . unfortunately , the second drawback is inherent to the type of method used : if the corrector equation has to be solved on a bounded domain @xmath4 , boundary conditions need to be imposed on the boundary @xmath16 . since their values are actually also part of the problem , a buffer zone seems mandatory with the notable exception of the periodization method , whose analysis is yet still unclear to us , especially when spatial correlations are introduced in the coefficients . in order to avoid the issue of boundary conditions , we adopt here another point of view on the problem : the random walk in random environment approach . this other point of view on the same homogenization problem has been analyzed in the celebrated paper @xcite by kipnis and varadhan , and then extended by de masi , ferrari , goldstein , and wick @xcite . the strategy of the present paper is to obtain an approximation of the homogenized coefficients by the numerical simulation of this random walk up to some large time . as we did in the case of the approach based on the corrector equation , a first step towards the analysis of this numerical method is to quantify the corresponding qualitative result , namely here kipnis - varadhan s convergence theorem . compared to the deterministic approach based on the approximate corrector equation , the advantage of the present approach is that its convergence rate and computational costs are dimension - independent . as we shall also see , as opposed to the approach based on the corrector equation , the environment only needs to be generated along the trajectory of the random walker , so that much less information has to be stored during the calculation . this may be quite an important feature of the monte carlo method in view of the discussion of ( * ? ? ? * section 4.3 ) . we consider the discrete elliptic operator @xmath17 , where @xmath18 and @xmath19 are the discrete backward divergence and forward gradient , respectively . for all @xmath20 , @xmath21 is the diagonal matrix whose entries are the conductances @xmath22 of the edges @xmath23 starting at @xmath24 , where @xmath25 denotes the canonical basis of @xmath3 . let @xmath26 denote the set of edges of @xmath3 . we call the family of conductances @xmath27 the _ environment_. the environment @xmath28 is random , and we write @xmath29 for its distribution ( with corresponding expectation @xmath30 ) . we make the following assumptions : * the measure @xmath29 is invariant under translations , * the conductances are i. i. d. , * there exists @xmath31 such that @xmath32 almost surely . under these conditions , standard homogenization results ensure that there exists some _ deterministic _ symmetric matrix @xmath33 such that the solution operator of the deterministic continuous differential operator @xmath34 describes the large scale behavior of the solution operator of the random discrete differential operator @xmath17 almost surely ( for this statement , ( h2 ) can in fact be replaced by the weaker assumption that the measure @xmath29 is ergodic with respect to the group of translations , see @xcite ) . the operator @xmath35 is the infinitesimal generator of a stochastic process @xmath36 which can be defined as follows . given an environment @xmath28 , it is the markov process whose jump rate from a site @xmath20 to a neighbouring site @xmath37 is given by @xmath38 . we write @xmath39 for the law of this process starting from @xmath20 . it is proved in @xcite that under the averaged measure @xmath40 , the rescaled process @xmath41 converges in law , as @xmath42 tends to @xmath43 , to a brownian motion whose infinitesimal generator is @xmath34 , or in other words , a brownian motion with covariance matrix @xmath44 ( see also @xcite for prior results ) . we will use this fact to construct computable approximations of @xmath33 . as proved in @xcite , this invariance principle holds as soon as ( h1 ) is true , ( h2 ) is replaced by the ergodicity of the measure @xmath29 , and ( h3 ) by the integrability of the conductances . under the assumptions ( h1-h3 ) , @xcite strengthens this result in another direction , showing that for almost every environment , @xmath41 converges in law under @xmath45 to a brownian motion with covariance matrix @xmath44 . this has been itself extended to environments which do not satisfy the uniform ellipticity condition ( h3 ) , see @xcite . let @xmath46 denote the sequence of consecutive sites visited by the random walk @xmath47 ( note that the `` times '' are different in nature for @xmath48 and @xmath49 ) . this sequence is itself a markov chain that satisfies for any two neighbours @xmath50 : @xmath51 = \frac{\omega_{x , y}}{p_\omega(x)},\ ] ] where @xmath52 . we simply write @xmath53 for @xmath54 . let us introduce a `` tilted '' version of the law @xmath29 on the environments , that we write @xmath55 and define by @xmath56 } \ \d { \mathbb{p}}(\omega).\ ] ] the reason why this measure is natural to consider is that it makes the environment seen from the position of the random walk @xmath57 a stationary process ( see ( [ defenvpart ] ) for a definition of this process ) . interpolating between two integers by a straight line , we can think of @xmath57 as a continuous function on @xmath58 . with this in mind , it is also true that there exists a matrix @xmath59 such that , as @xmath42 tends to @xmath43 , the rescaled process @xmath60 converges in law under @xmath61 to a brownian motion with covariance matrix @xmath62 . moreover , @xmath59 and @xmath33 are related by ( see ( * ? ? ? * theorem 4.5 ( ii ) ) ) : @xmath63 \ { a_\mathrm{hom}^\mathrm{disc}}.\ ] ] given that the numerical simulation of @xmath57 saves some operations compared to the simulation of @xmath64 ( there is no waiting time to compute , and the running time is equal to the number of steps ) , we will focus on approximating @xmath59 . more precisely , we fix once and for all some @xmath65 with @xmath66 , and define @xmath67 , \qquad \sigma^2 = 2 \xi \cdot { a_\mathrm{hom}^\mathrm{disc}}\xi.\ ] ] it follows from results of @xcite ( or ( * ? ? ? * theorem 2.1 ) ) that @xmath68 tends to @xmath69 as @xmath1 tends to infinity . our first contribution is to give a quantitative estimate of this convergence . in particular we shall show that , with i. i. d. coefficients and up to a logarithmic correction in dimension @xmath70 , the difference between @xmath68 and @xmath69 is of order @xmath71 . we now describe a monte - carlo method to approximate @xmath68 . using the definition of the tilted measure ( [ deftdp ] ) , one can see that @xmath72}{t } = \frac{{\mathbb{e}}{\mathbf{e}^\omega}_0[p(\omega ) ( \xi \cdot y(t))^2]}{t { \mathbb{e}}[p]}.\ ] ] assuming that we have easier access to the measure @xmath29 than to the tilted @xmath55 , we prefer to base our monte - carlo procedure on the r. h. s. of the second identity in ( [ enlevetilt ] ) . let @xmath73 be independent random walks evolving in the environments @xmath74 respectively . we write @xmath75 for their joint distribution , all random walks starting from @xmath43 , where @xmath76 stands for @xmath77 . the family of environments @xmath76 is itself random , and we let @xmath78 be the product distribution with marginal @xmath29 . in other words , under @xmath78 , the environments @xmath79 are independent and distributed according to @xmath29 . our computable approximation of @xmath68 is defined by @xmath80 the following step in the analysis is to quantify the random fluctuations of @xmath81 in terms of @xmath2 the number of random walks considered in the empirical average to approximate @xmath68 and @xmath1 . we shall prove a large deviation result which ensures that the @xmath82-probability that the difference between @xmath81 and @xmath68 exceeds @xmath71 is exponentially small in the ratio @xmath83 . the rest of this article is organized as follows . in section [ sec : quantkv ] , which can be read independently of the rest of the paper , we consider a general discrete or continuous - time reversible markov process . kipnis - varadhan s theorem ( and its subsequent development due to @xcite ) gives conditions for additive functionals of this process to satisfy an invariance principle . we show that , under additional conditions written in terms of a spectral measure , the statement can be made quantitative . more precisely , kipnis - varadhan s theorem relies on writing the additive functional under consideration as the sum of a martingale plus a remainder . this remainder , after suitable normalization , is shown to converge to @xmath43 in @xmath6 . under our additional assumptions , we give explicit bounds on the rate of decay . in section [ sec : syserr ] , we make use of this result , in the context of the approximation of homogenized coefficients , to estimate the systematic error @xmath84 . the central achievement of this section is to prove that the relevant spectral measure satisfies the conditions of our quantitative version of kipnis - varadhan s theorem . section [ sec : randfluc ] is dedicated to the estimate of the random fluctuations . these are controlled through large deviations estimates . relying on these results , we give in section [ sec : numtest ] a complete error analysis of the monte - carlo method to approximate the homogenized matrix @xmath59 , which we illustrate by numerical tests . let us quickly discuss the sharpness of these results . if @xmath85 was a periodic matrix ( or even a constant matrix ) the systematic error would also be of order @xmath71 ( without logarithmic correction for @xmath8 ) , and the fluctutations would decay exponentially fast in the ratio @xmath83 as well . this shows that our analysis is optimal ( the additional logarithm seems unavoidable for @xmath8 , as discussed in the introduction of @xcite ) . let us also point out that although the results of this paper are proved under assumptions ( h1)-(h3 ) , the assumption ( h2 ) on the statistics of @xmath28 is only used to obtain the variance estimate of ( * ? ? ? * lemma 2.3 ) . in particular , ( h2 ) can be weakened as follows : * the distribution of @xmath86 may in addition depend on @xmath87 , * independence can be replaced by finite correlation length @xmath88 , that is for all @xmath89 , @xmath90 and @xmath91 are independent if @xmath92 , * independence can be replaced by mixing in the sense of dobrushin and shlosman we refer the reader to work in progress by otto and the first author for this issue @xcite . * notation . * so far we have already introduced the probability measures @xmath45 ( distribution of @xmath57 ) , @xmath75 ( distribution of @xmath93 ) , @xmath29 ( i.i.d . distribution for @xmath27 ) , @xmath55 ( tilted measure defined in ( [ deftdp ] ) ) and @xmath78 ( product distribution of @xmath76 with marginal @xmath29 ) . it will be convenient to define @xmath94 the product distribution of @xmath76 with marginal @xmath55 . for convenience , we write @xmath95 as a short - hand notation for @xmath40 , @xmath96 for @xmath61 , @xmath97 for @xmath98 , and @xmath99 for @xmath100 . the corresponding expectations are written accordingly , replacing `` p '' by `` e '' with the appropriate typography . finally , we write @xmath101 for the euclidian norm of @xmath102 .

this article is devoted to the analysis of a monte - carlo method to approximate effective coefficients in stochastic homogenization of discrete elliptic equations . we consider the case of independent and identically distributed coefficients , and adopt the point of view of the random walk in a random environment . given some final time , a natural approximation of the homogenized coefficients is given by the empirical average of the final squared positions rescaled by of independent random walks in independent environments . relying on a new quantitative version of kipnis - varadhan s theorem ( which is of independent interest ) , we first give a sharp estimate of the error between the homogenized coefficients and the expectation of the rescaled final position of the random walk in terms of . we then complete the error analysis by quantifying the fluctuations of the empirical average in terms of and , and prove a large - deviation estimate . compared to other numerical strategies , this monte - carlo approach has the advantage to be dimension - independent in terms of convergence rate and computational cost . * keywords : * random walk , random environment , stochastic homogenization , effective coefficients , monte - carlo method , quantitative estimates . * 2010 mathematics subject classification : * 35b27 , 60k37 , 60h25 , 65c05 , 60h35 , 60g50 .

this article is devoted to the analysis of a monte - carlo method to approximate effective coefficients in stochastic homogenization of discrete elliptic equations . we consider the case of independent and identically distributed coefficients , and adopt the point of view of the random walk in a random environment . given some final time , a natural approximation of the homogenized coefficients is given by the empirical average of the final squared positions rescaled by of independent random walks in independent environments . relying on a new quantitative version of kipnis - varadhan s theorem ( which is of independent interest ) , we first give a sharp estimate of the error between the homogenized coefficients and the expectation of the rescaled final position of the random walk in terms of . we then complete the error analysis by quantifying the fluctuations of the empirical average in terms of and , and prove a large - deviation estimate . compared to other numerical strategies , this monte - carlo approach has the advantage to be dimension - independent in terms of convergence rate and computational cost . * keywords : * random walk , random environment , stochastic homogenization , effective coefficients , monte - carlo method , quantitative estimates . * 2010 mathematics subject classification : * 35b27 , 60k37 , 60h25 , 65c05 , 60h35 , 60g50 .

math0508330

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this paper addresses reduction theory for discrete mechanical systems with abelian symmetry groups and its relation to variational integration . to establish the setting of the problem , a few aspects of the continuous theory are first recalled ( see @xcite for general background ) . * continuous reduction theory . * consider a mechanical system with configuration manifold @xmath1 and a symmetry group @xmath2 ( with lie algebra @xmath3 ) acting freely and properly on @xmath1 and hence , by cotangent lift on @xmath4 , with corresponding ( standard , equivariant ) momentum map @xmath5 . recall from reduction theory ( see @xcite , and references therein ) that , under appropriate regularity and nonsingularity conditions , the flow of a @xmath2-invariant hamiltonian @xmath6 naturally induces a hamiltonian flow on the reduced space @xmath7 , where @xmath8 is the isotropy subgroup of a chosen point @xmath9 . in the abelian case , if one chooses a connection @xmath10 on the principal bundle @xmath11 , then @xmath12 is symplectically isomorphic to @xmath13 carrying the canonical symplectic structure modified by magnetic terms ; that is terms induced from the @xmath14-component of the curvature of @xmath10 . the lagrangian version of this theory is also well - developed . in the abelian case , it goes by the name of _ routh reduction _ , ( see , for instance @xcite , 8.9 ) . the reduced equations are again equations on @xmath15 and are obtained by dropping the variational principle , expressed in terms of the routhian , from @xmath1 to @xmath16 . the nonabelian version of this theory was originally developed in @xcite , with important contributions and improvements given in @xcite . of course , reduction has been enormously important for many topics in mechanics , such as stability and bifurcation of relative equilibria , integrable systems , etc . we need not review the importance of this process here as it is extensively documented in the literature . * purpose , main results , and examples . * this paper presents the theory and illustrative numerical implementation for the reduction of discrete mechanical systems with abelian symmetry groups . the discrete reduced space has a similar structure as in the continuous theory , but the curvature will be taken in a discrete sense . the paper studies two examples in detail , namely satellite dynamics in the presence of the bulge of the earth ( the @xmath17 effect ) and the double spherical pendulum ( which has a nontrivial magnetic term ) . in each case the benefit of studying the numerics of the reduced problem is shown . roughly , the reduced computations reveal dynamical structures that are hard to pick out in the unreduced dynamics in a way that is reminiscent of the phenomena of pattern evocation , as in @xcite . another interesting application of the theory is that of orbiting multibody systems , studied in @xcite . we refer to @xcite for a review of discrete mechanics , its numerical implementation , some history , as well as references to the literature . the value of geometric integrators has been documented in a number of references , such as @xcite . in the present paper , we shall focus , to be specific , on discrete euler lagrange and variational symplectic runge - kutta schemes and their reductions . one could , of course , use other schemes as well , such as newmark , strmer - verlet , or shake schemes . however , we wish to emphasize that _ without theoretical guidelines , coding algorithms for the reduced dynamics need not be a routine procedure since the reduced equations are not in canonical form because of nontrivial magnetic terms_. for example , using darboux theorem to put the structure into canonical form so that standard algorithms can be used is not practical . we also remind the reader that there are real advantages to taking the variational approach to the construction of symplectic integrators . for example , as in @xcite , the variational approach provides the design flexibility to take different time steps at spatially different points in an asynchronous way and still retain all the advantages of symplecticity even though the algorithms are not strictly symplectic in the naive sense ; such an approach is well - known to be useful in molecular systems , for instance . * motivation for discrete reduction . * besides its considerable theoretical interest , there are several practical reasons for carrying out discrete routh reduction . these are as follows : 1 . features that are clear in the reduced dynamics , such as relative equilibria and relative periodic orbits , can be obscured in the unreduced dynamics , and appear more complicated through the process of reconstruction and associated geometric phases . this is related to the phenomenon of _ pattern evocation _ that is an important practical feature of many examples , such as the double spherical pendulum @xcite and the stepping pendulum @xcite . going to a suitable ( but non - obvious ) rotating frame can `` evoke '' such phenomena ( see the movie at http://www.cds.caltech.edu/~marsden/research/demos/movies/wendlandt/pattern.mpg ) . this is essentially a window to the reduced dynamics , which the theory in the present paper allows one to compute directly . 2 . while directly studying the reduced dynamics can yield some benefits , it can be difficult to code using traditional methods . in particular , the presence of magnetic terms in the reduced symplectic form , as is the case with the double spherical pendulum , means that traditional symplectic methods for canonical systems do not directly apply ; if one attempts to do so , it may result ( and has in the literature ) in many inefficient coordinate changes when evoking darboux theorem to put things into canonical form . although simulating the reduced dynamics involves an initial investment of time in computing geometric quantities symbolically , these additional terms do not appreciably affect the sparsity of the system of equations to be solved . as such , direct coding of the reduced algorithms can be quite efficient , due to its reduced dimensionality . * two obvious generalizations . * the free and proper assumption that we make on the group action means that we are dealing with _ nonsingular _ , that is , _ regular _ reduction ( see @xcite for the general theory of singular reduction and references to the literature ) . it would be interesting to extend the work here to the case of singular reduction but already the regular case is nontrivial and interesting . while our examples have singular points and the dynamics near these points is interesting , there is no attempt to study this aspect in the present paper . secondly , it would be interesting to generalize the present work to the case of nonabelian groups and to develop a discrete version of nonabelian routh reduction , ( as in @xcite ) . we believe that such a generalization will require the further development of the theory of discrete connections , which is currently part of the research effort on discrete differential geometry ( see @xcite , and references therein . ) other future directions are discussed in the conclusions . * other discrete reduction results . * we briefly summarize some related results that have been obtained in the area of reduction for discrete mechanics . first of all , there is the important case of _ discrete euler - poincar and lie - poisson reduction _ that were obtained in @xcite . this theory is appropriate for rigid body mechanics , for instance . another important case is that of _ discrete semidirect product reduction _ that was obtained in @xcite and applied to the case of the heavy top , with interesting links to discrete elastica . this case is of interest in the present study since the heavy top , as with the general theory of semidirect product reduction ( see @xcite ) , one can view the @xmath18 reduction of this problem as routh reduction . linking these two approaches is an interesting topic for future research . * outline . * after recalling the notation from continuous reduction theory , [ s - disred ] develops discrete reduction theory , derives a reduced variational principle , and proves the symplecticity of the reduced flow . the relationship between continuous- and discrete - time reduction is also discussed . how the variational ( and hence symplectic ) runge - kutta algorithm induces a reduced algorithm in a natural way is shown in [ s - srkred ] . in [ s - summary ] we put together in a coherent way the main theoretical results of the paper up to that point . in [ s - examples ] the numerical example of satellite dynamics about an oblate earth is given , and in [ s - examples - dsp ] , the example of the double spherical pendulum , which has a non - trivial magnetic term , is given . lastly , in [ s - computational ] , we address some computational and efficiency issues .

this paper develops the theory of abelian routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry . these reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics . the methods are demonstrated for the dynamics of an earth orbiting satellite with a non - spherical correction , as well as the double spherical pendulum . the main feature of the double spherical pendulum example is that it has a nontrivial magnetic term in its reduced symplectic form . in contrast , a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking darboux theorem to transform the symplectic structure into canonical form , thereby incurring additional computational cost . our method allows one to design reduced symplectic integrators in a natural way , despite the noncanonical nature of the symplectic structure .

this paper develops the theory of abelian routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry . the reduction of variational runge - kutta discretizations is considered , as well as the extent to which symmetry reduction and discretization commute . these reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics . the methods are demonstrated for the dynamics of an earth orbiting satellite with a non - spherical correction , as well as the double spherical pendulum . the problem is interesting because in the unreduced picture , geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish , but this issue does not appear in the reduced algorithm , where one can directly observe interesting dynamical structures in the reduced phase space ( the cotangent bundle of shape space ) , in which the geometric phases have been removed . the main feature of the double spherical pendulum example is that it has a nontrivial magnetic term in its reduced symplectic form . our method is still efficient as it can directly handle the essential non - canonical nature of the symplectic structure . in contrast , a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking darboux theorem to transform the symplectic structure into canonical form , thereby incurring additional computational cost . our method allows one to design reduced symplectic integrators in a natural way , despite the noncanonical nature of the symplectic structure .

hep-th0006147

c

in this paper we have described the rational map ansatz applied to skyrmions on a @xmath0-sphere of radius @xmath2 . we have calculated the energy @xmath141 of a skyrmion as a function of @xmath2 for baryon number @xmath352 and found the following behaviour : for small @xmath2 the energy @xmath141 scales like @xmath57 . @xmath141 has a global minimum at an optimal radius @xmath273 . when the radius @xmath2 is further increased there is a bifurcation point at a critical length @xmath186 : below @xmath186 the skyrmion is symmetric under reflection at the plane through the equator of @xmath1 . above @xmath186 there are two degenerate skyrmions one of which is localized at the north pole whereas the other one is localized at the south pole . for @xmath8 the ansatz tends to the rational map ansatz for @xmath9 , @xcite . for @xmath89 and @xmath54 our ansatz reproduces the known exact solution @xcite . for @xmath187 our results are worse for small @xmath2 than the doubly axially - symmetric ansatz in @xcite . however , for @xmath388 the energies of our solutions are lower than any solutions known to date , including the doubly axially - symmetric solutions . we have also derived an analytic expression for the shape function by imposing that the metrics on the physical @xmath1 and on the target @xmath1 are conformal in an average sense . this quasi - conformal ansatz for the shape function depends only on one parameter @xmath207 . by varying @xmath207 we obtain very good agreement with the numerical results for a large range of @xmath2 , even for flat space . it is worth noting that the relative error of the quasi - conformal ansatz decreases with increasing baryon number . we have shown that the solution is localized at the equator if @xmath213 . for @xmath389 we have shown that the skyrmion really is symmetric below a critical value @xmath390 , _ i.e. _ @xmath213 gives the minimal energy solution . one particular property of the quasi - conformal shape function is that it becomes more and more localized around the equator as the baryon number increases . to be more precise , the derivative of the shape function , which is connected to the baryon density , has a peak at the equator . since this ansatz was derived with the assumption that the map between the metrics is `` as conformal as possible '' we have found a geometric explanation of why skyrmions on the @xmath0-sphere are shell - like . in flat space the map can not be conformal . however , one `` half '' of the skyrmion in flat space resembles `` half '' a skyrmion on a @xmath0-sphere with optimal radius . this fits well with the observation in section [ numericalresults ] that the parameter @xmath320 which is a measure of the size of the skyrmion agrees well with the optimal length @xmath347 . this line of thought can be carried even further . skyrmions on the @xmath0-sphere might be a reasonable model for nuclei , once they are quantized . the main advantage of this model is that on the @xmath0-sphere one - loop corrections are expected to play a far less important role than in flat space . in particular , if the skyrmion lives on the @xmath0-sphere with the optimal radius we expect these corrections to be so small that the predictions of the skyrme model could be compared with experiment . the main motivation for this claim are the promising results in @xcite for the @xmath89 skyrmion on the @xmath0-sphere , and the fact that they predict a different value for the skyrme coupling which is in agreement with one - loop calculations performed in @xcite and the skyrme coupling therein .

this paper discusses multi - skyrmions on the-sphere with variable radius using the rational map ansatz . for baryon number this ansatz produces the lowest energy solutions known so far . by considering the geometry of the model we find an approximate analytic formula for the shape function this provides an insight why skyrmions have a shell - like structure .

this paper discusses multi - skyrmions on the-sphere with variable radius using the rational map ansatz . for baryon number this ansatz produces the lowest energy solutions known so far . by considering the geometry of the model we find an approximate analytic formula for the shape function this provides an insight why skyrmions have a shell - like structure . pacs - number : 12.39.dc pages , 14 figures

astro-ph9905235

i

planets and brown dwarfs have now been detected around several main sequence stars ( e.g. mayor & queloz 1995 , butler & marcy 1996 , cochran et al . 1997 , rebolo et al . 1995 , 1996 , basri et al . 1996 , marcy et al . 1998 , butler et al . 1998 , delfosse et al . 1998 ) , and strikingly , a fraction of these `` hot jupiters '' orbit very close to the central star , at less than 1 au . this proximity to the central star poses a theoretical problem regarding the mechanism that brought these planets to these orbits , but it also raises the question of their fate . indeed , rasio et al . ( 1996 ) showed that the orbit of 51 peg s companion is tidally unstable and that the planet will ultimately be engulfed in the stellar envelope . the problem we address here is that of the effects of the accretion of a giant planet or a brown dwarf on the structure and evolution of solar mass stars on the red giant branch . this study is the continuation of our previous work ( siess & livio 1998 ) , in which we investigated the swallowing of massive planets / brown dwarfs by a 3 agb star . the general scenario for the accretion process is as follows : planets in close orbits ( as observed ) will be engulfed in the envelope of giant stars as the latter evolve away from the main sequence . due to viscous and tidal forces , angular momentum is imparted to the envelope and the planet spirals - in . previous studies of the spiralling - in process ( e.g. livio & soker 1984 ; soker , harpaz & livio 1984 ) have revealed that depending on the mass of the planet / brown dwarf three different evolutionary paths can take place . if the mass of the planet is larger than some critical value @xmath3 , the planet can accrete a fraction of the envelope mass . on the other hand , lower mass planets will either evaporate or collide with the stellar core . for the specific stellar model used in their computation , livio and soker ( 1984 ) estimated @xmath4 . however , these results must be taken with great caution since the physical processes were treated only approximatively . we also emphasize that such computations are very sensitive to the stellar model , notably to the size and mass of the convective envelope . more recently , sandquist et al . ( 1998 ) performed 3d hydrodynamical simulations of jupiter - like planets impacting onto solar type main sequence stars . they also found that depending on the initial stellar model , planets can be evaporated or survive the crossing of the convective zone . the present work has been motivated by the fact that planets surrounding low mass stars are more likely to be engulfed in the star s envelope during the red giant branch ( rgb ) phase than during the asymptotic giant branch ( agb ) phase . indeed , if we compare ( for different stars ) the ratio of the maximum radius a star can reach during the rgb to its maximum radius on the agb phase , this ratio is much closer to one for low mass stars ( @xmath5 ) than more massive stars ( e.g. soker 1998a ) . consequently , we expect that in most cases low mass stars will interact with close low - mass binary companions on the rgb . in the present paper , we used a spherically symmetric stellar evolution code to follow the evolution of a solar type star that accretes a giant planet or a brown dwarf on the red giant branch . in @xmath6[conditions ] , we describe briefly the computational approach and the initial models . then , in @xmath6[struc ] , we analyze the effects of accretion on the structure and the evolution of the star . we present results for different mass accretion rates and different initial stellar models on the rgb . the observational signatures expected from this process are investigated in detail in @xmath6[signature ] . a discussion and conclusions follow .

we analyze the effects of different accretion rates and different initial conditions . -1 cm -0.65 cm -0.65 cm 2h # 1 accretion - planetary systems - stars : low - mass , brown dwarfs - stars : late type - stars : evolution - stars : mass loss - stars : chemically peculiar - stars : rotation - x - ray : stars - infrared : stars

this paper extends our previous study of planet / brown dwarf accretion by giant stars to solar mass stars located on the red giant branch . the model assumes that the planet is dissipated at the bottom of the convective envelope of the giant star . the giant s evolution is then followed in detail . we analyze the effects of different accretion rates and different initial conditions . the computations indicate that the accretion process is accompanied by a substantial expansion of the star , and in the case of high accretion rates , hot bottom burning can be activated . the possible observational signatures that accompany the engulfing of a planet are also extensively investigated . they include : the ejection of a shell and a subsequent phase of ir emission , an increase in theli surface abundance and a potential stellar metallicity enrichment , spin - up of the star due to the deposition of orbital angular momentum , the possible generation of magnetic fields and a related x - ray activity due to the development of shear at the base of the convective envelope , and the effects on the morphology of the horizontal branch in globular clusters . we propose that the ir excess and high li abundance observed in 4 - 8% of the g and k giants originate from the accretion of a giant planet , a brown dwarf or a very low - mass star . -1 cm -0.65 cm -0.65 cm 2h # 1 accretion - planetary systems - stars : low - mass , brown dwarfs - stars : late type - stars : evolution - stars : mass loss - stars : chemically peculiar - stars : rotation - x - ray : stars - infrared : stars

astro-ph9905235

c

in this paper , we investigated the effects of the accretion of a planet or a brown dwarf by a solar type star located on the red giant branch . our computations show that the deposition of mass ( potential energy ) produces a substantial expansion of the envelope and , for higher accretion rates , nuclear burning at the base of the convective envelope can take place . the simulations show that the results are a sensitive function of the accretion rate and the structure of the star . generally , the higher the accretion rate and/or the more evolved the star , the larger is the expansion . after the end of the accretion process , the star relaxes and resumes a standard evolution . however , in one simulation ( case c0 ) , the star avoided the he flash but instead developed thermal instabilities . for this model , after a phase of thermal pulses , he burning was finally ignited at the center of the star . we discussed the possible observational signatures of the accretion of a planet / brown dwarf . in particular ( 1 ) we showed that the rotational velocity of the star can be substantially increased , provided that the accreted planet / brown dwarf is sufficiently massive . in this respect the accretion of a brown dwarf could account for the fast rotation of fk comae stars and more generally , the deposition of angular momentum via this process can explain unusually fast rotation rates . ( 2 ) investigating the x - ray properties of giant stars , we showed that a strong differential rotation may take place at the bottom of the convective envelope . the presence of shear in this region can turn - on the dynamo activity and this may ultimately generate x - ray emission . we showed that under some conditions the surface layers of the star could rotate slowly while a rapid rotation is maintained in the core . ( 3 ) we also showed that the accretion scenario can lead to the ejection of shells whose mass is in the range @xmath115 . the ir excesses observed in @xmath1488% of luminosity class iii stars could in part be due to this process . ( 4 ) we argued that the increase in the mass loss rate can also have indirect effects on the morphology of the horizontal branch and in this respect , the accretion process is a potential second parameter candidate . ( 5 ) we showed that the deposition of planet material in the convective envelope can efficiently increase the li surface abundance and more generally enhance the stellar metallicity of giant stars . ( 6 ) finally , on a related topic , we proposed that the accretion of a planet / brown dwarf can explain consistently both the ir excess and the high li abundance observed only in single red giant stars . in terms of physical processes , we suggested that planet / brown dwarf accretion may provide the triggering for a variety of processes . for example , the disruption of the planet and the associated instabilities could increase the he abundance in the giant s envelope and thus affect the morphology of the hb as proposed by sweigart ( 1997 , @xmath6[morpho ] ) . they could also be responsible for the production of lithium through the mechanism proposed by wasserburg et al . ( 1995 , @xmath6[lirich ] ) . finally , the rapid contraction of the star at the end of the accretion process could generate some pulsations . observations indicate that several of potential different signatures of an accretion event , e.g. a fast rotation rate , a significant x - ray emission , a high li abundance or a large ir excess , do not always occur simultaneously . as we have shown , this is not surprising . first , depending on the mass of the planet , the outcomes could be different . for example , a small planet that evaporates in the envelope before reaching its base will perturb the structure only slightly . in such a case , no shell will be ejected but the deposition of angular momentum and matter in the surface layers could still produce a relatively rapid rotation and a high lithium abundance , as observed in some chromospherically active giants ( fekel & balachandran 1993 ) . secondly , the timescales associated with the various phenomena ( ir excess , x - ray activity , rotational braking , particle transport ) can be different , and thus , not all the signatures will be observed at the same time . for example , if the spin - down timescale is longer than the timescale associated with the dissipation of the ejected shell , one can account for the absence of ir excess in some fast rotators . thirdly , the consequences of the accretion process depend on the evolutionary status of the star . giant stars located at the bottom of the rgb have much deeper convective envelopes than near the tip of the giant branch . thus , if we consider for example the deposition of li in the envelope , it is more difficult to obtain high li abundances in younger red giants ( it is also be more difficult to eject a shell ) . finally , our simulations show that the results are sensitive to the physics of the dissipation process , and more specifically , to the accretion rate and the location of the accretion process . at present , both these physical parameters are rather uncertain , and a better understanding of the dissipation process is definitively required . as a last point , we can attempt to use the expected observational signatures to infer some estimate for the frequency of planets around solar - type stars . in a search for lithium in 644 g and k giants , brown et al . ( 1989 ) found that 2% in the stars of their sample have log@xmath138(li)@xmath149 and 4% have log@xmath138(li)@xmath150 . if we adopt for our definition of li rich giants the value log@xmath138(li)@xmath151 , we find that @xmath117% of the stars surveyed by brown et al . belong to this group . in a more recent survey , castilho et al . ( 1998 ) report the detection of 5 li rich and 6 moderately li rich giants among 164 stars , indicating a proportion of li rich giants of @xmath152% . the study of plets et al . ( 1997 ) indicates that 8% of luminosity class iii giants have unexpected ir excess . finally , based on rotational velocity measurements of @xmath80 g and k giants , de medeiros et al . ( 1996a ) found that @xmath153 of late g and k giants located beyond the rotational dividing line are fast rotators with @xmath154 . thus , if the ir excess and/or high li abundance and/or unusually high rotational velocity among g and k giants result from the accretion of a planet / brown dwarf , the above numbers suggest that at least 4 - 8% of the single , solar - type stars must have a low mass companion , either a brown dwarf or a planet . if we were to take seriously the frequency of planets inferred by soker ( 1997 ) to account for the shaping of planetary nebulae ( @xmath155 of all progenitors of masses @xmath156 ) , our deduced frequency would indicate that either a large fraction of the planets do not interact during the red giant phase or , more probably , that the observational signatures of the accretion event are very short - lived compared to stellar evolutionary timescales . indeed , because of the large radii reached by solar type stars during the rgb , some planets will most likely be engulfed during the early giant phase rather than on the agb ( although jupiter will not be engulfed by our own sun ) . on the other hand , if we compare the timescales associated with both the li and ir excesses ( @xmath157yr ) to the red giant lifetime ( between @xmath158 and @xmath159yr for giants with masses between 1.0 and 2.5 ) , we conclude that the probability of detecting an accretion event is such that we are likely to miss most candidates .

this paper extends our previous study of planet / brown dwarf accretion by giant stars to solar mass stars located on the red giant branch . the model assumes that the planet is dissipated at the bottom of the convective envelope of the giant star . the giant s evolution is then followed in detail . the computations indicate that the accretion process is accompanied by a substantial expansion of the star , and in the case of high accretion rates , hot bottom burning can be activated . we propose that the ir excess and high li abundance observed in 4 - 8% of the g and k giants originate from the accretion of a giant planet , a brown dwarf or a very low - mass star .

this paper extends our previous study of planet / brown dwarf accretion by giant stars to solar mass stars located on the red giant branch . the model assumes that the planet is dissipated at the bottom of the convective envelope of the giant star . the giant s evolution is then followed in detail . we analyze the effects of different accretion rates and different initial conditions . the computations indicate that the accretion process is accompanied by a substantial expansion of the star , and in the case of high accretion rates , hot bottom burning can be activated . the possible observational signatures that accompany the engulfing of a planet are also extensively investigated . they include : the ejection of a shell and a subsequent phase of ir emission , an increase in theli surface abundance and a potential stellar metallicity enrichment , spin - up of the star due to the deposition of orbital angular momentum , the possible generation of magnetic fields and a related x - ray activity due to the development of shear at the base of the convective envelope , and the effects on the morphology of the horizontal branch in globular clusters . we propose that the ir excess and high li abundance observed in 4 - 8% of the g and k giants originate from the accretion of a giant planet , a brown dwarf or a very low - mass star . -1 cm -0.65 cm -0.65 cm 2h # 1 accretion - planetary systems - stars : low - mass , brown dwarfs - stars : late type - stars : evolution - stars : mass loss - stars : chemically peculiar - stars : rotation - x - ray : stars - infrared : stars

cs0602072

i

low - density parity - check ( ldpc ) codes as opposed to turbo codes have been studied extensively on the binary erasure channel ( bec ) . in @xcite , an iterative decoding algorithm for ldpc codes over the bec was proposed , and it was shown that this scheme approaches channel capacity arbitrarily close . although carefully optimized irregular ldpc codes with iterative decoding can achieve channel capacity on the bec as the code length tends to infinity , there is still some performance loss compared to maximum - likelihood ( ml ) decoding of a given fixed code of finite length . recently , some progress has been made towards efficient ml or near ml decoding of ldpc codes over the bec @xcite . the tanner graph representation of an ldpc code is a bipartite graph with left and right nodes . the left nodes correspond to codeword bits . the right nodes correspond to parity - check constraints . it is known that iterative belief - propagation ( bp ) decoding fails if and only if the set of erased bit - positions contains a _ stopping set _ @xcite . a stopping set is a subset of the bit - positions such that the corresponding left nodes in the tanner graph have the property that all neighboring nodes are connected to the set at least twice . in this work we consider turbo decoding over the bec . turbo codes have gained considerable attention since their introduction by berrou _ @xcite in 1993 due to their near - capacity performance and low decoding complexity . here we consider the conventional turbo code which is the parallel concatenation of two identical recursive systematic convolutional encoders separated by a pseudo - random interleaver . to accurately describe turbo decoding on the bec we introduce the concept of a _ turbo stopping set _ , and we identify an exact condition for decoding failure . assume that we transmit codewords of a turbo code over the bec . apply turbo decoding until either the codeword has been recovered , or the decoder fails to progress further . then the set of erased positions that will remain when the decoder stops is equal to the unique maximum - size turbo stopping set which is also a subset of the set of erased positions . we also consider improved turbo decoding on the bec . the algorithm applies turbo decoding until the transmitted codeword is recovered , or the decoder fails to progress further . then , an unknown ( systematic ) bit - position is identified and its value is guessed , after which turbo decoding is applied again . thus , the algorithm is based on guessing bit - values in erased bit - positions when turbo decoding does not progress further and has the same _ structure _ as the algorithms in @xcite . recently , several algorithms have been introduced to compute the first few terms of the weight distribution of both parallel and serial turbo codes . both exact algorithms ( e.g. , @xcite ) and approximate algorithms ( e.g. , @xcite ) have been presented . in this work we also show that basically all _ trellis - based _ algorithms can be adapted to find the first few terms of the turbo stopping set size enumerating function . in particular , we have considered in detail how to adapt the algorithm by garello _ introduced in @xcite and the improved algorithm in @xcite . also , an expression for the ( average ) turbo stopping set size enumerating function under the uniform interleaver assumption is presented . using linear programming ( lp ) to decode binary linear codes has recently been considered by feldman _ see also the seminal papers @xcite where lp decoding of turbo - like codes is considered . in particular , repeat - accumulate ( ra ) codes are considered . a description of lp decoding of arbitrary concatenated codes is given in ( * ? ? ? * ch . 6 ) . the obvious polytope for lp decoding is the convex hull of all codewords , in which case lp decoding is equivalent to ml decoding . however , the convex hull has a description complexity that is exponential in the codeword length for a general binary linear code . thus , feldman _ @xcite proposed a relaxed polytope which contains all valid codewords as vertices , but also additional non - codeword vertices . the vertices of the relaxed polytope are basically what the authors called _ pseudo - codewords _ in @xcite . one desirable property of the lp decoder is the ml certificate property , i.e. , when the lp decoder outputs a codeword , it is guaranteed to be the ml codeword . experimental results with ldpc codes show that the performance of the relaxed lp decoder is better than with the iterative min - sum algorithm , but slightly worse than with iterative bp decoding . recently , some understanding of the performance of iterative bp decoding of finite - length ldpc codes over general memoryless channels have been developed . finite graph covers of the tanner graph and the codes defined by these covers play an essential role in the analysis @xcite . the low complexity of iterative bp decoding is due to the fact that the algorithm operates _ locally _ on the tanner graph of the code . this property is also the main weakness of iterative bp decoding , since the decoder can not distinguish if it operates on the original tanner graph or on any of the finite covers . hence , codewords in the code defined by a finite cover of the tanner graph will influence on iterative decoding . these codewords are basically what vontobel and koetter referred to as pseudo - codewords in @xcite . it turns out that the set of pseudo - codewords of all finite covers of the tanner graph is equal to the set of points where all entries are rational numbers from the relaxed polytope of lp decoding of ldpc codes as introduced by feldman _ et al . _ in @xcite . a similar connection between the relaxed polytope of lp decoding of turbo codes , as described in ( * ? 6 ) , and the pseudo - codewords of all finite covers of the turbo code factor graph @xcite was established in @xcite . furthermore , rosnes also showed in @xcite that there is a many - to - one correspondence between these pseudo - codewords and turbo stopping sets in the following sense . the support set of any pseudo - codeword , i.e. , the set of non - zero coordinates , is a turbo stopping set , and for any turbo stopping set there is a pseudo - codeword with support set equal to the turbo stopping set . a similar connection also holds for pseudo - codewords of finite graph covers of tanner graphs and stopping sets @xcite . for ldpc codes it has been observed that stopping sets , to some degree , also reflect the performance of iterative decoding for other channels than the bec @xcite . it is therefore our hope that the notion of turbo stopping sets also can provide some useful insight into turbo decoding on the additive white gaussian noise ( awgn ) channel or on other memoryless channels . in @xcite , rosnes presented some simulation results to indicate that this may be the case . this paper is organized as follows . in section [ sec : decoding ] we define some basic notation and describe simplified turbo decoding on the bec . section [ sec : stopping ] introduces the concept of a turbo stopping set . we further give some of the basic properties and show that turbo stopping sets characterize exactly the performance of turbo decoding on the bec . an improved turbo decoding algorithm on the bec is introduced in section [ sec : improved ] , and its superiority compared to conventional turbo decoding is illustrated by simulation examples . finally , in section [ sec : alg ] , we consider enumeration of small - size turbo stopping sets for a particular interleaver and under the uniform interleaver assumption . conclusions and a discussion of future work are given in section [ sec : conclu ] .

we then adapt the concept of stopping sets to turbo decoding and state an exact condition for decoding failure . then the set of erased positions that will remain when the decoder stops is equal to the unique maximum - size _ turbo stopping set _ which is also a subset of the set of erased positions . finally , we give an expression for the turbo stopping set size enumerating function under the uniform interleaver assumption , and an efficient enumeration algorithm of small - size turbo stopping sets for a particular interleaver .

this paper is devoted to the finite - length analysis of turbo decoding over the binary erasure channel ( bec ) . the performance of iterative belief - propagation ( bp ) decoding of low - density parity - check ( ldpc ) codes over the bec can be characterized in terms of _ stopping sets_. we describe turbo decoding on the bec which is simpler than turbo decoding on other channels . we then adapt the concept of stopping sets to turbo decoding and state an exact condition for decoding failure . apply turbo decoding until the transmitted codeword has been recovered , or the decoder fails to progress further . then the set of erased positions that will remain when the decoder stops is equal to the unique maximum - size _ turbo stopping set _ which is also a subset of the set of erased positions . furthermore , we present some improvements of the basic turbo decoding algorithm on the bec . the proposed improved turbo decoding algorithm has substantially better error performance as illustrated by the given simulation results . finally , we give an expression for the turbo stopping set size enumerating function under the uniform interleaver assumption , and an efficient enumeration algorithm of small - size turbo stopping sets for a particular interleaver . the solution is based on the algorithm proposed by garello _ et al . _ in 2001 to compute an exhaustive list of _ all _ low - weight codewords in a turbo code . binary erasure channel , improved decoding , stopping set , turbo decoding , uniform interleaver , weight spectrum .

cs0602072

c

in this work we have considered the finite - length analysis of turbo decoding on the bec . in the same way as iterative bp decoding of ldpc codes is simpler on the bec than on other channels , turbo decoding can also be simplified on this channel . based on this simplified turbo decoding algorithm we have introduced turbo stopping sets by adapting the concept of stopping sets from the theory of iterative bp decoding of ldpc codes . these turbo stopping sets characterize turbo decoding on the bec , and an exact condition for decoding failure has been established as follows . apply turbo decoding until the transmitted codeword has been recovered , or the decoder fails to progress further . then the set of erased positions that will remain when the decoder stops is equal to the unique maximum - size turbo stopping set which is also a subset of the set of erased positions . furthermore , we have presented some improvements of the basic turbo decoding algorithm on the bec . the proposed improved turbo decoding algorithm has substantially better error performance as illustrated by simulation examples . in the second part of the paper an expression for the turbo stopping set size enumerating function under the uniform interleaver assumption was derived . also , an efficient enumeration algorithm of small - size turbo stopping sets for a particular interleaver was given . the solution is based on the algorithm proposed by garello _ _ in 2001 to compute an exhaustive list of _ all _ low - weight codewords in a turbo code . in fact , it turns out that every trellis - based weight spectrum computation or estimation algorithm for turbo codes can be adapted to the case of finding small - size turbo stopping sets . in particular , the impulse methods by berrou and vaton , vila - casado and garello , and crozier _ et al . _ can be adapted in a straightforward manner . one interesting topic for future work is the design of interleavers in which one considers both low - weight codewords and small - size turbo stopping sets . trellis - based interleaver design algorithms can in a similar manner be adapted to this problem using the extended trellis module . finally , we remark that the findings in this paper can be adapted in a fairly straightforward manner to other turbo - like codes , e.g. , ra codes , serial concatenated convolutional codes , and product codes . b. n. v. ravisankar and f. fekri , `` results on the improved decoding algorithm for low - density parity - check codes over the binary erasure channel , '' 2005 , _ ieee trans . theory _ , submitted for publication . c. di , d. proietti , i. e. telatar , t. j. richardson , and r. l. urbanke , `` finite - length analysis of low - density parity - check codes on the binary erasure channel , '' _ ieee trans . inform . theory _ 48 , no . 6 , pp . 15701579 , june 2002 . c. berrou , a. glavieux , and p. thitimajshima , `` near shannon limit error - correcting coding and decoding : turbo - codes . 1 , '' in _ proc ( icc ) _ , geneva , switzerland , may 1993 , pp . 10641070 . r. garello , p. pierleoni , and s. benedetto , `` computing the free distance of turbo codes and serially concatenated codes with interleavers : algorithms and applications , '' _ ieee j. select . areas commun . _ , vol . 19 , no . 5 , pp . 800812 , may 2001 . s. crozier , p. guinand , and a. hunt , `` computing the minimum distance of turbo - codes using iterative decoding techniques , '' in _ proc . 22th biennial symp . _ , kingston , ontario , canada , may - june 2004 , pp . 306308 . a. vila - casado and r. garello , `` the all - zero iterative decoding algorithm for turbo code minimum distance computation , '' in _ proc . ( icc ) _ , vol . 1 , paris , france , june 2004 , pp . 361364 . j. feldman and d. r. karger , `` decoding turbo - like codes via linear programming , '' in _ proc . 43rd annu . ieee symp . foundations of computer science ( focs ) _ , vancouver , bc , canada , nov . 2002 , pp . 251260 . j. feldman , m. j. wainwright , and d. r. karger , `` linear programming - based decoding of turbo - like codes and its relation to iterative approaches , '' in _ proc . allerton conf . on communications , control , and computing _ , monticello , il , oct . j. feldman , `` decoding error - correcting codes via linear programming , '' ph.d . dissertation , dept . of electrical engineering and computer science , massachusetts institute of technology ( mit ) , cambridge , ma , 2003 . o. vontobel and r. koetter , `` graph - cover decoding and finite - length analysis of message - passing iterative decoding of ldpc codes , '' 2005 , _ ieee trans . inform . theory _ , submitted for publication . [ online ] . available : http://arxiv.org/abs/cs.it/0512078/ e. rosnes , `` on the connection between finite graph covers , pseudo - codewords , and linear programming decoding of turbo codes , '' in _ proc . symp . on turbo codes & related topics _ , munich , germany , apr . 2006 . t. tian , c. r. jones , j. d. villasenor , and r. d. wesel , `` construction of irregular ldpc codes with low error floors , '' in _ proc . ( icc ) _ , vol . 5 , anchorage , ak , may 2003 , pp . 31253129 . h. d. l. hollmann and l. m. g. m. tolhuizen , `` on parity check collections for iterative erasure decoding that correct all correctable erasure patterns of a given size , '' 2005 , _ ieee trans . inform . theory _ , submitted for publication . [ online ] . available : http://arxiv.org/abs/cs.it/0507068/ s. crozier and p. guinand , `` distance upper bounds and true minimum distance results for turbo - codes designed with drp interleavers , '' in _ proc . 3rd int . symp . on turbo codes & related topics _ , brest , france , sept . 2003 , pp . 169172 . e. rosnes and . ytrehus , `` on the construction of good families of rate - compatible punctured turbo codes , '' in _ proc . symp . on inform . theory ( isit ) _ , adelaide , sa , australia , sept . 2005 , pp . 602606 . r. j. mceliece , `` the algebraic theory of convolutional codes , '' in _ handbook of coding theory _ , v. s. pless and w. c. huffman , eds . 1em plus 0.5em minus 0.4emnorth - holland , amsterdam : elsevier , 1998 , ch .

this paper is devoted to the finite - length analysis of turbo decoding over the binary erasure channel ( bec ) . the performance of iterative belief - propagation ( bp ) decoding of low - density parity - check ( ldpc ) codes over the bec can be characterized in terms of _ stopping sets_. we describe turbo decoding on the bec which is simpler than turbo decoding on other channels . apply turbo decoding until the transmitted codeword has been recovered , or the decoder fails to progress further . furthermore , we present some improvements of the basic turbo decoding algorithm on the bec . the proposed improved turbo decoding algorithm has substantially better error performance as illustrated by the given simulation results . the solution is based on the algorithm proposed by garello _ et al . _ in 2001 to compute an exhaustive list of _ all _ low - weight codewords in a turbo code . binary erasure channel , improved decoding , stopping set , turbo decoding , uniform interleaver , weight spectrum .

this paper is devoted to the finite - length analysis of turbo decoding over the binary erasure channel ( bec ) . the performance of iterative belief - propagation ( bp ) decoding of low - density parity - check ( ldpc ) codes over the bec can be characterized in terms of _ stopping sets_. we describe turbo decoding on the bec which is simpler than turbo decoding on other channels . we then adapt the concept of stopping sets to turbo decoding and state an exact condition for decoding failure . apply turbo decoding until the transmitted codeword has been recovered , or the decoder fails to progress further . then the set of erased positions that will remain when the decoder stops is equal to the unique maximum - size _ turbo stopping set _ which is also a subset of the set of erased positions . furthermore , we present some improvements of the basic turbo decoding algorithm on the bec . the proposed improved turbo decoding algorithm has substantially better error performance as illustrated by the given simulation results . finally , we give an expression for the turbo stopping set size enumerating function under the uniform interleaver assumption , and an efficient enumeration algorithm of small - size turbo stopping sets for a particular interleaver . the solution is based on the algorithm proposed by garello _ et al . _ in 2001 to compute an exhaustive list of _ all _ low - weight codewords in a turbo code . binary erasure channel , improved decoding , stopping set , turbo decoding , uniform interleaver , weight spectrum .

astro-ph0303550

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the observed difference of the @xmath1 contribution to the total light between binaries from a and b subsets may be understood as follows . the components of binaries from b subset are relatively much closer to each other than those from a subset and the proximity effects , depending on the gravitational distortion and overall geometry of the system , are much more distinct . thus proximity effects give us additional constraints to the solution . when we consider the third light @xmath1 we see that its influence on the light curve of well - detached systems is of little importance : equally good solutions can be obtained for wide range of @xmath1 values . the situation is different for closer systems small changes of @xmath1 produce noticeably systematic o - c residuals , especially near quadratures . this is an important reason for preferring such systems over classical well - detached systems in determination of the distance using individual eclipsing binaries , especially in the case of the extragalactic binaries observed usually on a rich stellar background of a host galaxy . the probability of blending with another star(s ) in such environment is high ( crowding effect ) . also the blend may be a member of the system itself as at least 30% of binaries ( batten 1973 ) are found to form hierarchical multiple systems of stars . indeed , neglecting of the third light contribution in the case of hv 2274 and hv 982 may be one of the prime sources of small differences on the level 1.5@xmath164 between distances derived for three lmc systems as was announced by ribas et al . ( 2002 ) . the idea of deriving the absolute properties of binary stars from knowledge of their photometric properties alone has long tradition ( e.g. gaposchkin 1938 , kopal 1959 - chapter 7 ) . the methods based on this idea use somewhat statistical approach : one or both components of a binary conform an empirical mass - luminosity relation and the temperature is imposed by observed spectral type . there are two important advantages of such statistical method 1 ) it may be used for large samples of binaries and 2 ) it gives fast , though approximate physical parameters of binaries . afterward we can choose from the sample most interesting systems and investigate them more accurately using spectroscopy , spectrophotometry or multicolor photometry . however , past methods neglected the interstellar reddening ( which influences both the brightness and the colours ) and , what is more important , the distance to the binary . as a matter of fact the distance is irrelevant to these methods and thus it can be derived simply by comparison with the apparent magnitude @xmath165 , even without any radial velocity measurements ( e.g. gaposchkin 1968 , dworak 1974 ) . moreover , they based their reasoning on quite crude spectral type - temperature calibrations and , of course , as the temperature come in high powers into equations involved in the method , the obtained parameters were usually very inaccurate . in present paper this `` old - fashioned '' method was innovated to account for the interstellar reddening @xmath138 and recent @xmath12 colour - temperature calibration ( flower 1996 ) . it turns out that such approach causes a big improvement in the temperature determination and overall physical parameters as was demonstrated by an accurate `` reproducing '' of absolute dimensions of three lmc eclipsing binaries . however , it was done for a little bit larger distance to lmc than the distance derived , on average , from these lmc stars . a shift of the distance modulus @xmath166 is quite small and comes probably from some inaccuracies of flower s temperature or / and bolometric corrections calibration for hot stars . anyway we should expect that this kind of method may give fast approximate determination of absolute dimensions for many binaries in the magellanic clouds , especially as we have large archives of binaries discovered by ogle , macho and eros projects at our disposal , and may be used also for eclipsing binaries in other close galaxies in the near future .

this paper presents a careful and detailed light curve analysis of bright detached eclipsing binaries ( deb ) in the small magellanic cloud , discovered by ogle collaboration , on the basis of recently available difference image analysis ( dia ) photometry . the physical properties of the stars were estimated on the basis of their photometric elements and indices assuming the distance modulus to smc and consistency between an empirical mass - luminosity relation and the flux scaling . such an approach may give fast and accurate estimates of absolute dimensions for large and homogeneous samples of eclipsing binaries in the magellanic clouds and other close galaxies .

this paper presents a careful and detailed light curve analysis of bright detached eclipsing binaries ( deb ) in the small magellanic cloud , discovered by ogle collaboration , on the basis of recently available difference image analysis ( dia ) photometry . the 19 binaries brighter than 16.4 mag in band and with the depth of primary and secondary eclipse greater than 0.25 mag were investigated . the solutions were obtained by a modified version of the wilson - devinney program . the quality of dia light curves a good phase coverage and relatively small scatter is enough to calculate realistic estimates for the third light and the argument of periastron . it was found that solutions of detached , eccentric systems with flat light curve between eclipses usually may suffer from indetermination of in contrast to those of similar systems having some proximity effects . the physical properties of the stars were estimated on the basis of their photometric elements and indices assuming the distance modulus to smc and consistency between an empirical mass - luminosity relation and the flux scaling . the method was tested on three lmc stars of known absolute dimensions and a good agreement was found for . such an approach may give fast and accurate estimates of absolute dimensions for large and homogeneous samples of eclipsing binaries in the magellanic clouds and other close galaxies . moreover , this method allows also for independent estimation of in the direction to a particular binary . the subset of six bright deb s worth future intensive investigations as likely distance indicators to smc , was chosen . they are sc3 139376 , sc4 53898 , sc5 129441 , sc6 67221 , sc6 215965 and sc9 175336 . [ firstpage ] binaries : eclipsing magellanic clouds

1501.02524

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it has been speculated that quantum computers , which harness physical phenomenon unique to quantum mechanics ( especially quantum interference and superposition ) to realize a fundamentally new mode of information processing , can overcome the limitation of classical computers in efficiently solving hard computational problems . in particular , polynomial - time algorithms have been offered to solve several np - intermediate problems by using quantum computers @xcite . a key challenge in building large - scale quantum computers is the environmental noise - more precisely , loss of quantum information due to unwanted interactions between the quantum system and its environment . this phenomenon is called _ quantum _ _ decoherence_. it has been shown that arbitrarily accurate quantum computation is possible , provided that the error per operation is below a _ threshold _ value @xcite and @xcite . in other words , quantum error correction works if the level of imperfections and noise in quantum gate operations and measurements are below a certain _ error threshold _ and if corrections can be applied repeatedly @xcite . based on the error threshold for each quantum circuit fabric technology , an appropriate encoding technique ( such as m - level concatenated steane code @xcite ) is selected to achieve fault tolerant realization of the quantum circuit . a typical quantum circuit fabric consists of a two - dimensional array of identical primitive structures ( called _ primitive cells _ in this paper ) , each structure containing some sites for generating / initializing qubits , measuring them , performing operations on one or two qubits , and channels for moving qubits or swapping their information . [ fig : fig3 ] for an example of such an array of primitive cells . unfortunately , dealing directly with this primitive cell array is very cumbersome and unwieldy . so in practice another 2-d array of super - templates ( which we call _ tiles _ ) is built . each tile comprises a number of primitive cells . instead of mapping a quantum circuit to the quantum fabric , the quantum circuit is mapped to this tiled architecture ( see below ) . a quantum logic synthesis tool ( surveyed in reference @xcite ) generates a quantum circuit . every qubit in the output is called a _ logical qubit _ , which is subsequently encoded into several _ physical qubits _ to detect and correct potential errors . to prevent the propagation of errors in the quantum circuit , the ( reversible ) _ logic gates _ in the synthesized circuit ( which are typically , not , cnot and toffoli gates ) must be converted into ft _ quantum operations_. a possible universal ( but redundant ) set of ft quantum operations includes cnot , h ( hadamard ) , t ( @xmath0/4 rotation ) , s ( phase ) , x , y and z gates . implementation of these ft quantum operations depend on the chosen error correction method . note that the set \{cnot , h , t } constitutes a universal basis for quantum circuit realization the other instructions are included to allow logic simplification during the process of converting the logic synthesis output to the ft quantum operation realization . a given quantum circuit fabric is natively capable of performing a universal set of one and two - qubit instructions ( also called _ native quantum instructions _ ) . this set differs among various quantum technologies ( e.g. , ion - trap vs. superconducting qubit vs. quantum dots ) . each ft quantum operation can be implemented by using a composition of these native quantum instructions . the transformation from logical gates ( which are the result of the quantum logic synthesis ) to the ft quantum operations and from the ft quantum operations to the native quantum instructions are called _ ft quantum synthesis _ and _ native quantum synthesis _ , respectively . ft and native quantum syntheses are outside of the scope of the present paper . each of the ft quantum operations performs a desired function on one or two logical qubits as the input producing one or two logical qubits as the output ; each of the input qubits is encoded with some number of physical qubits . the output qubits will also be encoded . moreover , each of these ft quantum operations requires subsequent _ syndrome extraction _ circuitry to detect and correct any errors ( up to a certain number ) that may have been introduced by the quantum operation itself . based on the adopted encoding scheme , implementation of each of the ft quantum operations may require hundreds to tens of thousands of native quantum instructions . different works in the literature e.g. , @xcite and @xcite have suggested using the _ tiled quantum architecture _ ( tqa ) , comprised of a regular two - dimensional array of _ universal logic blocks _ ( ulbs ) to avoid dealing with this complexity . notice that each ulb in the tqa is capable of performing _ any _ ft quantum operation . ulbs are separated by routing channels , which are used to move logical qubits ( or information about these qubits ) from some source ulbs to a target ulb in the tqa . a pictorial representation of the tqa is shown in fig . [ fig : fig1 ] . the quantum structures placed at the junctions of routing channels may be thought of as _ quantum crossbars _ ( possibly with some _ qubit purification _ @xcite capability ) . routing channels and quantum crossbars are also built from primitive cells . a ulb is analogous to a _ configurable logic block _ ( clb ) in a field programmable logic array ( fpga ) device , in that it can implement any of a set of desired functions . moreover , the same ulb ( as identified by its unique row and column indices in the ulb array ) can be configured to perform different ft quantum operations at different times as needed . this is analogous to an _ on - the - fly - reconfigurable clb_. trapped - ion technology is a very promising technology for implementing quantum circuits @xcite . hence , it is selected as the underlying technology for our quantum physical mapping tool . see section [ qcrep ] for more details of this technology . a trapped - ion quantum circuit fabric comprises of small quantum cells that are organized in a two - dimensional grid , similar to the tqa . although each primitive cell has the complete set of capabilities provided by the trapped - ion technology , it is not large enough to realize a complete ft operation with an acceptable latency . that is why we resort to the ulb abstraction . notice that each ulb itself is simply a fixed - size 2-d array of primitive cells , which can realize any ft operation with an acceptable latency . after appropriate high - level transformations , a quantum algorithm may be represented by a _ quantum operation dependency graph _ ( qodg ) , where nodes represent ft quantum operations and edges capture data dependencies . based on the target quantum fabric and error threshold , a particular quantum coding scheme is selected , and subsequently , a high - level tool maps the qodg into a tqa , where each ulb ( tile ) in this architecture can implement any desired one or two - input quantum operation in a fault - tolerant way . the latency of the quantum algorithm mapped to the tqa can be calculated as the length of the longest path in the qodg , where the length of an input - output path in the qodg is the summation of operation latencies plus routing latencies . the operation latencies are dependent on how precisely the required operation is realized within a ulb . this realization comprises static provisioning ( setting the size of the ulb in terms of an array of primitive structures in the target quantum fabric ) and mapping of the target operation into the ulb . on the other hand , the routing latencies are dependent on how long it takes for the logical qubits to move from source ulbs to a target ulb to perform the ft quantum operation . the routing latency , which depends on the actual move distances and the latency of moving a qubit through some link in the tqa , is highly sensitive to ulb size , operation placement , and qubit routing on the tqa . the focus of this paper is on finding the optimal ulb size for the tqa in the trapped - ion technology . the most important part of ulb design is to minimize the operation latency for a fixed ulb size by optimally mapping the quantum instructions to the underlying quantum fabric . this action is called _ quantum physical mapping_. the quantum physical mapping procedure is decomposed into three sub - procedures : ( a ) quantum instruction scheduling , ( b ) quantum instruction placement , and ( c ) dynamic qubit routing . next , based on operation usage frequencies in the target quantum algorithm and the average movement of logical qubits per operation in the tqa , the optimal size of the ulb is determined . each quantum fault - tolerant operation and its required syndrome extraction circuit can be modeled by a _ quantum instruction dependency graph _ ( or qidg ) . a qidg for an ft quantum operation is what a qodg is to a quantum algorithm . as an example , a cnot operation between two physical qubits may be implemented by using more than one native quantum instructions in the trapped - ion technology . moreover , this number of native quantum instructions is multiplied by a factor of seven if 7-qubit steane code [ [ 7,1,3 ] ] is used to implement the cnot in a fault - tolerant manner . adding syndrome extraction circuit for logical qubits increases the number of native quantum instructions even more . these numbers are far larger in the case of more complex ( i.e. , non - transversal ) ft quantum operations such as t operation in the [ [ 7,1,3 ] ] steane code , or more complex quantum encoding schemes such as the _ concatenated _ 7-qubit steane code . different solutions for quantum physical mapping are introduced in the literature see for example , @xcite . in this work , an iterative approach is proposed to schedule and place the instructions on quantum fabric to capture the relation between scheduling level of the instructions , instruction placement solution and qubit routing latencies . the proposed algorithms in each step are based on the state - of - the - art scheduling and placement solutions adding the unique characteristics of the quantum instructions scheduling and placement . to capture the quantum no - cloning theorem that forbids fan - out in quantum circuits , a pre - processing step is implemented on the qidg to resolve the multiple read dependencies between instructions by adding auxiliary edges between them considering the criticality factor of each instruction . a force - directed instruction scheduling approach is used as the scheduling algorithm to minimize the contention , i.e. the number of concurrent quantum instructions , and hence reduces the routing latency due to congestion among qubits . quantum instructions can only be executed at specific locations on the quantum circuit fabric called _ interaction wells_. the placement of the instructions in these interaction wells affects their start time due to the qubit routing latencies . hence , we present a placement approach based on a state - of - the - art placement engine with adaptive re - levelization of the operations . more precisely , the placement algorithm calls the quantum instruction scheduler several times to update the scheduling levels of instructions based on the current quantum placement solution . these algorithms are implemented as part of a quantum cad tool called _ quantum ulb factory designer _ ( qufd ) . to evaluate the performance of the proposed quantum instruction scheduling and placement algorithms , a quantum fabric emulator including a greedy router is developed . the result of the proposed algorithms with respect to previous work is evaluated . on average , 40% improvement with respect to the state - of - the - art quantum mapper is observed . moreover , considering toffoli profiling information , the best aspect ratio for a ulb to achieve the best latency is calculated and explained in the experimental section . the remainder of this paper is organized as follows . reviews of the most relevant prior work are presented in section [ prior ] . background on the quantum circuit representation and trapped - ion fabric is presented in section [ qcrep ] . the proposed flow for ulb design is presented in section [ cadflow ] . quantum physical mapping tool is discussed in section [ physicalmapping ] . quantum instruction scheduling and placement problem formulation and proposed algorithms are presented in sections [ sched ] and [ placement ] . experimental results are presented in section [ results ] and the paper is concluded in section [ concl ] .

this paper presents a physical mapping tool for quantum circuits , which generates the optimal universal logic block ( ulb ) that can , on average , perform any logical fault - tolerant ( ft ) quantum operations with the minimum latency . in addition to the quantum physical mapper , an approach is presented to determine the single best ulb size for a target quantum circuit by examining the latency of different ft quantum operations mapped onto different ulb sizes and using information about the occurrence frequency of operations on critical paths of the target quantum algorithm to weigh these latencies .

this paper presents a physical mapping tool for quantum circuits , which generates the optimal universal logic block ( ulb ) that can , on average , perform any logical fault - tolerant ( ft ) quantum operations with the minimum latency . the operation scheduling , placement , and qubit routing problems tackled by the quantum physical mapper are highly dependent on one another . more precisely , the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling whereas the operation placement and qubit routing solutions influence the scheduling solution due to resulting distances between predecessor and current operations , which in turn determines routing latencies . the proposed flow for the quantum physical mapper captures these dependencies by applying ( i ) a loose scheduling step , which transforms an initial quantum data flow graph into one that explicitly captures the no - cloning theorem of the quantum computing and then performs instruction scheduling based on a modified force - directed scheduling approach to minimize the resource contention and quantum circuit latency , ( ii ) a placement step , which uses timing - driven instruction placement to minimize the approximate routing latencies while making iterative calls to the aforesaid force - directed scheduler to correct scheduling levels of quantum operations as needed , and ( iii ) a routing step that finds dynamic values of routing latencies for the qubits . in addition to the quantum physical mapper , an approach is presented to determine the single best ulb size for a target quantum circuit by examining the latency of different ft quantum operations mapped onto different ulb sizes and using information about the occurrence frequency of operations on critical paths of the target quantum algorithm to weigh these latencies . experimental results show an average latency reduction of about 40% compared to previous work .

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qufd is implemented in java . trapped - ion parameters used for the simulations are as follows : move delay=10@xmath84 ; one - qubit primitive instruction delay=50@xmath85s@xmath86 and two - qubit primitive instruction delay=100@xmath84 . a workstation with intel core i7 - 2600 3.4ghz cpu and 8 gb ram was used to run the simulations . determining the concatenation level for the encoding , which is sufficient to get a correct result with high fidelity from the quantum circuit is a process based on the characteristics of the underlying quantum circuit technology and the implemented quantum circuit . this problem is outside the scope of this paper . in this experiment , we focus on one - level steane code [ [ 7,1,3 ] ] for quantum error correction and the steane syndrome extraction scheme . results for some other combinations of encoding and syndrome extraction schemes will also be presented . different ulb sizes are enumerated . for each ulb size , the latency of executing each of the ft operations ( cnot , t , s , x , y , and z ) encoded with steane code [ [ 7,1,3 ] ] are found by applying qufd . based on the results of the quantum physical mapper and target quantum circuit profiling results , the best ulb size is determined . the most important part of qufd is the quantum physical mapper for trapped - ion technology . there are different quantum mapping tools in the literature such as @xcite , quale @xcite , qpos @xcite , and qspr @xcite . in contrast to our work , all of these approaches rely on asap or alap scheduling and greedy placement of the qubits and instructions , which in turn results in long circuit latency . qspr improved on these approaches by repeating the scheduling and placement solution with random initial qubit placement solutions to reach a better initial qubit placement solution , which is critical in case of applying a greedy instruction placement solution . qspr algorithm provides about 41% improvement with respect to quale . in the following we provide a detailed comparison between qufd and qspr @xcite , which is the most advanced mapping tool in the literature . latencies of various ft operations implemented with different ulb sizes by using qufd and qspr are reported in fig . [ fig : fig12 ] . assuming simultaneous creation of ancillary qubits , there exist no feasible mapping solutions for the t instruction ( gate ) on 6@xmath876 and 8@xmath878 ulbs . this is because the number of the ancillary qubits for this instruction is more than the number of creation wells in the aforesaid ulbs . qspr fails to find any mapping solution for the 10@xmath8710 and 12@xmath8712 ulbs while qufd succeeds in these cases . the ft operation latencies obtained by qufd are from 35% ( for cnot ) to 41% ( for t instruction ) lower than those produced by qspr . although qufd uses larger computation time compared to qspr to produce its solutions , this is not a major concern , because we are only designing ulbs for seven ft operations and this procedure is done only once for the ft operation library design for each quantum circuit fabric . as mentioned in section [ sched ] , tightening the upper - bound on the number of instructions being scheduled in each scheduling level may decrease the total latency of the circuit by decreasing the routing time even though it may increase the number of scheduling levels at the end . this effect is examined for the cnot instruction mapped to a 10@xmath8710 ulb in fig . [ fig : fig13 ] . as can be seen in this figure , if the number of concurrent instructions is limited to 30% of the physical interaction wells on the fabric , the total latency is decreased by 18% . it is also seen that decreasing the maximum number of simultaneously active interaction wells does not change the circuit latency until this limit exceeds the maximum number of concurrent instruction in the qidg ( @xmath88 in fig . [ fig : fig13 ] ) . decreasing the maximum number of simultaneously active interaction wells after this value changes the scheduling , placement and routing solution by decreasing the resource contention in each scheduling level for placement and routing problems ( positive effect ) and possible qidg depth increase ( negative effect ) . the positive effect is dominant for a part of this process and after that the negative effect starts to dominate . as the coefficient of @xmath22,scaledwidth=70.0% ] to show the effect of enumerating different @xmath42 for the fds method , ( normalized ) total latency of the circuit with and without considering this factor for a complete set of ft operations ( cnot , h and t ) plus one of the pauli operations in a 10@xmath8710 ulb is reported in fig . [ fig : fig14 ] . as can be seen , for h and x operations , enumeration of different @xmath42 in the scheduling algorithm does not change the total latency but for cnot and t operations , this enumeration greatly reduces the total latency . in the scheduling algorithm on the circuit latency , scaledwidth=70.0% ] fig . [ fig : fig15 ] shows an exemplary case for the maximum scheduling level in different placement steps for the ft cnot instruction mapping on a 6@xmath876 ulb . clearly , as we go further in the placement iterations , the number of scheduling levels is increased when the deferred instruction(s ) is on the critical path of the circuit . the actual number of scheduling levels for this case is equal to 51 . the predicted number of scheduling levels after scheduling and placement solutions is increased from 26 ( without considering the routing latencies ) to 43 ( after iterative correction of the scheduling levels based on the placement solution ) . to show the effectiveness of the placement method that utilizes force - directed scheduling to modify the scheduling solution after each placement step , we implemented two other placement methods in the vlsi area . the first algorithm is based on the force - directed placement solution @xcite . in this approach , each instruction is considered to be a mass and data dependencies in the circuits are modeled by springs . the constant for each spring is set by the criticality factor of the source and the destination qubits . to avoid overlap between instructions with the same scheduling level , repulsive forces are used . the second algorithm is based on simpl algorithm @xcite with fixed scheduling levels for instructions . normalized latencies ( w.r.t . qufd results ) for a complete set of ft operations ( cnot , h and t ) plus one of the pauli operations in a 12@xmath8712 ulb for different placement mechanisms are presented in fig . [ fig : fig16 ] . as can be seen , the proposed placement method that modifies the scheduling level of instructions based on the placement solution generates on average 27% better results than the same placement method without using adaptive scheduling levels . moreover , the placement method based on the force - directed placement generates on average 72% worse results compared to the proposed placement solution . in this experiment , we focus on one - level steane encoding [ [ 7,1,3 ] ] and steane syndrome extraction scheme but to show the difference between encoding and syndrome extraction schemes , results of another concatenated code , that is , bacon - shor with the lowest concatenation level and different syndrome extraction schemes ( steane and knill ancilla ) are reported in fig . [ fig : fig17 ] . in this figure , latencies of cnot , h and x operations are measured in a 12@xmath8712 ulb . for the t operation , a 20@xmath8720 ulb is used because the number of required ancillary qubits for the t gate for some of the schemes is higher than the number of available creation wells on a 12@xmath8712 ulb . note , however , that these encoding / syndrome extraction schemes provide different levels of error detection / correction capabilities for the quantum circuit and can not be compared solely based on these latencies . based on the found latencies for ft operations , the total latency of the mapped toffoli circuit to a 2@xmath872 mesh tqa , which is calculated in section [ cadflow ] , is reported in fig . [ fig : fig18 ] . note that results for the 10@xmath8710 and 12@xmath8712 ulb sizes are not reported for qspr because this tool fails to find the total latency of the t instruction for these ulb sizes . as can be seen , the best ulb size for qufd is 10@xmath8710 and the best ulb size for qspr is 16@xmath8716 . moreover , the best total latency for the proposed qufd is 41% less than the best total latency of qspr .

more precisely , the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling whereas the operation placement and qubit routing solutions influence the scheduling solution due to resulting distances between predecessor and current operations , which in turn determines routing latencies .

this paper presents a physical mapping tool for quantum circuits , which generates the optimal universal logic block ( ulb ) that can , on average , perform any logical fault - tolerant ( ft ) quantum operations with the minimum latency . the operation scheduling , placement , and qubit routing problems tackled by the quantum physical mapper are highly dependent on one another . more precisely , the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling whereas the operation placement and qubit routing solutions influence the scheduling solution due to resulting distances between predecessor and current operations , which in turn determines routing latencies . the proposed flow for the quantum physical mapper captures these dependencies by applying ( i ) a loose scheduling step , which transforms an initial quantum data flow graph into one that explicitly captures the no - cloning theorem of the quantum computing and then performs instruction scheduling based on a modified force - directed scheduling approach to minimize the resource contention and quantum circuit latency , ( ii ) a placement step , which uses timing - driven instruction placement to minimize the approximate routing latencies while making iterative calls to the aforesaid force - directed scheduler to correct scheduling levels of quantum operations as needed , and ( iii ) a routing step that finds dynamic values of routing latencies for the qubits . in addition to the quantum physical mapper , an approach is presented to determine the single best ulb size for a target quantum circuit by examining the latency of different ft quantum operations mapped onto different ulb sizes and using information about the occurrence frequency of operations on critical paths of the target quantum algorithm to weigh these latencies . experimental results show an average latency reduction of about 40% compared to previous work .

1501.02524

c

this paper presented quantum scheduling and placement algorithms for mapping fault - tolerant quantum operations to a universal logic block ( ulb ) . analytical formulations for the scheduling and placement problems were also presented . effective and state - of - the - art algorithms used in standard cad tools for classical circuits were modified to be applicable to the quantum mapping problem ( a quantum cad problem ) . in particular , modified list scheduling and force - directed scheduling were applied to the quantum instruction scheduling problem to capture the no - cloning dependencies among quantum instructions and determine the scheduling levels to minimize the number of instruction levels and reduce the resource contention . to consider the large impact of the qubit routing on the total latency of the quantum circuit , a net - weighting timing - driven placement solution based on simpl package was employed . this technique adaptively modifies the scheduling level of the instructions . moreover , a technique was described to determine the best ulb size for implementing ft quantum operations . all of the aforementioned algorithms were implemented in a cad tool called qufd . experimental results showed that qufd dominated the prior art quantum mappers by as much as 41% in terms of the average latency reduction . with some modifications , qufd can be applied to large qodg s to produce a mapping solution for any tile - based quantum architectures . moreover , the proposed flow is applicable to quantum mapping and ulb design in other quantum fabric technologies with small changes due to different qubit / information movement cost . * acknowledgment * : this research was supported by the intelligence advanced research projects activity ( iarpa ) via department of interior national business center contract number d11pc20165 . government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation thereon . the views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements , either expressed or implied , of iarpa , doi / nbc , or the u.s . government . philipp schindler , julio t barreiro , thomas monz , volckmar nebendahl , daniel nigg , michael chwalla , markus hennrich , and rainer blatt . experimental repetitive quantum error correction . , 332(6033):10591061 , may 2011 . tzvetan s. metodi , darshan d. thaker , andrew w. cross , f. t. chong , and i. l. chuang . a quantum logic array microarchitecture : scalable quantum data movement and computation . in _ proceedings of the 38th annual ieee / acm international symposium on microarchitecture ( micro-38 ) _ , pages 305318 , washington , dc , usa , 2005 . ieee computer society . mark g. whitney , nemanja isailovic , yatish patel , and john kubiatowicz . a fault tolerant , area efficient architecture for shor s factoring algorithm . in _ proceedings of the 36th annual international symposium on computer architecture ( isca09 ) _ , pages 383394 , new york , ny , usa , 2009 . mark whitney , nemanja isailovic , yatish patel , and john kubiatowicz . automated generation of layout and control for quantum circuits . in _ proceedings of the 4th international conference on computing frontiers ( cf07 ) _ , pages 8394 , new york , ny , usa , 2007 . acm . m. j. dousti and massoud pedram . minimizing the latency of quantum circuits during mapping to the ion - trap circuit fabric . in _ design , automation and test in europe conference ( date12 ) _ , pages 840843 , march 2012 . larry mcmurchie and carl ebeling . pathfinder : a negotiation - based performance - driven router for fpgas . in _ proceedings of the 3rd acm international symposium on field - programmable gate arrays ( fpga95 ) _ , pages 111117 , new york , ny , usa , 1995 . m. a rowe , a. ben - kish , b. demarco , d. leibfried , v. meyer , j. beall , j. britton , j. hughes , w. m itano , b. jelenkovic , c. langer , t. rosenband , and d. j wineland . transport of quantum states and separation of ions in a dual rf ion trap . , may 2002 . w. k hensinger , s. olmschenk , d. stick , d. hucul , m. yeo , m. acton , l. deslauriers , c. monroe , and j. rabchuk . t - junction ion trap array for two - dimensional ion shuttling , storage , and manipulation . , 88(3):0341010341013 , january 2006 . d. r leibrandt , j. labaziewicz , r. j clark , i. l chuang , r. j epstein , c. ospelkaus , j. h wesenberg , j. j bollinger , d. leibfried , d. j wineland , d. stick , j. sterk , c. monroe , c. s pai , y. low , r. frahm , and r. e slusher . demonstration of a scalable , multiplexed ion trap for quantum information processing . , april 2009 . d. z. pan , halpin b. , and ren h. timing - driven placement . in alpert c. j. , mehta d. p. , and sapatnekar s. s. , editors , _ handbook of algorithms for vlsi physical automation _ , pages 223233 . crc press , 2007 .

the proposed flow for the quantum physical mapper captures these dependencies by applying ( i ) a loose scheduling step , which transforms an initial quantum data flow graph into one that explicitly captures the no - cloning theorem of the quantum computing and then performs instruction scheduling based on a modified force - directed scheduling approach to minimize the resource contention and quantum circuit latency , ( ii ) a placement step , which uses timing - driven instruction placement to minimize the approximate routing latencies while making iterative calls to the aforesaid force - directed scheduler to correct scheduling levels of quantum operations as needed , and ( iii ) a routing step that finds dynamic values of routing latencies for the qubits . experimental results show an average latency reduction of about 40% compared to previous work .

this paper presents a physical mapping tool for quantum circuits , which generates the optimal universal logic block ( ulb ) that can , on average , perform any logical fault - tolerant ( ft ) quantum operations with the minimum latency . the operation scheduling , placement , and qubit routing problems tackled by the quantum physical mapper are highly dependent on one another . more precisely , the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling whereas the operation placement and qubit routing solutions influence the scheduling solution due to resulting distances between predecessor and current operations , which in turn determines routing latencies . the proposed flow for the quantum physical mapper captures these dependencies by applying ( i ) a loose scheduling step , which transforms an initial quantum data flow graph into one that explicitly captures the no - cloning theorem of the quantum computing and then performs instruction scheduling based on a modified force - directed scheduling approach to minimize the resource contention and quantum circuit latency , ( ii ) a placement step , which uses timing - driven instruction placement to minimize the approximate routing latencies while making iterative calls to the aforesaid force - directed scheduler to correct scheduling levels of quantum operations as needed , and ( iii ) a routing step that finds dynamic values of routing latencies for the qubits . in addition to the quantum physical mapper , an approach is presented to determine the single best ulb size for a target quantum circuit by examining the latency of different ft quantum operations mapped onto different ulb sizes and using information about the occurrence frequency of operations on critical paths of the target quantum algorithm to weigh these latencies . experimental results show an average latency reduction of about 40% compared to previous work .

0705.1853

i

rank rigidity was first proved in the higher euclidean rank setting by ballman @xcite and , using different methods , by burns and spatzier @xcite . a manifold is said to have higher euclidean rank if a parallel , normal jacobi field can be found along every geodesic . ballman and burns - spatzier proved that if an irreducible , compact , nonpositively curved manifold has higher euclidean rank , then it is locally symmetric . ballman s proof works for finite volume as well and the most general version of this theorem is due to eberlein and heber , who prove it under only a dynamical condition on the isometry group of @xmath0 s universal cover @xcite . hamenstdt showed that a compact manifold with curvature bounded above by -1 is locally symmetric if along every geodesic there is a jacobi field making curvature -1 with the geodesic direction @xcite . she called this situation higher hyperbolic rank . shankar , spatzier and wilking extended rank rigidity into positive curvature by defining spherical rank . a manifold with curvature bounded above by 1 is said to have higher spherical rank if every geodesic has a conjugate point at @xmath5 , or equivalently , a parallel vector field making curvature 1 with the geodesic direction . they proved that a complete manifold with higher spherical rank is a compact , rank one locally symmetric space @xcite . these results settle many rank rigidity questions , but leave questions about other curvature settings open ( see @xcite for an excellent overview ) . in this paper we prove the following theorem , which can be applied to various settings in nonpositive curvature . let @xmath0 be a compact , ( euclidean ) rank 1 , nonpositively curved manifold . suppose that along every geodesic in @xmath0 there exists a parallel vector field making sectional curvature @xmath1 with the geodesic direction . if @xmath0 is odd dimensional , or if @xmath0 is even dimensional and satisfies the sectional curvature pinching condition @xmath2 with @xmath3 then @xmath0 has constant negative curvature equal to @xmath1 . in strict negative curvature , the proof of this theorem is considerably simpler . in fact , for negative curvature the full frame flow is ergodic under the conditions of theorem 1 in all dimensions but 7 and 8 ( @xcite for odd dimensions , @xcite for even dimensions ) . then the proof of theorem 1 is immediate by considering a frame with dense orbit . for dimensions 7 and 8 ergodicity of the @xmath6-frame flow holds under very strong curvature pinching ( see @xcite ) but under the curvature restrictions of theorem 1 one only has ergodicity of the 2-frame flow . note that ergodicity of this flow alone does not establish theorem 1 since the set of 2-frames giving the distinguished sectional curvature @xmath1 may , a priori , have zero measure . however , the ergodic theory of these types of flows , developed by brin , proceeds via explicit geometric descriptions of the ergodic components , and this allows theorem 1 to be obtained from the 2-frame flow dynamics alone . the proof proceeding via 2-frame flow gives the result in the exceptional dimensions 7 and 8 in negative curvature . in addition , it suggests an adaptation to the rank 1 nonpositive curvature setting , where the ergodic theory of frame flows has not been developed . the simplifications possible in the strictly negative curvature setting will be noted throughout the paper , but here we observe that although obtaining this paper s result for nonpositively curved rank 1 spaces necessitates a more technical proof , the resulting theorem forms a better complement to the rank rigidity theorem of ballmann and burns - spatzier . note that , unlike previous rank rigidity results , theorem 1 allows for situations where the distinguished curvature @xmath1 is not extremal . however , in the cases where @xmath1 is extremal the hypotheses of our theorem can be weakened , as demonstrated in section [ sec : parallel ] of this paper . the following two results are then easy corollaries of theorem 1 : let @xmath0 be a compact , rank 1 manifold with sectional curvature @xmath7 . suppose that along every geodesic in @xmath0 there exists a jacobi field making sectional curvature @xmath8 with the geodesic direction . if @xmath0 is odd dimensional , or if @xmath0 is even dimensional and satisfies the sectional curvature pinching condition @xmath9 then @xmath0 is hyperbolic . _ ( compare with hamenstdt @xcite ) _ let @xmath0 be a compact manifold with sectional curvature bounded above by @xmath8 . suppose that along every geodesic in @xmath0 there exists a jacobi field making sectional curvature @xmath8 with the geodesic direction . if @xmath0 is odd dimensional , or if @xmath0 is even dimensional and satisfies the sectional curvature pinching condition @xmath10 then @xmath0 is hyperbolic . in corollary 1 we obtain a new rank rigidity result analogous to those described above . this is the first positive result for lower rank , i.e. when the distinguished curvature value is the lower curvature bound ; @xcite provides a discussion of counterexamples to lower spherical and euclidean rank rigidity . in corollary 2 we obtain a shorter proof of hamenstdt s result , under an added pinching constraint in even dimension . in @xcite , connell showed that rank rigidity results can be obtained using only a dynamical assumption on the geodesic flow , namely an assumption on the lyapunov exponents at a full measure set of unit tangent vectors . his paper deals with the upper rank situations treated by ballman , burns - spatzier and hamenstdt . he proves that having the minimal lyapunov exponent allowed by the curvature restrictions attained at a full measure set of unit tangent vectors is sufficient to apply the results of ballman and burns - spatzier or hamenstdt . in the lower rank setting of this paper , this viewpoint translates into let @xmath0 be a compact , rank 1 manifold with sectional curvature @xmath11 , where @xmath12 . endow @xmath13 with a fully supported ergodic measure ; one can take the measure of maximal entropy or , if the curvature is known to be negative , the liouville measure . suppose that for a full measure set of unit tangent vectors @xmath14 on @xmath0 the maximal lyapunov exponent at @xmath14 is @xmath15 , the maximum allowed by the curvature restriction . if @xmath0 is odd dimensional , or if @xmath0 is even dimensional and satisfies the sectional curvature pinching condition @xmath16 with @xmath17 then @xmath0 is of constant curvature @xmath1 . the adaptation of connell s arguments for this setting is discussed in section [ sec : lyap ] . the proof of theorem 1 relies on dynamical properties of the geodesic and frame flows on nonpositively curved manifolds . the work of brin and others is the starting point for the proof ; the results needed are summarized in section [ sec : background ] ( see also @xcite for a survey of the area ) . although none of his work is undertaken for rank 1 nonpositively curved manifolds , the ideas used in this paper to deal with that situation are clearly inspired by brin s work . the proof will proceed as follows . we utilize the transitivity group @xmath18 , defined for any vector @xmath14 in the unit tangent bundle of @xmath0 , which acts on @xmath19 . essentially , elements of @xmath18 correspond to parallel translations around ideal polygons in @xmath0 s universal cover . in negative curvature , brin shows that this group is the structure group for the ergodic components of the frame flow ( see e.g @xcite or @xcite ) . for the rank 1 nonpositive curvature case the definition of this group must be adjusted and we use only that it is the structure group for a subbundle of the frame bundle . the considerations for the rank 1 case are discussed in section [ sec : rank1 ] . in section [ sec : trans ] we show that @xmath18 preserves the parallel fields that make curvature @xmath1 with the geodesic defined by @xmath14 . finally , we apply results of brin - gromov ( adapted to the rank 1 case ) and brin - karcher on the 2-frame flow which imply that @xmath18 acts transitively on @xmath20 and conclude that the curvature of @xmath0 is constant . i would like to thank chris connell for discussions helpful with the arguments in section [ sec : parallel ] of this paper , jeffrey rauch for the proof of lemma [ rauchlemma ] , and ben schmidt for helpful comments on this paper . in particular , special thanks are due to my advisor , ralf spatzier , for suggesting this problem , for help with several pieces of the argument and for helpful comments on this paper .

this paper presents hyperbolic rank rigidity results for rank 1 , nonpositively curved spaces . let be a compact , rank 1 manifold with nonpositive sectional curvature and suppose that along every geodesic in there is a parallel vector field making curvature with the geodesic direction . when is the upper curvature bound this gives a shorter proof of the hyperbolic rank rigidity theorem of hamenstdt , subject to the pinching condition in even dimension ; in all other cases it is a new result . we also present a rigidity result using only an assumption on maximal lyapunov exponents in direct analogy with work done by connell . the proof of the main theorem is simplified considerably by assuming strict negative curvature ; in fact , in all dimensions but 7 and 8 it is then an immediate consequence of ergodicity of the-frame flow . in these exceptional dimensions , [ section ] [ thm]definition [ thm]lemma [ thm]proposition [ thm]remark

this paper presents hyperbolic rank rigidity results for rank 1 , nonpositively curved spaces . let be a compact , rank 1 manifold with nonpositive sectional curvature and suppose that along every geodesic in there is a parallel vector field making curvature with the geodesic direction . we prove that has constant curvature equal to if is odd dimensional , or if is even dimensional and has sectional curvature pinched as follows : where . when is the upper curvature bound this gives a shorter proof of the hyperbolic rank rigidity theorem of hamenstdt , subject to the pinching condition in even dimension ; in all other cases it is a new result . we also present a rigidity result using only an assumption on maximal lyapunov exponents in direct analogy with work done by connell . the proof of the main theorem is simplified considerably by assuming strict negative curvature ; in fact , in all dimensions but 7 and 8 it is then an immediate consequence of ergodicity of the-frame flow . in these exceptional dimensions , recourse to the dynamics of the 2-frame flow must be made and the scheme of proof developed there can be generalized to deal with rank 1 , nonpositively curved spaces . [ section ] [ thm]definition [ thm]lemma [ thm]proposition [ thm]remark

cond-mat0504380

i

a better understanding of the electron - correlation driven volume collapse transitions in the compressed lanthanides may come from putting this behavior in context of their extended evolution from localized to itinerant character . to this end , the present paper has reported calculations for compressed ce ( @xmath0 ) , pr ( @xmath1 ) , and nd ( @xmath2 ) using a combination of the local density approximation ( lda ) and dynamical mean field theory ( dmft ) , so called lda+dmft . results for the @xmath3 moment @xmath259 , spectra , correlation energy , and equation of state among other quantities have been presented over a wide range of volume at a temperature of 632 k. this temperature is the lowest feasible with the present quantum monte carlo ( qmc ) implementation of the self energy , yet is still reasonably close to the low - temperature limit.@xcite while a face - centered cubic ( fcc ) structure was assumed , lda estimates of the important structural energy differences are significantly smaller than the relevant contributions to the correlation energy which may then be described as leading order volume - dependent effects . we find the three lanthanides to remain rather strongly localized under compression from ambient conditions up through the observed stability fields of the fcc ( @xmath4 ce ) phases , in the sense that the @xmath3 moments are close to the hund s rules values , there are fully formed hubbard sidebands which are themselves a signature of the local moments , and little @xmath3 spectral weight lying in between at the fermi level . subsequent compression brings about significant deviation of the moments from the hund s rules values , growth of @xmath3 spectral weight at the fermi level ( the kondo resonance ) at the expense of the hubbard sidebands , an associated softening in the total energy , and quenching of the spin orbit given that the kondo peak is of mixed-@xmath12 character in contrast to the predominantly @xmath5 lower hubbard band . the most dramatic evolution in these signatures is seen to coincide with the two - phase region of the @xmath4@xmath6 phase transition in the case of ce , consistent with earlier work,@xcite and in agreement with the kondo volume - collapse scenario.@xcite for pr and nd , on the other hand , these signatures change most rapidly over the volume range where the distorted fcc ( dfcc ) structure is experimentally observed to be stable , suggesting that this phase is transitional and not part of the localized trivalent lanthanide sequence . only on subsequent compression is pr experimentally observed to undergo a collapse from the dfcc phase to an @xmath6-u structure , while nd passes from dfcc to @xmath6-u through two other low symmetry phases without any substantial volume changes . due to the increasing but incompletely screened nuclear charge , the lanthanides shift towards the localized limit for larger atomic number , and we see a similar off - set to smaller volume of the above mentioned signatures from ce to pr , and then nd . in particular , a softening contribution to the total energy associated with growth of the kondo resonance must compete with the remaining contributions which become ever more dominant due to a steadily increasing bulk modulus as volume is reduced . if a region of low bulk modulus were to favor larger volume changes in structural transitions , then this would be qualitatively consistent with the observed sequence 15% ( ce ) , 9% ( pr ) , and none ( nd ) . this speculation is apparently contradicted by the 5% and 6% collapse transitions in gd ( @xmath260 ) and dy ( @xmath261 ) , respectively . however , these lanthanides correspond to filling a different spin - orbit subshell , which may significantly complicate matters given the profound manner in which spin - orbit is involved . there are still some correlation effects evident at even the smallest volumes considered here , such as residual hubbard side bands in the @xmath3 spectra and moments whose values have evolved only @xmath262% of the way from the strongly localized hund s rules values to those characteristic of totally uncorrelated electrons . nevertheless , standard paramagnetic lda does quite well within the bct phase of ce and the @xmath6-u phases of pr and nd , and so for all practical purposes these phases appear weakly correlated enough . the success of lda calculations for the structural parameters in these phases for ce as well as the light actinides is also well known.@xcite this work has also included a detailed quantitative comparison between the present lda+dmft results and experiment for the total energies and pressures of ce , pr , and nd . the comparison is encouraging , and serves to corroborate such theoretical observations as the systematic offset of kondo - like correlation signatures to smaller volume for increasing atomic number in these three lanthanides . there are also clear deficiencies , most notably the need to include intraatomic exchange , ideally in its full rotationally invariant form to enable rigorous calculation of the hund s rules moments in general cases . the need for accurate lda+dmft structural energy differences is also apparent . these improvements as well as making the lda and dmft parts mutually self - consistent will require a self - energy treatment that is both more precise and considerably less expensive , which unfortunately is likely to require giving up some of the rigor of the present qmc approach .

this paper reports calculations for compressed ce ( ) , pr ( ) , and nd ( ) using a combination of the local - density approximation ( lda ) and dynamical mean field theory ( dmft ) , or lda+dmft . the moment , spectra , and the total energy among other properties are examined as functions of volume and atomic number for an assumed face - centered cubic ( fcc ) structure . these materials are seen to be strongly localized at ambient pressure and for compressions up through the experimentally observed fcc phases ( phase for ce ) , in the sense of having fully formed hund s rules moments and little spectral weight at the fermi level . subsequent compression for all three lanthanides brings about significant deviation of the moments from their hund s rules values , a growing kondo resonance at the fermi level , an associated softening in the total energy , and quenching of the spin orbit since the kondo resonance is of mixed spin - orbit character while the lower hubbard band is predominantly . while the most dramatic changes for ce occur within the two - phase region of the volume collapse transition , as found in earlier work , those for pr and nd occur within the volume range of the experimentally observed distorted fcc ( dfcc ) phase , which is therefore seen here as transitional and not part of the localized trivalent lanthanide sequence . these lanthanides start closer to the localized limit for increasing atomic number , and so the theoretical signatures noted above are also offset to smaller volume as well , which is possibly related to the measured systematics of the size of the volume collapse being 15% , 9% , and none for ce , pr , and nd , respectively .

this paper reports calculations for compressed ce ( ) , pr ( ) , and nd ( ) using a combination of the local - density approximation ( lda ) and dynamical mean field theory ( dmft ) , or lda+dmft . the moment , spectra , and the total energy among other properties are examined as functions of volume and atomic number for an assumed face - centered cubic ( fcc ) structure . these materials are seen to be strongly localized at ambient pressure and for compressions up through the experimentally observed fcc phases ( phase for ce ) , in the sense of having fully formed hund s rules moments and little spectral weight at the fermi level . subsequent compression for all three lanthanides brings about significant deviation of the moments from their hund s rules values , a growing kondo resonance at the fermi level , an associated softening in the total energy , and quenching of the spin orbit since the kondo resonance is of mixed spin - orbit character while the lower hubbard band is predominantly . while the most dramatic changes for ce occur within the two - phase region of the volume collapse transition , as found in earlier work , those for pr and nd occur within the volume range of the experimentally observed distorted fcc ( dfcc ) phase , which is therefore seen here as transitional and not part of the localized trivalent lanthanide sequence . the experimentally observed collapse to the-u structure in pr occurs only on further compression , and no such collapse is found in nd . these lanthanides start closer to the localized limit for increasing atomic number , and so the theoretical signatures noted above are also offset to smaller volume as well , which is possibly related to the measured systematics of the size of the volume collapse being 15% , 9% , and none for ce , pr , and nd , respectively . + pacs numbers : 71.27.+a , 71.20.eh , 75.20.hr

gr-qc0312030

c

to date , the only fully general relativistic simulations of corotating binary , @xmath123 polytropes is @xcite . the study in @xcite differs from the present study in several important ways . one basic difference is that while we focus on the capability of simulating astrophysical realistic neutron star binaries , @xcite focuses on the dynamics of the final merger of the two neutron stars . thus , the initial data used in @xcite are cfqe configurations either at isco separation , or closer than isco separation ( isco separation here means simply the neutron star separation of the unique configuration that corresponds to a minimum of the binding energy in the constant rest mass cfqe - sequence , e.g. , in figure [ fig : cfqe_richard ] ) . also , in the study @xcite , it was found necessary to manually decrease the orbital angular momentum of each cfqe configuration at the level of several percent , in order to precipitate the binary merger more quickly . complementary to that approach , we are trying to use numerical relativity as a tool to assess the fidelity of the cfqe - sequence approximation itself . we found that in order to perform simulations of the neutron star binary systems compatible with realistic astrophysical scenarios , one must perform simulations using initial data at a distance considerably larger than the isco separation when using corotating cfqe configurations as initial data . we have outlined a generic method for analyzing the regime of validity of the cfqe - sequence approximation and have applied this method to the case of equal mass , corotating binary neutron stars . we have found that , for corotating neutron stars , the violation of the timelike helical killing vector field existence assumption was an order of magnitude larger than the violation of the assumption of conformal flatness . specifically , we have demonstrated that initial data specified by a cfqe configuration with neutron stars having an initial geodesic separation of less than @xmath207 ( which is slightly more than @xmath208 neutron star radii , or roughly twice the isco configuration separation ) would produce a solution to the einstein field equations that violates the killing vector field assumption by more than @xmath9 part in @xmath209 ; the conformal flatness assumption would be violated by more than @xmath9 part in @xmath210 . we thus conclude that , in the corotating case , the cfqe - sequence approximation for neutron star separations of @xmath207 and less violates the einstein field equations at a level larger than @xmath211 , and thus numerical simulations starting with similar cfqe configurations as initial data can not , therefore , be considered as approximating a realistic neutron star binary inspiral . we note that the violations of the assumptions of the cfqe - sequence approximation that we observe in our general relativistic calculations for the corotating binary systems occur on timescales that are two orders of magnitude shorter than the orbital timescale . we suspect that this may be due to interactions between the spin assumption of the individual neutron stars ( the corotating assumption ) and the cfqe assumptions . we have shown that the characteristic shape of the effective binding energy curve within the cfqe approximation is highly sensitive to the spin kinetic energy of the individual neutron stars . we have shown that if we subtract out the spin kinetic energy of the neutron stars in the construction of the effective binding energy ( which approximates the case where the neutron star spin does not increase as the orbital angular velocity increases ) , then the resulting binding energy curve will have no minimum , and thus the cfqe - sequence approximation would not predict the existence of an isco configuration . we speculate that specifying neutron stars with irrotational spin states in the cfqe - sequence approximation may yield a smaller violation of the einstein field equations for a fixed neutron star separation . the analysis we have developed in this paper can be used for a detailed investigation of this effect . more interestingly , the analysis we have developed might provide a way to determine a spin state most consistent with the cfqe approximations , and hence provide a more realistic set of initial data that can be used to start simulations at a smaller initial separations . we have shown that , for our specific neutron star models , we require a resolution of approximately @xmath212 in order to adequately resolve the neutron stars ( `` adequately resolve '' here refers to verifying that we are in the convergence regime through an appropriate richardson extrapolation technique ; this is a much more stringent condition than has been typically used in numerical relativity studies to date involving neutron stars and black holes ) . this resolution scale is over three orders of magnitude smaller than the characteristic wavelength of the gravitational radiation emitted during the last five to ten orbits of the neutron star inspiral process . we have also shown that the location of the outer boundary of the computational domain can have a significant impact on the details of the evolution of the compact objects on timescales of the orbital period . specifically , we have seen that changing the linear dimensions of our computational domain from @xmath213 to @xmath214 can significantly impact the dynamics of binary neutron stars during the first several orbits . this should serve as a warning to the numerical relativity community studying simulations of compact binaries with the hope of extracting gravitational wave information : not only will the outer boundary inhibit the actual process of extracting the gravitational waves , but they also directly affect the sources of the gravitational waves themselves . while our dynamical boundary conditions are not the best choice , and a more consistent treatment , e.g. constraint preserving boundary conditions , would most likely improve the situation , it may be that numerical relativists will be forced to push the outer boundary of the computational domain to the `` local wave zone '' ( which in this case means @xmath215 ) in order to provide realistic gravitational waveforms suitable for use as templates in gravitational wave detectors . unfortunately , this makes the numerical study of orbiting compact objects in numerical relativity particularly hard . note that every time we increase the resolution in our 3d simulations by a factor of two , keeping the outer boundary @xmath154 fixed , we must use 16 times the amount of computational resources to perform any particular simulation . also , every time we increase the outer boundary distance @xmath154 by a factor of two , we must use 8 times the amount of computational resources . therefore , if we wanted to simultaneously increase both the resolution and the outer boundary distance by a factor of 2 , we would require over two orders of magnitude more computational resources . while we have shown in this paper that it is possible to track the details of finite sized compact objects in full numerical relativity , what remains is to be able to do so in such a way that all of the numerical errors ( both truncation and boundary errors ) can be demonstrated to be small over a timescale of several orbital periods . this will be an extremely challenging task , given the current level of computational resources available . it may be necessary to employ mesh refinement in order to accurately simulate all of the physical degrees of freedom that we are interested in .

we show that the cfqe assumptions significantly violate the einstein field equations for corotating neutron stars at orbital separations nearly double that of the innermost stable circular orbit ( isco ) separation , thus calling into question the astrophysical relevance of the isco determined in the cfqe approach . with the need to start numerical simulations at large orbital separation in mind , we push for stable and long term integrations of the full einstein equations for the binary neutron star system .

this paper reports on our effort in modeling realistic astrophysical neutron star binaries in general relativity . we analyze under what conditions the conformally flat quasiequilibrium ( cfqe ) approach can generate `` astrophysically relevant '' initial data , by developing an analysis that determines the violation of the cfqe approximation in the evolution of the binary described by the full einstein theory . we show that the cfqe assumptions significantly violate the einstein field equations for corotating neutron stars at orbital separations nearly double that of the innermost stable circular orbit ( isco ) separation , thus calling into question the astrophysical relevance of the isco determined in the cfqe approach . with the need to start numerical simulations at large orbital separation in mind , we push for stable and long term integrations of the full einstein equations for the binary neutron star system . we demonstrate the stability of our numerical treatment and analyze the stringent requirements on resolution and size of the computational domain for an accurate simulation of the system .

1010.1294

i

we address here the following question : what is the asymptotic size and the limit laws of the smallest and largest gaps or spacings in the spectra of random matrices ? typical spacings between eigenvalues of random matrices have been well understood for invariant ensembles for quite some time . more recently , the behavior of these typical spacings has even been proved to be universal for much larger classes of random matrices ( @xcite , @xcite , @xcite ) . much less is known for atypically large or small spacings . this question was first considered for the smallest spacings in the unpublished phd thesis of j.vinson ( @xcite ) and raised by persi diaconis in @xcite for the largest ones . it was also discussed in an interesting debate during a conference at the courant institute in 2006 , in honor of percy deift . we solve here completely the question of the smallest spacings for the simplest invariant ensembles , i.e the cue and the gue . we give the scaling and the limit laws for the joint distribution of the smallest spacings . the answer is simple to state : it is given by the trivial poissonian ansatz where the spacings would be treated as i.i.d random variables . the answer we find for the largest spacings is less complete , since we can only obtain at this point a first - order approximation which gives the asymptotic size of the largest spacings and not their limit laws . we believe that the same poissonian ansatz should work as well for the largest gaps , but this question is left open . the question of the universality of the behavior of the extremal spacings is also left open . dyson @xcite showed that the repulsion between eigenvalues of the gaussian unitary ensemble ( the gue ) could be described asymptotically in terms of the _ determinantal _ point process associated with the sine kernel @xmath6 for this limiting determinantal point process , the probability of having no eigenvalue in an interval of size @xmath7 is known to be the fredholm determinant @xmath8 where @xmath9 is the convolution operator acting on @xmath10 with kernel @xmath11 . the density of the spacing between two successive points is then given by ( see @xcite ) @xmath12 this spacing distribution was shown to appear in a number - theoretic context : some statistics produced by odlyzko @xcite presented a correspondence between the histogram of normalized gaps between zeros of the riemann zeta function and @xmath13 . this gave further evidence for the analogy discovered by dyson and montgomery : they realized that the local dependence of the zeros of @xmath14 , previously calculated by montgomery , involved the sine kernel ( see @xcite , @xcite for an historical account and other steps of this fruitful analogy ) . at the same mean or typical gap scale , a precise analysis of the joint distribution of the gaps between eigenvalues was performed by katz - sarnak @xcite and soshnikov @xcite , for the circular unitary ensemble ( the cue ) . less attention was paid to eigenvalues statistics at smaller and larger scales . this paper concerns the extreme gaps . this study was initiated by j. vinson @xcite : he showed that the smallest gap between elements of the @xmath15 , multiplied by @xmath1 , converges in law to a random variable with distribution function @xmath16 , as the size @xmath17 of the unitary matrix increases . in his thesis , similar results for the smallest gap between eigenvalues of a generalization of the @xmath18 were obtained . vinson also gives interesting heuristics suggesting that the largest gap between @xmath15 eigenvalues should be of order @xmath19 , with poissonian fluctuations around this limit . using a different technique , soshnikov @xcite investigated the smallest gaps for determinantal point processes on the real line , with a translation invariant kernel : amongst points included in @xmath20 $ ] , this extreme spacing multiplied by @xmath21 converges weakly to the distribution with distribution function @xmath16 , as @xmath22 . heuristically , the above extreme gaps asymptotics can be obtained using the known asymptotics @xcite of the spacing distribution @xmath23 and treating the gaps as independent random variables . the difficulty to obtain rigorous results lies in showing that this poissonian ansatz is asymptotically correct for the extreme gaps , and in making the above estimates uniform in the dimension @xmath17 . we first consider the _ joint _ law of the smallest gaps ( theorem [ thm : unitary ] , corollary [ cor : smallestunitary ] ) between eigenvalues of unitary matrices . this relies both on soshnikov s method and a convergence of the process of small gaps to a poisson point process . the same reasoning equally applies to the small gaps between eigenvalues from the gaussian unitary ensemble ( theorem [ thm : g ] , corollary [ cor : smallestgue ] ) . the proofs of the small spacings asymptotics are in section 2 . the first order asymptotics of the largest gaps is then proved . concerning unitary random matrices ( theorem [ thm : largestgaps ] ) , this makes use of two important tools . a key ingredient , by deift & al @xcite , is the uniform asymptotics about the probability for a given arc of the circle to be free of eigenvalues . the proof also requires the negative correlation property for the event that two disjoint arcs are free of eigenangles . on account of the @xmath18 ( theorem [ thm : largestgapsgue ] ) , we also make a essential use of the negative correlation , and the large gap probability is evaluated by comparing the @xmath18 fredholm determinant with the unitary one . these large gaps asymptotics are proved in section 3 . the extreme spacings between random eigenvalues are important quantities for statistical physics , computational mathematics and number theory . for this reason , diaconis @xcite mentions the open question of maximal spacings , answered in theorem [ thm : largestgaps ] . after making our results explicit , successively for unitary matrices and the gue ensemble , we give applications of our extremal spacings statistics at the end of this introduction . let @xmath24 , a haar - distributed ( measure @xmath25 ) unitary matrix over @xmath26 . suppose @xmath24 has eigenvalues @xmath27 s , with ordered eigenangles @xmath28 consider the point process on @xmath29 @xmath30 our first result is about the convergence of @xmath31 to a poisson point process , thanks to this normalization by @xmath32 . [ thm : unitary ] suppose @xmath33 . as @xmath34 , the process @xmath31 converges to a poisson point process @xmath35 with intensity @xmath36 for any bounded borel sets @xmath37 and @xmath38 . the intensity is proportional to @xmath39 because of the rotational invariance of the haar measure . the corresponding factor will be less trivial in the case of the @xmath18 ensemble . our method to prove theorem [ thm : unitary ] relies on the _ s - modified _ random point field technique initiated by soshnikov @xcite : one can calculate the correlation functions of the process obtained by keeping only the @xmath40 s for which @xmath41 contains exactly one other eigenvalue . contrary to @xcite , we do not use the notion of cluster functions , because we characterize the convergence to poisson random variables thanks to the convergence of the factorial moments ; this allows also to consider easily non translation invariant kernels , like in the @xmath18 case . moreover , theorem [ thm : unitary ] gives information about the joint distribution of the number of gaps taking values in disjoint intervals ( convergence in terms of point processes ) . in particular we can compute the limiting joint law of the smallest gaps . let @xmath42 be the @xmath0 smallest eigenangles gaps ( i.e. of the form @xmath43 , where the indexes are modulo @xmath17 and gaps are defined as small as possible , i.e. @xmath44 $ ] ) . for the sake of brevity , write @xmath45 the limiting joint law of the @xmath46 s is a corollary of theorem [ thm : unitary ] . [ cor : smallestunitary ] for any @xmath47 , under the haar measure on @xmath48 , @xmath49 in particular , the @xmath50 smallest normalized space @xmath51 converges in law to @xmath46 , with density @xmath52 note that this result , for @xmath53 , is proved in vinson s thesis @xcite by a different method : he characterizes the number of small gaps as a symmetric function of the eigenvalues , and computes its moments . it is not clear how his method can be extended to provide the joint law of the @xmath0 smallest gaps . + we now turn to our next question about extreme gaps , i.e the asymptotic behavior of the largest gaps , which were guessed by vinson , based on the supposed asymptotic independence of distant gaps . we obtain thanks to the precise asymptotics of one gap probability , obtained by the steepest descent method for riemann hilbert problems in @xcite , and the negative association property of determinantal point processes ( see e.g. @xcite ) . note that both results are posterior to vinson s thesis . consider @xmath54 the largest gaps between successive eigenangles of @xmath55 , i.e. of the form @xmath56 , where the indexes are modulo @xmath17 and @xmath57 . then , as @xmath17 goes to infinity , the largest gap converges in @xmath58 to a constant , for any @xmath5 : @xmath59 actually the above limit holds for all the @xmath60 largest gaps if @xmath61 is subpolynomial . [ thm : largestgaps ] let @xmath62 be positive integers . then for any @xmath5 , @xmath63 as @xmath34 , @xmath64 the problem of the exact fluctuations will be addressed in a future work . ] . note that , for independent uniform eigenangles on the unit circle , the largest gap is of order @xmath65 , more than in the above theorem , as expected from the repulsion of the eigenvalues in the determinantal case . similar results hold for the @xmath18 . for this ensemble , the distribution of the eigenvalues has density @xmath66 with respect to the lebesgue product measure , on the simplex @xmath67 . the empirical spectral distribution @xmath68 converges in probability to the semicircle law ( see e.g. @xcite ) @xmath69 like for the unitary group , we first consider the smallest gaps , studying the point process @xmath70 for any arbitrarily small fixed @xmath71 ( this is a technical restriction allowing the use of the plancherel - rotach asymptotics of the hermite polynomials ) . [ thm : g ] as @xmath34 , the process @xmath72 converges to a poisson point @xmath73 process with intensity @xmath74 for any bounded borel sets @xmath75 and @xmath76 . the following corollary about the smallest gaps is an easy consequence of the previous theorem . as for the unitary group , introduce @xmath77 the @xmath0 nearest spacings in @xmath78 , i.e. of the form @xmath79 , @xmath80 , with @xmath81 , @xmath82 $ ] , @xmath83 . let @xmath84 [ cor : smallestgue ] for any @xmath47 , with the above notations and for the @xmath18 ensemble measure ( [ eqn : gue ] ) , @xmath85 in particular , the @xmath50 smallest normalized space @xmath86 converges in law to @xmath46 , with density @xmath52 the above result gives for @xmath53 the probability density of the normalized smallest gap in a given interval @xmath78 : @xmath87 . the following precises the distribution of this smallest spacing location in the bulk of the spectrum . [ cor : smallestlocation ] let @xmath88 be the index of the smallest gap between eigenvalues of the @xmath18 in a compact subset @xmath89 with nonempty interior : @xmath90 as @xmath34 , @xmath91 converges weakly to the probability measure with density proportional to @xmath92 we now turn to the largest gaps for the @xmath18 ensemble . the result is completely different inside the bulk and on the edge . indeed , for eigenvalues strictly inside the support of the limiting measure , the maximal spacings have order @xmath19 ( see the following theorem [ thm : largestgapsgue ] ) , while the eigenvalues on the border have an average distance of higher order , @xmath93 : for any @xmath0 , @xmath94 converges weakly as @xmath34 to a multivariate tracy - widom distribution ( see e.g. @xcite ) . strictly inside the bulk , the result is analogous to the circular case , the only difference being the normalization , due to the average density of eigenvalues . let @xmath95 be the largest gaps of type @xmath96 with @xmath97 , a compact subset of @xmath98 with nonempty interior . [ thm : largestgapsgue ] let @xmath99 be positive integers . then for any @xmath5 @xmath100 when seen in a window of size proportional to the average gap , the spacings between the zeros of dirichlet l - functions are distributed like particles of a determinantal point process with sine kernel , this is the montgomery - odlyzko law . here we want to discuss the accuracy of this analogy when looking at rare events , the extreme gaps between the zeta zeros , relying on theorems [ thm : unitary ] and [ thm : largestgaps ] . due to the availability of many numerical data , we focus on the riemann zeta function @xmath101 ( @xmath102 ) , which admits an analytic continuation to @xmath103 . let @xmath104 be the non trivial zeta zeros , @xmath105 , with @xmath106 then @xmath107 has an average value 1 . the quantity @xmath108 has been widely studied . conditionally to the generalized riemann hypothesis , the best known result is @xmath109 @xcite . from the @xmath18 hypothesis for the zeta zeros , it is expected that @xmath110 . however , to the best of our knowledge , more precise conjectures about the growth speed of large gaps between zeta zeros were not proposed . from theorem [ thm : largestgaps ] , amongst @xmath17 successive gaps with fermionic repulsion , the maximal gap has size about @xmath111 times the average gap , suggesting @xmath112 in particular @xmath113 odlyzko s numerical data @xcite give 3.303 for the maximal value of @xmath114 , @xmath115 , while @xmath116 , giving a difference of @xmath117 with the observed gaps . r0.5 [ fig : maximal ] further tests can be performed at distinct heights along the critical axis , thanks to numerical data of gourdon @xcite : he computed @xmath118 successive zeta zeros at height @xmath119 along the critical axis for each @xmath120 . the extreme normalized gaps are given on the joint graph , where the expectation from our random matrices result is the straight line @xmath121 . for example , amongst the @xmath122 gaps following the height @xmath123 , @xmath124 , i.e. a difference of @xmath125 with the expected value . concerning the smallest gaps , does the poisson intensity @xmath126 from theorem [ thm : unitary ] appear in the context of the zeta zeros ? note @xmath127 the normalized gaps . we know that , as @xmath34 , the set of gaps @xmath128 converges weakly to a poisson point process with intensity @xmath126 . we therefore expect that , as @xmath34 , @xmath129 converges to a poisson point process with the same intensity . r0.5 the joint graph gives the histogram of the @xmath130 smallest gaps , normalized as previously , amongst the @xmath131 first zeta zeros , based again on numerical data from @xcite . more precisely , the histogram gives the 3000 smallest values of @xmath132 . the straight line is the function @xmath133 ( the step of the histogram is 5 ) . this presents a good relevance of the @xmath18 hypothesis for the riemann zeta function , even at the scale of rare events , here the extreme spacings . the most classical method to diagonalize a matrix is the well - known qr algorithm . in the case of hermitian matrices , an alternative approach was proposed by deift & al @xcite , based on the isospectral property of the toda flow . more precisely , given a @xmath134 hermitian matrix @xmath135 , the first step is to reduce it in a tridiagonal form @xmath136 ( which is a robust and fast operation ) , conjugating with successive householder reflections , @xmath137,\ ] ] keeping the same spectrum as @xmath135 . after such a tridiagonalization , the @xmath138 and @xmath139 s are real . the above matrix is important in the analysis of the toda lattice : flaschka , hnon , and manakov proved independently in the 70 s that the following evolution of @xmath17 particles on a line ( @xmath140 , @xmath141 , @xmath142 ) , @xmath143 is an integrable system . more precisely , after the change of variables @xmath144 the differential equation takes the lax pair form @xmath145 where @xmath146.\ ] ] in particular and importantly , the spectrum of @xmath147 does not depend on time . moser proved that @xmath148 , @xmath149 as @xmath150 , with @xmath67 . this implies that @xmath151 converges to @xmath152 , hence @xmath136 converges to a diagonal matrix , whose entries give the eigenvalues of @xmath153 . deift @xcite asked about the speed of convergence of the toda flow till its equilibrium . more precisely , for a given @xmath154 , what is the necessary time @xmath155 such that @xmath156 for all @xmath157 ? as @xmath158 the speed of convergence to the spectrum is governed by the minimal gap between eigenvalues . a good choice for a _ typical _ hermitian matrix is a matrix from the @xmath18 , with independent ( up to symmetry ) complex gaussian entries ( of variance 2 on the diagonal , 1 elsewhere ) . from corollary [ cor : smallestgue ] , the minimal gap for such matrices is of order @xmath159 for a given required precision @xmath160 , the toda flow time necessary to evaluate the eigenvalues is expected to grow as @xmath161 with the dimension as a function of @xmath17 ] .

this paper studies the extreme gaps between eigenvalues of random matrices . we give the joint limiting law of the smallest gaps for haar - distributed unitary matrices and matrices from the gaussian unitary ensemble . in particular , theth smallest gap , normalized by a factor , has a limiting density proportional to . concerning the largest gaps , normalized by , they converge in to a constant for all . these results are compared with the extreme gaps between zeros of the riemann zeta function .

this paper studies the extreme gaps between eigenvalues of random matrices . we give the joint limiting law of the smallest gaps for haar - distributed unitary matrices and matrices from the gaussian unitary ensemble . in particular , theth smallest gap , normalized by a factor , has a limiting density proportional to . concerning the largest gaps , normalized by , they converge in to a constant for all . these results are compared with the extreme gaps between zeros of the riemann zeta function .

1311.0629

i

s. t. belyaev s contribution to theoretical physics is very impressive . in 1958 s. t. belyaev has published his classical works on the theory of nonideal bose - gas . in these works , s. t. belyaev demonstrates that peculiarity of bose systems comes from a microscopic number of particles in the condensed state with the momentum @xmath0 @xcite . to deal with such a system , he suggests splitting the system into two parts or subsystems , the condensate with @xmath0 and the rest with @xmath1 . it turns out that it is the condensate that creates the `` flavor '' of bose liquid , generating its vivid properties . one may try to figure out if physics like that of bose systems could be represented in fermi systems . belyaev s daring ideas of the two macroscopic parts in bose systems is adopted by a theory of fermion condensate that permits to construct the new class of strongly correlated fermi liquids with the fermion condensate ( fc ) @xcite , which quasiparticle system is also composed of two parts : one of them is represented by fc located at the chemical potential @xmath2 , and giving rise to the spiky density of states ( dos ) like that with @xmath0 of bose system . figure [ fig0 ] , panel * a * , shows dos of a fermi liquid with fc located at the momentum @xmath3 and energy @xmath4 . in contrast to the condensate of a bose system occupying the @xmath0 state , quasiparticles of fc with the energy @xmath4 must be spread out over the interval @xmath3 . [ ! ht ] at the momentum @xmath5 of a fermi liquid with fc . panel * b * , schematic plot of two - component fermi liquid at @xmath6 with fc . the system is separated into two parts shown by the arrows : the first part is a landau fermi liquid with the quasiparticle distribution function @xmath7 , and @xmath8 ; the second one is fc with @xmath9 and the single - particle spectrum @xmath10 . the fermi momentum @xmath11 satisfies the condition @xmath12.,title="fig:",scaledwidth=40.0% ] at the momentum @xmath5 of a fermi liquid with fc . panel * b * , schematic plot of two - component fermi liquid at @xmath6 with fc . the system is separated into two parts shown by the arrows : the first part is a landau fermi liquid with the quasiparticle distribution function @xmath7 , and @xmath8 ; the second one is fc with @xmath9 and the single - particle spectrum @xmath10 . the fermi momentum @xmath11 satisfies the condition @xmath12.,title="fig:",scaledwidth=37.0% ] the quasiparticle distribution function @xmath13 of fermi system with fc is determined by the ordinary equation for a minimum of the landau functional @xmath14 @xcite . in contrast to common functionals of the number density @xmath15 @xcite , the landau functional of the ground state energy @xmath14 becomes the exact functional of the occupation numbers @xmath16 . in case of homogeneous system a common functional becomes a function of @xmath17 , while e remains a functional , @xmath18 @xcite , @xmath19 equation represents an ordinary one to search the minimum of functional @xmath14 . in the case of bose system the equation @xmath20 describes a common instance . in the case of fermi systems such an equation , generally speaking , were not correct . thus , it is the binding constraint @xmath21 , taking place over some region @xmath3 , that makes eq . applicable for fermi systems . because of the binding constraint , fermi quasiparticles in the region @xmath3 can behave as bose one , occupying the same energy level @xmath4 , and eq . yields the quasiparticle distribution function @xmath22 that minimizes the ground - state energy @xmath14 . a possible solution @xmath22 of eq . ( [ fcm ] ) and the corresponding single - particle spectrum @xmath23 are depicted in fig . [ fig0 ] , panel * b*. as seen from the panel * b * , @xmath22 differs from the step function in the interval @xmath3 , where @xmath24 , and coincides with the step function outside this interval . thus , the fermi surface at @xmath25 transforms into the fermi volume at @xmath26 suggesting that the band is absolutely `` flat '' within this interval , giving rise to the spiky dos . the existence of such flat bands formed by inter - particle interaction has been predicted for the first time in ref . quasiparticles with momenta within the interval @xmath27 have the same single - particle energies equal to the chemical potential @xmath2 and form fc , while the distribution @xmath22 describes the new state of the fermi liquid with fc , and the fermi system is split up into to parts : a landau fermi liquid ( lfl ) and the fc part , as it is shown in fig . [ fig0 ] , panel * b * @xcite . in contrast to the landau , marginal , or luttinger fermi liquids , which exhibit the same topological structure of the green s function , in systems with fc , where the fermi surface spreads into the fermi volume , the green s function belongs to a different topological class . the topological class of the fermi liquid is characterized by the invariant @xcite @xmath28 where `` tr '' denotes the trace over the spin indices of the green s function and the integral is taken along an arbitrary contour @xmath29 encircling the singularity of the green s function . the invariant @xmath30 in takes integer values even when the singularity is not of the pole type , can not vary continuously , and is conserved in a transition from the landau fermi liquid to marginal liquids and under small perturbations of the green s function . as shown by volovik @xcite , the situation is quite different for systems with fc , where the invariant @xmath30 becomes a half - integer and the system with fc transforms into an entirely new class of fermi liquids with its own topological structure . in contrast to bose liquid , which entropy @xmath31 at temperature @xmath32 , a fermi liquid with fc possesses finite entropy @xmath33 at zero temperature @xcite . indeed , as it is seen from fig . [ fig0 ] , panel * b * , at @xmath6 , the ground state of a system with a flat band is degenerate , and the occupation numbers @xmath22 of single - particle states belonging to the flat band are continuous functions of momentum @xmath34 , in contrast to discrete standard lfl values 0 and 1 . such behavior of the occupation numbers leads to a @xmath35-independent entropy term @xmath36 with the entropy given by @xmath37.\label{s0}\ ] ] since the state of a system with fc is highly degenerate , fc serves as a stimulator of phase transitions that could lift the degeneracy of the spectrum and make @xmath33 vanish in accordance with the nernst theorem . for instance , fc can excite the formation of spin density waves , antiferromagnetic state and ferromagnetic state etc . , thus strongly stimulating the competition between phase transitions eliminating the degeneracy . the presence of fc facilitates a transition to the superconducting state , because the both phases have the same order parameter @xcite . thus , in contrast to bose systems with bose condensate , entropy of which at lowering temperatures @xmath31 , the @xmath33 peculiarity of fermi systems with fc incites to the emerging of great diversity of states . being generated by the same driving motive - @xmath33 - these , as we shall see , exhibit a universal behavior , and form a new state of matter demonstrated by many compounds . in this paper we briefly review the theory of fc that permits to describe a tremendously broad variety of experimental results in different systems . we assume that these systems are located near the fermion condensation quantum phase transition ( fcqpt ) , leading to the emergence of fc @xcite . the rest of the paper is organized as follows . in section 2 , we examine a scaling behavior of the effective mass and heavy fermion ( hf ) metals based on the extended quasiparticle paradigm that is employed to renovate the landau quasiparticle paradigm . in section 3 , we construct phase diagrams of fermi systems with fc , and compare these with the experimental ones , and show that fc leads to a new state of matter . in section 4 , we apply the fc theory to describe the thermodynamic properties of strongly correlated fermi systems represented by compounds holding a quantum spin liquid . section 5 is devoted to quasicrystals . section 6 summaries the main results .

belyaev s ideas associated with the condensate state in bose interacting systems have stimulated intensive studies of the possible manifestation of such a condensation in fermi systems . in many fermi systems and compounds at zero temperature a phase transition happens that leads to a quite specific state called fermion condensation . as a signal of such a fermion condensation quantum phase transition ( fcqpt ) serves unlimited increase of the effective mass of quasiparticles that determines the excitation spectrum and creates flat bands . we show that the class of fermi liquids with the fermion condensate forms a new state of matter . we discuss the phase diagrams and the physical properties of systems located near that phase transition . it is demonstrated that a huge amount of experimental data collected on different compounds suggests that they , starting from some temperature and down , form the new state of matter , and are governed by the fermion condensation .

this short review paper devoted to 90th anniversary of s. t. belyaev birthday . belyaev s ideas associated with the condensate state in bose interacting systems have stimulated intensive studies of the possible manifestation of such a condensation in fermi systems . in many fermi systems and compounds at zero temperature a phase transition happens that leads to a quite specific state called fermion condensation . as a signal of such a fermion condensation quantum phase transition ( fcqpt ) serves unlimited increase of the effective mass of quasiparticles that determines the excitation spectrum and creates flat bands . we show that the class of fermi liquids with the fermion condensate forms a new state of matter . we discuss the phase diagrams and the physical properties of systems located near that phase transition . a common and essential feature of such systems is quasiparticles different from those suggested by l. d. landau , by crucial dependence of their effective mass on temperature , external magnetic field , pressure etc . it is demonstrated that a huge amount of experimental data collected on different compounds suggests that they , starting from some temperature and down , form the new state of matter , and are governed by the fermion condensation . our discussion shows that the theory of fermion condensation develops completely good description of the nfl behavior of strongly correlated fermi systems . moreover , the fermion condensation can be considered as the universal reason for the nfl behavior observed in various hf metals , liquids , compounds with quantum spin liquids , and quasicrystals . we show that these systems exhibit universal scaling behavior of their thermodynamic properties . therefore , the quantum critical physics of different strongly correlated compounds is universal , and emerges regardless of the underlying microscopic details of the compounds . this uniform behavior , governed by the universal quantum critical physics , allows us to view it as the main characteristic of the new state of matter .

1311.0629

i

the condensate state in bose interacting systems , introduced by s. t. belyaev in his famous papers , forms the system s properties . it turns out that the fermion condensate takes place in many compounds , and generates the non - fermi liquid behavior by forming flat bands . we have for the first time theoretically carried out a systematic study of the phase diagrams of strongly correlated fermi systems , including hf metals , insulators with strongly correlated quantum spin liquid , and quasicrystals , and have demonstrated that these diagram have universal features . the obtained results are in good agreement with experimental facts . we have shown both analytically and using arguments based entirely on the experimental grounds that the data collected on very different heavy - fermion compounds , such as hf metals , compounds with quantum spin liquid and quasicrystals , have a universal scaling behavior , and materials with strongly correlated fermions can unexpectedly have a uniform behavior in spite of their microscopic diversity . thus , the quantum critical physics of different heavy - fermion compounds is universal , and emerges regardless of the underlying microscopic details of the compounds . this uniform behavior , induced by the universal quantum critical physics , allows us to view it as the main characteristic of the new state of matter . our analysis of strongly correlated systems is in the context of salient experimental results , and our calculations of the non - fermi liquid behavior are in good agreement with a broad variety of experimental facts . our theoretical analysis of numerous experimental facts shows that the theory of fermion condensation develops completely good description of the nfl behavior of strongly correlated fermi systems . moreover , the fermion condensate can be considered as the universal reason for the nfl behavior observed in various hf metals , liquids , insulators with quantum spin liquids , and quasicrystals .

our discussion shows that the theory of fermion condensation develops completely good description of the nfl behavior of strongly correlated fermi systems . moreover , the fermion condensation can be considered as the universal reason for the nfl behavior observed in various hf metals , liquids , compounds with quantum spin liquids , and quasicrystals . therefore , the quantum critical physics of different strongly correlated compounds is universal , and emerges regardless of the underlying microscopic details of the compounds . this uniform behavior , governed by the universal quantum critical physics , allows us to view it as the main characteristic of the new state of matter .

this short review paper devoted to 90th anniversary of s. t. belyaev birthday . belyaev s ideas associated with the condensate state in bose interacting systems have stimulated intensive studies of the possible manifestation of such a condensation in fermi systems . in many fermi systems and compounds at zero temperature a phase transition happens that leads to a quite specific state called fermion condensation . as a signal of such a fermion condensation quantum phase transition ( fcqpt ) serves unlimited increase of the effective mass of quasiparticles that determines the excitation spectrum and creates flat bands . we show that the class of fermi liquids with the fermion condensate forms a new state of matter . we discuss the phase diagrams and the physical properties of systems located near that phase transition . a common and essential feature of such systems is quasiparticles different from those suggested by l. d. landau , by crucial dependence of their effective mass on temperature , external magnetic field , pressure etc . it is demonstrated that a huge amount of experimental data collected on different compounds suggests that they , starting from some temperature and down , form the new state of matter , and are governed by the fermion condensation . our discussion shows that the theory of fermion condensation develops completely good description of the nfl behavior of strongly correlated fermi systems . moreover , the fermion condensation can be considered as the universal reason for the nfl behavior observed in various hf metals , liquids , compounds with quantum spin liquids , and quasicrystals . we show that these systems exhibit universal scaling behavior of their thermodynamic properties . therefore , the quantum critical physics of different strongly correlated compounds is universal , and emerges regardless of the underlying microscopic details of the compounds . this uniform behavior , governed by the universal quantum critical physics , allows us to view it as the main characteristic of the new state of matter .

1306.0721

i

ultrafast spectroscopy with a time resolution as high as @xmath0s is essential for understanding many quantum dynamical processes in chemical physics.@xcite although short time scales should simplify theoretical studies by requiring shorter simulations , solving the time - dependent schrdinger equation ( tdse ) is challenging even for short times due to the exponential scaling with the number of degrees of freedom . an attractive approach offering a compromise between accuracy and computational efficiency is provided by the semiclassical initial value representation methods , miller:1970,heller:1981,herman_kluk:1984,miller:2001,herman:1994,*thoss_wang:2004,*kay:2005,*ceotto_zhuang:2013 which benefit from the ultrafast character of the dynamics not only because of lower computational cost , but also because their accuracy deteriorates with increasing time . the so - called dephasing representation@xcite ( dr ) , is an efficient initial - value - type semiclassical approximation particularly fitted for calculations of time - resolved electronic spectra.@xcite the dr improves on a previous method@xcite inspired by the semiclassical perturbation theory of miller and coworkers.@xcite in electronic spectroscopy , the dr and closely related approximations are known as mukamel s phase averaging method@xcite or wigner - averaged classical limit , and were used by various authors.shemetulskis_loring:1992,rost:1995,wang_sun:1998,li_fang:1996,*egorov_rabani:1998,*egorov_rabani:1999,shi_geva:2005 shi and geva@xcite derived this approximation without invoking the semiclassical propagator by linearizingpoulsen_nyman:2003,bonella_coker:2005 the path integral quantum propagator . although the original formulation of the dr pertains to a single pair of potential energy surfaces , the generalization to multiple surfaces , and hence to nonadiabatic dynamics , exists.zimmermann_vanicek:2012,*zimmermann_vanicek:2012a the dr has many other applications ; the method successfully described , e.g. , the local density of states and the transition from the fermi - golden - rule to the lyapunov regime of fidelity decay.wang_casati:2005,*ares_wisniacki:2009,*wisniacki_ares:2010,*garcia-mata_wisniacki:2011 yet the most attractive feature of the dr is its efficiency : motivated by numerical comparisons with other semiclassical methods , wehrle_sulc:2011 it has been recently proved analyticallymollica_vanicek:2011 that the number of trajectories required for convergence of the dr is independent of the system s dimensionality , hamiltonian , or total evolution time . the efficiency was further increased in the cellular version of the dr,@xcite which was inspired by heller s cellular dynamics@xcite and which can significantly reduce the required number of trajectories . the original implementation of the _ cellular dr _ ( cdr ) , however , does not converge to the dr in the limit of infinite number of trajectories . unlike its efficiency , the accuracy of the dr is not always sufficient . the dr is exact in displaced harmonic oscillatorsmukamel:1982,*book_mukamel and often accurate in chaotic systems , vanicek:2004,*vanicek:2006 but it breaks down in as simple systems as harmonic oscillators with different force constants . this breakdown can be partially remedied by augmenting the dr with a prefactor , zambrano_almeida:2011 which , however , leads to a much higher computational cost per trajectory and also typically requires more trajectories to achieve convergence . the first goal of the present paper is to describe a general numerical implementation of the prefactor correction and apply it to the calculation of time - resolved electronic spectra . as the numerical evaluation of the cdr requires , incidentally , the same ingredients as the prefactor correction , the second goal is to combine the advantages of the cellular approach and prefactor correction into a single formula , and show that the resulting method , _ cellular dr with prefactor _ ( cdrp ) , is able to increase both the efficiency and accuracy of the dr . our third goal is presenting a major improvement of the cellularization process by employing the inverse weierstrass transform of the initial state as the optimal sampling weight instead of the widely used wigner or husimi functions , and by correlating the size of the cells with their number and the number of degrees of freedom , which guarantees the convergence of the cdr to the original dr in the limit of infinite number of trajectories . the remainder of the paper is organized as follows : the correlation function approach and the dr approximation for evaluating time - resolved stimulated emission spectra is reviewed in section [ sec : theory ] ; in particular , the dr , its prefactor correction , and its cellular version are deduced . after explaining how the new cellular approach provides optimal choices of the sampling weight and width of gaussian cells , we derive the cdrp , i.e. , a method combining the prefactor correction and cellularization into a single framework . section [ sec : examples ] contains several analytical and numerical results testing the theory developed in section [ sec : theory ] , while section [ sec : final_remarks ] provides conclusions .

we improve both the accuracy of this approximation with an amplitude correction derived from the phase - space propagator and its efficiency with an improved cellular scheme employing inverse weierstrass transform and optimal scaling of the cell size . we demonstrate the advantages of the new methodology by computing dispersed time - resolved stimulated emission spectra in the harmonic potential , pyrazine , and the nco molecule .

time - resolved electronic spectra can be obtained as the fourier transform of a special type of time correlation function known as fidelity amplitude , which , in turn , can be evaluated approximately and efficiently with the dephasing representation . here we improve both the accuracy of this approximation with an amplitude correction derived from the phase - space propagator and its efficiency with an improved cellular scheme employing inverse weierstrass transform and optimal scaling of the cell size . we demonstrate the advantages of the new methodology by computing dispersed time - resolved stimulated emission spectra in the harmonic potential , pyrazine , and the nco molecule . in contrast , we show that in strongly chaotic systems such as the quartic oscillator the original dephasing representation is more appropriate than either the cellular or prefactor - corrected methods .

astro-ph0612671

m

first we will look in a bit more detail into our equations of state before elaborating on the construction of the planet models . the total pressure , ( @xmath7 ) , can be expressed as : @xmath8 where @xmath9 is the pressure at zero - temperature and @xmath10 is the thermal pressure . for the degenerate interiors of massive planets , thermal effects are quite small for high atomic number species . for instance , zero - temperature equations of state for rock are thought to be accurate to within @xmath01 - 2% for use in uranus and neptune interior models @xcite , so we make no thermal corrections for rock and iron . for water , thermal pressure can be important at the @xmath010% level . @xcite find a relation for the @xmath11 of water that is suitable for the interior pressure - temperature ( _ p t _ ) profiles of uranus and neptune . this relation , @xmath12 where @xmath11 is in mbar , @xmath13 is in g @xmath14 , and @xmath15 in k , is relevant for `` typical planetary interior conditions . '' for @xmath16 g @xmath14 and @xmath17 k , @xmath18 mbar , or 10% of the total pressure , @xmath7 . for planets composed of any fraction of water , we assume that interior temperatures within the ice follow the uranus / neptune adiabat of @xcite , which reaches @xmath0550 k at 1 kar and 4000 k at 1 mbar , and add the thermal pressure correction of equation ( [ ice ] ) at every @xmath9 . this is our eos of `` warm ice . '' for the time being we will ignore the additional complexity of including the eos of methane and ammonia , solar system `` ices '' that are not as abundant as water . these molecules condense at colder temperatures and it is not clear how abundant these species may be in transiting planets , which are preferentially found relatively close to their parent stars . in we show our equations of state for cold ice , warm ice , rock , and iron . for hydrogen / helium envelopes , we compute internal adiabats with a helium mass fraction @xmath19 and do not include heavy elements . a description of this detailed h / he eos can be found in @xcite . the structure of spherically symmetric planets in hydrostatic equilibrium follow the relations set out below . equations ( [ dm1 ] ) and ( [ dm2 ] ) define mass conservation and hydrostatic equilibrium , respectively . equation ( [ dm3 ] ) defines energy conservation , which is employed in our evolution calculations of planets with a h / he envelope . @xmath20 @xmath21 @xmath22 here @xmath23 is the radius of a mass shell , @xmath24 mass of a given shell , @xmath13 the local mass density , @xmath7 the pressure , @xmath25 the gravitational constant , @xmath26 the planet s intrinsic luminosity , @xmath15 the temperature , @xmath27 the specific entropy , and @xmath28 the time . for planets composed only of water , rock , or iron , we do not utilize equation ( [ dm3 ] ) , as we assume a constant radius with age . given the small thermal component of the pressure for these materials , and the expected uncertainty in radius measurements , this assumption is valid . for planets where hydrogen and helium make up an appreciable mass fraction , following the thermal evolution and contraction of these planets is essential . we note that in these models we do not include additional interior energy sources such as tidal dissapation . this may be important for the hot jupiters . we also neglect helium phase separation , which will add @xmath01000 km in radius to cold giant planets at gyr ages @xcite . recall that for the planet with the most precisely determined radius hd 209458b , the 1@xmath29 radius uncertainty is still 1.9% ( @xmath01800 km ) , due to uncertainties in the stellar parameters @xcite . our evolution code for the calculation of the cooling and contraction of adiabatic giant planets is well - tested . it has been used to produce evolutionary models of jupiter and saturn @xcite , cool extrasolar giant planets @xcite , hot jupiters @xcite , and it is described in detail in @xcite and fortney04 . for all of these planets , it is the radiative atmosphere that serves as the bottleneck for cooling above the adiabatic h / he envelope . this is accounted for with our fully non - gray , self - consistent model atmosphere grids . the importance of using detailed atmosphere models for evolutionary calculations of hot jupiters is discussed in @xcite and @xcite . below the h / he envelope we assume that heavy elements are found within a distinct core . to model this core we use the eos of a 50/50 by mass ice / rock mix using the aneos zero - temperature water and olivine eoss @xcite . the compositions of the cores of jupiter and saturn are not known , and given that we model planets that likely formed at a variety of orbital distances , in which different ratios of ice / rock could be accumulated , this simple choice is a reasonable one . we ignore the heat content of the core on the thermal evolution of the planets . this is often done for evolutionary models of jupiter and saturn @xcite , as the error involved is small compared to other unknowns . please see @xcite for additional discussion on this point . we also neglect the `` transit radius '' effect : the apparent radius of a transiting planet is the radius where the slant optical depth through the planet s atmosphere reaches unity . the corresponding atmospheric pressure can vary across many orders of magnitude , depending on the wavelength @xcite . @xcite and @xcite have estimated this effect to be @xmath010% and 5% respectively , for hd 209458b , compared to some reference radius , such as the radiative - convective boundary or the 1 bar level . the _ hst _ light curve of @xcite and @xcite was obtained in a narrow wavelength band that overlaps the strong sodium d line absorptions at 589 nm . across a broad visible wavelength band , for most planets , the transit radius effect would likely be only a few percent . for the models presented here the radii correspond to a pressure of 1 bar . based on models from @xcite , an extension of @xmath05 - 6 atmosphere scale heights from the 1 bar level is needed to reach the optical transit radius . giant planets have been shown to be fully convective , or nearly so , beneath their thin radiative atmospheres ( for a review , see * ? ? ? the convection is thought to be quite efficient , and hence it is the radiative planetary atmosphere that serves as the bottleneck for escaping radiation and controls the cooling and contraction of the interior @xcite . as giant planet atmospheres have a number of atomic and molecular absorbers , including water , ammonia , methane , sodium , and potassium , these atmospheres are far from blackbodies @xcite . a model atmosphere grid , which serves as the upper boundary condition in these evolution calculations , relates the specific entropy ( @xmath27 ) of the planet s internal adiabat and atmospheric surface gravity ( @xmath30 ) to the planet s effective temperature ( @xmath31 ) . while @xmath27 and @xmath30 are calculated from the planetary structure , @xmath31 can only be accurately determined from a non - gray planetary atmosphere code . to compute the boundary condition for the evolution we compute self - consistent radiative - convective equilibrium atmospheric structure models on a large grid of gravities , intrinsic effective temperatures , and incident fluxes . each model computes an atmospheric temperature structure , accounting for deposition and re - radiation of incident starlight and convective transport and emission of internal thermal energy . the model , based on one developed for titan @xcite , was originally applied to the study of giant planet thermal structure by @xcite and has also been employed to study the atmospheres of the hot jupiters @xcite as well as brown dwarfs @xcite , albeit without incident radiation . the radiative transfer methods , chemical equilibrium calculations , and molecular and atomic opacities are summarized in the above publications as well as r. s. freedman & k. lodders , in prep . we assume solar metallicity atmospheres @xcite , and while the effect of condensation on atmospheric composition is included in the chemical equilibrium calculation @xcite we neglect the opacity of clouds . @xcite , @xcite , @xcite , and @xcite have previously discussed the importance of properly incorporating incident stellar flux into the hot jupiter atmosphere grids that serve as the upper boundary condition for the evolution of these planets , but this is also necessary at greater orbital separations for old and relatively low - mass planets . these planets have comparatively little internal energy , and their intrinsic effective temperature ( @xmath32 ) quickly falls below its equilibrium temperature ( @xmath33 ) , which is set entirely by absorption of stellar flux . here , by definition : @xmath34 when @xmath32 is small , incident stellar flux dominates over intrinsic flux and a deep atmospheric radiative zone grows , similar to a highly irradiated hot jupiter . this was previously discussed by j. b. pollack in the early 1990s and mentioned in @xcite , but we believe this is the first time this effect has been explicitly shown with detailed model atmospheres . shows model atmospheres computed at 0.1 au ( highly irradiated ) and 9.5 ( modestly irradiated ) . in both cases once @xmath35 , an isothermal region connects the deep interior adiabat to the upper atmosphere , whose structure is governed only by absorption of stellar flux ( see * ? ? ? note that the very low @xmath32 values in for this saturn - like planet would only occur after several hubble times of evolution . for all models we calculate a planet - wide average _ profile that is representative of the planet as a whole . in practice this means that the incident stellar flux is diluted by a factor of 1/4 ( see * ? ? ? * ) . the common approximation described in @xcite for including stellar flux into an atmosphere grid computed for _ isolated _ model atmospheres is only valid when @xmath36 . following the @xcite prescription to small @xmath32 leads to planetary radii that reach an asymptotic value governed by their bond albedo @xcite , and hence overestimates the radii of old , cold planets . we have computed model atmosphere grids across a range of surface gravities , for @xmath32 from 50 - 2000 k ( and as low at 10 k at low gravity ) , including the proper solar insolation for orbital distances of 0.02 , 0.045 , 0.1 , 1.0 , and 9.5 au ( which is saturn s orbital distance ) . extrapolation off the grid was performed as well . this generally only affected highly irradiated core - free low - mass planets . ] at gyr ages , we find bond albedos of @xmath00.05 - 0.1 at distances less than 0.1 au , and higher values of @xmath00.3 - 0.4 from 1 - 10 au , where cooler temperatures prevail and sodium and potassium , which absorb strongly in the optical , have condensed into clouds below the visible atmosphere @xcite . we have elected to ignore cloud opacity here , since considerable uncertainties remain concerning their effect on the atmospheric structure and albedos of egps . we will pursue this area in more detail in a later paper that focuses on the evolution of jupiter and saturn . a separate important issue is the opacity in the deep atmosphere at pressures near 1 kbar . while the temperature structure of highly irradiated atmospheres near @xmath371 kbar is of great importance for understanding giant planet thermal evolution @xcite , the opacities at these pressures remain highly uncertain @xcite . shows _ p t _ profiles computed for a jupiter - like planet from 0.02 to 10 au from the sun . the surface gravity @xmath30 is 25 m s@xmath38 and @xmath39 k in all models . these profiles are meant to roughly illustrate the atmospheres of jupiter - like planets at 4.5 gyr . @xmath39 k is very close to jupiter s current value @xcite , and we find that in our cooling calculations that the model planets reach a @xmath32 of @xmath0102 - 110 k at 4.5 gyr , which is only weakly dependent on stellar irradiation . a deep external radiative zone is found in the most highly irradiated models . for the planets at @xmath400.05 au convection does not begin until @xmath41 kbar . from 0.1 to 2 au the deep internal adiabat for all models begins at 300 + bar , but there is a 2nd , detached convective zone at pressures close to 1 bar . this detached convective zone grows at stellar distance increases , and by 3 au the convective zones have merged . only when these convective zones merge is the interior adiabat cooler as a function of orbital distance . the models from 0.1 to 2 au have essentially the same internal adiabat , meaning the planets would have the same radius at a given mass . as we will see , a striking consequence of this effect is that stellar irradiation at 2 au has approximately the same effect on retarding cooling and contraction as at 0.1 au , even though the incident fluxes vary by a factor of 400 !

masses ranging from 0.01 earth masses to 10 jupiter masses at orbital distances of 0.02 to 10 au are considered . for hydrogen - helium rich planets , our models are the first to couple planetary evolution to stellar irradiation over a wide range of orbital separations ( 0.02 to 10 au ) through a non - gray radiative - convective equilibrium atmosphere model . stellar irradiation retards the contraction of giant planets , but its effect is not a simple function of the irradiation level : a planet at 1 au contracts as slowly as a planet at 0.1 au . we confirm the assertion of guillot that very old giant planets under modest stellar irradiation ( like that received by jupiter and saturn ) develop isothermal atmospheric radiative zones once the planet s intrinsic flux drops to a small fraction of the incident flux . for hydrogen - helium planets ,

to aid in the physical interpretation of planetary radii constrained through observations of transiting planets , or eventually direct detections , we compute model radii of pure hydrogen - helium , water , rock , and iron planets , along with various mixtures . masses ranging from 0.01 earth masses to 10 jupiter masses at orbital distances of 0.02 to 10 au are considered . for hydrogen - helium rich planets , our models are the first to couple planetary evolution to stellar irradiation over a wide range of orbital separations ( 0.02 to 10 au ) through a non - gray radiative - convective equilibrium atmosphere model . stellar irradiation retards the contraction of giant planets , but its effect is not a simple function of the irradiation level : a planet at 1 au contracts as slowly as a planet at 0.1 au . we confirm the assertion of guillot that very old giant planets under modest stellar irradiation ( like that received by jupiter and saturn ) develop isothermal atmospheric radiative zones once the planet s intrinsic flux drops to a small fraction of the incident flux . for hydrogen - helium planets , we consider cores up to 90% of the total planet mass , comparable to those of uranus and neptune . if `` hot neptunes '' have maintained their original masses and are not remnants of more massive planets , radii of.30 - 0.45 are expected . water planets are% larger than rocky planets , independent of mass . finally , we provide tables of planetary radii at various ages and compositions , and for ice - rock - iron planets we fit our results to analytic functions , which will allow for quick composition estimates , given masses and radii , or mass estimates , given only planetary radii . these results will assist in the interpretation of observations for both the current transiting planet surveys as well as upcoming space missions , including corot and kepler .

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the rapidly improving experimental techniques to probe magnetic adatoms on non - magnetic surfaces allow for direct studies of fundamental magnetic exchange mechanisms on an atomic scale . besides access to the structural and the electronic properties of such adatoms and of the underlying substrate for a given system , the construction of tailored magnetic model systems represents an exciting perspective . @xcite magnetic structures of nanometer size provide extremely small systems suitable to store and to transport information and may realize efficient nano spintronics devices . @xcite the competition between an indirect magnetic exchange of the adatoms via the substrate electrons on the one hand and the screening of the adatom magnetic moment by the conduction - band electrons of the substrate on the other represents a prominent example for a physical problem becoming accessible to new real - space techniques . the scanning tunneling microscope ( stm ) @xcite has been used to investigate the kondo physics @xcite of single magnetic adatoms @xcite and the magnetic properties of the individual magnetic islands@xcite on non - magnetic substrates . using stm , it is possible to investigate the direct magnetic interaction of atom pairs . @xcite indirect magnetic exchange , i.e. the ruderman - kittel - kasuya - yosida ( rkky ) interaction @xcite between two adatoms , was detected through the kondo effect . @xcite a direct real - space study of the rkky coupling , however , comes in reach with spin - polarized scanning - tunneling spectroscopy only . @xcite ( orange ) at a distance @xmath0 coupled via a hybridization term of strength @xmath1 to a one - dimensional `` substrate '' consisting of @xmath2 non - interacting sites ( blue ) with nearest - neighbor hopping @xmath3 . in the r - dmft , the tiam is self - consistently mapped onto two single - impurity anderson models which are solved independently by means of exact diagonalization ( ed ) to get the local self - energies . these are used to set up the tiam dyson equation the solution of which gives the local green s functions which define via the r - dmft self - consistency conditions the parameters of the impurity models ( see text for details ) . , scaledwidth=40.0% ] the most simple model which captures this competition is displayed schematically in fig . [ fig : schematic_tiam ] . here the electronic and magnetic properties of a magnetic adatom are modeled by a single non - degenerate orbital . a local magnetic moment is formed by a strong local hubbard interaction . the adatom orbital hybridizes with a valence orbital of the nearest - neighboring substrate atom . the substrate electronic structure itself is modeled by a tight - binding valence band resulting from non - degenerate and uncorrelated orbitals on a bipartite lattice with nearest - neighbor hopping . considering two adatoms yields a variant of the two - impurity anderson model ( tiam ) @xcite in a surface geometry . the main goal of our study is to benchmark the real - space variant @xcite of the dynamical mean - field theory @xcite that can be employed for theoretical studies of the electronic and magnetic properties of a single , of two and or of more magnetic adatoms in different geometries on metal surfaces . for this purpose the tiam represents a fundamental starting point . in the kondo limit of the tiam , charge fluctuations on the adatom site are largely suppressed , and the adatom spin @xmath4 couples antiferromagnetically to the local spin at the nearest - neighboring substrate site @xmath5 via a spin - spin coupling @xmath6 given by the local exchange @xmath7 . the interplay between the kondo effect and the rkky interaction has extensively been studied in the kondo limit of the tiam or in the two - impurity kondo model by different analytical as well as numerical techniques . @xcite the physics is governed by two energy scales , the nonlocal indirect magnetic interaction @xmath8 and the kondo temperature @xmath9 below which the magnetic moment of the adatom ( impurity ) is screened locally . in the kondo regime for @xmath10 , the conventional picture is that the local magnetic moments at the two impurities are individually screened by forming local singlet states with two kondo clouds of itinerant electron spins from the substrate ( conduction band ) . for large @xmath11 , on the other hand , and in the antiferromagnetic case @xmath12 , the two adatom spins form a nonlocal singlet state and there is no kondo effect . if @xmath13 is ferromagnetic and large as compared to @xmath14 , a nonlocal spin - triplet state is formed . this may subsequently be kondo screened . in the generic case and as a function of @xmath15 there is no quantum phase transition but a smooth crossover from the rkky regime at weak @xmath15 to the kondo regime at strong @xmath15 . for a dense system , i.e. the kondo or anderson lattice model , a static mean - field approach would sharpen this to a phase transition . @xcite dynamical mean - field theory is a comprehensive , thermodynamically consistent and non - perturbative approximation for correlated lattice - fermion models . @xcite dmft treats the kondo effect exactly . on the other hand , one has to tolerate an approximate treatment of the effects of the rkky interaction . it is important to note that there is no approximation of rkky coupling itself : integrating out the non - interacting substrate degrees of freedom , the effective second - order - in-@xmath15 rkky coupling , @xmath16 , is given in terms of the nonlocal static susceptibility of the substrate . it was pointed out by peters and pruschke @xcite that @xmath17 is still finite but reduces to an interaction between nearest neighbors for the case of a lattice in infinite spatial dimensions where the dmft becomes exact . for finite dimensions , it is a long - ranged and oscillating function of the distance @xmath18 . what is neglected in fact for a finite - dimensional lattice , is the feedback of nonlocal , e.g. magnetic correlations , which result from the nonlocal rkky coupling , on the self - energy and thus on the one - particle green s function . this is a rather subtle approximation the quality of which can be estimated by concrete numerical calculations only . the same argumentation holds for the real - space dmft ( r - dmft ) . @xcite r - dmft generalizes the standard dmft to systems with missing or reduced translational symmetry by self - consistently mapping the original ( lattice ) model to a set of single - impurity anderson models ( siam ) , one for each of the geometrically or electronically inequivalent sites . even for the tiam ( see fig . [ fig : schematic_tiam ] ) , this real - space generalization is necessary if one wants to apply dmft in order to test the local approximation for the self - energy . previous applications of the r - dmft concentrated on the mott metal - insulator transition at surfaces and in thin films,@xcite on surface effects in correlated fermi liquids , @xcite on multilayered nanostructures , heterostructures and interfaces , @xcite on disordered systems , @xcite as well as on ultracold atomic gases in optical lattices with harmonic confinement . @xcite it has not been employed , however , to study the effects of the indirect magnetic exchange . the main purpose of the present study is to apply the r - dmft to the particle - hole symmetric tiam at half - filling and zero temperature and to study the magnetic response , i.e. different static magnetic susceptibilities , by applying a weak local magnetic field to one of the adatoms . calculations are performed as a function of the distance between the adatoms and as a function of the hybridization strength @xmath1 to cross over from the kondo to the rkky regime . to test the reliability of the dynamical mean - field approach , the substrate electronic structure is modeled as a one - dimensional tight - binding chain ( see fig . [ fig : schematic_tiam ] ) . the resulting essentially one - dimensional model is accessible to the density - matrix renormalization group ( dmrg ) . @xcite extensive comparison with numerically exact dmrg results obtained from an implementation based on matrix - product states , @xcite and operators along the lines described in ref . helps to benchmark the mean - field approach . our intention is that , by comparing with dmrg , the strengths but also the mean - field artifacts of r - dmft become more transparent . a failure of r - dmft for the weak - coupling limit , where non - local correlations due to the rkky coupling are strong , can be expected from the very beginning . however , there are several interesting questions left , e.g. : where precisely are the limits of the mean - field approach ? how does a failure of the approach manifest itself in the observables ? which physical effects are accessible to a description on the r - dmft level ? to what extent can the physics be reproduced quantitatively in the strong - coupling limit ? such benchmarking of the r - dmft , at the level of the two - impurity anderson model , will be important for future studies of similar systems in higher spatial dimensions , with more correlated adatoms forming more complex geometries such as chains or clusters etc . by choosing the one - dimensional two - impurity anderson model at half - filling , the above - mentioned questions are tackled in a situation that is very unfavorable for r - dmft . the benchmark will thus serve as a `` lower limit '' for the applicability of r - dmft for future applications . our interest in the r - dmft approach to study magnetic nanostructures on surfaces results from its extremely large flexibility . opposed to dmrg , for example , the r - dmft is able to investigate inhomogeneous systems in arbitrary geometries in higher dimensions . while this is actually characteristic for any mean - field approach , the r - dmft is distinguished by the fact that it is non - perturbative and thermodynamically consistent . to account for the effects of short - range correlations , the theory can be improved by certain cluster extensions , such as cellular dmft . @xcite this is , in principle , also conceivable for complicated inhomogeneous geometries but requires further methodical advances as there is no straightforward tiling of the lattice in most cases . the paper is organized as the follows : the next sections introduces the model , notations and quantities of interest . sec . [ rdmft ] and sec . [ dmrg ] briefly describe our real - space dmft and our dmrg approach to the problem , respectively . results of both approaches are presented , compared and discussed in detail in sec . [ results ] . finally , sec . [ con ] concludes the paper .

to analyze the physical properties arising from indirect magnetic exchange between several magnetic adatoms and between complex magnetic nanostructures on metallic surfaces , the real - space extension of dynamical mean - field theory ( r - dmft ) appears attractive as it can be applied to systems of almost arbitrary geometry and complexity . , we consider a simplified model system consisting of two magnetic hubbard sites ( `` adatoms '' ) hybridizing with a non - interacting tight - binding chain ( `` substrate surface '' ) . is used to benchmark r - dmft results for the magnetic coupling between the two adatoms and for the magnetic properties induced in the substrate . in particular , the dependence of the local adatom and the nonlocal adatom - adatom static susceptibilities as well as the magnetic response of the substrate on the distance between the adatoms and on the strength of their coupling with the substrate is studied . we find both , excellent agreement with the dmrg data even on subtle details of the competition between rkky exchange and the kondo effect but also complete failure of the r - dmft , depending on the parameter regime considered .

to analyze the physical properties arising from indirect magnetic exchange between several magnetic adatoms and between complex magnetic nanostructures on metallic surfaces , the real - space extension of dynamical mean - field theory ( r - dmft ) appears attractive as it can be applied to systems of almost arbitrary geometry and complexity . while r - dmft describes the kondo effect of a single adatom exactly , indirect magnetic ( rkky ) exchange is taken into account on an approximate level only . here , we consider a simplified model system consisting of two magnetic hubbard sites ( `` adatoms '' ) hybridizing with a non - interacting tight - binding chain ( `` substrate surface '' ) . this two - impurity anderson model incorporates the competition between the kondo effect and indirect exchange but is amenable to an exact numerical solution via the density - matrix renormalization group ( dmrg ) . the particle - hole symmetric model at half - filling and zero temperature is used to benchmark r - dmft results for the magnetic coupling between the two adatoms and for the magnetic properties induced in the substrate . in particular , the dependence of the local adatom and the nonlocal adatom - adatom static susceptibilities as well as the magnetic response of the substrate on the distance between the adatoms and on the strength of their coupling with the substrate is studied . we find both , excellent agreement with the dmrg data even on subtle details of the competition between rkky exchange and the kondo effect but also complete failure of the r - dmft , depending on the parameter regime considered . r - dmft calculations are performed using the lanczos method as impurity solver . with the real - space extension of the two - site dmft , we also benchmark a simplified r - dmft variant .

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conventional ( rkky ) theory of indirect magnetic exchange predicts an effective exchange interaction @xmath258 where @xmath259 is the nonlocal static susceptibility of the metallic host . this interaction survives , as a nearest - neighbor coupling , @xcite even in the case of two magnetic impurities embedded in an infinite - dimensional lattice and is thus accessible by dynamical mean - field theory . in the limit of infinite spatial dimensions or , at finite dimensions , within the dynamical mean - field approximation , one can therefore expect a finite response at one magnetic impurity subject to a local magnetic field at the other one , located at nearest - neighbor but also for larger distances . on the other hand , nonlocal effective interactions do not contribute to the single - particle self - energy on the dmft level : the dmft self - energy is just defined as the sum of the _ local _ skeleton diagrams only . this is a well - known shortcoming of mean - field theory which gives rise to artifacts in the rkky limit . namely , for @xmath187 the magnetic impurities are only weakly coupled to the host and thus become extremely susceptible . a tiny weiss field within dmft is then sufficient to drive the system to an artificial symmetry - broken state , i.e. an antiferromagnetic state rather than a nonlocal singlet of the impurity magnetic moments is formed . a state with the characteristic distance dependence of the rkky interaction , e.g. @xmath260 for a one - dimensional system at half - filling , can not be recovered within dmft as it is always preempted by spontaneous symmetry breaking . clearly , solutions with a finite magnetic moment could easily be suppressed in a mean - field approach . one should note , however , that the resulting magnetic susceptibility is unphysical , i.e. negative , as it refers to a thermodynamically unstable state . therefore , in any case , the physics of the rkky limit is not accessible by dmft . the present study has shown , however , that beyond the rkky limit , ( real - space ) dmft is well suited to study even quantitatively the effects of indirect magnetic exchange . here , we have concentrated on two magnetic `` adatoms '' on a one - dimensional `` substrate surface '' a minimal model to study indirect magnetic interactions in competition with the kondo effect for magnetic atoms on metallic surfaces and a model that is amenable to an exact numerical solution by means of the density - matrix renormalization group . dmrg has been used to compute spin - spin correlation functions and static spin susceptibilities , and particularly adatom - substrate site correlations and susceptibilities . depending on the distance @xmath0 between the two adatoms and depending on the hybridization strength @xmath1 , rather complicated profiles are obtained . comparing the results for the two - adatom ( two - impurity ) anderson model with those obtained for the corresponding single - adatom ( single - impurity ) anderson model , one can easily classify the different features of those profiles as single - impurity effects or as resulting from the adatom - adatom effective interaction . in this way , clear reminiscences of the rkky interaction , i.e. of nonlocal singlet formation , are found to compete with the formation of kondo clouds and screening of the adatom magnetic moments . in addition , the profiles are strongly affected by the finite system size ( chains with typically @xmath124 have been considered here ) and by effects resulting from strong surface friedel oscillations in the local density of states , especially if the adatoms are in the vicinity to one of the chain edges . this complex interplay of different physical mechanisms is almost perfectly recovered by the real - space dmft . qualitatively , the real - space dmft is reliable as long as the model parameters , in particular the local exchange coupling @xmath261 , are in a regime well separated from the artificial symmetry - broken state . this parameter regime , where the adatom susceptibilities are not too large or where the adatom magnetic moments are predominantly interacting with the substrate moments rather than among each other , however , goes well beyond the extreme kondo limit of non - overlapping kondo clouds . the critical value for @xmath240 in units of @xmath29 at @xmath154 gives an impression of a lower bound for the applicability of r - dmft . while the present study has focused on a one - dimensional model to allow for benchmarking against numerically exact dmrg results , future applications of the r - dmft should address higher - dimensional systems . with increasing coordination number of correlated sites , the parameter space accessible to the mean - field approach is expected to be become larger or mean - field artifacts less pronounced . for the case of atoms trapped in optical lattices , there are impressing examples where r - dmft has contributed to an understanding of the physics of inhomogeneous systems with @xmath116 correlated and geometrically inequivalent sites in two dimensions , for example . let us also point out that for anderson - type multi - impurity or lattice models , one typically expects non - local magnetic correlations to diminish rapidly as the electron filling on the correlated sites is changed away from half - filling . systems off half - filling are thus expected to be more amenable to an r - dmft approach . at the same time they are also interesting physically as reducing the filling away from half - filling affects local - moment formation as well . hence , the competition between non - local rkky interaction and kondo screening must be seen as strongly filling dependent . for complex magnetic nanostructures with several magnetic adatoms in different chain or cluster geometries on two- or on semi - infinite three - dimensional metallic surfaces , a mean - field approach is inevitable anyway . here the conceptual simplicity of a single - site mean - field theory , as compared to different possibilities for cluster extensions , is important as it allows to study almost arbitrary geometries . as in ab - initio studies , the accessible system size strongly depends on the remaining e.g. lateral spatial symmetries , and the computational effort scales nearly linearly with the number of inequivalent correlated sites only . the two - impurity one - dimensional anderson model represents a model that is rather unfavorable to a single - site r - dmft approach . even for this case , as the present study has shown , r - dmft can in fact almost quantitatively predict the effects of indirect magnetic exchange in competition with the kondo and with geometrical effects as long as the approximation predicts a fermi - liquid ground state .

while r - dmft describes the kondo effect of a single adatom exactly , indirect magnetic ( rkky ) exchange is taken into account on an approximate level only . here this two - impurity anderson model incorporates the competition between the kondo effect and indirect exchange but is amenable to an exact numerical solution via the density - matrix renormalization group ( dmrg ) . the particle - hole symmetric model at half - filling and zero temperature

to analyze the physical properties arising from indirect magnetic exchange between several magnetic adatoms and between complex magnetic nanostructures on metallic surfaces , the real - space extension of dynamical mean - field theory ( r - dmft ) appears attractive as it can be applied to systems of almost arbitrary geometry and complexity . while r - dmft describes the kondo effect of a single adatom exactly , indirect magnetic ( rkky ) exchange is taken into account on an approximate level only . here , we consider a simplified model system consisting of two magnetic hubbard sites ( `` adatoms '' ) hybridizing with a non - interacting tight - binding chain ( `` substrate surface '' ) . this two - impurity anderson model incorporates the competition between the kondo effect and indirect exchange but is amenable to an exact numerical solution via the density - matrix renormalization group ( dmrg ) . the particle - hole symmetric model at half - filling and zero temperature is used to benchmark r - dmft results for the magnetic coupling between the two adatoms and for the magnetic properties induced in the substrate . in particular , the dependence of the local adatom and the nonlocal adatom - adatom static susceptibilities as well as the magnetic response of the substrate on the distance between the adatoms and on the strength of their coupling with the substrate is studied . we find both , excellent agreement with the dmrg data even on subtle details of the competition between rkky exchange and the kondo effect but also complete failure of the r - dmft , depending on the parameter regime considered . r - dmft calculations are performed using the lanczos method as impurity solver . with the real - space extension of the two - site dmft , we also benchmark a simplified r - dmft variant .

astro-ph0606530

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we presented a study of the spatially - resolved dynamics in the optical emission line gas around the [email protected] powerful radio galaxy mrc1138 - 262 , using the near - infrared integral - field spectrograph spiffi on ut1 of the vlt . the large - scale kinematics in the emission line nebula of this galaxy are not consistent with the signatures of large - scale gravitational motion or starburst - driven winds . velocities and fwhms of @xmath279 indicate a vigorous outflow with an estimated total energy which is orders of magnitude higher than suggested for starburst - driven winds . based on timescale and energy arguments , we conclude that the observed outflow , which is a strict lower limit to the intrinsic amount of outflowing gas , is most plausibly driven by the agn . this implies a relatively efficient interaction between agn and interstellar medium , with efficiency @xmath280 , mostly mediated by mechanical energy injection through the radio jet . radiation - driven winds do not appear powerful enough to explain the observed velocities over the size of the optical line emitting gas . for mrc1138 - 262 we estimate from simple energetic arguments that the total energy needed to drive the observed outflow of optical emission line gas is of - order few @xmath24 @xmath216 ergs with a mass outflow rate , @xmath281 yr@xmath15 . if we assume that every luminous qso near the peak of their co - moving density at z@xmath392 has such an outflow phase with similar characteristics to mrc1138 - 262 we find that powerful agn eject @xmath282 ergs mpc@xmath237 of energy into the igm and @xmath283 mpc@xmath237 of gas , including @xmath284 mpc@xmath237 in metals . these energy and masses are significant compared to the the total binding energy and mass budget of @xmath253 early - type galaxies in the local universe . if mrc1138 - 262 is indeed archetypal , then agn winds have the potential to be of similar , perhaps even larger , cosmological signficance than starburst - driven winds , especially for the most massive galaxies . they accelerate the outflowing gas to much higher velocities than starburst - driven winds , and much of this material and energy are likely to escape the potential of even the most massive individual galaxy halo . outflows like in mrc1138 - 262 have the potential to explain the observed properties of low - redshift massive galaxies , namely their old , and narrow range of ages and low gas fractions . moreover , the large mass loss rates and short timescales of their outflows can naturally explain the observed enhancement of [ @xmath5/fe ] relative metal abundances observed in the most massive galaxies at low redshift . agn - driven outflows appear to be a plausible mechanism that efficiently suppresses star - formation within a few @xmath9 yrs . they also have high enough energies to perhaps stop the accretion flow of matter from the igm into their dark matter halos . thus , if accretion is followed by agn activity , then agn feedback may be an effective mechanism for regulating galaxy growth @xcite . our study comprises only one source , but we have indirect evidence for mrc1138 - 262 being far from unique . velocities of @xmath285 are not uncommon in the extended emission line gas of powerful radio galaxies , but are generally extracted from longslit spectra aligned with the radio jet axis only . simulating a longslit spectrum from the spiffi data cube , we find good agreement between mrc1138 - 262 and these samples . the bolometric and radio jet luminosities of mrc1138 - 262 are not unusual , and the source follows the @xmath286 relationship of high - redshift radio galaxies , if correcting for the luminous broad line emission . we are currently acquiring rest - frame optical , integral - field data for a larger sample of hzrgs , to make statistically more robust predictions . preliminary results strongly support the present analysis , giving further evidence that agn feedback plays a major role in the evolution of the most massive galaxies in the universe . martini , p. 2004 , invited review to appear in `` carnegie observatories astrophysics series , vol . 1 : coevolution of black holes and galaxies , '' ed . l. c. ho ( cambridge : cambridge univ . press ) , astro - ph/0304009

to explain the properties of the most massive low - redshift galaxies and the shape of their mass function , recent models of galaxy evolution include strong agn feedback to complement starburst - driven feedback in massive galaxies . using the near - infrared integral - field spectrograph spiffi on the vlt , we searched for direct evidence for such a feedback in the optical emission line gas around the z.16 powerful radio galaxy mrc1138 - 262 , likely a massive galaxy in formation . the kpc - scale kinematics , with fwhms and relative velocities and nearly spherical spatial distribution , do not resemble large - scale gravitational motion or starburst - driven winds . observed outflow properties are in gross agreement with the models , and suggest that agn winds might have a similar , or perhaps larger , cosmological significance than starburst - driven winds , if mrc1138 - 262 is indeed archetypal .

to explain the properties of the most massive low - redshift galaxies and the shape of their mass function , recent models of galaxy evolution include strong agn feedback to complement starburst - driven feedback in massive galaxies . using the near - infrared integral - field spectrograph spiffi on the vlt , we searched for direct evidence for such a feedback in the optical emission line gas around the z.16 powerful radio galaxy mrc1138 - 262 , likely a massive galaxy in formation . the kpc - scale kinematics , with fwhms and relative velocities and nearly spherical spatial distribution , do not resemble large - scale gravitational motion or starburst - driven winds . order - of - magnitude timescale and energy arguments favor the agn as the only plausible candidate to accelerate the gas , with a total energy injection of ergs or more , necessary to power the outflow , and relatively efficient coupling between radio jet and ism . observed outflow properties are in gross agreement with the models , and suggest that agn winds might have a similar , or perhaps larger , cosmological significance than starburst - driven winds , if mrc1138 - 262 is indeed archetypal . moreover , the outflow has the potential to remove significant gas fractions (% ) from a galaxy within a few 10 to 100 myrs , fast enough to preserve the observed [/fe ] overabundance in massive galaxies at low redshift . using simple arguments , it appears that feedback like that observed in mrc1138 - 262 may have sufficient energy to inhibit material from infalling into the dark matter halo and thus regulate galaxy growth as required in some recent models of hierarchical structure formation .

0912.2159

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, 76 sources , left panel ) and the @xmath87\lambda 5007 $ ] line luminosity ( @xmath88 $ ] , 46 sources , right panel ) for h@xmath2o maser sources ( solid lines ) , in units of ergs@xmath86 . for comparison , the distributions are also given for a seyfert 2 sample without known h@xmath2o maser emission ( dashed lines , 38 sources from mulchaey et al . all numbers are plotted on a percent scale ( % ) .,width=377 ] $ ] line luminosity , corrected for extinction , of h@xmath2o maser galaxies on a logarithmic scale . for comparison , the distribution is also given for a seyfert 2 sample without known h@xmath2o maser emission ( dashed lines , 38 sources from mulchaey et al . right panel : the fir versus extinction - corrected @xmath3 $ ] luminosity . the straight line shows a linear fit to the unweighted data.,width=453 ] for our h@xmath2o maser galaxies with available data , the luminosity distributions of both isotropic indicators , the @xmath3 $ ] line and the fir luminosities , are presented in fig . 1 . the left panel shows the histogram of the infrared luminosities for all 76 h@xmath2o maser galaxies with available data ( @xmath89 , hereafter luminosity in logarithmic scale and in units of ergs@xmath86 ) . @xmath90 ranges from 41.8 to 45.5 , with a mean value of [email protected] ( the error denotes the standard deviation of the mean ) . for the sub - sample of 10 masers associated with massive star formation , the mean value of @xmath9@xmath91@[email protected] is slightly fainter than that of the agn masers . however , the difference between both distributions ( not shown here ) is not significant . the histogram shown in the right panel presents the number of the h@xmath2o maser sources as a function of the @xmath3 $ ] line luminosity . it gives the range of @xmath9@xmath92}$]@xmath7 from 39 to 43.2 and a mean value of [email protected] , comparable to results of seyfert 2 galaxies not associated with detected h@xmath2o maser ( mulchaey et al . 1994 ) . for comparison , the latter sample is also presented in fig . 1 ( dashed lines ) . for the two tracers @xmath90 and @xmath93}$ ] , the ratio was calculated and the distribution of the ratio is shown as a histogram in fig . 2 ( left panel ) . no significant difference can be found for the distribution of the ratio between our h@xmath2o maser galaxies and the seyfert 2 galaxy sample not containing galaxies with known masers ( mulchaey et al . this is in agreement with the fact that most h@xmath2o maser sources have been found in seyfert 2 systems . the good agreement between seyfert 1 and seyfert 2 galaxies ( mulchaey et al . 1994 ) with respect to this parameter , in spite of different viewing angles , lends further support to an approximately isotropic emission of both tracers . in order to further compare those two isotropic tracers , the fir luminosity is plotted against the extinction - corrected @xmath3 $ ] luminosity of our maser sample in the right panel of fig.2 . a correlation is found , logl@xmath75=([email protected])+ ( [email protected])logl@xmath77}$ ] with a spearman s rank correlation coefficient r=0.66 and a chance probability @xmath9 5@xmath9410@xmath95 . assuming the corrected @xmath3 $ ] line luminosity to be a good isotropic tracer ( bassani et al . 1999 ) , the strong correlation between fir luminosity and @xmath3 $ ] line luminosity may suggest that the fir luminosity is to some extent also an indicator of intrinsic nuclear activity , even though the fir flux may be contaminated by a spatially extended starburst component . ) of the iron line versus the thickness parameters l@xmath96/l@xmath97}$ ] ( t1 , left panel ) and l@xmath96/l@xmath75 ( t2 , right panel ) . square and pentacle symbols represent compton - thick and -thin sources as identified by modeling their x - ray spectra ( e.g. , zhang et al . the bold squares show those compton - thick sources , which have high ew ( k@xmath5 ) and low t values . these are located in the upper - left regions of both panels . three _ exceptional _ sources ngc2639 , mrk3 , and ngc4945 are marked . for ngc4945 , the lower limit of its [ oiii ] luminosity is taken . details are given in sect.3.2.,width=604 ] as mentioned above , nuclear absorbing columns can be obtained by analyzing x - ray spectra . these analyses are model dependent . comparing the observed 2 - 10kev x - ray emission from the nuclear region , absorbed by the obscuring material along the line - of - sight , with the intrinsic nuclear power provides another method for evaluating the absorbing column density . the ratio of the observed 2 - 10kev luminosity and the luminosity of the nuclear isotropic indicators was assumed to represent the optical thickness parameter , which allows us to diagnose the gas absorption ( bassani et al . 1999 ) . here the l@xmath74/l@xmath97}$ ] and l@xmath74/l@xmath75 ratios are used as optical thickness parameters . in addition , high ew ( @xmath6 ) values of the iron emission line are considered as a qualitative feature indicating a heavily obscured nucleus ( e.g. , maiolino & risaliti 2007 ) . combining the ew ( @xmath6 ) and the optical thickness parameters , we probe the circumnuclear environment of the maser sources . for the maser galaxies with available data ( ew ( @xmath6 ) , l@xmath74 , l@xmath97}$ ] and l@xmath75 , in total 31 agn maser sources ) , the ew ( k@xmath5 ) of the iron lines is plotted against the optical thickness parameters in fig.3 . the prominent feature of the figure is the existence of an anti - correlation , which is similar to that obtained for the seyfert 2 sample of bassani et al . ( 1999 ) , which is predominantly containing targets without known maser lines . in the left panel ( ew ( @xmath6 ) v.s . l@xmath74/l@xmath97}$ ] ) , a least - squares fit shows log(ew ( @xmath6))=([email protected])+ ( [email protected])logl@xmath74/l@xmath97}$ ] , with spearman s rank correlation coefficient r=-0.57 and a chance probability of p @xmath10.001 . the possibly compton - thick sources ( shown by squares in fig.3 ) , determined by modeling their x - ray spectra , cluster in the upper left region , the region with high ew ( k@xmath5 ) and low l@xmath74/l@xmath97}$ ] values . this area is marked by dashed lines . the approximate boundaries between compton - thick and -thin sources , the latter shown by pentacles , are log(l@xmath74/l@xmath97}$])@xmath10.25 ( i.e. , @xmath8@xmath12@xmath10}$ ] ) and logew ( @xmath6)@xmath12.5 ( i.e , ew@xmath1300ev ) . for comparison with seyfert 2 galaxies without detected h@xmath2o maser emission , the seyfert 2 sample of bassani et al . ( 1999 ) is used , excluding those objects with maser emission . the trend is the same for this sample ( here not shown ) . compton - thick sources fall again into the upper left region with high ew ( k@xmath5 ) and low l@xmath74/l@xmath97}$ ] values , while compton - thin sources are located in the lower right . the right panel of fig.3 shows a similarly clear anti - correlation between ew ( k@xmath5 ) and l@xmath74/l@xmath75 . linear fitting results in log(ew ( @xmath6))=(1.71 @xmath44 0.26 ) + ( -0.36@xmath44 0.08)logl@xmath74/l@xmath75 , with r=-0.61 and p @xmath1 2 @xmath9410@xmath98 . most of those sources with high ew ( k@xmath5 ) and low l@xmath74/l@xmath75 value ( upper - left region , in square symbols ) are compton - thick sources , while those sources with low ew ( k@xmath5 ) and high l@xmath74/l@xmath75 value ( in pentacles ) are compton - thin as determined from x - ray spectral fitting . the approximate boundaries between compton - thick and -thin environments are in this case logl@xmath74/l@xmath75@xmath1 - 2.75 ( i.e. , @xmath11@xmath1600@xmath8 ) and logew ( @xmath6)@xmath12.5 , i.e. again ew@xmath1300ev . we like to emphasize that these boundaries are not arbitrary . among the 20 compton - thick candidate sources from our sample , classified by conventional x - ray spectroscopy , we find 19 in each of our limited `` compton - thick '' regions , related either to l@xmath74/l@xmath97}$ ] or to l@xmath74/l@xmath75 . 18 of these sources are identical ( see also sect.4 ) . the results obtained so far could be affected by systematic errors in the measurements . assuming for the [ oiii ] values uncertainties of @xmath120% ( dahari & de robertis 1988 ) results in l@xmath74/l@xmath97}$ ] errors of order 0.08dex . obviously , this does not affect the robust fundamental trend in our diagnostic fig.3 . compton - thick sources are still placed in the upper left and compton - thin sources in the lower right . the anti - correlation between the ew ( @xmath6 ) and the optical thickness parameters are readily explained . with an increase of the absorbing column density , the x - ray luminosity will decrease so that l@xmath74/l@xmath97}$ ] and l@xmath74/l@xmath75 are reduced with respect to l@xmath97}$ ] and l@xmath75 . on the other hand , the ew ( @xmath6 ) values will increase , since these are measured against a reduced 6.4kev continuum level . with compton - thick galaxies being located in the upper left part of the panels in fig . 3 , we find for our h@xmath2o maser galaxies three criteria hinting at a compton - thick nuclear environment : ew ( @xmath6)@xmath7300ev , @xmath8@xmath92@xmath10}$ ] and @xmath11@xmath7600 @xmath8 . these are independent of the detailed shape of the x - ray spectrum . the search for new extragalactic h@xmath2o masers is ongoing and important with respect to several key aspects of modern astrophysics ( see , e.g. , sect.1 and braatz et al . 2009 ) . here we therefore investigate possible indicators of h@xmath2o maser emission . we analyze relationships between h@xmath2o maser luminosity and the iron line ew ( k@xmath5 ) , fir , and @xmath99}$ ] luminosity . ) ( logarithmic scale , in units of ev ) for seyfert 2s with detected h@xmath2o maser emission ( 19 sources , solid lines ) and non - masing seyfert 2s ( 34 sources from bassani et al . 1999 , dashed lines).,width=302 ] for 33 maser sources with available ew ( @xmath6 ) of the iron line in table1 , we obtain an ew ( k@xmath5 ) mean value of @xmath100ev . x - ray observations show that strong iron line emission is common in the spectra of agn hosting h@xmath2o masers . it is interesting to check if the 6.4kev line can be used as a criterion to search for agn masers . have seyfert 2s with detected maser emission higher ew ( k@xmath5 ) values than non - maser seyfert 2s ? our statistical results show that the iron line ew ( @xmath6 ) of masing seyfert 2 galaxies ( mean value @xmath101ev and median value @xmath1800ev for our 19 maser sources ) is higher than that of the non - maser seyfert 2 sample ( mean value @xmath102ev and median value @xmath1200ev for 34 sources from bassani et al . figure 4 shows the distributions of both samples . while the difference seems to be obvious at first sight , we should cautiously avoid a definite conclusion due to the large scatter , the still too small number of sources , and the incompleteness of the studied samples . potential differences in sensitivity have also to be addressed . for our maser host seyfert 2s , the ew ( @xmath6 ) values were taken almost exclusively ( except four sources ) from _ xmm - newton _ or _ chandra _ observations . the results for seyfert 2s without known masers ( bassani s sample ) come mostly from asca data of lower sensitivity , which might lead to an increase in the real average ( only sources with a strong iron line could be detected ) . this strengthens our result and amplifies the difference between seyfert 2s with and without detected 22ghz h@xmath2o maser . nevertheless , we consider our result as tentative . ) of the iron line ( logarithmic scale , in units of ev ) versus isotropic luminosity of the h@xmath2o maser emission ( logarithmic scale , in @xmath103 ) . center : [ oiii ] line luminosity against @xmath104 ; bottom : fir luminosity against @xmath104 , empty circles show galactic h@xmath2o masers from jaffe et al . ( 1981 ) and the line marks the correlation of @xmath104/@xmath105}$]@xmath110@xmath106 . squares and triangles represent agn - masers and masers in star formation regions respectively . disk - masers , as a subsample of agn - masers , for which maser emission is anticipated to be particularly well connected with indicators of the intrinsic nuclear power , are marked by crosses over squares.,width=377 ] in order to investigate possible correlations between h@xmath2o maser and iron emission lines , the ew ( @xmath6 ) of the fe line was plotted against the isotropic h@xmath2o luminosity in fig.5 ( upper panel ) . as already mentioned , h@xmath2o maser emission can be produced by collisional pumping in a dense molecular layer , which is heated by irradiated x - rays from the nucleus ( neufeld et al . strong fe @xmath6 emission is believed to be produced via x - ray reflection by the cold iron in the circumnuclear region ( e.g. , fabian et al . 2000 ) . in those cases where h@xmath2o maser and iron line emission are detected , the nuclear x - ray emission plays a key role . correlations between maser and iron line emission are therefore expected . however , our results show no apparent trend between the iron line ew ( k@xmath5 ) and the isotropic h@xmath2o maser luminosity , neither for the entire sample nor the two subsamples , agn- and star - forming masers ( squares and triangles , respectively , in fig.5 ) . in view of alternative h@xmath2o excitation mechanisms ( see , e.g. , lo 2005 ) , the subsample of possible disk - masers ( with detected high velocity maser features ) was analyzed separately ( see the crosses in fig.5 ) . however , even in this case no significant correlation can be found . the [ oiii ] and fir luminosities were also plotted against h@xmath2o maser luminosity in fig.5 ( central and bottom panel respectively ) . there is no significant correlation between @xmath107}$ ] and @xmath104 , although maser sources related to star formation seem to have lower [ oiii ] luminosities than agn masers . for fir versus maser luminosities , there appears to be a correlation , similar to that previously found by henkel et al . ( 2005 ) , castangia et al . ( 2008 ) , bennert et al . ( 2009 ) and surcis et al . the relation was first found for galactic star forming regions by jaffe et al . 1981 , i.e. , luminous h@xmath2o masers form in star formation regions with high fir luminosity . for comparison , values of galactic h@xmath2o masers are also plotted in fig.5 ( empty circles ) and the line shows the correlation of @xmath104/@xmath105}$]@xmath110@xmath106 from jaffe et al . apparently , there exists a correlation between fir and h@xmath2o maser luminosity over many orders of magnitude . when considering agn - masers only ( squares in fig.5 , lowest panel ) , the strongest masers appear to be overluminous with respect to the @xmath108-@xmath109 correlation . this is likely caused by the different properties of agn versus star - forming masers .

can be established for compton - thick nuclear regions . there are no obvious correlations between the ew ( k ) , the $ ] luminosity and the isotropic ho maser luminosity . when comparing samples of seyfert 2s with and without detected ho maser lines , there seem to exist differences in ew ( k ) and the fraction of compton - thick nuclei . this should be studied further . for agn masers alone , there is no obvious correlation between fir and ho maser luminosities .

to shed light onto the circumnuclear environment of 22 ghz ( 1.3 cm ) ho maser galaxies , we have analyzed some of their multi - wavelength properties , including the far infrared luminosity ( fir ) , the luminosity of the\lambda5007 $ ] emission line , the nuclear x - ray luminosity , and the equivalent width of the neutral iron emission line ( ew ( k ) ) . our statistical analysis includes a total of 85 sources , most of them harboring an active galactic nucleus ( agn ) . there are strong anti - correlations between ew ( ) and two `` optical thickness parameters '' , i.e. the ratios of the x - ray luminosity versus the presumably more isotropically radiated $ ] and far infrared ( fir ) luminosities . based on these anti - correlations , a set of quantitative criteria , ew ()ev ,}$ ] and can be established for compton - thick nuclear regions . 18 ho maser galaxies belong to this category . there are no obvious correlations between the ew ( k ) , the $ ] luminosity and the isotropic ho maser luminosity . when comparing samples of seyfert 2s with and without detected ho maser lines , there seem to exist differences in ew ( k ) and the fraction of compton - thick nuclei . this should be studied further . for agn masers alone , there is no obvious correlation between fir and ho maser luminosities . however , including masers associated with star forming regions , a linear correlation is revealed . overall , the extragalactic fir - ho data agree with the corresponding relation for galactic maser sources , extrapolated by several orders of magnitude to higher luminosities .

0912.2159

i

in this paper , multi - wavelength data from the complete sample of galaxies ( @xmath111@xmath7100kpc ) so far reported to host 22ghz h@xmath2o masers are analyzed , including the equivalent width ( ew ) of the iron @xmath6 line , the @xmath3\lambda 5007 $ ] line , and the x - ray and fir emission . the latter two are considered to be the isotropic tracers of intrinsic nuclear power . the observed nuclear x - ray luminosity , compared with the luminosities of these two isotropic tracers ( our optical thickness parameters ) , can be used as a measure of the circumnuclear absorption . the ew ( @xmath6 ) and the optical thickness parameters ( @xmath110/@xmath112}$ ] , @xmath110/@xmath108 ) are combined here to probe the obscuration of maser host agn . the main results are summarized below : \(1 ) our statistical analysis shows obvious anti - correlations between the ew ( @xmath6 ) of the fe emission line and the two optical thickness parameters . without requiring a full x - ray spectrum , compton - thick nuclear environments can be identified with these parameters and are found to be characterized approximately by ew ( @xmath6)@xmath7300ev , @xmath8@xmath92@xmath113}$ ] and @xmath11@xmath7600@xmath8 ; \(2 ) 18 h@xmath2o maser sources matching these criteria are identified to be compton - thick . a comparison with zhang et al . ( 2006 ) shows , that among these there are five newly identified h@xmath2o maser galaxies which are compton - thick , i.e. , ngc591 , ugc5101 , ngc3072 , ic2560 and mrk266 . masers associated with seyfert 2 nuclei may be more likely compton - thick ( 60% ) than seyfert 2s without detected maser emission ( @xmath145% ) . however , this still has to be confirmed with larger samples ; \(3 ) in an attempt to guide future h@xmath2o maser surveys , new ways to find extragalactic h@xmath2o sources are also explored . maser sources may show larger ew ( k@xmath5 ) values than non - maser seyfert 2s , which , however , also needs further support . no significant correlations have been found between ew ( k@xmath5 ) , @xmath112}$ ] and @xmath104 . there appears a linear correlation between @xmath108 and @xmath104 , which is consistent with the correlation found for galactic h@xmath2o masers . however , the strongest h@xmath2o masers appear overluminous with respect to their @xmath108 . this may be related to their different origin when compared with masers associated with sites of massive star formation well outside the nuclear region of their parent galaxy . we wish to thank the anonymous referee for many detailed and constructive comments as well as p. castangia for critically reading the manuscript . this work is supported partly by the national natural scientific foundation of china ( 10633010 ) and guangdong province natural science foundation ( 8451009101001047 ) . we made use of the nasa / ipac extragalactic database ( ned ) , high - energy astrophysics science and research center ( heasarc ) and the nasa astrophysics data system bibliographic services ( ads ) . 2 alonso - herrero , a. , ward , m. j. & kotilainen , j. k. 1997 , mnras , 288 , 947 awaki , h. , ueno , s. , taniguchi , y. & weaver , k. a. 2000 , apj , 542 , 175 ballo , l. , braito , v. , della ceca , r. , maraschi , l. , tavecchio , f. & dadina , m. 2004 , apj , 600 , 634 bassani , l. , dadina , m. , maiolino , r. , salvati , m. , risaliti , g. , della ceca , r. , matt , g. & zamorani , g. 1999 , apjs , 121 , 473 beckmann , v. , gehrels , n. , favre , p. , walter , r. , courvoisier , t. j .- l . , petrucci , p .- o . & malzac , j. 2004 , apj , 614 , 641 bennert , n. , barvanis , r. , henkel , c. & antonucci , r. 2009 , apj , 695 , 276 bianchi , s. , balestra , i. , matt , g. , guainazzi , m. & perola , g. c. 2003 , a&a , 402 , 141 bianchi , s. , miniutti , g. , fabian , a. c. , & iwasawa , k. 2005 , mnras , 360 , 380 braatz , j. a. , wilson , a. s. , & henkel , c. 1997 , apjs , 110 , 321 braatz , j. a. & gugliucci , n. e. 2008 , apj , 678 , 96 braatz , j. a. , condon , j. j. , henkel , c. , lo , k .- y . & reid , m.j . 2009 , astro2010 , 23 cappi , m. et al . 1999 , a&a , 344 , 857 cappi , m. et al . 2006 , a&a , 446 , 459 castangia , p. , tarchi , a. , henkel , c. & menten , k. m. 2008 , a&a , 479 , 111 dahari , o. & de robertis , m. m. 1988 , apjs , 67 , 249 darling , j. , brogan , c. & johnson , k. 2008 , apjs 685 , 39 della ceca , r. et al . 2002 , apj , 581 , 9 diaz , a. i. , prieto , m. a. & wamsteker , w. 1988 , a&a , 195 , 5 done , c. , madejski , g. m. , zycki , p. t. , & greenhill , l. j. 2003 , apj , 588 , 763 fabian , a. c. , iwasawa , k. , reynolds , c. s. & young , a. j. 2000 , pasp , 112 , 1145 ghisellini , g. , haardt , f. & matt , g. 1994 , mnras , 267 743 greenhill , l. j. , tilak , a. & madejski , g. 2008 , apj , 686 , l13 guainazzi , m. , matt , g. , brandt , w. n. , antonelli , l. a. , barr , p. & bassani , l. 2000a , a&a , 356 , 463 guainazzi , m. , matt , g. , fiore , f. , & perola , g. c. , 2002 , a&a , 388 , 787 guainazzi , m. , rodriguez - pascual , p. , fabian , a. c. , iwasawa , k. & matt , g. 2004 , mnras , 355 , 297 guainazzi , m. , fabian , a. c. , iwasawa , k. , matt , g. & fiore , f. 2005a , mnras , 356 , 295 guainazzi , m. , matt , g. & perola , g. c. 2005b , a&a , 444 , 119 heckman , t. m. , balick , b. & crane , p. c. 1980 , a&as , 40 , 28 heckman , t. m. , ptak , a. , hornschemeier , a. & kauffmann , g. , 2005 , apj , 634 , 161 henkel , c. , peck , a. b. , tarchi , a. , nagar , n. m. , braatz , j. a. , castangia , p. & moscadelli , l. 2005 , a&a , 436 , 75 ho , l. c. , filippenko , a. v. & sargent , w. l. w. 1997 , apjs , 112 , 315 imanishi , m. , terashima , y. , anabuki , & n. , nakagawa , t. 2003 , apj , 596 , 167 impellizzeri , c. m. v. , mckean , j. p. , castangia , p. , roy , a. l. , henkel , c. , brunthaler , a. & wucknitz , o. 2008 , nature , 456 , 927 iwasawa , k. , maloney , p. r. & fabian , a. c. 2002 , mnras , 336 , 71 iyomoto , n. , fukazawa , y. , nakai , n. & ishihara , y. 2001 , apj , 561 , 69 jaffe , d. t. , guesten , r. & downes , d. 1981 , apj , 250 , 621 jenkins , l. f. , roberts , t. p. , ward , m. j. & zezas , a. 2004 , mnras , 352 , 1335 kim , d .- c . , sanders , d. b. , veilleux , s. , mazzarella , j. m. & soifer , b. t 1995 , apj , 98 , 129 kondratko , p.t . , greenhill , l. j. & moran , j. m. 2006 , apj , 652 , 136 kraft , r. p. , hardcastle , m. j. , worrall , d. m. & murray s. s. 2005 , apj , 622 , 149 lamastra , a. , bianchi , s. , matt , g. , perola , g. c. , barcons , x. & carrera , f. j. 2009 , a&a , 504 , 73 leahy , d. a. , & creighton , j. 1993 , mnras , 263 , 314 levenson , n. a. , heckman , t. m. , krolik , j. h. , krolik , j. h. , weaver , k. a. & zycki , p. t. 2006 , apj , 648 , 111 lightman , a. p. & white , t. r. 1988 , apj , 335 , 57 lo , k. y. 2005 , ara&a , 43 , 625 lumsden , s. l. & alexander , d. m. 2001 , mnras , 328 , l32 madejski , g. , done , c. , zycki , p. t. & greenhill , l. 2006 , apj , 636 , 75 maiolino , r. & rieke , g. h. , 1995 , apj , 454 , 95 maiolino , r. & risaliti , g. 2007 , in asp conf . , 373 , the central engine of activ e galactic nuclei , ed . l. c. ho & j .- m.wang ( sanfrancisco , ca : asp ) , 447 matt , g. , guainazzi , m. , perola , g. c. , fiore , f. , nicastro , f. , cappi , m. & piro , l. 2001 , a&a , 377 , 31 matt , g. 1997 , mem . ital . , 68 , 127 matt , g. , bianchi , s. , guainazzi , m. & molendi , s. , 2004 , a&a , 414 , 155 matsumoto , c. , nava , a. , maddox , l. a. , leighly , k. m. , grupe , d. , awaki , h. & ueno , s. 2004 , apj , 617 , 930 mulchaey , m. et al . 1994 , apj , 436 , 586 netzer , h. , mainieri , v. , rosati , p. & trakhtenbrot , b. 2006 , a&a , 453 , 525 neufeld , d. a. , maloney , p. r. , & conger , s. 1994 , apj , 436l , 127 ohno , m. , fukazawa , y. & iyomoto , n. 2004 , pasj , 56 , 425 panessa , f. , bassani , l. , cappi , m. , dadina , m. , barcons , x. , carrera , f. j. , ho , l. c. & iwasawa , k. 2006 , a&a , 455 , 173 polletta , m. , bassani , l. , malaguti , g. , palumbo , g. g. c. & caroli , e. 1996 , apj , 106 , 399 ptak , a. , heckman , t. , levenson , n. a. , weaver , k. & strickland , d. 2003 , apj , 592 , 782 risaliti , g. , maiolino , r. & salvati , m. 1999 , apj , 522 , 157 risaliti , g. , gilli , r. , maiolino , r. & salvati m. , 2000 , a&a , 357 , 13 shu , x. w. , wang , j. x. , jiang , p. , fan , l. l. & wang , t , g . , 2007 , apj , 657 , 167 smith , d. a. & done , c. , 1996 , mnras , 280 , 355 smith , d. a. & wilson , a. s. , 2001 , apj , 557 , 180 spergel , d. n. et al . 2003 , apjs , 148 , 175 storchi - bergmann , t. & pastoriza , m. g. 1989 , apj , 347 , 19 storchi - bergmann , t. , kinney , a. l. & challis , p. 1995 , apjs , 98 , 10 su , j. b. , zhang , j. s. & fan , j.h . , . j. astron . astrophys . , 8 , 547 surcis , n. , tarchi , a. , henkel , c. , ott , j. , lovell , j. & castangia , p. 2009 , a&a , 502 , 529 terlevich , r. , melnik , j. , masegosa , j. , moles , m. & copetti , m. v. f. 1991 , a&as , 91 , 285 terashima , y. , iyomoto , n. , ho , l. c. & ptak , a. f. , 2002 , apjs , 139 , 1 tran , h. d. 2001 , apj , 554 , l19 turner , t. j. , george , i. m. , nandra , k. & mushotzky , r. f. 1997 , apjs , 113 , 23 weaver , k. a. , gelbord , j. & yaqoob , t. 2001 , apj , 550 , 261 whittle , m. 1992 , apjs , 79 , 49 wilson , a. s. et al . 1998 , apj , 505 , 587 wouterloot , j. g. a. & walmsley , c. m. 1986 , a&a , 168 , 237 zhang , j. s. , henkel c. , kadler , m. , greenhill , l. j. , nagar , n. , wilson , a. s. & braatz , j. a. 2006 , a&a , 450 , 933 zhang , j. s. & fan , j. h. 2009 , sci chin . g , 6 , 960

there are strong anti - correlations between ew ( ) and two `` optical thickness parameters '' , i.e. the ratios of the x - ray luminosity versus the presumably more isotropically radiated $ ] and far infrared ( fir ) luminosities . based on these anti - correlations , a set of quantitative criteria , ew ()ev ,}$ ] and

to shed light onto the circumnuclear environment of 22 ghz ( 1.3 cm ) ho maser galaxies , we have analyzed some of their multi - wavelength properties , including the far infrared luminosity ( fir ) , the luminosity of the\lambda5007 $ ] emission line , the nuclear x - ray luminosity , and the equivalent width of the neutral iron emission line ( ew ( k ) ) . our statistical analysis includes a total of 85 sources , most of them harboring an active galactic nucleus ( agn ) . there are strong anti - correlations between ew ( ) and two `` optical thickness parameters '' , i.e. the ratios of the x - ray luminosity versus the presumably more isotropically radiated $ ] and far infrared ( fir ) luminosities . based on these anti - correlations , a set of quantitative criteria , ew ()ev ,}$ ] and can be established for compton - thick nuclear regions . 18 ho maser galaxies belong to this category . there are no obvious correlations between the ew ( k ) , the $ ] luminosity and the isotropic ho maser luminosity . when comparing samples of seyfert 2s with and without detected ho maser lines , there seem to exist differences in ew ( k ) and the fraction of compton - thick nuclei . this should be studied further . for agn masers alone , there is no obvious correlation between fir and ho maser luminosities . however , including masers associated with star forming regions , a linear correlation is revealed . overall , the extragalactic fir - ho data agree with the corresponding relation for galactic maser sources , extrapolated by several orders of magnitude to higher luminosities .

hep-th9907119

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many a time advances in mathematics and physics have occurred hand in hand . newton s theory of mechanics and the development of techniques of calculus are a classical example of this phenomenon . another example is the developments in differential geometry inspired by maxwell theory of electromagnetism and einstein theory of general relativity . a recent glorious example is the developments of topological quantum field theories and their relevance to the study of geometry and topology of low dimensional manifolds . the application of topological quantum field theories reflects the enormous interest generated both by mathematicians and field theoreticians in building a link between quantum physics through its path integral formulation on one hand and geometry and topology of low dimensional manifolds on the other . these are indeed deep links which are only now getting explored . it does appear that the properties of low dimensional manifolds can be very successfully unraveled by relating them to infinite dimensional manifolds of fields . this provides a powerful tool to study these manifolds notwithstanding the ` lack of mathematical rigour ' in defining the functional integrals of quantum field theory . indeed , an axiomatic formulation of topological quantum field theories has also been attempted . toplogical quantum field theories are independent of the metric of curved manifold on which these are defined ; the expectation value of the energy - momentum tensor is zero , @xmath1 . these possess no local propagating degrees of freedom ; only degrees of freedom are topological . operators of interest in such a theory are also metric independent . to illustrate how ideas of quantum field theory can be used to study topology , we shall focus our attention here on recent important developments in chern - simons gauge field theory as a topological quantum field theory on a three - manifold . this theory provides a field theoretic framework for the study of knots and links in a given three manifold@xcite - @xcite . it was a.s . schwarz who first conjectured @xcite that the now famous jones polynomial @xcite may be related to chern - simons theory . e. witten in his pioneering paper about ten years ago demonstrated this connection@xcite . in addition , he set up a general field theoretic framework to study knots and links . since then enormous effort has gone into developing an exact and explicit non - perturbative solution of this field theory . many of the standard techniques of field theory find applications in these developments . the interplay between quantum field theory and knot theory has paid rich dividends in both directions . many of the open problems in knot theory have found answers in the process . wilson loop operators are the topological operators of the chern - simons gauge field theory . their vacuum expectation values are the topological invariants for knots and links which do not depend on the exact shape , location or form of the knots and links but reflect only their topological properties . the power of this framework is so deep that it allows us to study these invariants not only on simple manifold such as three - sphere but also on any arbitrary three - manifold . the knot and link invariants obtained from these field theories are also intimately related to the integrable vertex models in two dimensions@xcite . these invariants have also been approached in different mathematical frameworks . a quantum group approach to these polynomial invariants has been developed@xcite . last decade or so has seen enormous activity in these directions in algebraic topology . a mathematically important development is that these link invariants provide a method of obtaining a specific topological invariant for three - manifolds@xcite in terms of invariants for framed unoriented links in @xmath0@xcite . in the following , we shall review these developments . not only in mathematics , chern - simons theory has also played a major role in quantum gravity . three - dimensional gravity with a negative cosmological constant , itself a topological field theory , can be described by two copies of @xmath2 chern - simons theory . even in four dimensional gravity , chern - simons theories find application . for example , the boundary degrees of freedom of a black hole in four dimensions , are described by an @xmath2 chern - simons field theory . this has allowed an exact calculation of quantum entropy of a non - rotating black hole . the formula so obtained for a schwarzschild black hole , while agreeing with the bekenstein - hawking formula for large areas , goes beyond the semi - classical result . before explaining how a field theoretic framework for knots and links can be developed , let us start with a brief discussion of knots and links .

chern - simons theories , which are examples of such field theories , provide a field theoretic framework for the study of knots and links in three dimensions . not only in mathematics , chern - simons theories find important applications in three and four dimensional quantum gravity also .

topological quantum field theories can be used as a powerful tool to probe geometry and topology in low dimensions . chern - simons theories , which are examples of such field theories , provide a field theoretic framework for the study of knots and links in three dimensions . these are rare examples of quantum field theories which can be exactly ( non - perturbatively ) and explicitly solved . abelian chern - simons theory provides a field theoretic interpretation of the linking and self - linking numbers of a link . in non - abelian theories , vacuum expectation values of wilson link operators yield a class of polynomial link invariants ; the simplest of them is the famous jones polynomial . other invariants obtained are more powerful than that of jones . powerful methods for completely analytical and non - perturbative computation of these knot and link invariants have been developed . in the process answers to some of the open problems in knot theory are obtained . from these invariants for unoriented and framed links in , an invariant for any three - manifold can be easily constructed by exploiting the lickorish - wallace surgery presentation of three - manifolds . this invariant up to a normalization is the partition function of the chern - simons field theory . even perturbative analysis of the chern - simons theories are rich in their mathematical structure ; these provide a field theoretic interpretation of vassiliev knot invariants . not only in mathematics , chern - simons theories find important applications in three and four dimensional quantum gravity also . -0.6 in -0.5 in = 20000 # 1|#1 # 1| # 1#2|#2 # 1#2#3#4 # 1#2#3#4 epsf 1.5 cm

1305.0133

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excitons are electrically neutral and have finite lifetimes . these are two obstacles which make the development of excitonic spintronics , or spin - optronics challenging . how possibly one can explore the current , which is carried by neutral particles , and whose amplitude changes with distance and time ? - is a fair question to ask . while electrons and holes have been considered as perfectly valid spin carriers , and exotic effects like the spin hall effect @xcite have been intensively studied for them @xcite , the spin currents carried by excitons @xcite and exciton - polaritons @xcite over tens or even hundreds of micrometers remained relatively less explored . there existed a huge imbalance of theoretical works on fermionic and bosonic spin transport . this is changing now . a number of phenomena have been observed and studied in the field of bosonic spin currents recently @xcite@xmath0wertz2012 . to summarize tens of publications in one sentence : bosonic systems bring new quantum coherent effects to the physics of spin transport . for instance , stimulation @xcite and amplification @xcite of spin currents are possible in exciton and exciton - polariton bose gases . bosonic spintronics or spin - optronics operates with electrically neutral spin carriers which makes control of spin currents carried by excitons a non - trivial task . fortunately , the exciton density replaces charge in many aspects : the density currents may be efficiently controlled by stationary or dynamic potential gradients as demonstrated in recent works kuznetsova2010 , leonard2012 . combined with evident advantages of bosonic amplification and low dephasing , this makes spin - optronics a valuable alternative to fermionic spintronics . besides bosonic effects , exciton spin transport has another important specific feature : it is dissipative by its nature , as the spin carriers have a finite ( and short for excitons in regular materials ) life - time . in continuous wave optical experiments stationary spin textures can appear : excitons are injected in the structure , they propagate ballistically or diffusively , and eventually disappear by radiative recombination . their polarization properties and spin are inherited by the emitted photons , that is why the polarization patterns observed in near field photoluminescence experiments directly characterize exciton spin currents in the plane of the structure . the goal of this work is to define what the exciton spin , magnetization and polarization currents are , and to explain how they can be described within the most frequently used spin density matrix ( dm ) approach and mean - field @xcite approximation . we consider a specific system , namely a planar zinc - blend semiconductor structure containing quantum wells , where excitons can be formed . this choice is motivated by recent experimental results in gaas / algaas based coupled quantum wells . we limit the scope of this paper to heavy - hole excitons , however , our approach can be easily extended to light - hole excitons or excitons in quantum wells of a different symmetry . we do not speak here about the large variety of recent experimental results and application of the formalism presented here to the description of one particular experiment , as this would make this paper too long and too specific . for a direct comparison of theoretical simulations with the experimental data we address the reader to ref . . the approaches formulated here are suitable for the description of a variety of excitonic spin effects in quantum wells . the paper is organized as follows . in section ii we introduce the spin dm formalism accounting for the different mechanisms of spin re - orientation and the relation to electron and hole spin currents . in section iii we present numerical results obtained within the spin dm formalism and analyze them . in section [ sec : gp ] we study the non - linear spin dynamics of propagating excitons using the gross - pitaevskii ( gp ) equations . the next three sections of the paper are devoted to exciton spin currents and polarization currents . conclusions are perspectives are given in section viii .

traditional spintronics relies on spin transport by charge carriers , such as electrons in semiconductor crystals . the challenges for the realization of long - range electron spin transport include rapid spin relaxation due to electron scattering . they can form coherent quantum liquids that carry spins over macroscopic distances .

traditional spintronics relies on spin transport by charge carriers , such as electrons in semiconductor crystals . the challenges for the realization of long - range electron spin transport include rapid spin relaxation due to electron scattering . scattering and , in turn , spin relaxation can be effectively suppressed in excitonic devices where the spin currents are carried by electrically neutral bosonic quasi - particles : excitons or exciton - polaritons . they can form coherent quantum liquids that carry spins over macroscopic distances . the price to pay is a finite life - time of the bosonic spin carriers . we present the theory of exciton ballistic spin transport which may be applied to a range of systems supporting bosonic spin transport , in particular , to indirect excitons in coupled quantum wells . we describe the effect of spin - orbit interaction for the electron and the hole on the exciton spin , account for the zeeman effect induced by external magnetic fields and long range and short range exchange splittings of the exciton resonances . we also consider exciton transport in the non - linear regime and discuss the definitions of the exciton spin current , polarization current and spin conductivity .

1305.0133

c

bosonic spin transport is a young and promising area of solid - state physics . the theories of mesoscopic transport of charge carriers and quantum transport are among the most interesting chapters of modern physics . substitution of fermions by bosons and of a scalar electric charge by a spin vector can not be formally done in these theories . basically , all mesoscopic and quantum transport effects need to be reconsidered if we speak about electrically neutral bosonic spin carriers like excitons or exciton - polaritons . this is why the area of spin - optronicsessentially remains _ terra incognita_. experimentally , direct measurements of transport of indirect excitons and exciton - polaritons in time - resolved imaging experiments have become possible in recent years . in this work , we have demonstrated that exciton polarization currents are inseparably connected with electron and hole spin currents . the intensity and direction of exciton polarization currents and electron and hole spin currents is governed by an interplay of spin - orbit effects , zeeman effects and exciton exchange effects . in the non - linear regime , the pattern of spin currents may also be affected by spin - dependent exciton - exciton interactions . we have developed two complementary approaches to the description of exciton spin currents and textures . the dm formalism allows for description of the spin transport effects in both classical exciton gases and condensates of non - interacting excitons , while the gp equations describe propagation of exciton condensates . we predict non - trivial topologies of interacting exciton spin in condensates , and suggest tools of their control , such as external magnetic and electric fields , and source intensity . we have demonstrated , that ballistic propagation of excitons may result in a build up of polarization patterns , which may be observed in near - field photoluminescence spectra . this work has been supported by the eu fp7 itn index , eu fp7 poditrodi , the e.p.s.r.c . , the eu fp7 marie curie epoques , anr-2011-nano-004 - 06 , and doe . j. r. l. acknowledges chateaubriand fellowship from the embassy of france in the united states . the authors are deeply grateful to t. ostatnicky , y.g . rubo , m.m . glazov , i.a . shelykh , and a. bramati for many useful discussions on the peculiarities of bosonic spin transport . d. sanvitto , s. pigeon , a. amo , d. ballarini , m. de giorgi , i. carusotto , r. hivet , f. pisanello , v. g. sala , p. s. s. guimaraes , r. houdr , e. giacobino , c. ciuti , a. bramati , and g. gigli , nature photon , * 5 * , 610 ( 2011 ) . a. g. winbow , j. r. leonard , m. remeika , y. y. kuznetsova , a. a. high , a. t. hammack , l. v. butov , j. wilkes , a. a. guenther , a. l. ivanov , m. hanson , and a. c. gossard , phys . lett . * 106 * , 196806 ( 2011 ) .

scattering and , in turn , spin relaxation can be effectively suppressed in excitonic devices where the spin currents are carried by electrically neutral bosonic quasi - particles : excitons or exciton - polaritons . we also consider exciton transport in the non - linear regime and discuss the definitions of the exciton spin current , polarization current and spin conductivity .

traditional spintronics relies on spin transport by charge carriers , such as electrons in semiconductor crystals . the challenges for the realization of long - range electron spin transport include rapid spin relaxation due to electron scattering . scattering and , in turn , spin relaxation can be effectively suppressed in excitonic devices where the spin currents are carried by electrically neutral bosonic quasi - particles : excitons or exciton - polaritons . they can form coherent quantum liquids that carry spins over macroscopic distances . the price to pay is a finite life - time of the bosonic spin carriers . we present the theory of exciton ballistic spin transport which may be applied to a range of systems supporting bosonic spin transport , in particular , to indirect excitons in coupled quantum wells . we describe the effect of spin - orbit interaction for the electron and the hole on the exciton spin , account for the zeeman effect induced by external magnetic fields and long range and short range exchange splittings of the exciton resonances . we also consider exciton transport in the non - linear regime and discuss the definitions of the exciton spin current , polarization current and spin conductivity .

0910.0332

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there is strong observational and theoretical evidence that magnetic fields play a crucial role in the acceleration and the collimation of extragalactic jets . most active galactic nuclei ( agn ) jet formation scenarios involve magnetic fields threading a rotating black hole ( in the ergosphere ) and its accretion disk , thereby removing from them angular momentum , allowing the central black hole to accrete . at least close to the jet launching region , the jet rotation profile persists , reflecting its ( general relativistic and/or magneto - rotational ) origin . thus both ingredients , magnetic fields and rotation , are very important in jet formation , as well as in jet propagation and stability . moreover , detailed astrophysical jet observations point out that relativistic jets are structured , in a direction perpendicular to the jet axis , typically consisting of a fast spine and slower outer flow . in the case of agns , this jet structuring plays an important role in explaining the morphology of the jet high energy radiation @xcite , with sometimes clear evidence for a very fast , light inner jet and a heavy slow outer outflow @xcite . furthermore , observations of the tev bl lacertae objects show brightenings and rapid variability in their tev emission . this variation in their high energy emission implies high lorentz factor flows occuring at smaller scale , suggesting ultra - relativistic bulk motion of the ( inner ) jet . at the same time , complementary ( radio ) observations with vlbi of the pc - scale jet structure indicate a broad , ` slowly ' ( albeit relativistic ) moving outflow . in combination , this clearly suggests the presence of a two component jet morphology @xcite . two - component jet structure has also been proposed in more theoretical work , addressing the physics of jet launching , collimation and propagation mechanisms @xcite . while our jet dynamics computations will be representative for agn jet conditions , radially structured jet flows are now known to exist in virtually all astrophysical jet outflows . transversely structured , ultra - relativistic jet - like outflow has been proposed in the context of gamma ray bursts @xcite , to explain the break observed in their afterglow light curve . in the case of stellar outflows , recent observations of some t tauri jets @xcite also suggest a fast inner outflow bounded by a slow outer outflow . in these young stellar objects , a clear signature of jet rotation around the symmetry axis was detected @xcite , fully supporting scenarios of magneto - centrifugal jet launch and acceleration . theoretical models of two - component jets in classical t tauri @xcite then postulate that the inner outflow is turbulent and pressure driven , associated with the young star wind . the inner jet then has a small opening angle , as it is collimated by the outer jet , which is in turn magneto - centrifugally driven from the surrounding disk . the outer disk wind then carries most of the mass loss in the jet . various authors @xcite have demonstrated using axisymmetric mhd simulations that the outer outflow is self collimated by its intrinsic magnetic field , and that the turbulent inner outflow gets collimated by the outer jet . furthermore , @xcite investigated the topological stability of two - component outflows for young stellar objects , performing extensive numerical simulations to determine whether analytic self - similar models demonstrate robustness in axisymmetric conditions . also for relativistic jet simulations , axisymmetry assumptions are often adopted , excluding the development of all non - axisymmetric perturbations . these can address details of how helical field configurations ( naturally expected from magneto - centrifugal launch mechanisms ) effectively may transport their helicity down the jet beam @xcite , with magnetically aided reacceleration by field compression across internal cross - shocks . while @xcite concentrated on kinetic energy dominated jets , initially poynting flux dominated jets were simulated by @xcite in axisymmetric relativistic mhd , finding that the transition to a matter - dominated jet regime occurs very close to the central engine ( within @xmath0 ) . our model computations will therefore assume kinetic energy dominated jets . as far as the magnetic field topology is concerned , we will restrict ourselves in this paper to purely poloidally magnetized jet components . our two - component jet model determining our initial conditions can actually allow for helical fields , as explained in sect . [ s - model ] ( we include this more general case here , for future reference in follow - up studies ) . as indicated before , during the first acceleration phase of agn jets , magneto - centrifugal mechanisms play an important role and a helical or even strongly toroidal magnetic field is likely produced . present 3d general relativistic mhd simulations for rapidly rotating black holes producing jets with strong toroidal fields . they find a prominent role of the accreted magnetic field geometry for achieving ` stable ' jets . helical or strongly toroidal field topologies can be subject to current - driven kink instabilities @xcite , with @xmath1 toroidal modes that helically displace the jet axis . this requires full 3d numerical simulations , such as performed by @xcite in non - relativistic mhd , or addressed by @xcite in relativistic mhd for a static force - free equilibrium . dispersion relations for non - axisymmetric modes and @xmath1 kinks in particular for relativistic mhd were analysed by @xcite for purely toroidal fields , and electromagnetically dominated , force - free jets were analysed spectrally by and more recently by @xcite . in our work , we will restrict attention to 2.5d scenarios with the somewhat unusual assumption of translational invariance along the jet axis . the overall configuration is schematically indicated in fig . [ fig1 ] , and we simulate a transverse cross - section of the jet at sufficient distance from the two - component jet source , where all three velocity components ( axial , azimuthal and radial ) are included , but their variation along the jet axis is ignored . our aim is to investigate all non - axisymmetric instabilities , primarily induced by the ( sheared ) rotation . this approximation is valid because in the poloidal direction , the flow is supersonic with high lorentz factor , and then the growth rate of poloidal instabilities is expected to be low . on the other hand , the rotation is subsonic , facilitating the growth of toroidal instabilities . we then address jet stability in a cross section of a rotating two - component jet , initially collimated by thermal pressure and/or poloidal magnetic field . consecutive snapshots of the cross - sectional evolution can be interpreted as mimicking the jet flow conditions at increasing distance from the source . note that this particular assumption allows us to follow both axisymmetric and all non - axisymmetric ( including @xmath1 ) mode development , but does exclude helical mode axis displacement typical for kink modes . our model therefore mimics jet evolution adequately as long as the radial axis displacement is smaller than the axial wavelength associated with possible @xmath1 kinks . our assumption does also neglect conical jet expansion , assuming cylindrical propagation . this is justified given the low observed values for jet opening angles . since we defer the study of toroidal and helical magnetic field configurations in 2.5d and 3d to later work , we start off with numerically investigating the influence of a purely poloidal magnetic field on the stability of rotating , two - component relativistic jets . our work complements the studies looking into kink development , by putting the emphasis on the azimuthal variation and on the effect of the two - component jet stratification . as far as a purely poloidal magnetic field topology is concerned , the work by @xcite suggests that jets should be collimated by poloidal magnetic field pressure , rather than by toroidal magnetic field , as toroidal jet magnetic fields can introduce kink instability ( but only slow mode growth was found for force - free jets by @xcite ) . to justify purely toroidal fields , we can argue that the toroidal magnetic field in the jet acceleration phase can be gradually dissipated involving reconnection , a mechanism which in turn contributes to ( axial ) jet acceleration @xcite . indeed , during the acceleration phase a fraction of the poynting flux ( angular momentum ) carried by the magnetic field is converted to kinetic energy by internal dissipation / reconnection of the toroidal magnetic field @xcite . in accord with this mechanism , we model the region where the eventual jet rotation is low . in this paper , we analyse five cases in detail , to determine the effects of differing poloidal magnetic field configurations in the two - component structure on its long - term stability , and on the overall deceleration of the jet as it propagates away from the central source regions . the role of poloidal magnetic field is in these cases most prominent in its added effect on total pressure and effective fluid inertia , and this is shown to play a prominent role in the two - component jet stability .

transverse stratification is a common intrinsic feature of astrophysical jets . there is growing evidence that jets in radio galaxies consist of a fast low density outflow at the jet axis , surrounded by a slower , denser , extended jet . we here investigate the stability of rotating , two - component relativistic outflows typical for jets in radio galaxies . for this purpose , we parametrically explore the long term evolution of a transverse cross - section of radially stratified jets numerically , extending our previous study where a single , purely hydrodynamic evolution was considered . , we revisit the interaction between the two jet components . we study the influence of dynamically important poloidal magnetic fields , with varying contributions of the inner component jet to the total kinetic energy flux of the jet , on their non - linear azimuthal stability .

transverse stratification is a common intrinsic feature of astrophysical jets . there is growing evidence that jets in radio galaxies consist of a fast low density outflow at the jet axis , surrounded by a slower , denser , extended jet . the inner and outer jet components then have a different origin and launching mechanism , making their effective inertia , magnetization , associated energy flux and angular momentum content different as well . their interface will develop differential rotation , where disruptions may occur . we here investigate the stability of rotating , two - component relativistic outflows typical for jets in radio galaxies . for this purpose , we parametrically explore the long term evolution of a transverse cross - section of radially stratified jets numerically , extending our previous study where a single , purely hydrodynamic evolution was considered . we include cases with poloidally magnetized jet components , covering hydro and magnetohydrodynamic models . with grid - adaptive relativistic magnetohydrodynamic simulations , augmented with approximate linear stability analysis , we revisit the interaction between the two jet components . we study the influence of dynamically important poloidal magnetic fields , with varying contributions of the inner component jet to the total kinetic energy flux of the jet , on their non - linear azimuthal stability . we demonstrate that two - component jets with high kinetic energy flux , and an inner jet effective inertia which is higher than the outer jet effective inertia are subject to the development of a relativistically enhanced , rotation - induced rayleigh - taylor type instability . this instability plays a major role in decelerating the inner jet and the overall jet decollimation . this novel deceleration scenario can partly explain the radio source dichotomy , relating it directly to the efficiency of the central engine in launching the inner jet component . the frii / fri transition could then occur when the relative kinetic energy flux of the inner to the outer jet grows beyond a certain treshold .

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we examined five configurations of magnetized two - component jets . all share the same density ratio between inner and outer component and identical rotation profiles . the magnetic and thermal pressure configuration in each model differs , though . this in turn translates to different distributions of the ( total , fixed ) kinetic energy flux over the inner and outer jet component . in fact , in case ( a ) the kinetic energy flux in the inner component is about @xmath22 , while it is @xmath164 for case ( b1 ) and @xmath165 in case ( b2 ) , and around @xmath166 for cases ( c ) and ( d ) . for the outer component , we thus have @xmath167 in case ( a ) , @xmath168 in case ( b1 ) and @xmath169 in case ( b2 ) , and only @xmath170 for cases ( c ) and ( d ) . the most important difference between the two model categories is then : cases ( a , c , d ) have an inner jet component with higher inertia @xmath171 than their outer jet component , while cases ( b1 ) and ( b2 ) have an inner jet component inertia which ends up lower than in the outer jet component . from the detailed analysis of the simulations , as well as from the approximate stability analysis , this criterion distinguishes between cases where relativistically enhanced rayleigh - taylor modes ultimately dominate the evolution , leading to complete mixing of both components and inner jet deceleration . this is quantified most clearly by showing the time evolution of the mean lorentz factor over the inner jet region for all cases in fig . [ lorentzfactor_evolution ] . this requires a clear criterion to distinguish inner versus outer jets in the turbulent evolutions . in cases ( a ) , ( c ) and ( d ) , we locate the outer jet component as having a lorentz factor @xmath172 and effective polytropic index @xmath173 . the inner component is the region defined by a lorentz factor @xmath174 and effective polytropic index @xmath175 . in the cases ( b1 ) and ( b2 ) , the effective polytropic index in the inner and outer jet can be locally of the same order there , hence we use that the inner jet is magnetized . in the cases ( b1 ) and ( b2 ) , the inner component jet and shear region are not totally mixed during the evolution , since the inner component is compressed and has higher magnetization and lorentz factor . thus to distinguish the inner component jet we put a condition on magnetic field strength @xmath176 , where @xmath177 is the magnetic strength assumed initially . under these precise quantifications of inner / outer jet regions , fig . [ lorentzfactor_evolution ] demonstrates clearly how stable cases ( for the relativistically enhanced rayleigh - taylor modes ) remain at high speed , while unstable cases decelerate . using the same means to distinguish inner versus outer jet regions at all times , we can quantify the inner jet radius for all cases , as well as the total jet radius for all cases . these are shown in figs . [ inradius_evolution]-[radius_evolution ] , and quantify the decollimation effects discussed in section [ simulations ] . during the entire evolutions , the toroidal and radial speeds remain weak as we have typically a maximal @xmath178 and @xmath179 . this means that the contribution of the laboratory frame charge separation force @xmath180 to the lorentz force is negligible at all times . under these conditions , in both radial and toroidal directions , the contribution of magnetic energy to fluid inertia is @xmath181 weaker than the contribution of the magnetic pressure to the total pressure . this explains why cases ( b1 ) and ( b2 ) are then more stable than the other cases . despite the fact that case ( b2 ) has similar axial total pressure than other cases ( a , c , d ) , the low contribution of thermal energy to total pressure makes the effective inertia ratio between the inner and outer jet low . this two - component jet is then stable against the relativistically enhanced rayleigh - taylor instability . extraction of angular momentum and energy from the inner jet to the shear shell is less efficient in cases ( b1 ) and ( b2 ) than in all other cases . as a result , in cases ( b1 ) and ( b2 ) the inner relativistic jet with high lorentz factor @xmath182 persists . in the other cases , the kinetic energy flux in the inner jet was initially relatively high , making them unstable and leading to deceleration to lorentz factors around @xmath135 we investigated the stability of two - component jets beyond the launching region , where both components are rotating differently and a clear two - component structure exists . we initialized this model in accord with magneto - centrifugal models for jet generation , also using the observed analogy between radio source jets and two - component jets in young stellar objects , where the rotation within the jet can actually be observed . we performed five very high resolution simulations of magnetized two - component jets with various magnetization and kinetic energy flux stratifications . the two - component jets with a low inner kinetic energy flux contribution are more stable and remain relativistic for long distances , whereas jets with a highly contributing inner jet to the total jet kinetic energy flux , are subject to a relativistic rayleigh - taylor type instability . this instability turns out to be very efficient to decollimate and decelerate the inner jet . jets that are subject to this instability become turbulent after propagating for a distance of about @xmath183 . this new result on two - component jet models is important because it can explain the classification of radio sources in fanaroff - riley i / ii categories according the energy stratification of the inner jet . this ultimately relates to the jet launch region and the properties of the inner accretion disk . in fact , by analogy between the fri / frii classification and the results of our model , an fri jet would correspond to a two - component jet with a high energy flux contribution from the inner jet , whereas the frii jet corresponds to relatively low energy fluxes in the inner jet . the model we propose here to explain the fri / frii dichotomy is different from the model we proposed earlier @xcite where the transition occurs due to external density stratification . that model explains the group of peculiar hybrid morphology radio source " ( hymors ) which appear to have an fr ii type on one side and an fr i type diffuse radio lobe on the other side of the active nucleus . since the launch conditions on each side are presumably similar in these kind of radio sources , the different fanaroff - riley morphologies on either side must be attributed to the change in the properties of the ambient media , as shown convincingly in @xcite . the results of the present paper nicely complement these earlier findings with a quantifiable role of the central engine contribution . we currently continue this study of the interaction between two component jets in full 3d . we thereby intend to explore the relative influence of azimuthal versus longitudinal instabilities for realistic multi - component jets . another extension is to allow for aximuthal magnetic fields , in accord with the initial profiles as given generally in this paper . it then rremains to be shown that ( 1 ) the newly discovered instability persists in 3d hydro and magnetohydrodynamic configurations , where the potential role of axial mode development is incorporated , and introduces helical jet axis displacements ; ( 2 ) how the instability gets modified ( stabilized or destabilized ) by the inclusion of toroidal field components , first in 2.5d neglecting helical axis displacements , and consecutively in 3d , where also current - driven kinks may occur . we acknowledge financial support from the fwo , grant g.027708 , and from the k.u.leuven goa/09/009 . part of the computations made use of the high performance computing vic cluster at k.u.leuven . z. meliani acknowledge financial support from hpc europa ( project number : 228398 ) . visualization was performed using paraview , see www.paraview.org . 99 appl , s. , & camenzind , m. , 1993 , a&a , 270 , 71 bacciotti , f. , mundt , r. , ray , t.p . , eiskffel , j. , solf , j. , camenzind , m. , 2000 , apj , 537 , l49 bacciotti , f. , ray , t.p . , mundt , r. , eiskffel , j. , solf , j. , 2002 , apj , 576 , 222 baty , h. , & keppens , r. , 2002 , apj , 580 , 800 begelman , m. c. , li . z. y. , 1994 , 426 , 269 begelman , m.c . , 1998 , apj , 493 , 291 biretta , j.a . , junor , w. , livio , m. , 2002 , newar , 46 , 239 bogovalov , s. , & tsinganos , k. , 2001 , mnras , 325 , 249 coffey , d. , bacciotti , f. , woitas , j. , ray , t.p . , eislffel , j. , 2004 , apj , 604 , 758 coffey , d. , bacciotti , f. , ray , t.p . , eislffel , j. , woitas , j. , 2007 , apj , 663 , 350 cranmer , s.r . , 2008 , apj , 689 , 316 fendt , c. , 1997 , a&a , 319 , 1025 fendt , c. , 2009 , apj , 692 , 346 gopal - krishna , wiita , p. j. , 2000 , a&a , 363 , 507 ghisellini , g. , tavecchio , f. , chiaberge , m. , 2005 , a&a , 432 , 401 giroletti , m. , giovannini , g. , feretti , l. , cotton , w.d . , edwards , p.g . , lara , l. , marscher , a.p . , mattox , j.r . , piner , b.g . , venturi , t. , 2004 , apj , 600 , 127 ghisellini , g. , tavecchio , f. , 2008 , mnras , 386 , l28 gnther , h.m . , matt , s.p . , li , z .- y . , 2009 , a&a , 493 , 579 hardcastle , m.j . , 2006 , mnras , 366 , 1465 hardee , p.e . , 2004 , ap&ass , 293 , 117 heyvaerts , j. , & norman , c. 2003 , apj , 596 , 1240 istomin , ya.n . , pariev , v.i . , 1996 , mnras , 281 , 1 jester , s. , harris , d.e . , marshall , h.l . , meisenheimer , k. , 2006 , apj , 648 , 900 jester , s. , meisenheimer , k. , martel , a.r . , perlman , e.s . , sparks , w.b . , 2007 , mnras , 380 , 828 kataoka j. , stawarz , l. , harris , d.e . , siemiginowska , a. , ostrowski , m. , swain , m.r . , hardcastle , m.j . , goodger , j.l . , iwasawa , k. , edwards , p.g . , 2008 , apj , 685 , 839 keppens , r. , meliani , z. , van der holst , b. , casse , f. , 2008 , a&a , 486 , 663 komissarov , s.s . , barkov , m.v . , vlahakis , n. , knigl , a. , 2007 , mnras , 380 , 51 matsakos , t. , tsinganos , k. , vlahakis , n. , massaglia , s. , mignone , a. , trussoni , e. , 2008 , a&a , 477 , 521 mckinney , j.c . , blandford , r.d . , 2009 , mnras , 394 , l126 mignone , a. , plewa , t. , bodo , g. , 2005 , apjs,160 , 199 mignone , a. , bodo , g. , 2005 , mnras , 364 , 126 mizuno , y. , lyubarsky , y. , nishikawa , k .- hardee , p.e . , 2009 , apj , 700 , 684 meliani , z. , sauty , c. , tsinganos , k. , vlahakis , n. , 2004 , a&a , 425 , 773 meliani , z. , sauty , c. , vlahakis , n. , tsinganos , k. , trussoni , e. , 2006a , a&a , 447 , 797 meliani , z. , casse , f. , sauty , c. , 2006b , a&a , 460 , 1 meliani , z. , keppens , r , casse , f. , giannios , d. , 2007 , mnras , 376 , 1189 meliani , z. , & keppens , r. , 2007 , a&a , 475 , 785 meliani , z. , keppens , r. , giacomazzo , b. , 2008 , a&a , 491 , 321 meier , d.l . , 2003 , newar , 47 , 667 narayan , r. , li , j. , tchekhovskoy , a. , 2009 , apj , 697 , 1681 osullivan , s. p. , gabuzda , d. c. , 2009 , arxiv:0907.5211 racusin , j. l. , et al . , 2008 , nature , 455 , 183 rawlings , s. , & saunders , r. , 1991 , nature , 349 , 138 siemiginowska , a. , stawarz , l. , cheung , c.c . , harris , d.e . , sikora , m. , aldcroft , t.l . , bechtold , j. , 2007 , apj , 657 , 145 sol , h. , pelletier , g. , assero , e. , 1989 , mnras , 237 , 411 spruit , h.c . , foglizzo , t. , stehle , r. , 1997 , mnras , 288 , 333 spruit , h.c . , 2008 , arxiv , 0804.3096 tavecchio , f. , maraschi , l. , sambruna , r.m . , urry , c.m . , cheung , c.c . , gambill , j.k . , scarpa , r. , 2004 , apj , 614 , 64 van der holst , b. , & keppens , r. , 2007 , jcp , 226 , 925 van der holst , b. , keppens , r. , meliani , z. , 2008 , cophc , 179 , 617 woitas , j. , bacciotti , f. , ray , t.p . , marconi , a. , coffey , d. , eislffel , j. , 2005 , a&a , 432 , 149

their interface will develop differential rotation , where disruptions may occur . we include cases with poloidally magnetized jet components , covering hydro and magnetohydrodynamic models . with grid - adaptive relativistic magnetohydrodynamic simulations , augmented with approximate linear stability analysis we demonstrate that two - component jets with high kinetic energy flux , and an inner jet effective inertia which is higher than the outer jet effective inertia are subject to the development of a relativistically enhanced , rotation - induced rayleigh - taylor type instability .

transverse stratification is a common intrinsic feature of astrophysical jets . there is growing evidence that jets in radio galaxies consist of a fast low density outflow at the jet axis , surrounded by a slower , denser , extended jet . the inner and outer jet components then have a different origin and launching mechanism , making their effective inertia , magnetization , associated energy flux and angular momentum content different as well . their interface will develop differential rotation , where disruptions may occur . we here investigate the stability of rotating , two - component relativistic outflows typical for jets in radio galaxies . for this purpose , we parametrically explore the long term evolution of a transverse cross - section of radially stratified jets numerically , extending our previous study where a single , purely hydrodynamic evolution was considered . we include cases with poloidally magnetized jet components , covering hydro and magnetohydrodynamic models . with grid - adaptive relativistic magnetohydrodynamic simulations , augmented with approximate linear stability analysis , we revisit the interaction between the two jet components . we study the influence of dynamically important poloidal magnetic fields , with varying contributions of the inner component jet to the total kinetic energy flux of the jet , on their non - linear azimuthal stability . we demonstrate that two - component jets with high kinetic energy flux , and an inner jet effective inertia which is higher than the outer jet effective inertia are subject to the development of a relativistically enhanced , rotation - induced rayleigh - taylor type instability . this instability plays a major role in decelerating the inner jet and the overall jet decollimation . this novel deceleration scenario can partly explain the radio source dichotomy , relating it directly to the efficiency of the central engine in launching the inner jet component . the frii / fri transition could then occur when the relative kinetic energy flux of the inner to the outer jet grows beyond a certain treshold .

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computational fluid dynamics ( cfd ) simulations have been widely used in aerospace , mechanical , and chemical industries to support engineering design , analysis , and optimization . two decades ago when large eddy simulations ( les ) started gaining popularity with the increasing availability of computational resources , it was widely expected that les would gradually displace and eventually replace reynolds - averaged navier - stokes ( rans ) equations in industrial computational fluid dynamics ( cfd ) work - flows for decades to come . in the past two decades , however , while les - based methods ( including resolved les , wall - modeled les , and hybrid les / rans methods ) did gain widespread applications , and the earlier hope certainly did not diminish , the predicted time when these methods would replace rans has been significantly delayed . this observation is particularly relevant in light of the recent discussions on the ending of the `` moore s law era '' with transistor sizes approaching their theoretical lower limit @xcite . rans solvers , particularly those based on standard eddy viscosity models ( e.g. , @xmath0@xmath1 @xcite , @xmath0@xmath2 @xcite , s a @xcite , and k@xmath2sst @xcite , are still and will remain the dominant tool for industrial cfd in the near future . this is likely to be true even in mission critical applications such as aircraft design . interestingly , even the advanced rans models such as reynolds stress transport models @xcite and explicit algebraic reynolds stress models @xcite have not seen much development in the past few decades . these advanced models are computationally more expensive and less robust compared to the standard eddy viscosity rans models . as such , it is still practically important to further develop the standard rans models for industrial cfd applications . however , improving the predictive capabilities of these models is critical yet technically challenging . while traditional development of turbulence models has focused on incorporating more physics to improve predictive capabilities , an alternative approach is to utilize data . in the past few years , a number of data - driven approaches have been proposed . researchers have investigated the use of both offline data ( i.e. , existing dns data for flows different from that to be predicted @xcite ) and online data ( streamed monitoring data from the flow to be predicted @xcite ) . dow and wang @xcite used direct numerical simulation ( dns ) data from a plane channel flow to infer the full - field discrepancy in the turbulent viscosity @xmath3 modeled by the @xmath0@xmath2 model . to predict flows in channels with wavy boundaries , they modeled the ( log-)discrepancies of @xmath3 in the new flows as gaussian random fields , with the discrepancy field inferred above as mean . duraisamy and co - workers @xcite introduced a full - field multiplicative discrepancy term @xmath4 into the production term of the transport equations of turbulent quantities ( e.g. , @xmath5 in the sa model and @xmath2 in the @xmath0@xmath2 models ) . they used dns data to calibrate and infer uncertainties in the @xmath4 term . it is expected that the inferred discrepancy field can provide valuable insights to the development of turbulence model and can be used to improve rans predictions in similar flows . xiao et al . @xcite used sparse velocity measurements ( online data ) to infer the full - field discrepancies @xmath6 in the rans - predicted reynolds stress tensors , or more precisely the physical projections thereof ( turbulent kinetic energy , anisotropy , and orientations ) . throughout this paper it is understood that @xmath7 indicates the physical projections and not the individual components of the reynolds stress tensor . good performance was demonstrated on several canonical flows including flow past periodic hills , flow in a square duct @xcite , and flow past a wing body junction @xcite . all three approaches @xcite discussed above can be considered starting points toward the same destination : the capability of predictive turbulence modeling by using standard rans models in conjunction with offline data . to this end , the respective discrepancies terms ( @xmath8 , @xmath4 , and @xmath6 ) are expected to be extrapolated to similar yet different flows . these contributions are all relatively recent and much of the research is still on - going . duraisamy et al . @xcite performed _ a priori _ studies to show the potential universality of their discrepancy term @xmath4 among a class of similar flows , but their performances in _ a posteriori _ tests , i.e. , using the calibrated discrepancy in one flow to predict another flow , have yet to be demonstrated . dow and wang @xcite extrapolated the logarithmic discrepancies @xmath8 calibrated in the plane channel flow to flows in channel with slightly wavy walls , where velocity predictions were made . similarly , further pursuing the approach of xiao et al . @xcite , wu et al . @xcite showed that the reynolds stress discrepancy calibrated with sparse velocity data can be extrapolated to flows at reynolds number more than an order of magnitude higher than that in the calibration case . the extrapolated discrepancy has lead to markedly improved predictions of velocities and other quantities of interest ( qois ) , showing the potential of the approach in enabling data - driven predictive turbulence modeling . however , an intrinsic limitation in the approach of wu et al . @xcite is that they inferred the functions @xmath9 , or simply denoted as @xmath10 , in the space of _ physical coordinates _ therefore , strictly speaking they only demonstrated that the discrepancy @xmath6 can be extrapolated to flows in the same geometry at the same location . consequently , their attempts of extrapolation to the flow in a different geometry ( e.g. , from a square duct to a rectangular duct ) encountered less success . the approach of dow and wang @xcite would share the same limitation since they built gaussian random fields indexed by the physical coordinates @xmath11 . a natural extension that overcomes the key limitation in the calibration prediction approach of wu et al . @xcite is to build such functions in a space of well - chosen features @xmath12 instead of physical coordinates @xmath11 . despite its limitations , a key factor in the success of the original approach is that the reynolds stress discrepancies are formulated on its projections such as the anisotropy parameters ( @xmath13 and @xmath14 ) and orientation ( @xmath15 ) of the reynolds stresses and not directly on the individual components . these projections are normalized quantities @xcite . we shall retain this merits in the current approach and thus use data to construct functions @xmath16 instead of @xmath17 . this extension would allow the calibrated discrepancies to be extrapolated to a much wide range of flows . in other words , the discrepancies of the rans - predicted reynolds stresses can be quantitatively explained by the mean flow physics . hence , these discrepancies are likely to be universal quantities that can be extrapolated from one flow to another , at least among different flows sharing the same characteristics ( e.g. , separation ) . as such , discrepancies in reynolds stress projections are suitable targets to build functions for . with the function targets identified , two challenges remain : ( 1 ) to identify a set of mean flow features based on which the discrepancies functions @xmath16 can be constructed and ( 2 ) to choose a suitable method for constructing such functions . duraisamy and co - workers @xcite identified several features and used neural network to construct functions for the multiplicative discrepancy term . ling and templeton @xcite provided a richer and much more complete set of features in their pioneering work , and they evaluated several machine learning algorithms to predict point - based binary confidence indicators of rans models @xcite . ling et al . @xcite further used machine learning techniques to predict the reynolds stress anisotropy in jet - in - cross flows . based on the success demonstrated by ling and co - workers @xcite , we will use machine learning to construct the functions @xmath16 in the current work . specifically , we will examine a class of supervised machine learning techniques , where the objective of the learning is to build a statistical model from data and to make predictions on a response based on one or more inputs @xcite . this is in contrast to unsupervised learning , where no response is used in the training or prediction , and the objective is to understand the relationship and structure of the input data . unsupervised learning will be explored as an alternative approach in future works . the objective of this contribution is to present an approach to predict reynolds stress modeling discrepancies in new flows by utilizing data from flows with similar characteristics as the prediction flow . this is achieved by training regression functions of reynolds stress discrepancies with the dns database from the training flows . in light of the consensus in the turbulence modeling community that the reynolds stresses are the main source of model - form uncertainty in rans simulations @xcite , the current work aims to improve the rans modeled reynolds stresses . in multi - physics applications the qois might well be the reynolds stresses and/or quantities that directly depend thereon . in these applications the current work is significant by itself in that it would enable the use of standard rans models in conjunction with an offline database to provide accurate reynolds stress predictions . moreover , the improvement of reynolds stresses enabled by the proposed method is an important step towards a data - driven turbulence modeling framework . however , the reynolds stresses corrected by the constructed discrepancy function from dns databases can not necessarily guarantee to obtain improved mean flow fields . there are a number of challenges associated with propagating the improvement of reynold stresses through rans equation to the mean velocity field , which will be addressed in future works . the rest of this paper is organized as follows . section 2 introduces the components of the predictive framework , including the choice of regression inputs and responses as well as the machine learning technique used to build the regression function . section 3 shows the numerical results to demonstrate the merits of the proposed method . further interpretation of the feature importance and its implications to turbulence model development are discussed in section 4 . finally , section 5 concludes the paper .

turbulence modeling is a critical component in numerical simulations of industrial flows based on reynolds - averaged navier - stokes ( rans ) equations . however , after decades of efforts in the turbulence modeling community , universally applicable rans models with predictive capabilities are still lacking . large discrepancies in the rans - modeled reynolds stresses are the main source that limits the predictive accuracy of rans models . identifying these discrepancies is of significance to possibly improve the rans modeling . in this work ,

turbulence modeling is a critical component in numerical simulations of industrial flows based on reynolds - averaged navier - stokes ( rans ) equations . however , after decades of efforts in the turbulence modeling community , universally applicable rans models with predictive capabilities are still lacking . large discrepancies in the rans - modeled reynolds stresses are the main source that limits the predictive accuracy of rans models . identifying these discrepancies is of significance to possibly improve the rans modeling . in this work , we propose a data - driven , physics - informed machine learning approach for reconstructing discrepancies in rans modeled reynolds stresses . the discrepancies are formulated as functions of the mean flow features . by using a modern machine learning technique based on random forests , the discrepancy functions are trained by existing dns databases and then used to predict reynolds stress discrepancies in different flows where data are not available . the proposed method is evaluated by two classes of flows : ( 1 ) fully developed turbulent flows in a square duct at various reynolds numbers and ( 2 ) flows with massive separations . in separated flows , two training flow scenarios of increasing difficulties are considered : ( 1 ) the flow in the same periodic hills geometry yet at a lower reynolds number , and ( 2 ) the flow in a different hill geometry with a similar recirculation zone . excellent predictive performances were observed in both scenarios , demonstrating the merits of the proposed method . model - form uncertainty , turbulence modeling , reynolds - averaged navier stokes equations , boussinesq assumption , data - driven modeling , machine learning

1606.07987

c

in this work , we proposed a physics - informed machine learning approach to reconstruct reynolds stresses modeling discrepancies by utilizing dns databases of training flows sharing similar characteristics as the flow to be predicted . for this purpose , we formulated discrepancy of reynolds stresses ( or more precisely its magnitude and the shape and orientation of the anisotropy ) as target functions of mean flow features and used modern machine learning techniques based on random forest regression to learn the functions . the obtained functions are then used to predict reynolds stress discrepancies in new flows . to evaluate the performance of the proposed approach , the method is tested by two classes of flows : ( 1 ) fully developed turbulent flows in a square duct at various reynolds numbers and ( 2 ) flows with massive separations . in the separated flows , two training flow scenarios of increasing difficulties are considered : in the less challenging scenario , data from two flows in the same periodic hill geometry at lower reynolds numbers ( @xmath185 and 5600 ) are used for training . in a more challenging scenario , the training data come from separated flows in different geometries ( wavy channel and curved backward facing step ) . in all test cases the corrected reynolds stresses are significantly improved compared to the baseline rans predictions , demonstrating the merits of the proposed approach . in the scenario , where the training flows and the prediction flow have different geometries , the improvement is not as drastic as in the the scenario with the same geometry . this is expected since the prediction involves more extrapolations in the feature space for this more challenging scenario . in other words , compared to the first scenario where the training and prediction flows have identical geometry , the prediction flow is less `` similar '' to the training flows in this scenario . the extent to which the training and prediction flows are `` similar '' to each other can be assessed _ a priori _ based on their respective rans predicted mean flow field , and methods for such assessment are presented in companion publications @xcite . as the inaccuracy in modeled reynolds stresses is the dominant source of model - form uncertainty in rans simulations , the proposed method for improving rans - predicted reynolds stresses is an important step towards the goal of enabling predictive capabilities of rans models . moreover , the random forests regression technique adopted in this work can provide physical insights regarding the relative importance of mean flow features that contributed to the discrepancies in the rans predicted reynolds stresses . this information can be used to assist future model development in that developers can devise models that are aware of and correctly respond to these flow features . however , a number of challenges need to be tackled before the improved reynolds stresses can be used to predict more accurate quantities of interests that are needed in engineering design ( e.g. , draft and lift coefficients ) . this topic will be investigated in future research .

we propose a data - driven , physics - informed machine learning approach for reconstructing discrepancies in rans modeled reynolds stresses . the discrepancies are formulated as functions of the mean flow features . by using a modern machine learning technique based on random forests , the discrepancy functions are trained by existing dns databases and then used to predict reynolds stress discrepancies in different flows where data are not available . the proposed method is evaluated by two classes of flows : ( 1 ) fully developed turbulent flows in a square duct at various reynolds numbers and ( 2 ) flows with massive separations . in separated flows , two training flow scenarios of increasing difficulties are considered : ( 1 ) the flow in the same periodic hills geometry yet at a lower reynolds number , and ( 2 ) the flow in a different hill geometry with a similar recirculation zone .

turbulence modeling is a critical component in numerical simulations of industrial flows based on reynolds - averaged navier - stokes ( rans ) equations . however , after decades of efforts in the turbulence modeling community , universally applicable rans models with predictive capabilities are still lacking . large discrepancies in the rans - modeled reynolds stresses are the main source that limits the predictive accuracy of rans models . identifying these discrepancies is of significance to possibly improve the rans modeling . in this work , we propose a data - driven , physics - informed machine learning approach for reconstructing discrepancies in rans modeled reynolds stresses . the discrepancies are formulated as functions of the mean flow features . by using a modern machine learning technique based on random forests , the discrepancy functions are trained by existing dns databases and then used to predict reynolds stress discrepancies in different flows where data are not available . the proposed method is evaluated by two classes of flows : ( 1 ) fully developed turbulent flows in a square duct at various reynolds numbers and ( 2 ) flows with massive separations . in separated flows , two training flow scenarios of increasing difficulties are considered : ( 1 ) the flow in the same periodic hills geometry yet at a lower reynolds number , and ( 2 ) the flow in a different hill geometry with a similar recirculation zone . excellent predictive performances were observed in both scenarios , demonstrating the merits of the proposed method . model - form uncertainty , turbulence modeling , reynolds - averaged navier stokes equations , boussinesq assumption , data - driven modeling , machine learning

astro-ph0002385

i

perhaps the most perplexing and long - standing problem associated with galactic and cluster cooling flows is the uncertain physical nature and spatial distribution of the gas that cools . the apparent absence of large masses of cooled gas in elliptical galaxies has led some to argue that little or no cooling actually occurs and to postulate some source of heating that offsets the radiative losses in x - ray emission . but the energy required to balance radiative losses is prohibitively large and appropriate heating sources may not be universally available . if the expected radiative cooling actually occurs , two questions arise : ( 1 ) what is the nature of the objects that condense from the hot gas ? and ( 2 ) where is most of the cooled mass located in the galaxy ? regarding the first question , a variety of physical arguments support the hypothesis , or even the inevitability , of low mass star formation ( fabian , nulsen & canizares 1982 ; thomas 1986 ; cowie & binney 1988 ; vedder , trester , & canizares 1988 ; sarazin & ashe 1989 ; ferland , fabian & johnstone 1994 ; mathews & brighenti 1999 ) . here we shall address the second question in the context of cooling flows in elliptical galaxies where the known stellar mass and light profiles strongly constrain the spatial distribution of cooled gas . we adopt the generally accepted hypothesis that only stars of very low mass ( e.g. @xmath5 @xmath6 ) form in cooling flows ( e.g. ferland , fabian & johnstone 1994 ) , so that the mass to light ratio of the young stellar population formed from the cooling gas is essentially infinite . in view of the difficulties we encounter with this hypothesis , described below , it seems more likely that the stellar population formed from cooled gas extends to somewhat more massive stars that are optically luminous . our gas dynamical models for the evolution of hot interstellar gas in giant ellipticals indicate that the origin of the gas varies with galactic radius . most of the gas in the inner , optically luminous regions originates from the ejected envelopes of evolving stars ; gas in the outer halo is supplied by cosmological secondary infall or tidal acquisitions from neighboring galaxies ( mathews & brighenti 1998b ) . circumgalactic gas around massive ellipticals is enriched by type ii supernovae that accompanied early star formation . the variability of circumgalactic gas among luminous ellipticals is responsible for some of the enormous dispersion in x - ray luminosity @xmath7 among ellipticals of similar optical luminosity @xmath8 ( mathews & brighenti 1998a ) . since the hot interstellar gas in a bright elliptical emits observable x - rays , it is clearly losing energy . however , as the gas loses energy it is compressed toward the galactic center by gravitational forces and @xmath9 work maintains the high temperatures observed , @xmath10 k , producing a galactic cooling flow . the positive interstellar temperature gradients typically observed within a few effective radii are often cited as evidence of radiative cooling in a cooling flow , but this cooling is due instead to the mixing of somewhat cooler , locally virialized gas ejected from stars with hotter gas arriving from larger galactic radii ( mathews & brighenti 1998b ; brighenti & mathews 1998 , 1999a ) . if large entropy fluctuations are present in the hot gas , catastrophic cooling can occur at any radius in the flow . regions of low entropy ( low temperature , high density ) radiate more and cool sooner . the amplitude distribution of entropy fluctuations in the interstellar gas determines the radius where cooling mass dropout occurs in the cooling flow . for example , if the entropy in some region in the flow is only slightly less than in the ambient flow , the differential radiative cooling will be small and the region will cool out of the flow at small galactic radii ; conversely , localized regions with entropy much lower than the ambient flow cool rapidly and deposit their mass at large radii . some possible sources of interstellar entropy variations are stellar winds , explosions of type ia supernovae , non - uniform snii heating at early times , and mergers with small , gas - rich galaxies . the total rate that mass cools and drops out of the flow is closely related to the x - ray luminosity @xmath7 . the x - ray luminosity can be approximately expressed as the product of the total cooling rate @xmath11 and the enthalpy per gram in the hot gas , or @xmath12 here we have used data from the giant virgo elliptical ngc 4472 : @xmath13 k ; @xmath14 ; @xmath15 . if @xmath7 and @xmath16 are reasonably constant over the hubble time , a mass @xmath17 @xmath6 of cold gas is expected to condense from the hot ism somewhere within ngc 4472 . although this mass is very large , it is only about 4 percent of the total stellar mass in ngc 4472 today . the mass that cools can therefore be ignored if it is widely distributed throughout the galactic volume . however , the central concentration of h@xmath18 emission in ellipticals ( e.g. macchetto et al . 1996 ) suggests that the cooling is concentrated toward the galactic center where the interstellar density is highest and the bulk of the x - ray energy is emitted . the motivation of this paper is to explore a variety of options for the mass dropout profile of cooled gas in bright ellipticals appropriately constrained by the known radial distributions of total stellar and non - baryonic mass . the radial mass dropout profile of cooled gas can not be determined from first principles because the distribution and amplitude of the entropy and magnetic fluctuations in the hot gas are unknown and difficult to evaluate from simple physical arguments . nevertheless , the total mass of cooled gas inside an effective ( half - light ) radius @xmath3 must be consistent with the mass to light ratio determined from stellar velocities and with the total mass inferred from x - ray observations within @xmath3 . assuming that the stellar mass to light ratio is uniform with radius , the stellar mass @xmath19 and the x - ray mass @xmath20 appear to be in nearly perfect agreement for two bright virgo ellipticals in the range @xmath21 ( brighenti & mathews 1997a ) . because of constraints on the mass distribution of cooled gas provided by x - ray and stellar dynamical observations , galactic cooling flows provide a critical venue for testing the physics of mass deposition in cooling flows . the mass of cold ( @xmath22 k ) gas @xmath23 actually observed in ellipticals is many orders of magnitude less than the total cooled mass estimated above . for example , neither hi nor h@xmath24 gas has been observed in ngc 4472 , only upper limits , @xmath25 @xmath6 ( bregman , roberts & giovanelli 1988 ; braine , henkel & wiklind 1988 ) . if stars form they must either be indistinguishable from the old stellar population or non - luminous . we explore here the possibility that most of the cooled gas forms dense baryonic clouds or stars that are dark at optical and radio frequencies . the very low mass stars advanced by ferland , fabian & johnstone ( 1994 ) satisfy this invisibility criterion , while the star formation models of mathews & brighenti ( 1999 ) indicate that ( luminous ) stars of mass @xmath26 @xmath6 can form in galactic cooling flows . x - ray studies indicate significant masses of cold , absorbing gas in cluster and galactic cooling flows ( e.g. white et al . 1991 ; allen et al . 1993 ; fabian et al . 1994 ; allen & fabian 1997 ; buote 1999 ) , but these results are inconsistent with the absence of radio frequency emission from the cold gas ( braine & dupraz 1994 ; donahue & vogt 1997 ) and should be regarded as controversial until this inconsistency is resolved . even taken at face value , the total mass of cooled gas implied by the x - ray absorption in cluster cooling flows is typically only a small fraction of the total mass that should have cooled in a hubble time ( allen & fabian 1997 ; wise & sarazin 1999 ) , implying that most of the cooled gas may have formed stars . if cooled gas forms into small stars , these stars will have apogalatica near their point of origin where they will spend most of their orbital time . we shall assume that the gas mass that cools and drops out of the flow contributes optically dark ( stellar ) mass at the radius where the cooling occurred . in the following we describe a series of gas dynamical calculations for the evolution of x - ray emitting interstellar gas over the hubble time and investigate a variety of assumptions about the radial distribution of optically dark cooled gas . to be specific , we compare our models with the well - observed massive elliptical ngc 4472 . we find that the mass of cooled gas contributes significantly to dynamical mass to light determinations within @xmath3 based on stellar velocities .

typically percent of the total baryonic mass in luminous elliptical galaxies is in the form of cooled interstellar gas . although the mass contributed by cooled gas is small relative to the mass of the old stellar system in these galaxies , it is almost certainly concentrated within the optical effective radius where it can influence the local dynamical mass . however , the mass of cooled gas can not be confined to very small galactic radii ( ) since its mass would greatly exceed that of known central mass concentrations in giant ellipticals , normally attributed to massive black holes . , we find that the mass of cooled gas contributes significantly ( percent ) to stellar dynamical mass to light ratios which , as a result , are expected to vary with galactic radius . however , .2 in

typically percent of the total baryonic mass in luminous elliptical galaxies is in the form of cooled interstellar gas . although the mass contributed by cooled gas is small relative to the mass of the old stellar system in these galaxies , it is almost certainly concentrated within the optical effective radius where it can influence the local dynamical mass . however , the mass of cooled gas can not be confined to very small galactic radii ( ) since its mass would greatly exceed that of known central mass concentrations in giant ellipticals , normally attributed to massive black holes . we explore the proposition that a population of very low mass , optically dark stars is created from the cooled gas . for a wide variety of assumed radial distributions for the interstellar cooling , we find that the mass of cooled gas contributes significantly ( percent ) to stellar dynamical mass to light ratios which , as a result , are expected to vary with galactic radius . however , if the stars formed from cooled interstellar gas are optically luminous , their pertubation on the the mass to light ratio of the old stellar population may be reduced . cooling mass dropout also perturbs the local apparent x - ray surface brightness distribution , often in a positive sense for centrally concentrated cooling . in general the computed x - ray surface brightness exceeds observed values within , suggesting the presence of additional support by magnetic stresses or non - thermal pressure . the mass of cooled gas inside is sensitive to rate that old stars lose mass , but this rate is nearly independent of the initial mass function of the old stellar population . .2 in

1408.0352

i

coronal mass ejections ( cmes ) are huge magnetized plasma expulsions from the sun into the heliosphere and are considered as primary drivers of geomagnetic storms and various other space weather effects @xcite . it is therefore required to improve the physics and our understanding of evolution of cmes in the solar wind , which is found to be dependent on heliospheric environment @xcite . various techniques based on stereoscopic observations which estimate the 3d kinematics of cmes in the heliosphere have been developed @xcite . using these techniques , association of remote observations of cmes with in situ observations has been carried out by @xcite . also , several models have been developed for predicting the arrival time of cmes at 1 au @xcite . sometimes , cmes are observed to erupt in quick succession which under certain favorable initial conditions , can interact or merge with each other during their propagation in the heliosphere . in such a scenario , space weather prediction schemes may not be successful without taking into account the post - interaction cmes characteristics . the compound streams ( interaction of cme - cir or cme - cme ) were first inferred by @xcite using observations from helios and iseee 3 spacecraft . their study suggested that a large geomagnetic storm may be associated with compound streams . the observational evidence for merging of cmes ( or cannibalism ) was first given by @xcite based on the long - wavelength radio and soho / lasco observations . thus , these interactions are of great importance from space weather point of view . before the era of wide angle imaging far from the sun , the understanding of involved physical mechanisms in cme - cme or cme - shock interaction was achieved mostly from magnetohydrodynamic ( mhd ) numerical simulations of the interaction of a shock wave with an magnetic cloud ( mc ) @xcite , the interaction of two ejecta @xcite , and the interaction of two mcs @xcite . @xcite have shown that a forward shock can cause an intense southward magnetic field of long duration in the preceding magnetic cloud . such modifications in the preceding cloud are important for space weather prediction . therefore , events involving cme - cme and cme - shock interactions are important candidates to investigate their kinematics and arrival time at near earth . after the launch of _ solar terrestrial relation observatory ( stereo ) _ in 2006 @xcite , it is possible to continuously image the cmes and to determine the 3d locations of their features in the heliosphere and hence have direct evidence of cme interaction using images from heliospheric imager ( hi ) on sun earth connection coronal and heliospheric investigation ( secchi ) package @xcite . however , immediately after the launch of stereo , during deep extended solar minimum , not many interacting cmes were observed . as the current solar cycle progressed , interaction of cmes now appears a fairly common phenomenon , in particular around solar maximum . the interacting cmes of 2010 august 1 have been studied extensively by using primarily the stereo white light imaging , near earth in situ and , s - waves radio observations @xcite . also , @xcite have reported a clear deflection of 2010 may 23 - 24 cmes after their interaction . as mentioned above , therefore , only a few studies on cme interaction have been reported . several key questions regarding cme interaction need to be addressed , which are not well understood quantitatively , viz . ( 1 ) how the dynamics of cmes change after interaction ? what is the regime of interaction , i.e. elastic , inelastic or super - elastic ? @xcite ( 2 ) what are the consequences of the interaction of cme - shock structure ? how the overtaking shock changes the plasma and the magnetic field properties into preceding magnetic cloud ? @xcite ( 3 ) what are the favorable conditions for the cme cannibalism and the role of magnetic reconnection in it ? @xcite ( 4 ) what is the possibility for production of reverse shock at cme - cme interaction site ? @xcite ( 5 ) whether these interacted structures produce different geomagnetic consequences than individual cmes , on their arrival to magnetosphere ? @xcite . ( 6 ) what are the favorable conditions for the cme s deflection and enhanced radio emission during cme - cme interaction in light of aforementioned questions and only a few studies reported , it is clear that the prediction of arrival time of interacting cmes and association of remote observations of such cmes with in situ is challenging . in the present study , we focus on the identification , evolution and propagation of two cmes launched on 2010 november 9 and 10 , as they travel from the corona to the inner heliosphere . this study , in which the launch time of the selected cmes are separated by about 14 hr , gives an opportunity to understand the cme - cme interaction unambiguously for simpler scenario , contrary to complex events around 2010 august 1 , wherein four cmes were launched in quick succession . we find that cmes of november 9 and 10 are directed towards the earth and their initial characteristics indicate a probability of their interaction . in section [ intcmes ] , observations and estimated kinematics of these cmes are presented to investigate if they interacted during their propagation in the heliosphere . in section [ momentum ] , nature of collision , momentum and energy transfer during collision phase of cmes are described using their estimated true mass and kinematics . in section [ insitu ] , in situ observations of remotely tracked cme features are described . using the derived kinematics combined with drag based model ( dbm ) of @xcite , the arrival time and transit speed of tracked features of cmes at l1 is predicted in section [ arrtime ] . the geomagnetic response of interacted cmes structures is described in section [ geomagnetic ] . in section [ results ] , the results and discussions of the present study are emphasized and conclusions are given in section [ conclu ] .

it is found that kinematics of cmes can change when they interact or collide with each other as they propagate in the heliosphere . in this paper our analysis shows an improvement in arrival time prediction of cmes using their post - collision dynamics than using pre - collision dynamics . estimating the true masses and speeds of these colliding cmes the investigation also places in perspective the geomagnetic consequences of the two cmes and their interaction in terms of occurrence of geomagnetic storm and triggering of magnetospheric substorms .

understanding of the kinematic evolution of coronal mass ejections ( cmes ) in the heliosphere is important to estimate their arrival time at the earth . it is found that kinematics of cmes can change when they interact or collide with each other as they propagate in the heliosphere . in this paper , we analyze the collision and post - interaction characteristics of two earth - directed cmes , launched successively on 2012 november 9 and 10 , using white light imaging observations from stereo / secchi and in situ observations taken from wind spacecraft . we tracked two density enhanced features associated with leading and trailing edge of november 9 cme and one density enhanced feature associated with leading edge of november 10 cme by constructing j - maps . we found that the leading edge of november 10 cme interacted with the trailing edge of november 9 cme . we also estimated the kinematics of these features of the cmes and found a significant change in their dynamics after interaction . in in situ observations , we identified distinct structures associated with interacted cmes and also noticed their heating and compression as signatures of cme - cme interaction . our analysis shows an improvement in arrival time prediction of cmes using their post - collision dynamics than using pre - collision dynamics . estimating the true masses and speeds of these colliding cmes , we investigated the nature of observed collision which is found to be close to perfectly inelastic . the investigation also places in perspective the geomagnetic consequences of the two cmes and their interaction in terms of occurrence of geomagnetic storm and triggering of magnetospheric substorms .

1408.0352

r

in this paper , we have studied the interactions between two successively launched earth directed cmes from the sun on 2012 november 9 and 10 , respectively . the analysis involved remote sensing observations of cme propagation in inner heliosphere from secchi / cor2 and hi images and the associated in situ measurements from wind spacecraft . the first cme ( cme1 ) associated with a filament eruption is observed to be slower ( 600 km s@xmath15 ) than the successive cme ( cme2 ) launched on november 10 with a higher velocity ( 900 km s@xmath15 ) . both the cmes were launched in approximately the same direction towards the earth , indicating a possibility of interaction because of their relative speeds and the same direction . different features were tracked as brightness enhancements in j - maps obtained from cor2 and hi images and subsequently hm technique was applied to estimate the kinematics of the tracked features of the cmes . from the estimated kinematics , the site of collision of cmes could be located at a distance of approximately 35 r@xmath14 at 12:00 ut on november 10 , which is at least 85 r@xmath14 before and 15 hours earlier than as predicted by using the initial kinematics of cmes in cor2 fov . the estimated kinematics were then used as inputs in the dbm to determine the arrival times of the tracked features . after the interaction , cme2 transferred some of its velocity to cme1 and both were observed to propagate together , showing a distinct deceleration of cme2 . as described earlier , cme1 le is found to be propagating with higher speed than cme1 te . therefore , cme1 le ( green track ) did not collide with cme2 le ( blue track ) . with the start of collision phase , the le of cme1 is also found to accelerate and after the collision phase , significant acceleration of cme1 le is noticed . this may occur either because of sudden impact ( push ) from cme1 te to cme1 le during collision or due to the passage of a shock driven by the cme2 or a combined effect of both . beyond the collision phase , up to an estimated distance of nearly 100 r@xmath14 , le of cme2 was found moving behind the te of cme1 and both these features propagated together decelerating slowly . for few hours after the observed collision phase , it is noticed that speed of the le and te of cme1 is slightly higher than le of cme2 , which can increase the observed separation of these structures . the j - maps show that both these features can be tracked for further elongations after interaction . however , due to the limitation of the hm method for higher elongations @xcite , we restricted our measurements on the tracked features up to 100 r@xmath14 . our analyses show an evidence that after the interaction , the two features did not merge . it appears that le of cme2 interacted with te of cme1 and continued to propagate with a reduced speed of 500 km s@xmath15 . in the secchi / hi - b images these features can not be well distinguished and therefore it is difficult to use any stereoscopic method to infer about a possible longitudinal deflection ( based on stereoscopic methods ) of these features after interaction . during the collision between cme1 and cme2 , we noticed a large deceleration of fast cme2 while relatively less acceleration of slow cme1 , till both approached an equal speed . this is expected to occur if the mass of cme1 is larger than that of cme2 , which is indeed the case . in section [ momentum ] we have shown that the mass of cme1 is @xmath16 2.0 times larger than the mass of cme2 . this result is an important finding and is in agreement with the second scenario of interaction described in @xcite . it also must be noted that we have estimated the mass of cmes in cor2 fov while interaction takes place in hi fov . further , we can not ignore the possibility of increase in mass of cme due to mass accretion at its front via snowplough effect in the solar wind beyond cor fov @xcite . we must also mention that in our calculation of momentum and energy transfer , although we use the total mass of cme1 but only a part of cme1 ( i.e. te of cme1 ) takes part in collision with cme2 . considering the uncertainties in the derived speeds and mass of the cmes , our analysis reveals that the nature of collision remains close to perfectly inelastic . however , we also acknowledge that defining collision phase is crucial and seems to play an important role in this calculation . in this context , it must be emphasized that marking of the start of collision is often difficult . this is because the following fast speed cme2 starts to decelerate , well before the actual merging or collision is revealed in imaging observations . this is also shown in earlier studies for other interacting cmes @xcite . the interaction of cme2 with streamers or overlying coronal magnetic field lines @xcite may be responsible for deceleration of following cme2 before its collision with cme1 takes place . however , the contribution of other factors , e.g. , the solar wind drag acting on cme2 , interaction of cme2 with trailing edge of preceding cme1 , and magnetic interaction of cme2 with preceding cme1 can not be completely ignored . also , possibly a shock launched by the following cme2 can contribute in acceleration of the preceding cme1 before the actual merging of both cmes . therefore , different timing and large time - interval of acceleration of one cme and deceleration of other , prevent us to pinpoint the exact start and end of the collision phase . we concluded that the collision of interacting cmes of 2012 november 9 - 10 is close to perfectly inelastic in nature . here , it is noted that we are dealing with large scale magnetized three - dimensional structures , however , in the present study we have reduced the calculations to one - dimensional collision which seems to be accurate as tracked features of both cme1 and cme2 are considered to move along approximately the same trajectory . this implies that there will be a small difference between velocity of tracked feature of one cme and its component along the direction of propagation ( i.e. longitude ) of tracked feature of other cme . we must admit that possibility of change in longitude of tracked features during their collision can partially contribute to some errors in the estimated speed . in light of earlier reported observations @xcite , it seems that collision of cmes can occur in all i.e. elastic , inelastic or super - elastic regimes . an in - depth study is required further for understanding the nature of cme - cme collision which may depend on the characteristics of cmes , locations and duration of collision phase in the heliosphere . at the last point of measurement in hi fov around 120 r@xmath14 , the estimated speed of te of cme1 and le of cme2 are approximately equal ( @xmath16 470 km s@xmath15 ) . therefore , both features are expected to arrive at l1 at approximately the same time . comparing to in situ measured actual arrival time , the delayed arrival of le of cme2 is possible due to higher drag force acting on it resulting in its deceleration . however , the propagation direction of cme2 in southward hemisphere , as noticed in hi1-a images and also estimated in cor2 fov using 3d reconstruction , can also account for flank encounter of cme2 and thus its delayed sampling by wind spacecraft at l1 . this is consistent with our interpretation in section [ insitu ] . since , in the hm method , the front of the cme is assumed spherical which may not be the real case for cme2 , as it was moving with fast speed and has large probability to distort and flatten its front while interacting with structured solar wind @xcite . in this case , the estimated speed using hm method will lead to some error and can result in the delayed arrival of le of cme2 . keeping all these issues in mind , we believe that it is quite probable that the tracked feature corresponding to le of cme2 ( blue track in j - map ) is not sampled by in situ spacecraft . therefore , erroneous predicted arrival time for le of cme2 is related to incorrect identification of tracked cme2 le in in situ data which is taken as a reference ( actual ) for remotely observed tracked cme2 le . the present study not only estimates the kinematics and arrival times based on hi observations and their application to the dbm model of cme propagation , it also attempts to associate tracked brightness enhancements as observed in remote sensing cor and hi ( j - maps ) with the in situ observations @xcite . the association of hi observations with in - situ measurements from wind leads to many interesting results . in spite of two cmes launched from the sun in succession in the earthward direction , we observe only one shock in in situ data which may suggest the merging of shocks driven by cme1 and cme2 , if both cmes would have driven shocks . however , such a claim can not be made unless we are well familiar with the in situ signatures of merged shock and plasma structure following it . the sweeping of plasma to high density at the front of cme1 and its compressed heating is most likely due to passage of cme2 driven shock through the mc associated with cme1 . based on the predicted arrival time of tracked features , it seems that the cme2 driven shock and cme1-sheath region is tracked as cme1 le in j - map . therefore , we infer that cme1 le is propagating probably into an unperturbed solar wind . our study also provides a possibility of formation of interaction region ( ir ) at the junction of trailing edge of preceding cme and leading edge of following cme . we show that during collision of the cmes , kinetic energy exchange up to 50% and momentum exchange between 23 to 30% . our study also demonstrate that the arrival time prediction significantly improved using his on - board stereo compared to cor2 observations , and also emphasizes the importance of understanding of post - collision kinematics in further improving the arrival time prediction for a reliable space weather prediction scheme . our study reveals clear signatures of interaction of these cmes in remote and in situ observations and also helps in identification of separate structures corresponding to these cmes . in spite of the interaction of the two cmes in the interplanetary medium which generally results in complex structures as suggested by @xcite , in our case , we could identify interacted cmes as distinguished structures in wind spacecraft data . even after collision of these cmes , they did not merge which may be possibly because of strong magnetic field and higher density of cme1 than cme2 . this needs further confirmation , and therefore , it is worth to investigate what decides the formation of merged cme structure or complex ejecta during cme - cme interaction . due to single point in situ observations of cme , we acknowledge the possibility of ambiguity in marking the boundaries of cmes . in the present case , the boundaries for cme1 and ir are distinctly clear . also , slight ambiguity in the boundary of cme2 ( flank encounter ) will not change our interpretation because the main geomagnetic response is caused due to enhanced negative bz in trailing portion of cme1 and its extension in ir . here , we also point out that temperature in ir is lesser than the temperature for cme2 region but temperatures in both regions are elevated as compared to a normal non - interacting cme . the observations of unexpected larger temperature in cme2 region than ir region may be due to the possibility that sheath region of cme2 is intersected by in situ spacecraft , as we have interpreted . the association of geomagnetic storms with isolated single cmes has been carried out extensively for a long time @xcite . however , only few studies have been dedicated to understand the role of interacting cmes in the generation of geomagnetic storms @xcite . our study is important as it focuses on the role of interacting cmes in the generation of geomagnetic storms as well as substorms . in the context of substorms , our study highlights that persistence of imf bz in the southward direction is more important than the amplitude in driving the substorm activity as manifested by the al intensification . using windmi model , @xcite have shown that the ip shock and sheath features for cmes contribute significantly to the development of storms and substorms . but , in our study , sharp and large southward excursions in the midst of fluctuating imf bz associated with shock ( shock - sheath region before cme1 ) were found less effective in producing strong substorm activity . therefore , further investigations are required regarding characteristics ( geometry , intensity ) of shock and preceding cme in the context of triggering of substorms , as has been shown in earlier studies @xcite . regarding geomagnetic storms , our study suggests that the trailing edge of preceding cme ( cme1 ) and ir formed between two interacting cmes are efficient candidates for intense geomagnetic storms . is that the nearly equal amplitude responses of the pc index corresponding to the shock - sheath region ( imf bz sharply fluctuating between southward and northward directions ) preceding the cme1 interval vis - - vis the cme1 interval ( imf bz steadily turning southward ) . this is interesting as the responses of sym - h and al during these two intervals are quite different in terms of amplitudes of variations . @xcite have inferred that the pc index for the sunlit polar cap ( summer hemisphere , high polar ionospheric conductance ) responds mainly to the geo - effective interplanetary electric field whereas the pc index for the dark winter cap ( winter hemisphere , low polar ionospheric conductance ) responds better to the particle precipitation in the auroral zone like the ae and al indices . it is to be noted here that , in the present study , no distinction is made between the variations of pc index in the northern ( pcn ) and southern ( pcs ) hemispheres . on the other hand , it is known that al index is constructed based on magnetometer observations around the northern auroral oval only . the discrepancy between the variations in the pc index and the al index may , therefore , suggest towards the hemispherical asymmetry in the response of polar ionosphere corresponding to this event . this is not unexpected as asymmetric auroral intensities in the northern and southern hemispheres are reported in literature @xcite . further investigations are needed to understand this aspect .

, we analyze the collision and post - interaction characteristics of two earth - directed cmes , launched successively on 2012 november 9 and 10 , using white light imaging observations from stereo / secchi and in situ observations taken from wind spacecraft . we also estimated the kinematics of these features of the cmes and found a significant change in their dynamics after interaction . in in situ observations , we identified distinct structures associated with interacted cmes and also noticed their heating and compression as signatures of cme - cme interaction .

understanding of the kinematic evolution of coronal mass ejections ( cmes ) in the heliosphere is important to estimate their arrival time at the earth . it is found that kinematics of cmes can change when they interact or collide with each other as they propagate in the heliosphere . in this paper , we analyze the collision and post - interaction characteristics of two earth - directed cmes , launched successively on 2012 november 9 and 10 , using white light imaging observations from stereo / secchi and in situ observations taken from wind spacecraft . we tracked two density enhanced features associated with leading and trailing edge of november 9 cme and one density enhanced feature associated with leading edge of november 10 cme by constructing j - maps . we found that the leading edge of november 10 cme interacted with the trailing edge of november 9 cme . we also estimated the kinematics of these features of the cmes and found a significant change in their dynamics after interaction . in in situ observations , we identified distinct structures associated with interacted cmes and also noticed their heating and compression as signatures of cme - cme interaction . our analysis shows an improvement in arrival time prediction of cmes using their post - collision dynamics than using pre - collision dynamics . estimating the true masses and speeds of these colliding cmes , we investigated the nature of observed collision which is found to be close to perfectly inelastic . the investigation also places in perspective the geomagnetic consequences of the two cmes and their interaction in terms of occurrence of geomagnetic storm and triggering of magnetospheric substorms .

1401.6866

i

since several decades polymer brushes find abiding interest for various applications , and have been studied very intensively by experiment , analytical theory , and computer simulations @xcite . the structure of these soft polymeric layers and their response to various external perturbations depends in a delicate way on various control parameters such as molecular weight , grafting density , quality of the solvent , and character of the interactions between monomeric units and the substrate to which the macromolecules are grafted . however , inspired by the early works @xcite , mostly brushes formed from completely flexible chains were considered , where the elastic response is entirely entropic , due to the configurational degrees of freedom of the tethered chain molecules . in such brushes , chains may be nevertheless strongly stretched in the direction perpendicular to the substrate , to avoid unfavorable monomer - monomer overlap in the case of sufficiently dense grafting . effects of intrinsic chain stiffness , as are expected for semi - flexible polymers @xcite , did find rather little attention @xcite , apart from the case where one considers grafted semi - flexible chains in nematic solvents @xcite and their liquid crystalline order @xcite . we also draw attention to some related problems where rod - like molecules densely packed and anchoring at substrates play a role , such as in langmuir monolayers of surfactants and related systems @xcite . experimentally , the interactions between dna - grafted colloids @xcite , or poly(acrylic acid ) brushes with variable rigidity @xcite , have been comprehensively investigated by f. kremer and collaborators . in recent years , semi - flexible polymers find increasing interest particularly in the context of biophysical systems , such as cytoskeleton actin bundles @xcite biofilaments @xcite , and also biobased polymer brushes were recently created @xcite . thus , a more comprehensive simulation study of brushes formed from semi - flexible polymers would be desirable to theoretically clarify the effect of chain stiffness on structure and dynamics of such systems , including also their response to external perturbations , such as shear and compressive forces . as is well known , one important possible application of polymer brushes formed from flexible polymers is their use as a lubricant @xcite , although the theoretical aspects of this response to shear and compression are still under discussion @xcite . in our preliminary publication @xcite , indeed , an anomalous response of brushes formed from rather stiff chains was found , caused by an onset of orientational order parallel to the substrate . in the present paper we shall give a more complete account of this problem , focusing mainly on the structure and static behavior of such stiff brushes subject to compression . in the next section [ sec_model ] , the model that is studied will be introduced and the simulation method will be described . section [ sec_structure ] examines the parallel and perpendicular chain linear dimensions in rigid brushes as a function of bending rigidity and grafting density over a wide range , as well as the profiles of monomer density in the direction perpendicular to the grafting substrate , and the end monomer distribution . then in section [ sec_compress ] we elaborate the topic that was already briefly addressed in our preliminary study , compression of such brushes by a piston , presenting new results , including also the variation with grafting density and chain length . the hysteresis associated with the transition towards orientational order will also be investigated . section [ sec_theory ] is devoted to an attempt for theoretical consideration within the mean - field approximation of the brush response to deformation . a brief account on the recovery dynamics of compressed stiff brushes is then given in section [ sec_dynamics ] . our conclusions are summarized in section [ sec_summary ] .

using a coarse - grained bead - spring model for semi - flexible macromolecules forming a polymer brush , structure and dynamics of the polymers is investigated , varying chain stiffness and grafting density . the anchoring condition for the grafted chains is chosen such that their first bonds are oriented along the normal to the substrate plane . the pressure , required to keep the stiff brush at a given degree of compression , is thereby significantly _ smaller _ than for an otherwise identical brush made of entirely flexible polymer chains ! while both the brush height and the chain linear dimension in the-direction perpendicular to the substrate increase monotonically with increasing chain stiffness , lateral chain linear dimensions exhibit a maximum at intermediate chain stiffness .

using a coarse - grained bead - spring model for semi - flexible macromolecules forming a polymer brush , structure and dynamics of the polymers is investigated , varying chain stiffness and grafting density . the anchoring condition for the grafted chains is chosen such that their first bonds are oriented along the normal to the substrate plane . compression of such a semi - flexible brush by a planar piston is observed to be a two - stage process : for small compressions the chains contract by `` buckling '' deformation whereas for larger compression the chains exhibit a collective ( almost uniform ) bending deformation . thus , the stiff polymer brush undergoes a-nd order phase transition of collective bond reorientation . the pressure , required to keep the stiff brush at a given degree of compression , is thereby significantly _ smaller _ than for an otherwise identical brush made of entirely flexible polymer chains ! while both the brush height and the chain linear dimension in the-direction perpendicular to the substrate increase monotonically with increasing chain stiffness , lateral chain linear dimensions exhibit a maximum at intermediate chain stiffness . increasing the grafting density leads to a strong decrease of these lateral dimensions , compatible with an exponential decay . also the recovery kinetics after removal of the compressing piston is studied , and found to follow a power - law / exponential decay with time . a simple mean - field theoretical consideration , accounting for the buckling / bending behavior of semi - flexible polymer brushes under compression , is suggested .

astro-ph0203319

c

the advent of x - ray telescopes with large effective areas and instruments for high resolution spectroscopy opens a new window on the intergalactic medium , one that could reveal a large reservoir of previously hidden baryons . we have used a hydrodynamic simulation of the @xmath0cdm cosmological model to predict the properties of the x - ray forest at @xmath11 . in agreement with previous studies based on numerical simulations ( hgm ; fbc ) and analytic methods @xcite , we find that the oxygen species and produce the strongest x - ray forest lines , thanks to the high cosmic abundance of oxygen , the oscillator strengths of the transitions at 21.60 ( ) and 18.97 ( ) , and the relatively frequent occurrence of temperature and density regimes where these species have large fractional abundance . if the igm metallicity at these temperatures and densities is @xmath4 , as we assume in most of our calculations , then and are the only x - ray forest lines likely to be detectable with existing instruments , and even these will be difficult to study in any comprehensive fashion . other promising lines for study with future instruments include the helium - like and hydrogen - like species of carbon , nitrogen , and neon ( , , , , , ) , , which has lower abundance but a large oscillator strength , and possibly . we have not examined highly ionized species like and , which occur only at high temperatures that are poorly represented in our @xmath128 box ( see @xcite for analytic predictions ) . our conclusions about the detectability of these x - ray forest lines are summarized by the rightmost column of table [ ions ] , which lists the equivalent width threshold at which we predict one line per unit redshift , and table [ equivwidth ] , which gives approximate @xmath116 detection thresholds for observations with _ chandra _ , _ xmm - newton _ , _ constellation - x _ , and _ xeus _ , assuming 500 ksec exposures and the source spectrum of the x - ray bright quasar h1821 + 643 ( @xmath163 ) . target - of - opportunity searches that observe blazars in very high states could potentially reach lower equivalent width thresholds ( nicastro , private communication ) . the full distribution functions for absorber equivalent widths are shown in figures [ optdisto][optdistnesife ] . the largest uncertainty in the predictions is the unknown metallicity distribution of the igm at the relevant temperatures and densities . this distribution can itself be predicted by tracking the dispersal of metals in cosmological simulations ( as done by , e.g. , hgm and @xcite ) , but the uncertainties in the escape of metals from the galaxies themselves make these results quite uncertain . we predict a lower frequency of detectable x - ray forest lines than fbc , mainly because we assume @xmath4 instead of the higher metallicity found in the central regions of hot x - ray clusters . for the same metallicity , the two simulations give similar predictions for the number of strong absorbers , though the inclusion of radiative cooling and photoionization in our calculations tends to reduce the column densities of the strongest systems and substantially increase the number of weak absorbers . our predicted equivalent width distribution agrees with that of hgm at low @xmath113 but falls below it at high @xmath113 , perhaps because of differences in the assumed cosmological parameters and in the simulation methods , but perhaps because their strongest absorbers arise in regions of higher than average metallicity . our assumption of a uniform metallicity of @xmath132 with solar abundance ratios ( instead of the @xmath49-enhanced ratios characteristic of type ii sn enrichment ) is probably conservative , and perhaps unduly pessimistic . the predicted equivalent width thresholds in table [ ions ] are approximately proportional to the assumed metallicity , except that they grow more slowly for @xmath214 as saturation becomes significant ( see figure [ colo78 ] ) . as shown in figure [ optdisto ] , the predicted number of systems at high equivalent width is sensitive to the scatter in igm metallicity as well as its mean value . for example , if we include 0.4 dex of scatter about 0.1 solar metallicity , then the and equivalent width thresholds corresponding to one line per unit redshift are about a factor of two higher than the values quoted in table [ ions ] . because the intrinsic equivalent width distribution is steep , the first x - ray forest systems to be detected are likely to lie on the high tail of the igm metallicity distribution we have devoted much of our attention to the physical state of the gas producing and absorption , as illustrated in figures [ zoombox][o1 - 678 ] , especially figure [ ophysprpty ] . strong and absorbers , with @xmath215 , arise mainly in gas with @xmath3 and temperature @xmath2 , where collisional ionization dominates over photoionization . weaker absorbers arise in lower density gas ( @xmath216 for @xmath217 ) over a wider range of temperatures , with photoionization often playing a significant role . for @xmath213 , all absorbers and most absorbers arise in the temperature regime @xmath10 identified by @xcite as the `` warm - hot igm , '' which contains a substantial fraction of the low redshift baryons in cosmological simulations @xcite . however , one should keep in mind that the absorbers potentially detectable with _ chandra _ or _ xmm - newton _ trace only the high density regions of the whim , with overdensities characteristic of virialized groups rather than intergalactic filaments . in agreement with @xcite and @xcite , we find that the @xmath0cdm model can plausibly account for the high incidence of ( 1032 , 1038 ) absorbers at low redshift @xcite , as shown in figure [ o6 ] . the absorbers exhibit a well - defined trend between equivalent width and overdensity , though there are some extreme outliers ( figure [ ophysprpty ] ) . at every equivalent width there is a substantial range of gas temperatures ( about a factor of ten ) , with photoionization dominating in the cooler systems . at @xmath217 ( @xmath218 ) , much of the absorption arises in gas with overdensity @xmath195 . in searches with _ chandra _ or _ xmm - newton , absorbers will play a crucial role as signposts for or absorption . if the igm metallicity is @xmath132 , or even @xmath219 , then the predicted number of x - ray forest systems strong enough to be detected at the @xmath5 level needed in a `` blind '' survey is very small . however , if one is searching at the redshift of a known system , then a @xmath220 detection is already significant , and the steepness of the equivalent width distribution translates a small change in detection threshold to a large change in predicted line density . ly@xmath49 absorption can also serve as a signpost , but the higher density of ly@xmath49 lines and the large scatter between and or ( figure [ o1 - 678 ] ) makes it less useful for this purpose than . recent observations provide several tentative detections of intergalactic and absorption . the most convincing detections are those of @xcite , who find absorption features of , , and in their _ chandra _ spectrum of pks 2155 - 304 , at wavelengths consistent with zero redshift . the implied and column densities are @xmath221 . _ xmm - newton _ and _ chandra _ observations also show @xmath11 absorption along lines of sight towards mrk 421 and 3c 273 @xcite . these observations suggest that highly ionized gas is fairly ubiquitous along lines of sight through the local group , as one might expect when looking out from a local maximum in the igm density ( see , e.g. , @xcite ) , though at least some of the absorption could be galactic in origin @xcite . our simulations predict that oxygen lines of this strength should be rare along random lines of sight beyond the local group ( fig . [ optdisto ] ) , and here the observational situation is more ambiguous . @xcite find a statistically significant absorption feature in the _ chandra _ spectrum of pks 2155 - 304 that could correspond to absorption coincident with a known galaxy group at @xmath222 , with an implied column density @xmath223 . however , the _ xmm - newton _ spectrum appears to rule out the existence of an absorption feature at this level ( rasmussen , private communication ; see @xcite ) . @xcite use a _ chandra _ spectrum of h1821 + 643 to search for absorption at the redshifts of previously known systems @xcite , obtaining apparent detections of one system in and another in both and . the statistical significance of the features is only @xmath224 in each case , but because the absorption redshifts are known _ a priori _ from the measurements , the probability that they are simply noise fluctuations is small ( @xmath225 ) . the rest - frame equivalent widths are @xmath226 and @xmath227 for the lines and @xmath228 for the line , with corresponding column densities @xmath229 ( ) and @xmath230 ( ) , assuming no saturation . the existence of two such strong systems in a path length @xmath231 is surprising relative to our predictions in figure [ optdisto ] , unless the metallicity in these systems is substantially higher than 0.1 solar , though it is worth noting that this line of sight also has an unusually high incidence of absorption @xcite . further measurements of or limits on and absorption associated with will take us much further towards understanding this newly discovered population of low redshift absorbers , providing constraints on their densities , temperatures , and ionization mechanisms and on their contribution to the cosmic baryon budget . however , absorbers trace only the low temperature end of the x - ray forest ; many strong and systems have very weak absorption , and , conversely , many strong systems will be undetectable in or ( figure [ ocorr ] ) . a full accounting of the strong and absorbers will probably require a mission with the capabilities of _ constellation - x _ , which may also begin to detect x - ray absorption from other elements in the same systems . even at the @xmath232 threshold of _ constellation - x _ , the detectable x - ray forest absorbers at @xmath4 correspond mainly to gas in the outer regions of groups and poor clusters , with some contribution from more diffuse gas in filaments . the powerful _ satellite would allow a comprehensive investigation of x - ray forest absorption by a number of ionization species , providing great insight into the distribution of shock - heated baryons and the enrichment of the intergalactic medium . we are grateful to smita mathur for helpful advice at many stages in this work , especially in matters related to observational capabilities . we also thank jordi miralda - escud for several valuable discussions and joop schaye for comments on the manuscript . we thank todd tripp for providing the observational data points used in figure [ o6 ] and taotao fang for providing the numerical results from @xcite and fbc ( discussed in [ sec : ewdist ] and shown in figure [ o6 ] ) . this work was supported by nasa ltsa grant nag5 - 3525 , nsf grant ast-9802568 , and chandra observatory grant g01 - 2118x from smithsonian astrophysical observatory . x.c . was supported at osu by the department of energy under grant de - fg02 - 91er40690 , and at itp / ucsb by the nsf under grant phy99 - 07949 . d.w . acknowledges the hospitality of the institute for advanced study and the financial support of the ambrose monell foundation during the completion of this work . r.d . was supported by nasa through hubble fellowship grant number hst - hf-01128.01-a awarded by the space telescope science institute , which is operated by aura , inc . , under nasa contract nas5 - 26555 . the simulation was performed at the san diego supercomputer center and ncsa . barlow , t. a. & tytler , d. , 1998 , , 115 , 1725 burles , s. , & tytler , d. 1997 , , 114 , 1330 burles , s. , & tytler , d. 1998 , , 507 , 732 cen , r. , miralda - escud , j. , ostriker , j. p. , & rauch , m. , 1994 , , 427 , l9 hellsten , u. , dav , r. , hernquist , l. , weinberg , d. h. , & katz , n. 1997 , , 487 , 482 hernquist , l. , & katz , n. 1989 , , 70 , 419 hernquist , l. , katz , n. , weinberg , d. h. , & miralda - escud , j. , 1996 , , 457 , l51 press , w. h. , & schechter , p. 1974 , , 187 , 425 rasmussen , a. , kahn , s. m. , & paerels , f. 2003 , to appear in the igm / galaxy connection : the distribution of baryons at @xmath11 , ( kluwer : dordrecht ) , astro - ph/0301183 equivalent widths corresponding to @xmath159 , computed from eq . ( [ eqn : wmin ] ) using the resolution and effective area values of table [ instrument ] , a 500 ksec integration time , and a quasar spectrum @xmath233 similar to that of the @xmath163 quasar h1821 + 643 .

using a hydrodynamic simulation of a cold dark matter universe with a cosmological constant (cdm ) , we investigate the `` x - ray forest '' absorption imprinted on the spectra of background quasars by the intervening intergalactic medium ( igm ) , at redshift . in agreement with previous studies , we find that and produce the strongest absorption features . chandra _ or _ xmm - newton _ arise in gas with and overdensities that are characteristic of galaxy groups . future x - ray missions could detect weaker oxygen absorption produced by gas with a wider range of temperatures and the lower densities of unvirialized structures ; they could also detect x - ray forest absorption by carbon , nitrogen , neon , iron , and possibly silicon . if the igm metallicity is , as we assume in most of our calculations , then the predicted number of systems strong enough for a detection with _ chandra _ or _ xmm - newton _ is extremely low . our simulation reproduces the high observed incidence of ( 1032 , 1038 ) absorbers , and the most promising strategy for finding the x - ray forest is to search at the redshifts of known systems , thus reducing the signal - to - noise threshold required for a significant detection . however , while many absorbers have associated or absorption , the systems trace only the low temperature phases of the x - ray forest , and a full accounting of the strong and systems will require a mission with the anticipated capabilities of _ constellation - x_. the large effective area of the _ xeus _ satellite would make it an extremely powerful instrument for studying the igm , measuring x - ray forest absorption by a variety of elements and revealing the shock - heated filaments that may be an important reservoir of cosmic baryons .

using a hydrodynamic simulation of a cold dark matter universe with a cosmological constant (cdm ) , we investigate the `` x - ray forest '' absorption imprinted on the spectra of background quasars by the intervening intergalactic medium ( igm ) , at redshift . in agreement with previous studies , we find that and produce the strongest absorption features . the strong oxygen absorbers that might be detectable with _ chandra _ or _ xmm - newton _ arise in gas with and overdensities that are characteristic of galaxy groups . future x - ray missions could detect weaker oxygen absorption produced by gas with a wider range of temperatures and the lower densities of unvirialized structures ; they could also detect x - ray forest absorption by carbon , nitrogen , neon , iron , and possibly silicon . if the igm metallicity is , as we assume in most of our calculations , then the predicted number of systems strong enough for a detection with _ chandra _ or _ xmm - newton _ is extremely low . however , scatter in metallicity increases the number of strong absorbers even if the mean metallicity remains the same , making the predictions somewhat more optimistic . our simulation reproduces the high observed incidence of ( 1032 , 1038 ) absorbers , and the most promising strategy for finding the x - ray forest is to search at the redshifts of known systems , thus reducing the signal - to - noise threshold required for a significant detection . however , while many absorbers have associated or absorption , the systems trace only the low temperature phases of the x - ray forest , and a full accounting of the strong and systems will require a mission with the anticipated capabilities of _ constellation - x_. the large effective area of the _ xeus _ satellite would make it an extremely powerful instrument for studying the igm , measuring x - ray forest absorption by a variety of elements and revealing the shock - heated filaments that may be an important reservoir of cosmic baryons .

astro-ph0206344

c

we have used gemini - north to study the stellar populations in the central regions of m33 . the surface brightness profiles from @xmath4 to @xmath5 , formed from the combination of our data and those of @xcite , show that the data need to be modeled using a three - component , core + spheroid + disk model . the best - fit parameters are listed in table [ tab : decomposition ] . these high - resolution observations allow us to accurately measure individual stars to @xmath278 . artificial star tests ( [ sec : artstartests ] ) show that our completeness is relatively uniform across the field ( 50% at @xmath232 ) , although within @xmath47 from the nucleus the completeness is dramatically lower due to severe crowding . artificial fields are used to understand the observational effects associated with adaptive optics measurements in crowded fields . based on the slope of the giant branch in the infrared color magnitude diagram , we estimate the mean metallicity to be @xmath1 ( [ sec : metallicity ] ) . using the bolometric luminosities and density of stars on the agb , we hypothesize two bursts of star formation ; at @xmath3 and @xmath2 gyr ago ( [ sec : age ] ) . we note however , that this component of young stars may have influenced our metallicity estimate due to the sensitivity of the gb slope on age . the stellar luminosity function in m33 is shown to be significantly different from that measured in the galactic bulge as viewed through baade s window ( [ sec : lfs ] ) . the difference in their maximum luminosities is due to differences in ages of the two regions . we speculate that this is also the origin of their different slopes as well . in section [ sec : comparison ] we compare our data with previous observations . recent work by @xcite is in good agreement with our data , although our observations go @xmath279 magnitudes deeper ( [ sec : davidge ] ) . we also combine our data with optical hst - wfpc2 measurements @xcite , and present the optical - ir cmd in [ sec : mighell ] . this cmd clearly shows that the central regions of m33 are composed of young , intermediate , and old aged stellar populations . dividing the inner @xmath280 ( @xmath281 pc ) into equal area rings around the nucleus , we look for radial variations in the stellar properties ( [ sec : radial_variations ] ) . however , based on the distribution of stellar luminosities and the morphology of the cmd , we find that all stars are consistent with being drawn from a single population . in the last section ( [ sec : blending ] ) we perform calculations to estimate the severity of blending at various imaging resolutions and locations in m33 . using the formulations of @xcite and our composite surface brightness profile , these calculations call into question some previous claims of very luminous stars in the central regions of m33 . this paper was based on observations obtained at the gemini observatory , which is operated by the association of universities for research in astronomy , inc . , under a cooperative agreement with the nsf on behalf of the gemini partnership : the national science foundation ( united states ) , the particle physics and astronomy research council ( united kingdom ) , the national research council ( canada ) , conicyt ( chile ) , the australian research council ( australia ) , cnpq ( brazil ) and conicet ( argentina ) . observations used the adaptive optics system hokupaa / quirc , developed and operated by the university of hawaii adaptive optics group , with support from the national science foundation . many thanks to the gemini queue observers , peter stetson for supplying and helping us with his photometry package , allframe , and to ken mighell for providing us with his hst - wfpc2 images and photometry lists before publication . thanks to michael regan for helping with his surface brightness decomposition . valuable comments from ken mighell , darren depoy , dante minniti , and an anonymous referee were also greatly appreciated .

based on the slope of the giant branch we estimate the mean metallicity to be , and from the luminosities of the most luminous stars , we estimate that there were two bursts of star formation and gyr ago . we combine our infrared gemini data with optical hst - wfpc2 measurements revealing a cmd populated with young , intermediate , and old age stellar populations . using surface brightness profiles from to , we perform simple decompositions and show that the data are best fit by a three - component , core + bulge + disk model .

using gemini quickstart infrared observations of the central of m33 , we analyze the stellar populations in this controversial region . based on the slope of the giant branch we estimate the mean metallicity to be , and from the luminosities of the most luminous stars , we estimate that there were two bursts of star formation and gyr ago . we show that the stellar luminosity function not only has a different bright end cutoff , but also a significantly different slope than that of the galactic bulge , and suggest that this difference is due to the young stellar component in m33 . we combine our infrared gemini data with optical hst - wfpc2 measurements revealing a cmd populated with young , intermediate , and old age stellar populations . using surface brightness profiles from to , we perform simple decompositions and show that the data are best fit by a three - component , core + bulge + disk model . finally , we find no evidence for radial variations of the stellar populations in the inner of m33 based on a spatial analysis of the color - magnitude diagrams and luminosity functions .

1608.01473

c

* detailed look into water flux across the tm domain . * in order to glean the molecular origin of receptor state - dependent water flux , we first visualize the geometry of water channel . the radius of water channel , calculated using the program hole @xcite ( see figure [ water_flux_analysis]a ) , reveals that the geometrical bottleneck ( @xmath70 ) in the midst of tm domain ( @xmath71 ) ( figure [ water_flux_analysis]a , see the black arrow ) is formed around w246@xmath72 and y288@xmath73 in the agonist - bound active form . this is compatible with our finding that the water flux is substantially reduced in the agonist - bound form ( figure [ flux ] ) . w246@xmath72 , a key microswitch that senses an agonist and relays its signal to other microswitches @xcite , is located deep inside the orthosteric binding vestibule , regulates the entry of water from the ec domain ; whereas y288@xmath73 is located at the lower part of tm channel , regulating the entry of water from the ic domain . although the geometry of channel in each receptor state provides a glimpse of pipeline across the tm region , the actual water flux through the channel is not fully explained by the radii of the channel alone . for example , the apo state , overall , has greater radii along the channel and does not have a particularly more restrictive geometrical bottleneck than those in the antagonist - bound state ( figure [ water_flux_analysis]a ) ; yet the flux is smaller than the one observed in the antagonist - bound state . depending on the extent of hydrophobicity or electrostatic nature of residues comprising each region of the channel surface , stochastic wetting - dewetting transition @xcite can occur along the channel . furthermore , a stable water cluster in the channel , not exchanging water molecules with the surroundings , would impede the water dynamics through the channel . explicit calculations of water occupancy along the @xmath62-axis @xcite visualize how water molecules actually fill the tm channel at time @xmath31 ( figure [ water_flux_analysis]b ) . as expected , in the apo state ( figure [ water_flux_analysis]b , top ) the ec region ( @xmath74 ) is always filled with a high density of water since the empty ligand binding pocket is accessible from the bulk ; however , ic region ( @xmath75 ) remains dry " , indicating that the entry of water through the ic region is blocked . this dry zone corresponds to the second hydrophobic layer ( hl2 ) around npxxy motif above y288@xmath73 , illustrated by yuan _ _ @xcite . in the agonist - bound form , another water - free layer is observed right above the hl2 ( @xmath76 ) ( figure [ water_flux_analysis]b , middle ) . this is the region below which the water cluster is formed . on the other hand , the first hydrophobic layer ( hl1 ) @xcite , corresponding to another dry zone between the orthosteric and the allosteric sites @xcite(@xmath71 ) is observed in the inactive state . notably , despite the hl1 , the water occupancy map of the antagonist - bound form ( figure [ water_flux_analysis]b , bottom ) finds multiple instances ( @xmath77 ns ) that both hl1 and hl2 are filled with water bridging across the entire tm region . this accounts for the greater water flux in the inactive state . the location of the hydrophobic layer and the receptor state - dependent water flux are affected by the alignment of polar residues along the channel . the tm domain is mostly composed of non - polar hydrophobic residues , but there are polar / charged amino acids buried inside the tm domain as well . the streams of water molecules are found along an y " shaped array of these polar and charged residues that bridge through the tm domain ( figure s3 ) . this array of polar / charged residues corresponds to the buried ionizable networks in gpcrs which have recently been underscored @xcite . our study reveals that these networks shape the passages of water molecules through the tm domain . a misalignment of polar residues in the agonist - bound state is led to dehydration of the ic zone around @xmath78 , which gives rise to the hl2 ( figure s3 left ) . the rotameric state of y288@xmath73 sidechain in the antagonist - bound form enables a single file of water molecules constituting a water wire to flow across the hl2 ( figure s3 right , si movie m3 . see also figure s4 ) . the formation of the y - shaped bridge made of polar residues including the npxxy motif is the molecular origin underlying the hydrophobic gating " @xcite that regulates the water flux through the ic region of a@xmath0ar . + * microscopic origin of receptor state - dependent water flux . * to further glean the microscopic underpinnings of the receptor state - dependent water flux ( figure [ flux ] ) , configurations of microswitches at three key locations in the tm domain are probed ( figure [ three_switches ] ) : ( i ) the ionic lock ( r102@xmath79-e228@xmath80 ) ( figure [ three_switches]a , top panel ) , the hallmark of the inactive state of gpcrs , is intact in the antagonist - bound form , maintaining the inter - residue distance @xmath81 . in the apo form , the ionic - lock repeatedly disrupts and rebinds , suggestive of the receptor s basal activity @xcite . in the agonist - bound form , the ionic lock is completely disrupted ; ( ii ) the distance between r102@xmath79 and y288@xmath73 depends on the receptor state ( figure [ three_switches]a , the second panel from the top ) , and importantly y288@xmath73 gates the entry of water from the ic region . in the active form , r102@xmath79 released from the influence of e228@xmath80 can interact with and stabilize the side chain orientation of y288@xmath73 , resulting in blocking the passage of water stream as well as misaligning the bridge made of npxxy motif ( see supporting movie m2 , figure [ three_switches]b , figure s3 ) ; ( iii ) the side chain of w246@xmath72 residue gates the entry of water from the ec domain . in the active form , w246@xmath72 blocks the water passage from the ec region , but it allows water to flow more freely in the inactive form . in the apo form , the rotamer angle of w246@xmath72 undergoes sharp transitions ( @xmath82 in figure [ three_switches]a , black trace ) multiple times during the simulation ( @xmath83 ns ) , displaying correlations with the ionic - lock ( @xmath84 in figure [ three_switches]a , black line ) and with the increased level of water flux ( notice the sudden increase of the flux at @xmath85 nsec from ec to ic ( black trace in solid line in figure [ flux ] ) ) . for example , when the ionic - lock was stabilized at @xmath86 nsec in the apo form ( figure [ three_switches]a , top panel , black trace ) , the rotameric angle of w246@xmath72 also displayed a sharp change from @xmath87 to @xmath88 ( cyan arrow in the @xmath82 plot of figure [ three_switches]a ) . this is the moment when @xmath89 in the apo form has increased ( @xmath90 nsec in figure [ flux ] ) . the movies ( si movies m1 , m2 , and m3 ) from simulations of the water dynamics across tm region provide nice visualizations of receptor state - dependent water flux , which is recapitulated in the cartoons in figure [ water_flux_map ] . in the apo form , the water molecules freely navigate the wide volume of the empty ligand binding cleft in the ec domain , but a further penetration across the tm region is regulated by the narrow channel gated by w246@xmath72 . when the agonist or antagonist occupies the binding cleft , however , water flux is divided into the major ( solid lines in figure [ water_flux_map ] ) and minor streams ( dashed lines in figure [ water_flux_map ] ) ; the major stream is formed between tm1 , 2 , and 7 , and the minor stream is formed between tm3 , 5 , and 6 . in the agonist - bound form , the w246@xmath72 blocks the minor stream and the water flow along the major stream is tightly regulated by the several other microswitch residues ( n24@xmath91 , d52@xmath92 , n280@xmath93 , s281@xmath94 , and n284@xmath95 ) , which creates the stable water cluster . in case of the antagonist - bound form , no water cluster is observed ; w246@xmath72 gate is open and lets water molecules flow in and out of the tm channel . the water flux from the ic region is regulated by the side chain configuration of y288@xmath73 . in the active state whose ionic - lock is disrupted , r102@xmath79 interacts with y288@xmath73 , which in turn blocks the passage of water flux in the ic domain . + * allosteric interface reinforced by water - mediated interactions . * in order to underscore the contribution of water - mediated contacts between tm residues to the receptor s allosteric signaling and function we conducted a graph theoretical analysis on the ensemble of gpcr structures . as shown by our previous study @xcite the microswitches of gpcrs in general are identified by graph theoretical analysis using betweenness centrality to be the key sites for intra - molecular orthosteric ( allosteric ) signal transmission ( see methods ) . allosteric interface can be visualized by highlighting those allosteric hotspots @xcite . while waters inside channel are generally dynamic , some water molecules , especially around microswitches in the active state , display slow relaxation kinetics and even can be trapped for an extended amount of time ( @xmath96 ns ) ( see si text , figure s5 and figure s6 ) . as long as water dynamics is sufficiently slow , stable water - mediated contacts can be made between two residues that are not in direct contact . defining a water - mediated contact when two residues share a water oxygen within 3.5 from any heavy atom in each residue , we constructed a water - mediated residue interaction network for a given structure . using an ensemble of structure obtained from simulations , we calculated an average betweenness centrality ( @xmath48 ) at the @xmath40-th residue ( see si text , figure [ allosteric_interface]a ) . at present , there are many ways to consider the protein allostery ; some of them consider thermodynamic aspect of protein allostery @xcite , and others focus more on identification of allosteric hotspot of a given structure @xcite . the graph theoretical method @xcite can also be employed to identify an allosteric hotspot of a given network structure , and in this method a residue with high @xmath97 value corresponds to a site important for allosteric signal transmission @xcite . in the agonist - bound active state , the @xmath48 values calculated with ( @xmath98 ) and without ( @xmath99 ) water - mediated contacts ( see figure s7 ) show clear differences ( @xmath100 ) along the microswitches in tm7 ( figure [ allosteric_interface]b , c ) , which is in accord with our findings that a number of slow water molecules stably coordinating with microswitches along the water channels are present in the active state . highlighted in figure [ allosteric_interface]c with magenta surface is the allosteric interface in the active state reinforced by water - mediated interactions ( @xmath101 ) . the interface mainly formed from along the tm7 helix , reaches r102@xmath79 in the tm3 helix via y288@xmath102 and a231@xmath103 , spanning the whole tm domain . we surmise that this wide - spread interface across the tm domain enables a robust long - range signal transmission " ( compare the map of agonist - bound active state with those for apo and antagonist - bound inactive states in figure [ allosteric_interface]c ) . notably , recent calculation of energy tranport in homodimeric hemoglobin also underscores the importance of interface water cluster , substantiating our proposal of ultra - slow water mediated allosteric signaling @xcite .

water molecules inside g - protein coupled receptor have recently been spotlighted in a series of crystal structures . to decipher the dynamics and functional roles of internal waters in gpcr activity our study finds that the amount of water flux across the transmembrane ( tm ) domain varies depending on the receptor state , and that the water molecules of the tm channel in the active state flow three times slower than those in the inactive state . depending on the location in solvent - protein interface as well as the receptor state , the average residence time of water in each residue varies from psec to nsec . a continuous allosteric network spanning the tm domain , arising from water - mediated contacts , is unique in the active state , underscoring the importance of slow waters in the gpcr activation .

water molecules inside g - protein coupled receptor have recently been spotlighted in a series of crystal structures . to decipher the dynamics and functional roles of internal waters in gpcr activity , we studied a adenosine receptor usingsec - molecular dynamics simulations . our study finds that the amount of water flux across the transmembrane ( tm ) domain varies depending on the receptor state , and that the water molecules of the tm channel in the active state flow three times slower than those in the inactive state . depending on the location in solvent - protein interface as well as the receptor state , the average residence time of water in each residue varies from psec to nsec . especially , water molecules , exhibiting ultraslow relaxation ( nsec ) in the active state , are found around the microswitch residues that are considered activity hotspots for gpcr function . a continuous allosteric network spanning the tm domain , arising from water - mediated contacts , is unique in the active state , underscoring the importance of slow waters in the gpcr activation .

1103.0672

i

this article is a continuation of @xcite , in which we introduced the notion of symplectic microfolds and symplectic micromorphisms between them . recall that a symplectic microfold is essentially the same thing as a germ @xmath0 $ ] of symplectic manifolds @xmath1 around a lagrangian submanifold @xmath2 , called the core . a symplectic micromorphism from @xmath0 $ ] to @xmath3 $ ] is a germ around the graph of a smooth map @xmath4 , the core map , of a canonical relation of a symplectic manifold @xmath5 is the manifold @xmath1 endowed with the opposite symplectic form @xmath6 . ] @xmath7 containing the graph of @xmath8 and satisfying a certain transversality condition ; we review the definitions in section [ subsec - definitions ] below . in contrast with their macroworld counterparts ( i.e. canonical relations ) , symplectic micromorphisms always compose well , forming thus , with the symplectic microfolds as objects , an honest symmetric monoidal category : the microsymplectic category , which can be thought as the appropriate `` microworld '' analog to the symplectic `` category '' of symplectic manifolds and canonical relations @xcite . this makes the microsymplectic category a natural setting for questions related to the functorial behavior of quantization schemes in symplectic geometry . by `` quantization scheme '' , we mean here any well - defined correspondence between a certain type of geometric structures in the symplectic realm ( such as poisson structures ) and a certain type of algebraic structures in the realm of analysis ( such as @xmath9-algebras ) . two important ingredients involved in these quantization questions have been the generating functions and the fourier integral operators associated with a given lagrangian submanifold ( see @xcite ) . in this paper , we extend the notion of generating functions to the microworld . our first main result is that _ any _ symplectic micromorphism admits a _ global _ generating function . this is the best possible case when it comes to quantization via fourier integral operators ( as will be shown in a sequel @xcite ) . a second result ( theorem [ thm : normal form ] ) states that the underlying lagrangian submicrofold of a symplectic micromorphism can always be decomposed into a fibration by graphs of actual smooth map germs . the main example here is the cotangent lift @xmath10 of a smooth map @xmath4 , whose underlying lagrangian submicrofold is the germ of the lagrangian submanifold @xmath11 around the graph of @xmath8 . when @xmath8 is not a diffeomorphism , @xmath12 is not the graph of a symplectomorphism , although the cotangent maps @xmath13 to @xmath8 at each @xmath14 _ are _ actual maps . this gives us a decomposition @xmath15 of @xmath12 associated with the lagrangian fibration of @xmath16 by its cotangent fibers . more generally , a similar decomposition holds for general symplectic micromorphisms from @xmath0 $ ] to @xmath3 $ ] , which is uniquely associated with the data of a lagrangian fibration of @xmath3 $ ] . this special geometry of the underlying lagrangian submicrofolds may be of help in questions related to the continuity of their corresponding fourier integral operators . namely , in various instances ( @xcite,@xcite,@xcite ) , the continuity in @xmath17-spaces of some classes of fios has been related to their wave - fronts being local graphs . from a different perspective , this decomposition is reminiscent of the notion of co - morphisms of chen and liu introduced in @xcite in the context of lie groupoids . we derive the existence of global generating functions for symplectic micromorphisms from a more general result : the _ equivalence theorem _ for clean lagrangian submicrofolds ( theorem [ thm : equivalence theorem ] ) . it states that the data of a germ @xmath18 $ ] of a lagrangian submanifold @xmath19 that intersects the zero section _ cleanly _ in @xmath20 is equivalent to the data @xmath21 of a symplectomorphism germ , when it is clear from the context , we write @xmath22 to denote the microfold @xmath23 $ ] , where @xmath24 is the zero section of @xmath22 . moreover , we also identify @xmath24 with @xmath2 and the submanifolds @xmath25 with the corresponding submanifolds of @xmath24 , yielding the notation @xmath26 $ ] . ] @xmath27 $ ] ( of the type prescribed by the lagrangian embedding theorem @xcite applied to the conormal bundle @xmath28 and satisfying an extra condition ) together with a function germ @xmath29 around the zero section ( and vanishing on it , as well as its differential ) . actually , we prove that for each @xmath30 there exists a unique @xmath31 such that @xmath32 . this defines the global generating function @xmath31 of the clean lagrangian submicrofold @xmath18 $ ] associated with the symplectomorphism germ @xmath30 . it turns out that the symplectic micromorphisms from @xmath33 to @xmath16 with core map @xmath8 are nothing but the _ clean _ lagrangian submicrofolds in @xmath34 with core @xmath35 . while giving another ( and simpler ) characterization of symplectic micromorphisms , the equivalence theorem also tells us that they admit global generating functions ( associated with special symplectomorphism germs @xmath30 as before ) . another application of the equivalence theorem comes from considering the restriction of a symplectic micromorphism to a local chart . the restriction is again a symplectic micromorphism , but now we have a canonical symplectomorphism germ @xmath30 coming from the affine structure of the local chart . this allows us to define the _ local _ generating function of the symplectic micromorphism in the local chart as the global generating function of its restriction . we conclude this paper by associating with any hamiltonian flow on a cotangent bundle a symplectic micromorphism , the evolution micromorphism , which encodes the dynamics for asymptotically short times . we show that the local generating functions of the evolution micromorphism coincide with the solutions of the hamilton - jacobi equation for the flow in local charts . moreover , by considering a particular monoid object in the microsymplectic category , the energy monoid @xmath36 , we show that the @xmath36-modules are essentially the same thing as germs of hamiltonian flows with time - independent hamiltonian . this gives us a categorical formulation for the temporal evolution in classical mechanics . finally , we briefly describe how symmetries in classical mechanics can be formalized using the language of symplectic microgeometry . this approach to symmetry , which will be developed in full details somewhere else , is very close in spirit to the work of benenti on the hamilton - jacobi equation for an hamiltonian action ( @xcite ) . a.s.c . acknowledges partial support from snf grant 200020_131813/1 . thanks pedro de m. rios for useful discussions on generating families and acknowledges partial support from nwo grant 613.000.602 carried out at utrecht university and from fapesp grant 2010/15069 - 8 hosted by the icmc of sao paulo university at sao carlos . acknowledges partial support from nsf grant dms-0707137 and the hospitality of the institut mathmatique de jussieu .

we adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry . we show that a symplectic micromorphism always admits a global generating function . as an application , we describe hamiltonian flows as special symplectic micromorphisms whose local generating functions are the solutions of hamilton - jacobi equations . we obtain a purely categorical formulation of the temporal evolution in classical mechanics .

we adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry . we show that a symplectic micromorphism always admits a global generating function . as an application , we describe hamiltonian flows as special symplectic micromorphisms whose local generating functions are the solutions of hamilton - jacobi equations . we obtain a purely categorical formulation of the temporal evolution in classical mechanics .

1101.4102

i

congestion phenomena in population dynamics cover a wide range of mechanisms , which can be classified according to their stiffness : 1 . soft congestion : as the distance between individuals becomes smaller , the behavior of a single person is affected by the presence of others ; 2 . hard congestion : actual contacts between individuals occur , and the overall motion is perturbed by the fact that two persons may not occupy the same place at the same time . soft congestion models can be included in both microscopic and macroscopic models . in the first class there are discrete - space models like cellular automata - based models which constrain pedestrians to be located at squares of a fixed grid @xcite . we can also mention models based on networks as route choice models @xcite or queuing models @xcite . a lot of evacuation softwares rest on such models as for example buildingexodus in @xcite . some microscopic models are space continous as the social force model introduced in @xcite and its forerunner which has been proposed by @xcite . in @xcite , people are identified to particles submitted to the laws of newtonian mechanics . as for macroscopic models , soft congestion is also usually favored . some of these models ( see for example @xcite , @xcite and @xcite ) own their origins in vehicular traffic models , and deal with the one - dimensional case . in higher dimension , similarly to the microscopic case , many models rely on social forces . one solution , used e.g. by bellomo and dogbe in @xcite and @xcite , or degond in @xcite , is to add to the equation satisfied by the velocity a repulsive term that forces people to avoid high density areas . another possibility is to modify directly the velocity by adding a term that make people deviate from their preferred path as soon as they approach a crowded area . the modeling of the velocity is the key point of these strategies , see for example the work of hughes @xcite , @xcite , coscia @xcite , or piccoli @xcite , @xcite . we aim here at addressing the particular issues pertaining to _ hard _ congestion . in this spirit , we shall make very crude assumptions on the social aspects triggering crowd dynamics ( see section [ sec : ext ] for possible improvements on these aspects ) , and simply consider that , at any time , a spontaneous ( or desired ) velocity field is given , and that it is purely _ reptilian _ : everyone s priority is to achieve his own goals , without accounting for others . actual behavior shall result from some sort of compromise between individual tendencies and congestion constraints . more precisely , we shall consider that the actual velocity is defined as the projection of the spontaneous one onto the set of feasible velocities ( i.e. which do not lead to a violation of the non - overlapping constraint ) . those basic principles can be applied to microscopic and macroscopic descriptions of the crowd . in the microscopic setting , the degrees of freedom are the positions of individuals ( identified to rigid disks ) , and the non - overlapping constraints can be written straightforwardly by prescribing a minimal value for the distance between centers . the problem takes the form of a differential inclusion which fits into the general framework of sweeping processes introduced by moreau in the 70 s ( see @xcite ) . this approach has been extended more recently to non convex cases , namely the case of uniformly prox - regular sets in @xcite , in @xcite and later in @xcite . the perturbed ( i.e. inhomogeneous ) problem has been studied in @xcite . as we shall see , it gives a natural framework for the microscopic model we propose . in the macroscopic setting , the crowd is seen as a population density and the non - overlapping constraint consists in prescribing a maximal value for this density . although both microscopic and macroscopic models express the same type of modeling assumptions , the mathematical structure of the macroscopic model is less obvious . expressed in the eulerian framework as a transport equation by the actual velocity field , which is defined as the projection of the spontaneous one onto the set of feasible velocities , it involves a conservative transport equation by a field whose regularity can not be controlled a priori , so that classical results can not be used . a first attempt to address those issues was proposed in @xcite , in the case where the spontaneous velocity is the gradient of a given dissatisfaction function ( typically the distance to the exit for the evacuation of a building ) : the framework of optimal transportation allows to reformulate the problem as a gradient flow in the wasserstein space of measures ( see e.g. @xcite for an overview of the theory of optimal transport , and @xcite for the notion of gradient flow in this setting ) . we show here that the sweeping process framework , which does not rely on any assumption on the gradient nature of the forcing term , can be extended in the macroscopic situation . stemming from similar principles , both microscopic and macroscopic models present nevertheless deep differences . for instance we shall point out the fact that the notion of maximal density is not properly defined in the microscopic setting . thus the macroscopic one can not be expected to be obtained from the microscopic one by any homogenization process . we shall focus here on the particular issues related to hard congestion . in order to highlight the very problems it raises , we will favor a very basic form of the crowd motion model . in particular we shall disregard in the main part of this paper any social or strategical aspects of human behavior . we are aware of the very crude character of these assumptions , and we gathered in section [ sec : ext ] other aspects of pedestrian behavior that could be included in our approach . besides , we hope that the framework presented here , and the issues we raise in attempting to establish links between microscopic and macroscopic settings , may be fruitful in other contexts , e.g. micro - macro issues in granular flows or modeling of chemotactic motion of large populations of cells .

we develop those principles in the microscopic and macroscopic settings , and we present how the framework of wasserstein distance between measures allows to recover the _ sweeping process _ micro and macro approaches are compared , and we investigate the similarities together with deep differences of those two levels of description . b. maury , a. roudneff - chupin , f. santambrogio j. venel

we address here the issue of congestion in the modeling of crowd motion , in the non - smooth framework : contacts between people are not anticipated and avoided , they actually occur , and they are explicitly taken into account in the model . we limit our approach to very basic principles in terms of behavior , to focus on the particular problems raised by the non - smooth character of the models . we consider that individuals tend to move according to a desired , or spontanous , velocity . we account for congestion by assuming that the evolution realizes at each time an instantaneous balance between individual tendencies and global constraints ( overlapping is forbidden ) : the actual velocity is defined as the closest to the desired velocity among all admissible ones , in a least square sense . we develop those principles in the microscopic and macroscopic settings , and we present how the framework of wasserstein distance between measures allows to recover the _ sweeping process _ nature of the problem on the macroscopic level , which makes it possible to obtain existence results in spite of the non - smooth character of the evolution process . micro and macro approaches are compared , and we investigate the similarities together with deep differences of those two levels of description . b. maury , a. roudneff - chupin , f. santambrogio j. venel

0806.2608

i

the stability of the electroweak scale has driven the high energy physics community , both theorists and experimentalists alike , for nearly the past two decades . with the advent of the large hadron collider ( lhc ) , we can finally probe the mechanism of electroweak symmetry breaking ( ewsb ) and possibly new physics at the tev scale that stabilizes the electroweak scale . however , as such new physics is still a mystery , we need to be prepared for all the possibilities . in addition , with the multitude of models of new physics and the possible associated experimental signatures , we are also faced with the ` inverse problem ' of distinguishing models of new physics using the experimental data . in this work , we investigate one of the possible scenarios at the lhc , and attempt to disentangle three generic models of new physics based on experimental measurements of a higgs boson . we suppose that , after the first few years of operation with an integrated luminosity of 10 @xmath2 , the lhc has only discovered a lone scalar boson with couplings to the @xmath3- and @xmath4-bosons that are of the same magnitude as predicted in the standard model ( sm ) . while discovering only a higgs boson at the lhc ( with an integrated luminosity of several 100 @xmath2 ) has been dubbed a `` nightmare scenario @xcite , '' here we are only assuming no new physics , other than this higgs boson , is seen at this stage of operation of the lhc , and leave open the possibility that new physics may be uncovered with further operation time . indeed , one of the main goals of works of this type is to optimize further search strategies based on the information we have at hand from the discovered higgs boson . let us denote @xmath5 as the product of the higgs boson production cross section @xmath6 and the di - photon decay branching ratio @xmath7 . the main question that we attempt to answer in this work is : from the measurement of @xmath5 and its deviation from the sm prediction , can we identify this scalar boson as _ the _ higgs boson in the sm , minimal universal extra dimensions ( mued ) , littlest higgs with @xmath1-parity ( lht ) , or the lightest @xmath8-even boson in the minimal supersymmetric standard model ( mssm ) ? if not , we investigate whether we can use this measurement as a hint or bias , and devise further search strategies of new physics based on its deviation from the sm , regardless whether such deviation is statistically significant . questions of this type are in spirit similar to the lhc inverse problem @xcite , but with an emphasis on distinguishing the models rather than mapping the regions of parameter spaces of a particular model from the data . while such lhc inverse problems have been studied in the literature , they attempt to distinguish models through properties , such as spin , of the new resonances discovered at the lhc . our work here is also of similar spirit to mantry et al . @xcite @xcite and randall @xcite , where they discuss how the properties of the higgs boson can be modified due to states that are not directly observable at the lhc . our work is organized as follows . in section [ sec : precision ] , we discuss the precision to which the signal @xmath5 can be measured at the lhc after 10 @xmath2 of data . in section [ sec : hgg - model ] , we discuss the general pattern of deviations of the signal @xmath5 in the parameter spaces of the models , and roughly map out regions in parameter spaces that such deviation can be significant . we also apply the results of lhc reaches in these models to map out regions of parameter spaces that can be consistent with the aforementioned lone higgs scenario . in section [ sec : hgg - lone ] , we apply the lone higgs scenario as constraints on the parameter spaces , and see how the signal is affected . in particular , we find that in the lone higgs scenario with a large deviation in @xmath5 , we can potentially rule out mued , and , in some cases , distinguish between the mssm and lht . also in section [ sec : hgg - lone ] , we propose some parameter - independent tests that can also be used to distinguish these models . we conclude in section [ sec : conc ] with a summary of our results and offer outlook for projects of this type .

we address the possible scenario that the large hadron collider ( lhc ) discovers only a higgs boson after 10 fb of operation , and attempt to identify this higgs boson as that of the standard model ( sm ) , the minimal universal extra dimension model ( mued ) , the littlest higgs model with-parity ( lht ) , or the minimal supersymmetric standard model ( mssm ) , using only the measurement of the product of gluon - fusion production cross section and the di - photon branching ratio . in mued , by decoupling any new physics sufficiently to evade the discovery reach at the lhc , the deviation of the signal from the sm is not statistically significant .

we address the possible scenario that the large hadron collider ( lhc ) discovers only a higgs boson after 10 fb of operation , and attempt to identify this higgs boson as that of the standard model ( sm ) , the minimal universal extra dimension model ( mued ) , the littlest higgs model with-parity ( lht ) , or the minimal supersymmetric standard model ( mssm ) , using only the measurement of the product of gluon - fusion production cross section and the di - photon branching ratio . in mued , by decoupling any new physics sufficiently to evade the discovery reach at the lhc , the deviation of the signal from the sm is not statistically significant . however , in lht and mssm , it is possible to have a significant deviation in the signal that is consistent with this `` lone higgs scenario '' , and , in the case of a very large suppression , we can distinguish mssm and lht before the discovery of any new resonances . starting with the lone higgs scenario and the deviation in this measurement from the standard model prediction ( whether or not statistically significant ) , we offer tests that may discriminate the models and search strategies of discovering new physics signatures with increasing integrated luminosity .

1103.0088

i

it is a classical fact in complex geometry that the singular kummer surface @xmath5 attached to an abelian surface @xmath6 has sixteen rational double points , and an irreducible principal polarization embeds it as a quartic surface in @xmath4 , compare hudson s classical monography @xcite , or for a modern account @xcite . our starting point was an analogous computation in characteristic @xmath7 for the diagonal action of the additive group @xmath8 on the selfproduct @xmath9 , where @xmath10 is the supersingular elliptic curve , viewed as an artin schreier covering . it turns out that this is a special case of a rather general construction , which works for all primes @xmath0 , in fact for all prime powers @xmath11 . it starts with certain _ artin schreier curves _ and leads , with a few exceptions for small prime powers , to _ surfaces of general type_. the goal of this paper is to describe the geometry of these surfaces , and we obtain a fairly complete description . the construction goes as follows : fix an algebraically closed ground field @xmath12 of characteristic @xmath13 and consider artin schreier curves of the form @xmath14 where @xmath15 is a monic polynomial of degree @xmath16 . these curves carry a translation action of the additive group @xmath17 , and we consider the diagonal action on the product @xmath18 of two such artin schreier curves . the quotient @xmath19 is a normal surface containing a unique singularity . such singularities are examples of _ wild quotient singularities _ , i.e. , the characteristic of the ground field divides the order of the group @xmath20 . few examples of wild quotient singularities occur in the literature , and little is known in general . artin @xcite gave a complete classification for wild @xmath21-quotient singularities in dimension two , and general @xmath22-quotient singularities were studied further by peskin @xcite . peculiar properties of wild @xmath23-quotient singularities in relation to punctual hilbert schemes appear in @xcite . in light of the scarcity of examples , it is useful to have more classes of wild quotient singularities in which computations are feasible . lorenzini initiated a general investigation of wild quotient singularities on surfaces @xcite , which play an important role in understanding the reduction behaviour of curves over discrete valuation fields . he compiled a list of open questions @xcite . in a recent paper , lorenzini studied wild @xmath22-quotient singularities resulting from diagonal actions on products of @xmath18 , where one or both factors are ordinary curves @xcite . in some sense , we treat the opposite situation , as artin - schreier curves have vanishing @xmath0-rank , and our main concern is the interplay between the local structure coming from the the wild quotient singuarity and the global geometry of the algebraic surface . we have choosen artin schreier coverings that are concrete enough so that explicit computations are possible . note that our set - up includes wild quotient singularities with respect to elementary abelian groups , and not ony cyclic groups . consider the minimal resolution of singularities @xmath24 of our normal surface . according to lorenzini s general observation , the exceptional divisor of a wild quotient singularity in dimension two consists of projective lines , and its dual graph is a tree @xcite . using an explicit formal equation for the singularitiy , we show that the dual graph is even star - shaped , with @xmath25 terminal chains attached to the central node , each of length @xmath3 , as depicted in figure 1 . the two basic numerical invariants of surface singularities are the genus @xmath26 of the fundamental cycle @xmath27 and the _ geometric genus _ @xmath28 , @xmath29 . the latter is usually very difficult to compute . we obtain @xmath30 the latter under the assumption that our prime power @xmath3 is prime . this relies on a computation of the global @xmath31-adic euler characteristic of the surface , combined with a determination of the @xmath20-invariant part in @xmath32 , which in turn depends on a problem in modular representation theory related to tensor products of jordan matrices . in contrast , the singularities occuring in @xcite , where at least one factor in @xmath18 is an ordinary curve , are all rational . having a good hold on the structure of the resolution of singularities , we determine the global invariants of the smooth surface @xmath33 . it turns out that @xmath34 , and that @xmath35 is a free abelian group of finite rank . moreover , the algebraic fundamental group @xmath36 vanishes . passing to the minimal model @xmath37 we show that the minimal surface @xmath38 is of general type for @xmath39 , a k3 surface for @xmath40 , and a weak del pezzo surface for @xmath41 . their chern invariants are given by the formula @xmath42 the resulting _ chern slopes _ asymptotically tend to @xmath43 , and one may say that our surfaces show no pathological behaviour with respect to surface geography . the determination of the euler characteristic @xmath44 depends on dolgachev s formula @xmath45 for @xmath31-adic euler characteristic for schemes fibered over curves @xcite , where @xmath46 is _ serre s measure of wild ramification_. its computation is quite easy in our situation , given the explicit nature of the artin schreier curves . the surface @xmath38 has a surprisingly simple _ projective description _ , which is reminiscent to kummer s quartic surfaces @xmath47 . passing to the normal surface @xmath48 with @xmath1 rational double points of type @xmath2 obtained by contracting all terminal chains in the fundamental cycle , the image @xmath49 of the fundamental cycle remains cartier , and defines the embedding : the invertible sheaf @xmath50 is very ample , has @xmath51 and embeds the normal surface @xmath48 as a divisor of degree @xmath3 in @xmath4 , sending the rational double points into a line . in fact , a canonical divisor is @xmath52 . so for @xmath39 , the closed embedding @xmath53 can be viewed as an _ @xmath54-canonical map _ , for the fractional value @xmath55 . in the simplest case @xmath56 , this is in line with classification results of horikawa on minimal surfaces of general type with @xmath57 and vanishing irregularity @xcite . the projective description also allows us to deduce that our surfaces @xmath38 admit a lifting into characteristic zero , at least in the category of algebraic spaces . it would be interesting to determine the homogeneous polynomial describing the image @xmath58 , but we have made no attempt to do so . the paper is organized as follows : in section [ artin schreier curves ] we review some relevant facts on artin schreier curve , all of them well - known . in section [ products of artin schreier curves ] we study the normal surface @xmath19 , obtained as the quotient of the product of two artin schreier curves with respect to the diagonal action . we find an explicit equation for the singularitiy , and a dimension formula for the global sections of the dualizing sheaf . section [ invariants of the singularity ] contains an analysis of the minimal resolution of singularities @xmath59 . notable results are formulas for the fundamental cycle and its genus , as well as some bounds on the arithmetic genus . in section [ vanishing of irregularity ] we prove that @xmath34 , such that the picard scheme is reduced and 0-dimensional . this relies on a general fact about group actions with fixed points , which seems to be of independent interest , and is verified with grothendieck s theory of @xmath20-equivariant cohomology . in section [ place in the enriques classification ] we determine the place of the smooth surface @xmath33 in the enriques classification . among other things , this depends on the geometry of the fibration @xmath60 induced from the projections on @xmath18 . section [ canonical model and canonical map ] contains our analysis of projective models for the surfaces . finally , in section [ numerical invariants and geography ] we take up questions from surface geography and compute chern invariants . this mainly relies on dolgachev s formula for @xmath31-adic euler characteristics for fibered schemes . the first author would like to thank the mathematisches institut of the heinrich heine universitt dsseldorf , where this work has begun , for its warm hospitality . research of the first author was partially supported by grand - in - aid for scientific research ( c ) 20540044 , the ministry of education , culture , sports , science and technology . we thank the referee for bringing to our attention lorenzini s preprints @xcite , @xcite , @xcite .

we analyse the diagonal quotient for the product of certain artin schreier curves . the calculation of numerical invariants relies on a close examination of the relevant wild quotient singularity in characteristic . it turns out that the canonical model has rational double points of type , and embeds as a divisor of degree in , which is in some sense reminiscent of the classical kummer quartic .

we analyse the diagonal quotient for the product of certain artin schreier curves . the smooth models are almost always surfaces of general type , with chern slopes tending asymptotically to 1 . the calculation of numerical invariants relies on a close examination of the relevant wild quotient singularity in characteristic . it turns out that the canonical model has rational double points of type , and embeds as a divisor of degree in , which is in some sense reminiscent of the classical kummer quartic .

cond-mat0108023

i

quantifying correlations between different stocks is a topic of interest not only for scientific reasons of understanding the economy as a complex dynamical system , but also for practical reasons such as asset allocation and portfolio - risk estimation @xcite . unlike most physical systems , where one relates correlations between subunits to basic interactions , the underlying `` interactions '' for the stock market problem are not known . here , we analyze cross - correlations between stocks by applying concepts and methods of random matrix theory , developed in the context of complex quantum systems where the precise nature of the interactions between subunits are not known . in order to quantify correlations , we first calculate the price change ( `` return '' ) of stock @xmath2 over a time scale @xmath3 @xmath4 where @xmath5 denotes the price of stock @xmath6 . since different stocks have varying levels of volatility ( standard deviation ) , we define a normalized return @xmath7 where @xmath8 is the standard deviation of @xmath9 , and @xmath10 denotes a time average over the period studied . we then compute the equal - time cross - correlation matrix * c * with elements @xmath11 by construction , the elements @xmath12 are restricted to the domain @xmath13 , where @xmath14 corresponds to perfect correlations , @xmath15 corresponds to perfect anti - correlations , and @xmath16 corresponds to uncorrelated pairs of stocks . the difficulties in analyzing the significance and meaning of the empirical cross - correlation coefficients @xmath12 are due to several reasons , which include the following : \(i ) market conditions change with time and the cross - correlations that exist between any pair of stocks may not be stationary . \(ii ) the finite length of time series available to estimate cross - correlations introduces `` measurement noise '' . if we use a long time series to circumvent the problem of finite length , our estimates will be affected by the non - stationarity of cross - correlations . for these reasons , the empirically - measured cross - correlations will contain `` random '' contributions , and it is a difficult problem in general to estimate from * c * the cross - correlations that are not a result of randomness . how can we identify from @xmath12 , those stocks that remained correlated ( on the average ) in the time period studied ? to answer this question , we test the statistics of * c * against the `` null hypothesis '' of a random correlation matrix a correlation matrix constructed from mutually uncorrelated time series . if the properties of * c * conform to those of a random correlation matrix , then it follows that the contents of the empirically - measured * c * are random . conversely , deviations of the properties of * c * from those of a random correlation matrix convey information about `` genuine '' correlations . thus , our goal shall be to compare the properties of * c * with those of a random correlation matrix and separate the content of * c * into two groups : ( a ) the part of * c * that conforms to the properties of random correlation matrices ( `` noise '' ) and ( b ) the part of * c * that deviates ( `` information '' ) . the study of statistical properties of matrices with independent random elements _ random matrices _ has a rich history originating in nuclear physics @xcite . in nuclear physics , the problem of interest 50 years ago was to understand the energy levels of complex nuclei , which the existing models failed to explain . rmt was developed in this context by wigner , dyson , mehta , and others in order to explain the statistics of energy levels of complex quantum systems . they postulated that the hamiltonian describing a heavy nucleus can be described by a matrix * h * with independent random elements @xmath17 drawn from a probability distribution @xcite . based on this assumption , a series of remarkable predictions were made which are found to be in agreement with the experimental data @xcite . for complex quantum systems , rmt predictions represent an average over all possible interactions @xcite . deviations from the _ universal _ predictions of rmt identify system - specific , non - random properties of the system under consideration , providing clues about the underlying interactions @xcite . recent studies @xcite applying rmt methods to analyze the properties of * c * show that @xmath18% of the eigenvalues of * c * agree with rmt predictions , suggesting a considerable degree of randomness in the measured cross - correlations . it is also found that there are deviations from rmt predictions for @xmath19% of the largest eigenvalues . these results prompt the following questions : * what is a possible interpretation for the deviations from rmt ? * are the deviations from rmt stable in time ? * what can we infer about the structure of * c * from these results ? * what are the practical implications of these results ? in the following , we address these questions in detail . we find that the largest eigenvalue of * c * represents the influence of the entire market that is common to all stocks . our analysis of the contents of the remaining eigenvalues that deviate from rmt shows the existence of cross - correlations between stocks of the same type of industry , stocks having large market capitalization , and stocks of firms having business in certain geographical areas @xcite . by calculating the scalar product of the eigenvectors from one time period to the next , we find that the `` deviating eigenvectors '' have varying degrees of time stability , quantified by the magnitude of the scalar product . the largest 2 - 3 eigenvectors are stable for extended periods of time , while for the rest of the deviating eigenvectors , the time stability decreases as the the corresponding eigenvalues are closer to the rmt upper bound . to test that the deviating eigenvalues are the only `` genuine '' information contained in * c * , we compare the eigenvalue statistics of * c * with the known universal properties of real symmetric random matrices , and we find good agreement with the rmt results . using the notion of the inverse participation ratio , we analyze the eigenvectors of * c * and find large values of inverse participation ratio at both edges of the eigenvalue spectrum suggesting a `` random band '' matrix structure for * c*. lastly , we discuss applications to the practical goal of finding an investment that provides a given return without exposure to unnecessary risk . in addition , it is possible that our methods can also be applied for filtering out ` noise ' in empirically - measured cross - correlation matrices in a wide variety of applications . this paper is organized as follows . section ii contains a brief description of the data analyzed . section iii discusses the statistics of cross - correlation coefficients . section iv discusses the eigenvalue distribution of * c * and compares with rmt results . section v tests the eigenvalue statistics * c * for universal properties of real symmetric random matrices and section vi contains a detailed analysis of the contents of eigenvectors that deviate from rmt . section vii discusses the time stability of the deviating eigenvectors . section viii contains applications of rmt methods to construct ` optimal ' portfolios that have a stable ratio of risk to return . finally , section ix contains some concluding remarks .

we test the statistics of the eigenvalues of * c * against a `` null hypothesis '' a random correlation matrix constructed from mutually uncorrelated time series . we test the eigenvalues of * c * within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross - correlation coefficients .

we analyze cross - correlations between price fluctuations of different stocks using methods of random matrix theory ( rmt ) . using two large databases , we calculate cross - correlation matrices * c * of returns constructed from ( i ) 30-min returns of 1000 us stocks for the 2-yr period 199495 ( ii ) 30-min returns of 881 us stocks for the 2-yr period 199697 , and ( iii ) 1-day returns of 422 us stocks for the 35-yr period 196296 . we test the statistics of the eigenvalues of * c * against a `` null hypothesis '' a random correlation matrix constructed from mutually uncorrelated time series . we find that a majority of the eigenvalues of * c * fall within the rmt bounds $ ] for the eigenvalues of random correlation matrices . we test the eigenvalues of * c * within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross - correlation coefficients . further , we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction . in addition , we find that these `` deviating eigenvectors '' are stable in time . we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks . our analysis of the remaining deviating eigenvectors shows distinct groups , whose identities correspond to conventionally - identified business sectors . finally , we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return . 2

cond-mat0108023

c

how can we understand the deviating eigenvalues i.e. , correlations that are stable in time ? one approach is to postulate that returns can be separated into idiosyncratic and common components i.e. , that returns can be separated into different additive `` factors '' , which represent various economic influences that are common to a set of stocks such as the type of industry , or the effect of news @xcite . on the other hand , in physical systems one starts from the interactions between the constituents , and then relates interactions to correlated `` modes '' of the system . in economic systems , we ask if a similar mechanism can give rise to the correlated behavior . in order to answer this question , we model stock price dynamics by a family of stochastic differential equations @xcite , which describe the ` instantaneous' returns @xmath260 as a random walk with couplings @xmath261 @xmath262 here , @xmath263 are gaussian random variables with correlation function @xmath264 , and @xmath265 sets the time scale of the problem . in the context of a soft spin model , the first two terms in the _ rhs _ of eq . ( [ langevin ] ) arise from the derivative of a double - well potential , enforcing the soft spin constraint . the interaction among soft - spins is given by the couplings @xmath261 . in the absence of the cubic term , and without interactions , @xmath266 are relaxation times of the @xmath267 correlation function . the return @xmath9 at a finite time interval @xmath3 is given by the integral of @xmath268 over @xmath3 . equation ( [ langevin ] ) is similar to the linearized description of interacting `` soft spins '' @xcite and is a generalized case of the models of refs . @xcite . without interactions , the variance of price changes on a scale @xmath269 is given by @xmath270 , in agreement with recent studies @xcite , where stock price changes are described by an anomalous diffusion and the variance of price changes is decomposed into a product of trading frequency ( analog of @xmath271 ) and the square of an `` impact parameter '' which is related to liquidity ( analog of @xmath272 ) . as the coupling strengths increase , the soft - spin system undergoes a transition to an ordered state with permanent local magnetizations . at the transition point , the spin dynamics are very `` slow '' as reflected in a power law decay of the spin autocorrelation function in time . to test whether this signature of strong interactions is present for the stock market problem , we analyze the correlation functions @xmath273 , where @xmath274 is the time series defined by eigenvector * u@xmath121*. instead of analyzing @xmath275 directly , we apply the detrended fluctuation analysis ( dfa ) method @xcite . figure [ autocorr ] shows that the correlation functions @xmath275 indeed decay as power laws @xcite for the deviating eigenvectors * u@xmath121 * in sharp contrast to the behavior of @xmath275 for the rest of the eigenvectors and the autocorrelation functions of individual stocks , which show only short - ranged correlations . we interpret this as evidence for strong interactions @xcite . in the absence of the non - linearities ( cubic term ) , we obtain only exponentially - decaying correlation functions for the `` modes '' corresponding to the large eigenvalues , which is inconsistent with our finding of power - law correlations . to summarize , we have tested the eigenvalue statistics of the empirically - measured correlation matrix * c * against the null hypothesis of a random correlation matrix . this allows us to distinguish genuine correlations from `` apparent '' correlations that are present even for random matrices . we find that the bulk of the eigenvalue spectrum of * c * shares universal properties with the gaussian orthogonal ensemble of random matrices . further , we analyze the deviations from rmt , and find that ( i ) the largest eigenvalue and its corresponding eigenvector represent the influence of the entire market on all stocks , and ( ii ) using the rest of the deviating eigenvectors , we can partition the set of all stocks studied into distinct subsets whose identity corresponds to conventionally - identified business sectors . these sectors are stable in time , in some cases for as many as 30 years . finally , we have seen that the deviating eigenvectors are useful for the construction of optimal portfolios which have a stable ratio of risk to return .

in addition , we find that these `` deviating eigenvectors '' are stable in time . we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks . our analysis of the remaining deviating eigenvectors shows distinct groups , whose identities correspond to conventionally - identified business sectors . finally , we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return . 2

we analyze cross - correlations between price fluctuations of different stocks using methods of random matrix theory ( rmt ) . using two large databases , we calculate cross - correlation matrices * c * of returns constructed from ( i ) 30-min returns of 1000 us stocks for the 2-yr period 199495 ( ii ) 30-min returns of 881 us stocks for the 2-yr period 199697 , and ( iii ) 1-day returns of 422 us stocks for the 35-yr period 196296 . we test the statistics of the eigenvalues of * c * against a `` null hypothesis '' a random correlation matrix constructed from mutually uncorrelated time series . we find that a majority of the eigenvalues of * c * fall within the rmt bounds $ ] for the eigenvalues of random correlation matrices . we test the eigenvalues of * c * within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross - correlation coefficients . further , we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction . in addition , we find that these `` deviating eigenvectors '' are stable in time . we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks . our analysis of the remaining deviating eigenvectors shows distinct groups , whose identities correspond to conventionally - identified business sectors . finally , we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return . 2

1208.0983

c

we have observed line - of - sight emission spectra in 31 nearby , low metallicity dirr galaxies in order to search for cold defined by a velocity dispersion of less than 6 km s@xmath1 . we have detected it in 23 of 27 galaxies after quality control cuts were applied . the cold may be the future sites of molecular cloud and star formation and to date , are the only way to potentially trace star forming gas at low metallicity . based upon our observations , we find : * the cold gas is found in localized regions and usually at total column densities above the canonical threshold of star formation of 10@xmath55 cm@xmath15 @xcite . the cold in a given galaxy is also not typically associated with the very highest surface density gas ( see figures [ 2plots ] & [ cdplot ] ) . * the cold has a typical velocity dispersion of @xmath44.5 km s@xmath1 ( t @xmath0 800 k ) . * we derive an average value to the volume filling fraction of the cold of 9% ( assuming our lower limit detections ) . * we find lower limits to the cold gas mass fractions of a few percent , consistent with some models of the multi - phase ism @xcite . * the sfe@xmath70 is roughly constant as a function of the total cold mass over the observed gas mass ranges . * the cold contributes @xmath420% of the line - of - sight flux in locations where we detect both a cold and warm component . * cold gas that lacks a warm component is typically found at radii larger than the 25 mag arcsec@xmath15 optical radius . barone , l. t. , heithausen , a. , httemeister , s. , fritz , t. , & klein , u. 2000 , , 317 , 649 begum , a. , chengalur , j. n. , karachentsev , i. d. , kaisin , s. s. , & sharina , m. e. 2006 , , 365 , 1220 begum , a. , chengalur , j. n. , karachentsev , i. d. , sharina , m. e. , & kaisin , s. s. 2008 , , 386 , 1667 begum , a. , stanimirovi , s. , goss , w. m. , et al . 2010 , , 725 , 1779 berg , d. a. , skillman , e. d. , marble , a. r. , et al . 2012 , arxiv:1205.6782 bigiel , f. , leroy , a. , walter , f. , et al . 2008 , , 136 , 2846 braun , r. 1997 , , 484 , 637 briggs , d. s. 1995 , ph.d . thesis , new mexico institute of mining and tchnology brinks , e. , & bajaja , e. 1986 , , 169 , 14 dalcanton , j. j. , williams , b. f. , seth , a. c. , et al . 2009 , , 183 , 67 de avillez , m. a. , & breitschwerdt , d. 2004 , , 425 , 899 de blok , w. j. g. , & walter , f. 2006 , , 131 , 363 dickey , j. m. , mebold , u. , stanimirovic , s. , & staveley - smith , l. 2000 , , 536 , 756 engelbracht , c. w. , gordon , k. d. , rieke , g. h. , et al . 2005 , , 628 , l29 gil de paz , a. , boissier , s. , madore , b. f. , et al . 2007 , , 173 , 185 glover , s. c. o. , & mac low , m .- 2011 , , 412 , 337 gordon , k. d. , prez - gonzlez , p. g. , misselt , k. a. , et al . 2004 , , 154 , 215 israel , f. p. , tacconi , l. j. , & baas , f. 1995 , , 295 , 599 jackson , d. c. , cannon , j. m. , skillman , e. d. , et al . 2006 , , 646 , 192 jansen , r. a. 2000 , ph.d . thesis , kapteyn astronomical institute , univ . groningen kanekar , n. , braun , r. , & roy , n. 2011 , , 737 , l33 karachentsev , i. d. , karachentseva , v. e. , huchtmeier , w. k. , & makarov , d. i. 2004 , , 127 , 2031 kennicutt , r. c. , jr . 1998 , , 498 , 541 kennicutt , r. c. , jr . , armus , l. , bendo , g. , al . 2003 , , 115 , 928 kennicutt , r. c. , jr . , lee , j. c. , funes , s. j. , et al . 2008 , , 178 , 247 kennicutt , r. c. , jr . , & evans , n. j. , ii 2012 , arxiv:1204.3552 kro , m. , & goldsmith , p. f. 2010 , , 724 , 1402 krumholz , m. r. , mckee , c. f. , & tumlinson , j. 2009 , , 693 , 216 lee , h. , skillman , e. d. , cannon , j. m. , et al . 2006 , , 647 , 970 lee , j. c. , gil de paz , a. , tremonti , c. , et al . 2009 , , 706 , 599 lee , j. c. , gil de paz , a. , kennicutt , r. c. , jr . , et al . 2011 , , 192 , 6 leroy , a. , bolatto , a. d. , simon , j. d. , & blitz , l. 2005 , , 625 , 763 leroy , a. k. , walter , f. , brinks , e. , et al . 2008 , , 136 , 2782 leroy , a. k. , walter , f. , bigiel , f. , et al . 2009 , , 137 , 4670 li , d. , & goldsmith , p. f. 2003 , , 585 , 823 maloney , p. , & black , j. h. 1988 , , 325 , 389 mckee , c. f. , & ostriker , j. p. 1977 , , 218 , 148 merrifield , m. r. 1993 , , 261 , 233 relano , m. , kennicutt , r. c. , jr . , eldridge , j. j. , lee , j. c. , & verley , s. 2012 , arxiv:1204.4502 roychowdhury , s. , chengalur , j. n. , begum , a. , & karachentsev , i. d. 2009 , , 397 , 1435 salim , s. , rich , r. m. , charlot , s. , et al . 2007 , , 173 , 267 schruba , a. , leroy , a. k. , walter , f. , et al . 2012 , arxiv:1203.4231 skillman , e. d. 1987 , in lonsdale persson c.j . , ed . , star formation in galaxies . nasa conference publication , 2466 , 263 spaans , m. , & norman , c. a. 1997 , , 483 , 87 tamburro , d. , rix , h .- w . , leroy , a. k. , et al . 2009 , , 137 , 4424 taylor , c. l. , kobulnicky , h. a. , & skillman , e. d. 1998 , , 116 , 2746 van der marel , r. p. , & franx , m. 1993 , , 407 , 525 verter , f. , & hodge , p. 1995 , , 446 , 616 walter , f. , taylor , c. l. , httemeister , s. , scoville , n. , & mcintyre , v. 2001 , , 121 , 727 walter , f. , brinks , e. , de blok , w. j. g. , et al . 2008 , , 136 , 2563 warren , s. r. , weisz , d. r. , skillman , e. d. , et al . 2011 , , 738 , 10 wolfire , m. g. , mckee , c. f. , hollenbach , d. , & tielens , a. g. g. m. 2003 , , 587 , 278 young , l. m. , & lo , k. y. 1996 , , 462 , 203 young , l. m. , & lo , k. y. 1997 , , 490 , 710 young , l. m. , van zee , l. , lo , k. y. , dohm - palmer , r. c. , & beierle , m. e. 2003 , , 592 , 111 /a@xmath39 ) as a function of the ratio of the broad and narrow velocity dispersions ( @xmath40/@xmath41 ) for the 1.3 km s@xmath1 velocity resolution simulation in four different s / n bins . the grey dots are all of the simulated spectra . the red dots are those spectra identified as containing two components by our fitting routines , and the blue dots are the simulated spectra that were identified only containing a single gaussian component with a velocity dispersion of less than 6 km s@xmath1 . the values in the parentheses are the recovery percentages for the best fit double ( left ) and single ( right ) gaussians . we clearly identify more of the spectra at higher s / n values . our routines have a harder time recovering the two gaussian components when the velocity dispersions are similar . [ mcarlo2],width=661 ] . the velocity resolution ( @xmath7 ) is listed below the galaxy names . typically , the broad component velocity dispersions overlap with the single gaussian profile velocity dispersions indicating they arise from the same gas phase . [ veldisp],width=661 ] @xmath7@xmath30 , as a function of radius for the warm ( black ) and cold ( red ) gas for each of our velocity resolutions . we have omitted the locations best fit by a single gaussian with a velocity dispersion of less than 6 km s@xmath1 . the averages are taken over 200 pc bins ( the beam size ) . the error bars are the dispersions of the values in the bins . the velocity of the warm component decreases with radius indicating a possible decrease in turbulence as the radius increases from the main stellar body . some of the errorbars at large radii for the 2.6 km s@xmath1 velocity resolution overlap with values below our 6 km s@xmath1 cutoff . this is due to the dispersions being affected by a few larger values in these bins . [ disprad],width=661 ] ) and the lower limit to the fraction of gas in the cold phase ( @xmath49 ) as a function m@xmath2 ( left ) and @xmath60 ( right ) . the areal filling fraction and mass fractions do not correlate with m@xmath2 or @xmath60 . [ fracs],width=661 ] km s@xmath1 ) component as a function of radius . the x - axis has been normalized by the 25 mag arcsec@xmath15 radius ( vertical dashed line ) . the galaxies have been ordered faint ( m81 dwarf a ) to bright ( ngc 247 ) absolute @xmath14-band magnitude . a significant fraction of the cold is outside of the optical radius of each galaxy , except for ngc 247 . [ muchoblooshto],width=661 ] only . the contours represent the 10@xmath54 and 10@xmath55 cm@xmath15 total column densities . the green circle approximates the 25 mag arcsec@xmath15 optical level . the beam is shown at lower left . the majority of the cold detections described by a single gaussian profile are outside of the bulk of the stellar distribution . [ n42142plot],width=661 ] ( filled circles ) and sfr@xmath67 ( open squares ) as a function of the cold mass . _ middle : _ the sfr efficiency ( sfe@xmath70 ) defined as the sfr divided by the total gas mass as a function of the cold gas mass . _ bottom : _ the sfr as a function of the total gas mass . the sfr shows a linear trend with both cold and total mass . [ sfrfig],width=661 ]

cold is found in 23 of 27 (% ) galaxies after a reduction of the sample size due to quality control cuts . the cold contributes% of the total line - of - sight flux when found with warm . we find a lower limit for the mass fraction of cold - to - total gas of only a few percent in each galaxy .

we analyze line - of - sight atomic hydrogen ( ) line profiles of 31 nearby , low - mass galaxies selected from the very large array - acs nearby galaxy survey treasury ( vla - angst ) and the nearby galaxy survey ( things ) to trace regions containing cold ( t 1400 k ) from observations with a uniform linear scale of 200 pc beam . our galaxy sample spans four orders of magnitude in total mass and nine magnitudes in m . we fit single and multiple component functions to each spectrum to isolate the cold , neutral medium given by a low dispersion ( km s ) component of the spectrum . most spectra are adequately fit by a single gaussian with a dispersion of 8 - 12 km s . cold is found in 23 of 27 (% ) galaxies after a reduction of the sample size due to quality control cuts . the cold contributes% of the total line - of - sight flux when found with warm . spectra best fit by a single gaussian , but dominated by cold emission ( i.e. , have velocity dispersions km s ) are found primarily beyond the optical radius of the host galaxy . the cold is typically found in localized regions and is generally not coincident with the very highest surface density peaks of the global distribution ( which are usually areas of recent star formation ) . we find a lower limit for the mass fraction of cold - to - total gas of only a few percent in each galaxy .

hep-th9908194

i

cosmic strings are a special case of the vorticity phenomenon , which appears in many forms - in the flow of rivers and streams , in smoke rings , in hurricanes and tornadoes , etc . a special case of vorticity are the _ quantum vortices _ @xcite which include vortices in superfluids , flux tubes in superconductors and cosmic strings . global cosmic strings are analogues to vortices in superfluids while local cosmic strings are analogues to flux tubes in superconductors @xcite . all these vortices are described by a complex wave function or scalar field with a multivalued phase function @xmath0 , such that @xmath1 over a closed contour surrounding the string . as a result different physical quantities get quantized : the circulation of a superfluid vortex , the magnetic flux in a superconductor , the magnetic flux in a local cosmic string . vorticity was first investigated by helmholz and kelvin who set down the foundations for the study of vorticity in hydrodynamics . in this work we try to implement concepts born in the field of classical hydrodynamics to cosmic strings . as we shall see the interaction between these two fields can be very rewarding . turbulent fluid is regarded as full of vortex filaments @xcite . quantum turbulence in superfluids has likewise been defined as a superfluid state featuring a tangle of quantum vortex filaments @xcite . this paper is concerned with helicity of a tangle of cosmic strings . the concept of _ fluid helicity _ was introduced by moffatt @xcite as a useful measure of the degree of linkage of ordinary fluid vortice loops . it is defined as the volume integral of the scalar product of a velocity field @xmath2 and its curl , the vorticity @xmath3 . following this , moffatt @xcite and others @xcite considered helicity integrals in general , i.e. the space integral over the scalar product of a vector field and its curl @xmath4 and found them to have a topological interpretation as the linking of the field lines of the divergence free field @xmath5 . thus the conservation of helicity can be explained for systems in which the field lines may not cross each other , such as vortex lines in an inviscid fluid and the magnetic field lines in a perfectly conducting fluid @xcite . for these flows the field lines are said to be frozen into the flow , and the helicity is a topological invariant mathematically related to the hopf invariant @xcite classifying the nontrivial homotopy classes of maps from @xmath6 to @xmath7 . , which are isomorphic to circles in @xmath6 . the hopf invariant is equivalent to the helicity integral of a vector field who s field lines lie tangent to the preimage circles . in this sense the hopf invariant is a helicity integral term , but the inverse is usually not the case . ] superfluids and cosmic strings are both described by field theories of a complex field @xmath8 which obeys a nonlinear field equation @xcite , e.g. the nonlinear ginzburg - pitaevskii equation @xcite or the higgs equation . cosmic strings and superfluid vortices both occur in the presence of spontaneous symmetry breaking @xcite . a vortex filament or cosmic string is a configuration of @xmath9 which approaches asymptotically the broken symmetry vacuum , and is characterized by a phase @xmath0 which changes by @xmath10 ( @xmath11 ) when one goes once around the filament or string axis . @xmath12 , is termed the _ winding number of the string_. single valuedness of the field @xmath9 on the filament axis requires that @xmath13 along it . the curves along which @xmath13 define the position of the strings . a vortex filament or cosmic string must either be infinite in both directions , close on itself ( cosmic string loop , vortex ring ) , or terminate on a boundary of the system . otherwise the behavior of the phase just beyond the filament s free ends would be ambiguous . we assume throughout that all strings are closed un - knotted loops confined to a finite region . the analogy between vortices in superfluids and global cosmic strings has inspired the construction of a _ helicity _ for global cosmic strings . bekenstein @xcite defined a helicity for global strings , and vachaspati and field @xcite , sato and yahikozawa @xcite and sato @xcite did this for local strings . these works tried to relate helicity for cosmic strings with the topological and geometrical structure of these strings ( such as linking , knotting , writhing and twisting ) . in all these works bizarre physical conclusions were drawn . bekenstein concluded that an isolated unknotted loop of global string is restricted to a plane @xcite i.e. , only planar configurations may exist . this is strange since dynamically there seems to be no constraint on a loop accumulating a distortion continuously in an arbitrary direction . furthermore simulations of the formation and evolution of cosmic strings show the formation of loops which are not planar @xcite . bekenstein also claimed that the contortion of a single knot is quantized in integers . this is also strange because it says a single knot may not wiggle freely about , but is frozen in a configuration of integer contortion . for local cosmic strings there is a relation between the electroweak magnetic helicity of a tangle of strings and the violation of baryon number conservation via what is known as the chiral anomaly @xcite . vachaspati and field , sato and yahikozawa and sato found the helicity to change continuously with the shape of the strings , which implies that baryon number changes continuously too . this clashes with the expectation that baryon number is quantized in integers . we show here that the topological interpretation of helicity as the linking of field lines themselves is not fully incorporated in these works , and hence an important term was left out , which accounts for all the mentioned unacceptable conclusions . helicity arises from internal structure within a string , determined by the twist and writhe of the string , in addition to the external relations between strings , i.e. linking and knotting . the missing term arises from the internal structure of field lines within the strings which we name _ internal helicity_. it was previously believed @xcite that since the strings length is much greater than its width , the internal structure of the string becomes unimportant and physical quantities of interest can be averaged over the string cross - section . however , as we will see this is not always the case . in order to clarify the contribution of internal helicity , the relation of helicity to the topological structure of field lines will be further developed here . field lines of vector fields which are divergence - free do not have endpoints . this property allows us to examine such field structures in terms of the topology of closed curves . the link between helicity and topological invariants of curves was first conjectured by moffatt in 1981 @xcite and then developed by berger and field in 1984 @xcite . in 1992 moffatt and ricca @xcite managed to derive the extra term , arising from the internal structure of magnetic flux tubes , directly from the field equations of motion for a magnetohydrodynamic fluid . this is not possible when calculating the helicity of cosmic strings since their equations are second order non - linear equations , and therefore the calculation is too complicated . however , using formulas describing curves , developed by mathematical biologists investigating the structure of dna @xcite , the internal helicity may be calculated . by adding it to the external helicity we correct the mentioned results . in section [ sec_2 ] we review the concept of _ helicity _ of a solenoidal ( divergence free ) vector field , and dwell on the relation of the helicity to the linking of the field lines of the solenoidal field . in section [ sec_3 ] we review the construction and calculation of the helicity for a tangle of global cosmic string loops , as a function of different geometrical and topological properties of the strings @xcite . next we correct the previously mentioned conclusions of bekenstein by means of the internal helicity . in section [ sec_4 ] we deduce new constraints on the permitted linkages of string loops . we find that the linking possibilities of string loops depends on their winding numbers . in section [ sec_5 ] we review how the electroweak helicity of local cosmic strings in the weinberg - salam model is related to the baryon number , and clarify how baryon number conservation is violated . the baryon number is found to be quantized , in contrast to previous results . again , we show how internal helicity accounts for the new results .

we apply the concept of helicity from classical hydrodynamics to elucidate two problematical issues in cosmic string physics . helicity , the space integral of the scalar product of a velocity - like field with its vorticity field ( curl ) , can be defined for a complex scalar field in analogy with fluids . we dwell on the topological interpretation of helicity as related to the linking of field lines of the vorticity field . earlier works failed to fully implement this interpretation for cosmic strings by missing a term connected with the linking of these lines inside the strings . as a result , we find a new constraint on the permitted linkages of cosmic strings in a string tangle .

we apply the concept of helicity from classical hydrodynamics to elucidate two problematical issues in cosmic string physics . helicity , the space integral of the scalar product of a velocity - like field with its vorticity field ( curl ) , can be defined for a complex scalar field in analogy with fluids . we dwell on the topological interpretation of helicity as related to the linking of field lines of the vorticity field . earlier works failed to fully implement this interpretation for cosmic strings by missing a term connected with the linking of these lines inside the strings . as a result paradoxical conclusions were drawn : global cosmic string loops may not take on certain simple shapes , and baryon number is not quantized in integers in the presence of local cosmic strings in gauge theory . we show that both paradoxes are removed when internal contributions to helicity are properly taken into account . in particular , quantization of baryon number can be understood within a special case of the glashow - weinberg - salam model if cosmic strings are the unique mechanism for baryosynthesis . in addition , we find a new constraint on the permitted linkages of cosmic strings in a string tangle .

1406.7707

c

.[tab : gate_error]summary of the quantum gate errors [ cols="^,^,^,^,^",options="header " , ] we have applied the quantum optimal control method to implement fast and high - fidelity single - qubit and two - qubit gates for two inductively coupled superconducting flux qubits with fixed static off - diagonal qubit - qubit coupling and fixed qubit transition frequencies . table [ tab : gate_error ] summarizes the gate errors calculated with realistic experimental parameters for ideal unitary case , and for the cases considering the effect of leakage state and the effect of qubit decoherence . our optimal control scheme has the following great advantages . ( 1 ) our scheme that shares the same advantage of other directly coupling scheme requires no additional coupler subcircuit and control lines and thus is simple in experimental design . the control lines needed are only for the manipulation of individual qubits ( e.g. , the time - dependent magnetic flux or field through each qubit ) . ( 2 ) quantum gates constructed via our scheme are all with very high fidelity ( very low error ) as our optimal control scheme takes into account the fixed qubit detuning and fixed two - qubit interaction as well as all other time - dependent magnetic - field - induced single - qubit interactions and two - qubit couplings when performing single - qubit and two - qubit gates . ( 3 ) our scheme can cope with noise and decoherence very well as the qubits are biased at the optimal coherence point to reduce the influence of low - frequency flux noise , and the gate operation time ( @xmath3 ns ) is much shorter than the corresponding qubit decoherence time ( a few @xmath233s or larger ) @xcite so that the decoherence effect on such a fast gate is significantly diminished . ( 4 ) a cnot gate or other general quantum gates can be implemented in a single run of pulse sequence rather than being decomposed into several single - qubit and some entangled two - qubit operations in series by composite pulse sequences . a natural question then arises : how to generate these optimal control pulses experimentally ? the pulse sequences shown in fig . [ fig : x1 ] and , and in fig . [ fig : cnot ] and look experimentally challenging , but not impossible . commercial devices ( e.g. , tektronix awg70001a ) for generating arbitrary wave forms with 10 bits of vertical resolution at a sample rate of 50 gsa / s , a bit rate of 12.5 gb / s and a rise / fall time smaller than 27 ps are now available . such a device should enable generation of complex signals in a time scale of sub - nanoseconds to nanoseconds . this high - end arbitrary wave form generator combining with ultrafast josephson electronics should be or about to be able to fulfill the necessary specifications for implementing the optimal control pulse sequences we obtain for the quantum gate operations presented here . another challenge for the experimental implementations and applications of the quantum optimal control theory is one s imprecise knowledge of the quantum system s parameters . typically , the quantum gates constructed by the quantum optimal control theory are computed to very high precision assuming the parameters in the model hamiltonian are exactly known . however , for real systems controlled in the experiments , the parameters and also the hamiltonians usually are not known exactly . this poses a challenge to implement such high - fidelity gates successfully in the laboratory . recently , a hybrid open / closed - loop optimal control method called adaptation by hybrid optimal control ( ad - hoc ) has been proposed @xcite to overcome not only the problem of inaccurate knowledge of the system parameters but also shortcomings of the assumed physical model and errors on the controls themselves . the basic idea is to use the open - loop quantum optimal control theory to find the optimal control pulses with the best available model and parameters of the system . then the pulses are sent to the experiment and their performance are efficiently measured by using , for example , the method of randomized benchmarking @xcite . the closed - loop pulse calibration of ad - hoc , similar to adaptive model - free feedback control ( also referred to as closed - loop laboratory control or learning control ) @xcite , uses the physical system itself as a feedback to calibrate control pulses and optimize their performance . by using , e.g. , the robust and efficient nelder - mead algorithm @xcite , the control pulses are updated experimentally and the procedure is iterated until a target performance is reached or convergence stops . after the calibration is finished , the optimized pulses can then be used . even though the precise experimental parameters are never identified , ad - hoc can reduce the initial gate errors of the numerically obtained optimal control pulses implemented in an experiment by at least an order of magnitude @xcite . thus the quantum optimal control theory is practical and applicable experimentally through , e.g. , the ad - hoc protocol @xcite . a recent experiment demonstrating single - qubit operations ( with fidelity of 0.99 ) and two - qubit entanglement for the electron spins of two proximal nitrogen - vacancy centers in diamond using optimal control has been reported @xcite . it is thus believed that high - fidelity quantum gates with optimal control pulses obtained via our scheme will be realized experimentally in the near future . we are very grateful to prof . yu - xi liu for sending us his note for the derivation of the coupled flux - qubit hamiltonian of ref . @xcite . we acknowledge support from the national science council in taiwan under grant no . 100 - 2112-m-002 - 003-my3 , from the national taiwan university under grants no . 103r891400 , no . 103r891402 and 102r3253 , and from the focus group program of the national center for theoretical sciences , taiwan . 99 j. q. you and f. nori , phys . today * 58 * , 11 , 42 ( 2005 ) ; 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m. neeley , r. c. bialczak , m. lenander , e. lucero , m. mariantoni , a. d. oconnell , d. sank , h. wang , m. weides , j. wenner , y. yin , t. yamamoto , a. n. cleland , and j. m. martinis , nature * 467 * , 570 ( 2010 ) . a. p. peirce , m. a. dahleh , and h. rabitz , phys . a * 37 * , 4950 ( 1988 ) . d. j. tannor , v. a. kazakov and v. orlov , in _ time - dependent quantum molecular dynamics _ , edited by j. broeckhove and l. lathouwers , nato advanced studies institute , series b : physics ( plenum press , new york , 1992 ) , vol . 347 - 360 . j. p. palao and r. kosloff , phys . lett . * 89 * , 188301 ( 2002 ) ; j. p. palao and r. kosloff , phys . a * 68 * , 062308 ( 2003 ) . n. khaneja , t. reiss , c. kehlet , t. schulte - herbrggen , and s. j. glaser , j. magn . reson . * 172 * , 296 ( 2005 ) ; d .- b . tsai , p .- w . chen , and h .- s . goan , phys . a * 79 * , 060306(r ) ( 2009 ) . a. sprl , t. schulte - herbrggen , s. j. glaser , v. bergholm , m. j. storcz , j. ferber , and f. k. wilhelm , phys . a * 75 * , 012302 ( 2007 ) . r. eitan , m. mundt , and d. j. tannor , phys . a * 83 * , 053426 ( 2011 ) . m. wenin and w. ptz , phys . a * 78 * , 012358 ( 2008 ) ; 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we apply the quantum optimal control theory based on the krotov method to implement single - qubit and gates and two - qubit cnot gates for inductively coupled superconducting flux qubits with fixed qubit transition frequencies and fixed off - diagonal qubit - qubit coupling . our scheme that shares the same advantage of other directly coupling schemes requires no additional coupler subcircuit and control lines . the control lines needed are only for the manipulation of individual qubits ( e.g. , a time - dependent magnetic flux or field applied on each qubit ) . the qubits are operated at the optimal coherence points and the gate operation times ( single - qubit gates ns ; cnot gates ns ) are much shorter than the corresponding qubit decoherence time . a cnot gate or other general quantum gates can be implemented in a single run of pulse sequence rather than being decomposed into several single - qubit and some entangled two - qubit operations in series by composite pulse sequences . quantum gates constructed via our scheme are all with very high fidelity ( very low error ) as our optimal control scheme takes into account the fixed qubit detuning and fixed two - qubit interaction as well as all other time - dependent magnetic - field - induced single - qubit interactions and two - qubit couplings .

we apply the quantum optimal control theory based on the krotov method to implement single - qubit and gates and two - qubit cnot gates for inductively coupled superconducting flux qubits with fixed qubit transition frequencies and fixed off - diagonal qubit - qubit coupling . our scheme that shares the same advantage of other directly coupling schemes requires no additional coupler subcircuit and control lines . the control lines needed are only for the manipulation of individual qubits ( e.g. , a time - dependent magnetic flux or field applied on each qubit ) . the qubits are operated at the optimal coherence points and the gate operation times ( single - qubit gates ns ; cnot gates ns ) are much shorter than the corresponding qubit decoherence time . a cnot gate or other general quantum gates can be implemented in a single run of pulse sequence rather than being decomposed into several single - qubit and some entangled two - qubit operations in series by composite pulse sequences . quantum gates constructed via our scheme are all with very high fidelity ( very low error ) as our optimal control scheme takes into account the fixed qubit detuning and fixed two - qubit interaction as well as all other time - dependent magnetic - field - induced single - qubit interactions and two - qubit couplings . the effect of leakage to higher energy - level states and the effect of qubit decoherence on the quantum gate operations are also discussed .

1309.4805

i

in this paper , the validity of various exchange - correlation functionals ( lda , pbe , pbesol , wc , am05 , and htbs ) has been investigated for computing the structural , vibrational , dielectric , and thermodynamical properties of various materials ( silicon , sio@xmath0 @xmath1-quartz and stishovite , zrsio@xmath2 zircon , mgo periclase , and copper ) in the framework of dfpt . for the structural properties , pbesol and wc are found to provide the results closest to the experiments and am05 performs only slightly worse . these three functionals constitute an improvement over lda and pbe in contrast with htbs which has been shown to be really problematic for @xmath1-quartz . for the vibrational and thermodynamical properties , lda performs surprisingly very well . in the majority of cases , it outperforms pbe significantly and yields slightly better results than the wc , pbesol , and am05 functionals . for the latter functionals , this slight improvement is however detrimental for the structural parameters . on the other hand , htbs performs also poorly for vibrational quantities . for the dielectric properties , all the functionals fail to reproduce the electronic dielectric constant due to the well - known band gap problem . they all tend to overestimate the oscillator strengths and hence the static dielectric constant . overall , lda provides very good performances in dfpt computations provided the lda lattice parameter is used . if accurate lattice parameters are also sought for , the pbesol , wc and am05 provide the most accurate structural results while still improving in terms of vibrational quantities compared to pbe .

we assess the validity of various exchange - correlation functionals for computing the structural , vibrational , dielectric , and thermodynamical properties of materials in the framework of density - functional perturbation theory ( dfpt ) . we investigate a wide variety of materials including a semiconductor ( silicon ) , a metal ( copper ) , and various insulators ( sio-quartz and stishovite , zrsio zircon , and mgo periclase ) . for the structural properties , we find that pbesol and wc are the closest to the experiments and am05 performs only slightly worse . all three functionals actually improve over lda and pbe in contrast with htbs , which is shown to fail dramatically for-quartz . for the vibrational and thermodynamical properties , lda performs surprisingly very good . in the majority of the test cases , it outperforms pbe significantly and also the wc , pbesol and am05 functionals though by a smaller margin ( and to the detriment of structural parameters ) . on the other hand , htbs performs also poorly for vibrational quantities . for the dielectric properties they all ( i ) fail to reproduce the electronic dielectric constant due to the well - known band gap problem and ( ii ) tend to overestimate the oscillator strengths ( and hence the static dielectric constant ) .

we assess the validity of various exchange - correlation functionals for computing the structural , vibrational , dielectric , and thermodynamical properties of materials in the framework of density - functional perturbation theory ( dfpt ) . we consider five generalized - gradient approximation ( gga ) functionals ( pbe , pbesol , wc , am05 , and htbs ) as well as the local density approximation ( lda ) functional . we investigate a wide variety of materials including a semiconductor ( silicon ) , a metal ( copper ) , and various insulators ( sio-quartz and stishovite , zrsio zircon , and mgo periclase ) . for the structural properties , we find that pbesol and wc are the closest to the experiments and am05 performs only slightly worse . all three functionals actually improve over lda and pbe in contrast with htbs , which is shown to fail dramatically for-quartz . for the vibrational and thermodynamical properties , lda performs surprisingly very good . in the majority of the test cases , it outperforms pbe significantly and also the wc , pbesol and am05 functionals though by a smaller margin ( and to the detriment of structural parameters ) . on the other hand , htbs performs also poorly for vibrational quantities . for the dielectric properties , none of the functionals can be put forward . they all ( i ) fail to reproduce the electronic dielectric constant due to the well - known band gap problem and ( ii ) tend to overestimate the oscillator strengths ( and hence the static dielectric constant ) .

1601.06845

i

0.1 cm the parity - violating ( chiral ) gauge symmetries and spontaneous / explicit breaking of these symmetries for the hierarchy of fermion masses have been at the center of a conceptual elaboration that has played a major role in donating to mankind the beauty of the sm for particle physics . the nambu - jona - lasinio ( njl ) model @xcite of dimension-6 four - fermion operators at high energies and its effective counterpart , the phenomenological model @xcite of the elementary higgs boson and its yukawa - coupling to fermions at low energies , provide an elegant and simple description for the electroweak symmetry breaking and intermediate gauge boson masses . after a great experimental effort for many years , using data recorded at @xmath9 tev experiments of @xmath1-collision at the large hadron collider ( lhc ) , the atlas @xcite and cms @xcite collaborations have shown the first observations of a 125 gev scalar particle in the search for the sm higgs boson . this far - reaching result begins to shed light on this most elusive and fascinating arena of fundamental particle physics . recently , in the run-2 of the upgraded lhc , the preliminary results on @xmath0 tev @xmath1 collision data are prepared by atlas @xcite and cms @xcite to search for new ( beyond the sm ) resonant and/or nonresonant phenomena that might manifest themselves in the high - energy regime with final states of diboson , dilepton , dijet and so forth . the diphoton channel shows the trace of a new resonance at the diphoton invariant mass @xmath10 gev , which however needs to be confirmed by increasing the integrated luminosity of @xmath1 collisions in time . in refs . @xcite , we have already presented discussions on the possible decay channels of composite bosons and fermions into final states of jets and leptons in the framework of effective four - fermion operators in high energies . in this article , we focus on the discussions on the possible channels of composite bosons and fermions decaying into the final states of two sm gauge bosons ( diboson channels ) , and/or jets , in connection with the atlas amd cms on going @xmath0 tev experiments . it is shown that the diphoton channel of composite bosons decay should have the largest branching ratio , however other diboson channels should contribute to the invariant mass @xmath11 of possible composite - boson resonance . instead composite fermions decay into a quark(jet ) or a lepton and a composite boson , the latter is an intermediate state , which then decays into two bosons , i.e. , the peculiar jet - diboson or lepton - diboson channel . the kinematic relation of composite boson and fermion decays is thus definitely fixed , so that the theoretical scenario of composite bosons and fermions can be verified or excluded , provided that the diboson channel of composite boson decay and the jet - diboson or ( lepton - diboson ) channel of composite fermion decay can be experimentally verified . in secs . [ eff4o ] and [ smeff4o ] , we present the sm gauge - symmetric operators of four - fermion interactions and the discussion of their possible origin . some clarifications of the low - energy domain for the sm and the high - energy ( tev ) domain for an effective field theory of composite particles are given in secs . [ ird ] , [ uvd ] and riro . after showing the composite particle spectrum and effective lagrangian in secs . [ composite ] and [ efflag ] , we discuss the composite boson and fermion decay in secs . ( [ cbd ] ) and ( [ cfd ] ) , as well as their annihilation in sec . ( [ acf ] ) . in the final section , we present some discussions and speculations on the possible channels of composite particles that could be relevant to some experiments at energy scale tev .

we briefly recall the previous publications plb1996,2013,2014,2015,npb1997,2000 and prd2000,2001,2016 on the effective field theory of massive ( tev ) composite particles and their sm gauge couplings in the domain of uv - stable fixed point of relevant four - fermion operators , and on the resonant and nonresonant phenomena for experimental searches , in particular the final states of multijets . we calculate the rates of composite bosons ( fermions ) produced by lhc-collision decaying ( annihilating ) into two gauge bosons , , , and give the definite ratios of decay ( annihilation ) rates of different channels . it is shown that a composite fermion decays into an elementary fermion and a composite boson , the latter being an intermediate state decays into two gauge bosons , leading to a peculiar kinematics of final states of a jet ( or a lepton ) and two gauge bosons . we also give some speculative discussions on the channels of composite fermions decaying to , and two boson - tagged jets with quark jets , or to four - quark jets .

we briefly recall the previous publications plb1996,2013,2014,2015,npb1997,2000 and prd2000,2001,2016 on the effective field theory of massive ( tev ) composite particles and their sm gauge couplings in the domain of uv - stable fixed point of relevant four - fermion operators , and on the resonant and nonresonant phenomena for experimental searches , in particular the final states of multijets . we then focus the discussions on the decay and annihilation channels of composite particles into the final states of the sm gauge bosons , leptons and quarks in connection with the on - going searches of the atlas and cms experiments at energy tev . we calculate the rates of composite bosons ( fermions ) produced by lhc-collision decaying ( annihilating ) into two gauge bosons , , , and give the definite ratios of decay ( annihilation ) rates of different channels . it is shown that a composite fermion decays into an elementary fermion and a composite boson , the latter being an intermediate state decays into two gauge bosons , leading to a peculiar kinematics of final states of a jet ( or a lepton ) and two gauge bosons . these provide the justification for the verification or falsification of such a theoretical framework beyond the sm . we also give some speculative discussions on the channels of composite fermions decaying to , and two boson - tagged jets with quark jets , or to four - quark jets . moreover , at the same tev energy scale , the composite particles can be formed by high - energy sterile neutrino ( dark matter ) collisions , then they decay , leading to an excess of cosmic ray particles in space , producing signals of sm particles in underground .

1601.06845

r

0.1 cm for readers convenience , we first give a very brief review of effective four - fermion operators and the effective theory of composite particles , which were presented in previous papers . we then focus the discussions on the decay and annihilation channels of composite bosons and fermions into the final states of the sm gauge bosons , leptons and quarks , in connection with the on - going searches of the atlas and cms experiments at energy @xmath0 tev . the justifications are provided for the verification or falsification of such a theoretical framework of massive composite particles and sm gauge couplings in the uv - domain of effective four - fermion operators . we end this article by making some speculative considerations for experiments . in the lhc @xmath1 collisions , the most probably channels of producing composite particles are the composite bosons and fermions ( [ boundb]-[boundm ] ) in the first family via the four - fermion operators @xcite @xmath313 + g(\bar\psi^{ia}_l\nu_{r})(\bar \nu_{r}\psi^{ia}_{l } ) , \label{uhlx}\end{aligned}\ ] ] and the channels of producing composite particles by other quark and lepton families have smaller rate because of involving small gauge interactions . the last term of eq . ( [ uhlx ] ) represents the interaction of quarks and dark - matter particle @xmath169 , which stands for the right - handed sterile neutrino of the first fermion family . due to the @xmath237- and @xmath239-boson couplings @xmath314 to two constituent quarks ( @xmath315 ) of composite fermions , in particular @xmath237-boson coupling to @xmath36 doublet @xmath316 , massive composite dirac fermions have the decay channels of final states : ( i ) dijets tagged by two highly boosted bosons ww , wz or zz produced by high - energy constituent quarks ( @xmath315 ) of composite dirac fermions , together with additional quark jets ; ( ii ) four quark jets formed by four high - energy constituent quarks ( @xmath315 ) of composite dirac fermions with a peculiar kinematic distribution @xcite . the former should have smaller rate because of the gauge coupling @xmath314 , although we are not able to calculate the rates of these channels . the final states can also be high - energy leptons , however the branching ratio of @xmath237 and @xmath239 decaying to leptons is about several times smaller than that to hadrons ( jets ) @xcite . the composite dirac fermion can also decay in the channel wh @xcite , where the higgs boson is produced by @xmath315-quarks fusing into a top - quark pair via a gluon , and its production rate is then related to the qcd coupling @xmath317 . we can have similar discussions for the case of composite bosons . these composite dirac fermions could be experimentally verified by possibly observing the resonances in the invariant masses ( @xmath318 ) and kinematic distributions of final channels measured . if the cm energy @xmath319 of lhc @xmath1-collisions is close to the masses @xmath11 of composite dirac fermions ( @xmath320 ) , then the invariant masses @xmath321 . suppose that the recent atlas and cms preliminary results @xcite of diboson resonances ( dijets tagged by two bosons ) with invariant masses in the range from 1.3 to 3.0 tev could be further confirmed . these resonances are expected to be also seen in the channels of four quark jets , whose invariant mass and event rate should be larger , provided that these resonances are attributed to massive composite dirac fermions at tev scale . the cms result @xcite of resonances with final states being two jets could include the event of four quark jets , two of them are geometrically close together to form a `` wide jet '' , which should be tagged through a study of its substructure and flavor . moreover , if composite dirac fermions are formed by the last operator in eq . ( [ uhlx ] ) , in addition to jets in final state , dark - matter particles @xmath169 carry away missing energy - momentum @xcite . we can have similar discussions for the case of composite bosons . last but not least , all sterile neutrinos ( @xmath322 ) and gauge - singlet ( neutral ) states of massive composite dirac fermions , e.g. , @xmath323 $ ] , can be possible candidates of warm and cold dark matter @xcite . they can couple or decay to the sm elementary particles in the following ways . ( i ) gauge - singlet ( neutral ) states of massive composite dirac fermions become unstable and decay to sm elementary particles . ( ii ) sterile neutrinos interact with the sm elementary particles via the last term of eq . ( [ uhlx ] ) for @xmath324 being quark or lepton @xmath36-doublets . ( iii ) the terms in eqs . ( [ bhlxl ] ) and ( [ bhlbv ] ) give the interactions @xmath325 , \label{bhlbv'}\end{aligned}\ ] ] among sterile neutrinos @xmath326 ( dark matter ) and sm particles , where the lepton @xmath36 doublets @xmath43 , singlets @xmath44 and the conjugate fields of sterile neutrinos @xmath45 ( @xmath327 ) , and quark fields @xmath50 and @xmath51 . it is thus expected that at the same tev scale where composite bosons and fermions ( [ boundb]-[boundm ] ) appear as resonances in the lhc @xmath1 collisions , the composite boson @xmath328 or @xmath329 and the composite fermion @xmath330 $ ] or @xmath331 $ ] should be formed by high - energy sterile neutrino inelastic collisions , e.g. @xmath332 via the first or second term in eq . ( [ bhlbv ] ) , and then decay to produce an excess of cosmic ray electron and positrons @xcite in space laboratories . in addition , recent ams-02 results @xcite show that at tev scale the proton flux in terms of energy changes its power - law index . this implies that there would be `` excess '' tev protons whose origin can be also explained by the resonance of composite bosons and fermions due to the interactions ( [ uhlx ] ) and ( [ bhlbv ] ) of dark - matter and normal - matter particles at tev scale . we also expect that at the same tev scale via the last term in eq . ( [ uhlx ] ) , the third and fourth terms in eq . ( [ bhlbv ] ) , composite dirac fermions , e.g. , @xmath333 $ ] , @xmath334 $ ] or @xmath335 $ ] should be formed as resonances by high - energy sterile neutrinos inelastic collisions with nucleons ( xenon ) at the largest cross - section , then they decay to produce some other detectable sm particles in underground laboratories @xcite . similarly , in the icecube experiment @xcite , we expect the events that tev neutrinos change ( lose ) their directions ( energies ) by the first term of the interaction ( [ bhlxl ] ) to form the resonances of composite bosons and fermions at tev scale . in these inelastic collisions , if the accessible cm energy @xmath336 , the cross section for the allowed inelastic processes forming massive composite bosons and fermions will be geometrical in magnitude , of order @xmath337 in the cm frame where massive composite bosons and fermions are approximately at rest . we have to confess that the detailed theoretical analysis of the composite boson and fermion phenomenology has not completely performed yet , due to its nonperturbative nature . this is analogous to the hadron physics in nonperturbative qcd .

we then focus the discussions on the decay and annihilation channels of composite particles into the final states of the sm gauge bosons , leptons and quarks in connection with the on - going searches of the atlas and cms experiments at energy tev . these provide the justification for the verification or falsification of such a theoretical framework beyond the sm . moreover , at the same tev energy scale , the composite particles can be formed by high - energy sterile neutrino ( dark matter ) collisions , then they decay , leading to an excess of cosmic ray particles in space , producing signals of sm particles in underground .

we briefly recall the previous publications plb1996,2013,2014,2015,npb1997,2000 and prd2000,2001,2016 on the effective field theory of massive ( tev ) composite particles and their sm gauge couplings in the domain of uv - stable fixed point of relevant four - fermion operators , and on the resonant and nonresonant phenomena for experimental searches , in particular the final states of multijets . we then focus the discussions on the decay and annihilation channels of composite particles into the final states of the sm gauge bosons , leptons and quarks in connection with the on - going searches of the atlas and cms experiments at energy tev . we calculate the rates of composite bosons ( fermions ) produced by lhc-collision decaying ( annihilating ) into two gauge bosons , , , and give the definite ratios of decay ( annihilation ) rates of different channels . it is shown that a composite fermion decays into an elementary fermion and a composite boson , the latter being an intermediate state decays into two gauge bosons , leading to a peculiar kinematics of final states of a jet ( or a lepton ) and two gauge bosons . these provide the justification for the verification or falsification of such a theoretical framework beyond the sm . we also give some speculative discussions on the channels of composite fermions decaying to , and two boson - tagged jets with quark jets , or to four - quark jets . moreover , at the same tev energy scale , the composite particles can be formed by high - energy sterile neutrino ( dark matter ) collisions , then they decay , leading to an excess of cosmic ray particles in space , producing signals of sm particles in underground .

hep-th9802076

i

the chern - simons formulation of 2 + 1 dimensional gravity @xcite has provided many interesting new insights into the problem of quantum gravity . ( for a review see @xcite . ) most notably , making use of the relationship between 2 + 1 dimensional chern - simons theory and the 1 + 1 dimensional wzw model @xcite , carlip has argued for a statistical mechanical interpretation of the entropy of a 2 + 1 dimensional black hole , backed up by a pair of tantalising calculations which yielded the correct value for the black hole entropy , both in lorentzian @xcite , and euclidean @xcite formalisms . furthermore , the derivation given in @xcite has been recently applied with success to de sitter space @xcite , and may provide a tool for understanding black hole entropy in string theory far from extremality @xcite . the most important assumption in carlip s analysis is that those degrees of freedom responsible for the black hole entropy are located at the horizon . this idea is certainly appealing and has been advocated by many authors . however , at a technical and conceptual level , it is difficult to see what states are counted in carlip s calculation , and what is being held fixed . in principle , it should be possible to count states in a micro - canonical ensemble , holding the mass and spin of the black hole fixed , or to infer the number of states in a grand - canonical ensemble , holding fixed the black hole temperature and angular velocity . a different approach to understanding the statistical mechanical origin of the 2 + 1 dimensional black hole entropy was recently proposed by strominger @xcite . in this approach , the basic ingredient is the discovery by brown and henneaux @xcite that the asymptotic symmetry group of 2 + 1 dimensional gravity with a negative cosmological constant @xcite is the conformal group with a ( classical ) central charge @xmath0 where @xmath1 is the cosmological constant . note that in the weak coupling limit @xmath2 , @xmath3 becomes very large . strominger has pointed out that if one counts states by regarding the theory as equivalent to @xmath3 free bosons , then at a fixed value of @xmath4 and @xmath5 , the degeneracy of states gives rise to exactly the bekenstein hawking entropy . since in 2 + 1 dimensions @xmath6 and @xmath7 where @xmath8 and @xmath9 are , respectively , the black hole mass and angular momentum @xcite , strominger s computation is clearly a micro - canonical calculation . in this approach one would like to find the underlying conformal field theory with a central charge equal to ( [ c ] ) , and its connection is to a counting of states at the black hole horizon . since it is clear that one can not obtain the correct black hole entropy in general by looking only at asymptotic isometries , it seems that strominger s calculation succeeds because the trivial nature of gravity in 2 + 1 dimensions results in an isomorphism between boundary theories at infinity and at the horizon . this paper has two goals . on the one hand , in sec . 2 we present a micro - canonical calculation of the black hole entropy . starting with a chern - simons theory , we find the algebra of global charges present at any constant radius boundary surface in the black hole spacetime . we prove that a subset of this infinite set of conserved charges satisfies the virasoro algebra with a central charge equal to ( [ c ] ) . this central charge , as in @xcite , arises classically @xcite . the advantage of considering the chern - simons formulation is that the underlying conformal field theory is , at least at the classical level , an @xmath10 wzw model whose relation to the virasoro generators is via a twisted sugawara construction @xcite . further , it is possible , to show that this virasoro algebra arises from a reduction of the wzw theory to a liouville theory @xcite . the counting of black hole microstates then follows just as in @xcite . as stressed before , since this counting needs @xmath8 and @xmath9 fixed , the relevant states live in a micro - canonical ensemble . the subset of global charges satisfying the virasoro algebra are shown to be precisely those charges that , at infinity , leave the leading order form of the metric invariant , agreeing with the asymptotic isometries found in ref . @xcite . however , the construction leading to a virasoro algebra of surface deformations is equally valid at any radius , and in particular at the horizon . thus , we are able to derive the bekenstein hawking entropy from the algebra of horizon deformations . we give the explicit form of the generators of the virasoro algebra and of the diffeomorphisms that they generate , valid at a boundary surface located at any radius . our second goal is to find the grand - canonical partition function for the 2 + 1 dimensional black hole . in sec . 3 , we compute the partition function @xmath11 for three dimensional euclidean gravity on a solid torus with a fixed value of the modular parameter @xmath12 of the torus . we show that this parameter is related to the black hole inverse temperature @xmath13 and angular velocity @xmath14 by @xmath15 and therefore @xmath11 is clearly the grand - canonical partition function . the computation of @xmath11 is not straightforward because the relevant group is @xmath16 which is not compact . we use here the trick of replacing @xmath17 @xcite and show that the partition function correctly accounts for the 2 + 1 dimensional black hole entropy , after continuing the spin of the @xmath18 representations back to complex values . in this case , we find the correct answer only if we include a source term at the black hole horizon which has a particularly interesting interpretation in terms of the wzw theory . it tracks the spin of each representation and is the analogue of a @xmath19 operator in fermionic theories , twisting the wzw theory in the time direction .

we define the partition function by using a surface term at infinity that is compatible with fixing the temperature and angular velocity of the black hole . we then compute the partition function directly in a boundary wess - zumino - witten theory , and find that we obtain the correct result only after we include a source term at the horizon that induces a non - trivial spin - structure on the wzw partition function . 8.5 in 6.5 in -.35 in ^(-)a # 1#1 mximo baados 0.2 cm _ departamento de fsica terica , facultad de ciencias , + universidad de zaragoza , zaragoza 50009 , spain _ + e - mail : [email protected] thorsten brotz 0.2 cm _ blackett laboratory , imperial college of science , technology and medicine , + prince consort road , london sw7 2bz , uk _ + e - mail : [email protected] miguel e. ortiz 0.2 cm _ blackett laboratory , imperial college of science , technology and medicine , + prince consort road , london sw7 2bz , uk _ + e - mail : [email protected] 0.5truecm 0.5truecm

we calculate the density of states of the 2 + 1 dimensional btz black hole in the micro- and grand - canonical ensembles . our starting point is the relation between 2 + 1 dimensional quantum gravity and quantised chern - simons theory . in the micro - canonical ensemble , we find the bekenstein hawking entropy by relating a kac - moody algebra of global gauge charges to a virasoro algebra with a classical central charge via a twisted sugawara construction . this construction is valid at all values of the black hole radius . at infinity it gives the asymptotic isometries of the black hole , and at the horizon it gives an explicit form for a set of deformations of the horizon whose algebra is the same virasoro algebra . in the grand - canonical ensemble we define the partition function by using a surface term at infinity that is compatible with fixing the temperature and angular velocity of the black hole . we then compute the partition function directly in a boundary wess - zumino - witten theory , and find that we obtain the correct result only after we include a source term at the horizon that induces a non - trivial spin - structure on the wzw partition function . 8.5 in 6.5 in -.35 in ^(-)a # 1#1 mximo baados 0.2 cm _ departamento de fsica terica , facultad de ciencias , + universidad de zaragoza , zaragoza 50009 , spain _ + e - mail : [email protected] thorsten brotz 0.2 cm _ blackett laboratory , imperial college of science , technology and medicine , + prince consort road , london sw7 2bz , uk _ + e - mail : [email protected] miguel e. ortiz 0.2 cm _ blackett laboratory , imperial college of science , technology and medicine , + prince consort road , london sw7 2bz , uk _ + e - mail : [email protected] 0.5truecm 0.5truecm

hep-th9802076

c

we have performed two separate calculations of the entropy of the 2 + 1 dimensional black hole using the relation between 2 + 1 dimensional gravity and chern - simons theory . in sec . 2 , we have worked in the micro - canonical ensemble , and have calculated the density of states starting from the kac - moody algebra of global charges ( wzw theory ) . we have computed the correct density of states by relating the global charges to a particular virasoro algebra via a twisted sugawara construction , in a way first considered in @xcite . this virasoro algebra turns out to generate the same asymptotic isometries considered in refs . @xcite , if the analysis of global charges is performed at infinity . we have shown that it is also present on any other boundary surface at constant radius , including the black hole horizon . in sec . 3 , we have worked in the grand - canonical ensemble , which we have defined by adding an appropriate boundary term at infinity . we have found that in order to obtain the correct partition function we must also add a source term at the horizon . this source term gives the correct value of the partition function both semi - classically and in an exact quantum mechanical calculation . it is the analogue of the term equal to @xmath326 that is sometimes added to the canonical einstein hilbert action to yield the correct semi - classical partition function for black holes in arbitrary dimensions . in the micro - canonical calculation we saw that we obtain the correct density of states at a given value of mass and spin after we make a reduction from the wzw theory to a theory of boundary deformations that satisfies the virasoro algebra , or equivalently to a liouville theory . since this reduction involves additional constraints on the allowed global charges , it one expects that the density of states should be greater in the wzw theory ( although possibly equal to leading order ) . why , then , can one not calculate the density of states directly in terms of representations of the kac - moody algebra ? in the wzw theory , it seems clear that there are an insufficient number of states ( and for this reason , in the grand - canonical ensemble the correct partition function required the addition of a source term to give a larger apparent degeneracy ) . the answer presumably lies in the use of a twisted sugawara construction to connect the kac - moody and virasoro algebras . although the states we eventually count are unitary states with respect to the standard quantisation of the virasoro algebra , they most probably correspond to a non - unitary , twisted representation of the kac - moody algebra only if the vacuum has @xmath327 , which translates to a negative eigenvalue for @xmath328 defined in an untwisted sugawara construction from the underlying wzw theory . however , it is interesting to note from ( [ m224 ] ) that the condition @xmath327 corresponds to @xmath329 , @xmath330 ( anti - de sitter space ) and @xmath331 , while the black hole vacuum @xmath332 has @xmath333 but @xmath334 . this strongly suggests that our ensemble includes anti - de sitter space as its true vacuum . ] . thus in order to find the correct density of states , we should look at a different set of states to those usually constructed in representations of the kac - moody algebra . of course , this calculation is further complicated by the fact that representations of @xmath89 wzw theory are poorly understood . in contrast to the micro - canonical case , in the grand - canonical calculation we have managed to obtain the correct density of states directly in a standard ( not twisted ) wzw theory , using standard expressions for the partition function ( and an analytic continuation ) . however , this result came from a partition function with a `` spin - structure '' term , twisting the wzw theory in the time direction . it seems likely that the twists in the space and time directions that we have discussed are related by a modular transformation is the time coordinate and to verify that this can yield the same partition function . ] . in this context , it is also interesting to speculate on the correct interpretation of the source or wilson line term that gives rise to the non - trivial `` spin - structure '' . we saw in our semiclassical and quantum mechanical calculations that this term produces the black hole entropy not as a density of states , but rather as an operator eigenvalue . we conjecture that this source term can be understood in a different context as an effective action term . if we begin with the micro - canonical picture of a twisted wzw model with trivial spin - structure , then it should be possible to get back to an untwisted wzw theory by integrating out the additional degrees of freedom arising from the spatial twisting of the wzw theory . the effect of integrating out these states would be to introduce the spin - structure term . it would be extremely nice to see this connection explicitly . finally , we comment on what these various calculations tell us about the location of the degrees of freedom giving rise to the black hole entropy . while carlip @xcite has advocated that these degrees of freedom should be located on the black hole horizon , strominger @xcite has shown that the algebra of asymptotic isometries of the metric leads to the correct density of states . our discussion of the global charges and of the reduction to liouville theory in sec . 2 showed explicitly that the virasoro algebra responsible for the density of states can live at any value of the radius @xmath27 . a similar conclusion is suggested by the @xmath27 independence of the grand - canonical calculation . we were able to obtain an explicit form for a set of deformations of the horizon whose classical algebra is the virasoro algebra , with the same classical central charge as the set of asymptotic isometries , that gives the correct bekenstein hawking entropy . the discovery of an algebra of operators at the horizon , whose representations yield the correct density of states , makes an extension of these ideas to higher dimensions look more plausible . whereas it is unlikely that the algebra of asymptotic isometries of black holes in higher dimensions could lead to the correct density of states , it seems more likely that an algebra of deformations of the horizon could have the required properties . although these two algebras are identical in our case , this is because of the trivial dynamics of 2 + 1 dimensional gravity and would certainly not be true in general . in higher dimensional applications , one would then have to relate these charges at the horizon to the mass and spin of the black hole . this problem is solved in our case by the same trivial dynamics of the theory . what is not so clear from our analysis is the physical interpretation of the subset of deformations that lead to the virasoro algebra at any finite radius . however , as mentioned above in the context of wzw theory , the restriction to this subset of deformations will reduce the density of states , but it may well not change it to the leading semi - classical order . in that case , the complete algebra of deformations of the horizon would lead to the correct density of states . however , checking this probably requires getting a handle on the problem of state counting in the wzw theory . we are hopeful that a generalisation to arbitrary dimensions of the calculations that have been developed for the 2 + 1 dimensional black hole may come about through the algebra of deformations of the horizon . indeed , this algebra may have a very direct application for black holes in higher dimensions whose near - horizon behaviour is similar to the 2 + 1 dimensional black hole . in this case we would be able to talk of states localised at the horizon .

we calculate the density of states of the 2 + 1 dimensional btz black hole in the micro- and grand - canonical ensembles . our starting point is the relation between 2 + 1 dimensional quantum gravity and quantised chern - simons theory . in the micro - canonical ensemble , we find the bekenstein hawking entropy by relating a kac - moody algebra of global gauge charges to a virasoro algebra with a classical central charge via a twisted sugawara construction . it gives the asymptotic isometries of the black hole , and at the horizon it gives an explicit form for a set of deformations of the horizon whose algebra is the same virasoro algebra . in the grand - canonical ensemble

we calculate the density of states of the 2 + 1 dimensional btz black hole in the micro- and grand - canonical ensembles . our starting point is the relation between 2 + 1 dimensional quantum gravity and quantised chern - simons theory . in the micro - canonical ensemble , we find the bekenstein hawking entropy by relating a kac - moody algebra of global gauge charges to a virasoro algebra with a classical central charge via a twisted sugawara construction . this construction is valid at all values of the black hole radius . at infinity it gives the asymptotic isometries of the black hole , and at the horizon it gives an explicit form for a set of deformations of the horizon whose algebra is the same virasoro algebra . in the grand - canonical ensemble we define the partition function by using a surface term at infinity that is compatible with fixing the temperature and angular velocity of the black hole . we then compute the partition function directly in a boundary wess - zumino - witten theory , and find that we obtain the correct result only after we include a source term at the horizon that induces a non - trivial spin - structure on the wzw partition function . 8.5 in 6.5 in -.35 in ^(-)a # 1#1 mximo baados 0.2 cm _ departamento de fsica terica , facultad de ciencias , + universidad de zaragoza , zaragoza 50009 , spain _ + e - mail : [email protected] thorsten brotz 0.2 cm _ blackett laboratory , imperial college of science , technology and medicine , + prince consort road , london sw7 2bz , uk _ + e - mail : [email protected] miguel e. ortiz 0.2 cm _ blackett laboratory , imperial college of science , technology and medicine , + prince consort road , london sw7 2bz , uk _ + e - mail : [email protected] 0.5truecm 0.5truecm

cond-mat0411069

i

we calculated the critical current @xmath0 versus ( 001 ) in - plane tilt angle @xmath163 for symmetric and asymmetric grain boundary junctions , assuming the order parameter has either the @xmath1- , extended-@xmath1- , or @xmath2-wave form . we used two fermi surfaces appropriate for hole - doped cuprates , one appropriate for electron - doped cuprates , and an extreme fermi surface for comparison purposes , and took account of the surface boundary conditions appropriate for the interfaces . we studied both tunneling limits of specular and random tunneling . an important feature of our results is that the presence of the surface boundary conditions allows for a finite @xmath122-wave critical current across junctions in which the microscopic tunneling is random . this is especially important because the tunneling across nearly all in - plane ( 001 ) tilt junctions is expected to be random on an atomic scale , even within each reconstructed facet . although our results for electron - doped cuprates are in complete agreement with the interpretation of the observation of the tricrystal experiments on those compounds , our results for hole - doped cuprates differ qualitatively with those obtained from ginzburg - landau models,@xcite and indicate that the interpretation of the tricrystal experiments is complicated , depending upon strong assumptions about the details of the fermi surface topology and the nature of the tunneling processes . in addition , corresponding problems in the interpretation of the tetracrystal experiments on hole - doped cuprates persist , leading to expectations of an @xmath158 inconsistent with many experiments.@xcite we urge further in - plane @xmath247 tilt grain boundary experiments using films deposited by liquid phase epitaxy to be made , and for high resolution transmission electron microscopy studies of the pertinent grain boundaries to be presented.@xcite

we calculate the josephson critical current across in - plane ( 001 ) tilt grain boundary junctions of high temperature superconductors . our results are generally in agreement with the sigrist - rice form for ideal junctions that has been used to interpret `` phase - sensitive '' experiments consisting of such in - plane grain boundary junctions . our results for asymmetric junctions of electron - doped cuprates are in agreement with the sigrist - rice form . however , our results for asymmetric junctions of hole - doped cuprates show that the details of the fermi surface topology and of the tunneling processes are both very important , so that the `` phase - sensitive '' experiments based upon in - plane josephson junctions are less definitive than has generally been thought .

we calculate the josephson critical current across in - plane ( 001 ) tilt grain boundary junctions of high temperature superconductors . we solve for the electronic states corresponding to the electron - doped cuprates , two slightly different hole - doped cuprates , and an extremely underdoped hole - doped cuprate in each half - space , and weakly connect the two half - spaces by either specular or random josephson tunneling . we treat symmetric , straight , and fully asymmetric junctions with- , extended- , or-wave order parameters . for symmetric junctions with random grain boundary tunneling , our results are generally in agreement with the sigrist - rice form for ideal junctions that has been used to interpret `` phase - sensitive '' experiments consisting of such in - plane grain boundary junctions . for specular grain boundary tunneling across symmetric junctions , our results depend upon the fermi surface topology , but are usually rather consistent with the random facet model of tsuei _ et al . _ [ phys . rev . lett . * 73 * , 593 ( 1994 ) ] . our results for asymmetric junctions of electron - doped cuprates are in agreement with the sigrist - rice form . however , our results for asymmetric junctions of hole - doped cuprates show that the details of the fermi surface topology and of the tunneling processes are both very important , so that the `` phase - sensitive '' experiments based upon in - plane josephson junctions are less definitive than has generally been thought .

astro-ph0505089

i

we have calculated in a consistent way five near - infrared theoretical isochrones for filter sets @xmath68 , @xmath121 , @xmath122 , f160w@xmath14f205w , and f160w@xmath14f222 m . we presented isochrones for @xmath51 of 0.0001 to 0.03 , and age of @xmath74 to @xmath59 yr . even in the same vega magnitude system , near - infrared colors of the same isochrone can be different by up to 0.18 mag at the bright end of the isochrone for different filter sets . the difference of intrinsic colors for a red giant between atmospheric filters and the space filters is generally @xmath600.1 - 0.15 mag . we provided magnitude transformations between @xmath2-band filters as a function of color from @xmath5 & @xmath2 band filters . we also presented isochrones with @xmath123 of up to 6 mag . isochrones for larger extinction values are found to be more vertically straight . we found that care is needed when comparing extinction values that are estimated using different filter sets , in particular when comparing those between atmospheric and space filter sets : extinction values inferred using space filters can be in error by up to 0.3 mag . to alleviate this problem , we introduced an `` effective extinction slope '' for each filter set and isochrone model , which describes the extinction - dependent behaviour of isochrones in the observed cmd . thanks hwankyung sung for helpful discussion . we thank jeff valenti for identifying h@xmath73 as a source of opacity in cool stars . we thank the anonymous referee whose suggestions and comments significantly improved the content of the present paper . this work was supported by the research fund from kyung hee university . s.s.k . was supported by the astrophysical research center for the structure and evolution of the cosmos ( arcsec ) of korea science and engineering foundation through the science research center ( src ) program . m.g.l . was in part supported by the abrl ( r14 - 2002 - 058 - 01000 - 0 ) and the bk21 program . allard , f. , haushildt , p. h. , alexander , d. r. , tamanai , a. , & ferguson , j. w. 2000 , in proc . of from gian planets to cool stars , eds . c. a. griffith , & m. s. marley , asp conf . ser . , 212 , 127 bessell , m. s. , & brett , j. m. 1988 , pasp , 100 , 1134 bessell , m. s. , brett , j. m. , scholz , m. , wood , p. r. 1989 , a&as , 77 , 1 bessell , m. s. , brett , j. m. , scholz , m. , wood , p. r. 1991 , a&as , 89 , 335 castelli , f. , gratton , r. g. , & kurucz , r. l. 1997 , a&a , 318 , 841 dickinson , m. , ed . 2002 , nicmos data handbook ( ver . 5.0 ; baltimore : stsci ) fluks , m. a. , plez , b. , the , p. s. , de winter , d. , westerlund , b. e. , & steenman , h. c. 1994 , a&as , 105 , 311 girardi , l. , bertelli , g. , bressan , a. , chiosi , c. , groenewegen , m. a. t. , marigo , p. , salsasnich , b. , & weiss , a. 2002 , a&a , 391 , 195 johnson , h. l. , iriarte , b. , mitchell , r. i. , & wisniewskj , w. z. 1966 , comm . lunar plan . lab . , 4 , 99 kurucz , r. l. 1993 , in the stellar populations of galaxies , eds . b. barbuy , & a. renzini , ( dordrecht , kluwer ) , iau symp . , 149 , 225 origlia , l. , & leitherer . c. 2000 , aj , 119 , 2018 persson , s. e. , murphy , d. c. , krzeminski , w. , roth , m. , & rieke , m. j. 1998 , aj , 116 , 2475 rieke , g. h. , rieke , m. j. , & paul , a. e. 1989 , apj , 336 , 752 stephens , a. w. , grogel , j. a. , ortolani , s. , davies , r. , jablonka , p. , renzini , a. , & rich , r. m. 2000 , aj , 119 , 419 wainscoat , r. j. , & cowie , l. l. 1992 , aj , 103 , 332 cclrrrcc @xmath124 & @xmath3 @xmath14@xmath2 & 0.0001 & @xmath125 & @xmath126 & @xmath127 & @xmath128 & @xmath129 + @xmath124 & @xmath3 @xmath14@xmath2 & 0.001 & @xmath130 & @xmath131 & @xmath132 & @xmath133 & @xmath134 + @xmath124 & @xmath3 @xmath14@xmath2 & 0.019 & @xmath135 & @xmath136 & @xmath137 & @xmath138 & @xmath139 + @xmath124 & @xmath3 @xmath14@xmath2 & 0.03 & @xmath140 & @xmath141 & @xmath142 & @xmath143 & @xmath144 + @xmath124 & @xmath4@xmath14@xmath2 & 0.0001 & @xmath145 & @xmath146 & @xmath147 & @xmath128 & @xmath129 + @xmath124 & @xmath4@xmath14@xmath2 & 0.001 & @xmath130 & @xmath148 & @xmath149 & @xmath150 & @xmath134 + @xmath124 & @xmath4@xmath14@xmath2 & 0.019 & @xmath135 & @xmath151 & @xmath152 & @xmath153 & @xmath139 + @xmath124 & @xmath4@xmath14@xmath2 & 0.03 & @xmath154 & @xmath155 & @xmath156 & @xmath157 & @xmath144 + @xmath124 & f205w@xmath14@xmath2 & 0.0001 & @xmath158 & @xmath159 & @xmath160 & @xmath161 & @xmath129 + @xmath124 & f205w@xmath14@xmath2 & 0.001 & @xmath162 & @xmath163 & @xmath164 & @xmath165 & @xmath134 + @xmath124 & f205w@xmath14@xmath2 & 0.019 & @xmath166 & @xmath167 & @xmath168 & @xmath169 & @xmath139 + @xmath124 & f205w@xmath14@xmath2 & 0.03 & @xmath158 & @xmath170 & @xmath171 & @xmath172 & @xmath144 + @xmath124 & f222m@xmath14@xmath2 & 0.0001 & @xmath173 & @xmath174 & @xmath175 & @xmath176 & @xmath129 + @xmath124 & f222m@xmath14@xmath2 & 0.001 & @xmath177 & @xmath178 & @xmath179 & @xmath150 & @xmath134 + @xmath124 & f222m@xmath14@xmath2 & 0.019 & @xmath180 & @xmath181 & @xmath182 & @xmath183 & @xmath139 + @xmath124 & f222m@xmath14@xmath2 & 0.03 & @xmath184 & @xmath185 & @xmath186 & @xmath143 & @xmath144 + @xmath187 & @xmath2 @xmath14@xmath3 & 0.0001 & @xmath145 & @xmath188 & @xmath189 & @xmath128 & @xmath190 + @xmath187 & @xmath2 @xmath14@xmath3 & 0.001 & @xmath140 & @xmath191 & @xmath192 & @xmath165 & @xmath193 + @xmath187 & @xmath2 @xmath14@xmath3 & 0.019 & @xmath194 & @xmath195 & @xmath196 & @xmath197 & @xmath198 + @xmath187 & @xmath2 @xmath14@xmath3 & 0.03 & @xmath194 & @xmath199 & @xmath200 & @xmath201 & @xmath202 + @xmath187 & @xmath4@xmath14@xmath3 & 0.0001 & @xmath203 & @xmath204 & @xmath205 & @xmath128 & @xmath190 + @xmath187 & @xmath4@xmath14@xmath3 & 0.001 & @xmath125 & @xmath206 & @xmath207 & @xmath208 & @xmath193 + @xmath187 & @xmath4@xmath14@xmath3 & 0.019 & @xmath145 & @xmath180 & @xmath209 & @xmath128 & @xmath198 + @xmath187 & @xmath4@xmath14@xmath3 & 0.03 & @xmath145 & @xmath158 & @xmath210 & @xmath128 & @xmath202 + @xmath187 & f205w@xmath14@xmath3 & 0.0001 & @xmath158 & @xmath211 & @xmath212 & @xmath128 & @xmath190 + @xmath187 & f205w@xmath14@xmath3 & 0.001 & @xmath158 & @xmath213 & @xmath214 & @xmath128 & @xmath193 + @xmath187 & f205w@xmath14@xmath3 & 0.019 & @xmath177 & @xmath215 & @xmath216 & @xmath161 & @xmath198 + @xmath187 & f205w@xmath14@xmath3 & 0.03 & @xmath177 & @xmath217 & @xmath173 & @xmath161 & @xmath202 + @xmath187 & f222m@xmath14@xmath3 & 0.0001 & @xmath173 & @xmath218 & @xmath181 & @xmath176 & @xmath190 + @xmath187 & f222m@xmath14@xmath3 & 0.001 & @xmath219 & @xmath220 & @xmath221 & @xmath176 & @xmath193 + @xmath187 & f222m@xmath14@xmath3 & 0.019 & @xmath222 & @xmath223 & @xmath224 & @xmath176 & @xmath198 + @xmath187 & f222m@xmath14@xmath3 & 0.03 & @xmath219 & @xmath225 & @xmath226 & @xmath176 & @xmath202 + @xmath227 & @xmath2 @xmath14@xmath4 & 0.0001 & @xmath125 & @xmath228 & @xmath229 & @xmath128 & @xmath230 + @xmath227 & @xmath2 @xmath14@xmath4 & 0.001 & @xmath140 & @xmath125 & @xmath231 & @xmath176 & @xmath232 + @xmath227 & @xmath2 @xmath14@xmath4 & 0.019 & @xmath203 & @xmath233 & @xmath234 & @xmath169 & @xmath235 + @xmath227 & @xmath2 @xmath14@xmath4 & 0.03 & @xmath194 & @xmath236 & @xmath237 & @xmath133 & @xmath238 + @xmath227 & @xmath3 @xmath14@xmath4 & 0.0001 & @xmath135 & @xmath239 & @xmath240 & @xmath208 & @xmath230 + @xmath227 & @xmath3 @xmath14@xmath4 & 0.001 & @xmath145 & @xmath241 & @xmath242 & @xmath208 & @xmath232 + @xmath227 & @xmath3 @xmath14@xmath4 & 0.019 & @xmath125 & @xmath243 & @xmath244 & @xmath128 & @xmath235 + @xmath227 & @xmath3 @xmath14@xmath4 & 0.03 & @xmath125 & @xmath245 & @xmath246 & @xmath128 & @xmath238 + @xmath227 & f205w@xmath14@xmath4 & 0.0001 & @xmath158 & @xmath247 & @xmath248 & @xmath176 & @xmath230 + @xmath227 & f205w@xmath14@xmath4 & 0.001 & @xmath158 & @xmath249 & @xmath250 & @xmath128 & @xmath232 + @xmath227 & f205w@xmath14@xmath4 & 0.019 & @xmath166 & @xmath251 & @xmath252 & @xmath128 & @xmath235 + @xmath227 & f205w@xmath14@xmath4 & 0.03 & @xmath166 & @xmath253 & @xmath254 & @xmath128 & @xmath238 + @xmath227 & f222m@xmath14@xmath4 & 0.0001 & @xmath219 & @xmath255 & @xmath256 & @xmath165 & @xmath230 + @xmath227 & f222m@xmath14@xmath4 & 0.001 & @xmath219 & @xmath257 & @xmath258 & @xmath165 & @xmath232 + @xmath227 & f222m@xmath14@xmath4 & 0.019 & @xmath222 & @xmath136 & @xmath148 & @xmath259 & @xmath235 + @xmath227 & f222m@xmath14@xmath4 & 0.03 & @xmath222 & @xmath260 & @xmath261 & @xmath259 & @xmath238 + f160w@xmath14f205w & @xmath2 @xmath14f205w & 0.0001 & @xmath262 & @xmath263 & @xmath264 & @xmath259 & @xmath265 + f160w@xmath14f205w & @xmath2 @xmath14f205w & 0.001 & @xmath266 & @xmath267 & @xmath268 & @xmath161 & @xmath269 + f160w@xmath14f205w & @xmath2 @xmath14f205w & 0.019 & @xmath262 & @xmath255 & @xmath270 & @xmath157 & @xmath271 + f160w@xmath14f205w & @xmath2 @xmath14f205w & 0.03 & @xmath262 & @xmath272 & @xmath273 & @xmath133 & @xmath274 + f160w@xmath14f205w & @xmath3 @xmath14f205w & 0.0001 & @xmath245 & @xmath275 & @xmath276 & @xmath161 & @xmath265 + f160w@xmath14f205w & @xmath3 @xmath14f205w & 0.001 & @xmath245 & @xmath277 & @xmath278 & @xmath161 & @xmath269 + f160w@xmath14f205w & @xmath3 @xmath14f205w & 0.019 & @xmath245 & @xmath279 & @xmath131 & @xmath176 & @xmath271 + f160w@xmath14f205w & @xmath3 @xmath14f205w & 0.03 & @xmath266 & @xmath280 & @xmath281 & @xmath161 & @xmath274 + f160w@xmath14f205w & @xmath4@xmath14f205w & 0.0001 & @xmath262 & @xmath282 & @xmath283 & @xmath259 & @xmath265 + f160w@xmath14f205w & @xmath4@xmath14f205w & 0.001 & @xmath262 & @xmath280 & @xmath284 & @xmath176 & @xmath269 + f160w@xmath14f205w & @xmath4@xmath14f205w & 0.019 & @xmath245 & @xmath155 & @xmath285 & @xmath161 & @xmath271 + f160w@xmath14f205w & @xmath4@xmath14f205w & 0.03 & @xmath245 & @xmath155 & @xmath286 & @xmath176 & @xmath274 + f160w@xmath14f205w & f222m@xmath14f205w & 0.0001 & @xmath135 & @xmath287 & @xmath288 & @xmath176 & @xmath265 + f160w@xmath14f205w & f222m@xmath14f205w & 0.001 & @xmath135 & @xmath289 & @xmath211 & @xmath208 & @xmath269 + f160w@xmath14f205w & f222m@xmath14f205w & 0.019 & @xmath140 & @xmath290 & @xmath291 & @xmath176 & @xmath271 + f160w@xmath14f205w & f222m@xmath14f205w & 0.03 & @xmath154 & @xmath292 & @xmath293 & @xmath128 & @xmath274 + f160w@xmath14f222 m & @xmath2 @xmath14f222 m & 0.0001 & @xmath294 & @xmath295 & @xmath296 & @xmath176 & @xmath297 + f160w@xmath14f222 m & @xmath2 @xmath14f222 m & 0.001 & @xmath245 & @xmath298 & @xmath299 & @xmath176 & @xmath300 + f160w@xmath14f222 m & @xmath2 @xmath14f222 m & 0.019 & @xmath243 & @xmath301 & @xmath302 & @xmath201 & @xmath303 + f160w@xmath14f222 m & @xmath2 @xmath14f222 m & 0.03 & @xmath243 & @xmath304 & @xmath283 & @xmath172 & @xmath305 + f160w@xmath14f222 m & @xmath3 @xmath14f222 m & 0.0001 & @xmath262 & @xmath126 & @xmath306 & @xmath128 & @xmath297 + f160w@xmath14f222 m & @xmath3 @xmath14f222 m & 0.001 & @xmath294 & @xmath307 & @xmath308 & @xmath128 & @xmath300 + f160w@xmath14f222 m & @xmath3 @xmath14f222 m & 0.019 & @xmath294 & @xmath233 & @xmath309 & @xmath128 & @xmath303 + f160w@xmath14f222 m & @xmath3 @xmath14f222 m & 0.03 & @xmath294 & @xmath211 & @xmath160 & @xmath128 & @xmath305 + f160w@xmath14f222 m & @xmath4@xmath14f222 m & 0.0001 & @xmath294 & @xmath310 & @xmath311 & @xmath176 & @xmath297 + f160w@xmath14f222 m & @xmath4@xmath14f222 m & 0.001 & @xmath294 & @xmath312 & @xmath313 & @xmath176 & @xmath300 + f160w@xmath14f222 m & @xmath4@xmath14f222 m & 0.019 & @xmath243 & @xmath314 & @xmath219 & @xmath176 & @xmath303 + f160w@xmath14f222 m & @xmath4@xmath14f222 m & 0.03 & @xmath294 & @xmath315 & @xmath316 & @xmath176 & @xmath305 + f160w@xmath14f222 m & f205w@xmath14f222 m & 0.0001 & @xmath145 & @xmath317 & @xmath140 & @xmath161 & @xmath297 + f160w@xmath14f222 m & f205w@xmath14f222 m & 0.001 & @xmath203 & @xmath317 & @xmath318 & @xmath208 & @xmath300 + f160w@xmath14f222 m & f205w@xmath14f222 m & 0.019 & @xmath194 & @xmath285 & @xmath319 & @xmath176 & @xmath303 + f160w@xmath14f222 m & f205w@xmath14f222 m & 0.03 & @xmath194 & @xmath320 & @xmath321 & @xmath128 & @xmath305 + cclrrcc @xmath124 & @xmath3 @xmath14@xmath2 & 0.0001 & @xmath203 & @xmath322 & @xmath323 & @xmath324 + @xmath124 & @xmath3 @xmath14@xmath2 & 0.001 & @xmath135 & @xmath325 & @xmath128 & @xmath326 + @xmath124 & @xmath3 @xmath14@xmath2 & 0.019 & @xmath327 & @xmath328 & @xmath161 & @xmath329 + @xmath124 & @xmath3 @xmath14@xmath2 & 0.03 & @xmath330 & @xmath331 & @xmath176 & @xmath332 + @xmath124 & @xmath4@xmath14@xmath2 & 0.0001 & @xmath194 & @xmath216 & @xmath323 & @xmath324 + @xmath124 & @xmath4@xmath14@xmath2 & 0.001 & @xmath203 & @xmath245 & @xmath208 & @xmath326 + @xmath124 & @xmath4@xmath14@xmath2 & 0.019 & @xmath333 & @xmath167 & @xmath128 & @xmath329 + @xmath124 & @xmath4@xmath14@xmath2 & 0.03 & @xmath334 & @xmath167 & @xmath161 & @xmath332 + @xmath124 & f205w@xmath14@xmath2 & 0.0001 & @xmath177 & @xmath335 & @xmath323 & @xmath324 + @xmath124 & f205w@xmath14@xmath2 & 0.001 & @xmath336 & @xmath293 & @xmath128 & @xmath326 + @xmath124 & f205w@xmath14@xmath2 & 0.019 & @xmath228 & @xmath337 & @xmath161 & @xmath329 + @xmath124 & f205w@xmath14@xmath2 & 0.03 & @xmath174 & @xmath338 & @xmath161 & @xmath332 + @xmath124 & f222m@xmath14@xmath2 & 0.0001 & @xmath219 & @xmath339 & @xmath323 & @xmath324 + @xmath124 & f222m@xmath14@xmath2 & 0.001 & @xmath222 & @xmath340 & @xmath128 & @xmath326 + @xmath124 & f222m@xmath14@xmath2 & 0.019 & @xmath341 & @xmath342 & @xmath128 & @xmath329 + @xmath124 & f222m@xmath14@xmath2 & 0.03 & @xmath206 & @xmath343 & @xmath128 & @xmath332 + @xmath187 & @xmath2 @xmath14@xmath3 & 0.0001 & @xmath135 & @xmath282 & @xmath323 & @xmath344 + @xmath187 & @xmath2 @xmath14@xmath3 & 0.001 & @xmath203 & @xmath250 & @xmath128 & @xmath345 + @xmath187 & @xmath2 @xmath14@xmath3 & 0.019 & @xmath346 & @xmath347 & @xmath176 & @xmath348 + @xmath187 & @xmath2 @xmath14@xmath3 & 0.03 & @xmath295 & @xmath349 & @xmath161 & @xmath350 + @xmath187 & @xmath4@xmath14@xmath3 & 0.0001 & @xmath145 & @xmath340 & @xmath323 & @xmath344 + @xmath187 & @xmath4@xmath14@xmath3 & 0.001 & @xmath194 & @xmath147 & @xmath208 & @xmath345 + @xmath187 & @xmath4@xmath14@xmath3 & 0.019 & @xmath130 & @xmath351 & @xmath323 & @xmath348 + @xmath187 & @xmath4@xmath14@xmath3 & 0.03 & @xmath352 & @xmath257 & @xmath323 & @xmath350 + @xmath187 & f205w@xmath14@xmath3 & 0.0001 & @xmath166 & @xmath301 & @xmath323 & @xmath344 + @xmath187 & f205w@xmath14@xmath3 & 0.001 & @xmath158 & @xmath213 & @xmath323 & @xmath345 + @xmath187 & f205w@xmath14@xmath3 & 0.019 & @xmath166 & @xmath353 & @xmath323 & @xmath348 + @xmath187 & f205w@xmath14@xmath3 & 0.03 & @xmath177 & @xmath322 & @xmath323 & @xmath350 + @xmath187 & f222m@xmath14@xmath3 & 0.0001 & @xmath222 & @xmath354 & @xmath323 & @xmath344 + @xmath187 & f222m@xmath14@xmath3 & 0.001 & @xmath219 & @xmath355 & @xmath208 & @xmath345 + @xmath187 & f222m@xmath14@xmath3 & 0.019 & @xmath166 & @xmath356 & @xmath208 & @xmath348 + @xmath187 & f222m@xmath14@xmath3 & 0.03 & @xmath166 & @xmath357 & @xmath208 & @xmath350 + @xmath227 & @xmath2 @xmath14@xmath4 & 0.0001 & @xmath154 & @xmath358 & @xmath323 & @xmath359 + @xmath227 & @xmath2 @xmath14@xmath4 & 0.001 & @xmath135 & @xmath336 & @xmath208 & @xmath360 + @xmath227 & @xmath2 @xmath14@xmath4 & 0.019 & @xmath361 & @xmath362 & @xmath161 & @xmath363 + @xmath227 & @xmath2 @xmath14@xmath4 & 0.03 & @xmath364 & @xmath365 & @xmath161 & @xmath366 + @xmath227 & @xmath3 @xmath14@xmath4 & 0.0001 & @xmath125 & @xmath367 & @xmath323 & @xmath359 + @xmath227 & @xmath3 @xmath14@xmath4 & 0.001 & @xmath154 & @xmath314 & @xmath208 & @xmath360 + @xmath227 & @xmath3 @xmath14@xmath4 & 0.019 & @xmath368 & @xmath369 & @xmath323 & @xmath363 + @xmath227 & @xmath3 @xmath14@xmath4 & 0.03 & @xmath370 & @xmath371 & @xmath323 & @xmath366 + @xmath227 & f205w@xmath14@xmath4 & 0.0001 & @xmath166 & @xmath372 & @xmath323 & @xmath359 + @xmath227 & f205w@xmath14@xmath4 & 0.001 & @xmath336 & @xmath373 & @xmath208 & @xmath360 + @xmath227 & f205w@xmath14@xmath4 & 0.019 & @xmath219 & @xmath374 & @xmath323 & @xmath363 + @xmath227 & f205w@xmath14@xmath4 & 0.03 & @xmath173 & @xmath210 & @xmath323 & @xmath366 + @xmath227 & f222m@xmath14@xmath4 & 0.0001 & @xmath180 & @xmath375 & @xmath323 & @xmath359 + @xmath227 & f222m@xmath14@xmath4 & 0.001 & @xmath180 & @xmath376 & @xmath323 & @xmath360 + @xmath227 & f222m@xmath14@xmath4 & 0.019 & @xmath222 & @xmath240 & @xmath323 & @xmath363 + @xmath227 & f222m@xmath14@xmath4 & 0.03 & @xmath180 & @xmath377 & @xmath323 & @xmath366 + f160w@xmath14f205w & @xmath2 @xmath14f205w & 0.0001 & @xmath243 & @xmath378 & @xmath323 & @xmath379 + f160w@xmath14f205w & @xmath2 @xmath14f205w & 0.001 & @xmath380 & @xmath381 & @xmath176 & @xmath382 + f160w@xmath14f205w & @xmath2 @xmath14f205w & 0.019 & @xmath383 & @xmath384 & @xmath133 & @xmath385 + f160w@xmath14f205w & @xmath2 @xmath14f205w & 0.03 & @xmath386 & @xmath387 & @xmath133 & @xmath388 + f160w@xmath14f205w & @xmath3 @xmath14f205w & 0.0001 & @xmath262 & @xmath389 & @xmath323 & @xmath379 + f160w@xmath14f205w & @xmath3 @xmath14f205w & 0.001 & @xmath243 & @xmath136 & @xmath128 & @xmath382 + f160w@xmath14f205w & @xmath3 @xmath14f205w & 0.019 & @xmath306 & @xmath390 & @xmath208 & @xmath385 + f160w@xmath14f205w & @xmath3 @xmath14f205w & 0.03 & @xmath391 & @xmath392 & @xmath208 & @xmath388 + f160w@xmath14f205w & @xmath4@xmath14f205w & 0.0001 & @xmath243 & @xmath393 & @xmath323 & @xmath379 + f160w@xmath14f205w & @xmath4@xmath14f205w & 0.001 & @xmath380 & @xmath127 & @xmath161 & @xmath382 + f160w@xmath14f205w & @xmath4@xmath14f205w & 0.019 & @xmath241 & @xmath394 & @xmath161 & @xmath385 + f160w@xmath14f205w & @xmath4@xmath14f205w & 0.03 & @xmath241 & @xmath395 & @xmath161 & @xmath388 + f160w@xmath14f205w & f222m@xmath14f205w & 0.0001 & @xmath203 & @xmath384 & @xmath323 & @xmath379 + f160w@xmath14f205w & f222m@xmath14f205w & 0.001 & @xmath352 & @xmath396 & @xmath176 & @xmath382 + f160w@xmath14f205w & f222m@xmath14f205w & 0.019 & @xmath346 & @xmath244 & @xmath165 & @xmath385 + f160w@xmath14f205w & f222m@xmath14f205w & 0.03 & @xmath131 & @xmath397 & @xmath259 & @xmath388 + f160w@xmath14f222 m & @xmath2 @xmath14f222 m & 0.0001 & @xmath294 & @xmath398 & @xmath323 & @xmath399 + f160w@xmath14f222 m & @xmath2 @xmath14f222 m & 0.001 & @xmath294 & @xmath400 & @xmath208 & @xmath401 + f160w@xmath14f222 m & @xmath2 @xmath14f222 m & 0.019 & @xmath402 & @xmath391 & @xmath128 & @xmath403 + f160w@xmath14f222 m & @xmath2 @xmath14f222 m & 0.03 & @xmath404 & @xmath391 & @xmath208 & @xmath405 + f160w@xmath14f222 m & @xmath3 @xmath14f222 m & 0.0001 & @xmath245 & @xmath406 & @xmath323 & @xmath399 + f160w@xmath14f222 m & @xmath3 @xmath14f222 m & 0.001 & @xmath266 & @xmath407 & @xmath128 & @xmath401 + f160w@xmath14f222 m & @xmath3 @xmath14f222 m & 0.019 & @xmath295 & @xmath247 & @xmath161 & @xmath403 + f160w@xmath14f222 m & @xmath3 @xmath14f222 m & 0.03 & @xmath408 & @xmath284 & @xmath161 & @xmath405 + f160w@xmath14f222 m & @xmath4@xmath14f222 m & 0.0001 & @xmath294 & @xmath409 & @xmath323 & @xmath399 + f160w@xmath14f222 m & @xmath4@xmath14f222 m & 0.001 & @xmath294 & @xmath369 & @xmath323 & @xmath401 + f160w@xmath14f222 m & @xmath4@xmath14f222 m & 0.019 & @xmath266 & @xmath410 & @xmath208 & @xmath403 + f160w@xmath14f222 m & @xmath4@xmath14f222 m & 0.03 & @xmath266 & @xmath286 & @xmath208 & @xmath405 + f160w@xmath14f222 m & f205w@xmath14f222 m & 0.0001 & @xmath135 & @xmath411 & @xmath323 & @xmath399 + f160w@xmath14f222 m & f205w@xmath14f222 m & 0.001 & @xmath368 & @xmath412 & @xmath161 & @xmath401 + f160w@xmath14f222 m & f205w@xmath14f222 m & 0.019 & @xmath334 & @xmath413 & @xmath176 & @xmath403 + f160w@xmath14f222 m & f205w@xmath14f222 m & 0.03 & @xmath327 & @xmath414 & @xmath176 & @xmath405 + lcccccc 0.0001 & @xmath74 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.0001 & @xmath75 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.0001 & @xmath64 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.0001 & @xmath59 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.001 & @xmath416 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.001 & @xmath75 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.001 & @xmath64 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.001 & @xmath59 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.019 & @xmath74 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.019 & @xmath75 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.019 & @xmath64 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.019 & @xmath59 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.03 & @xmath416 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.03 & @xmath75 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.03 & @xmath64 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] + 0.03 & @xmath59 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] +

even when displayed in the same vega magnitude system , the near - infrared colors of the same isochrone can differ by up to 0.18 mag at its bright end , depending on the filter . we present magnitude transformations between-band filters as a function of color from & band filters . we find that care is needed when comparing extinction values that are estimated using different filter sets in the-band , in particular when comparing those between atmospheric and space filter sets : extinction values for space filters can be in error by up to 0.3 mag . to reduce this error , we introduce an `` effective extinction slope '' for each filter set and isochrone model , which describes the extinction behaviour of isochrones in the color - magnitude diagram more correctly than the actual extinction law .

we calculate theoretical isochrones , in a consistent way , for five filters in the atmospheric window between and , , , , f205w , and f222 m , using the padova stellar evolutionary models by girardi et al . even when displayed in the same vega magnitude system , the near - infrared colors of the same isochrone can differ by up to 0.18 mag at its bright end , depending on the filter . we present magnitude transformations between-band filters as a function of color from & band filters . isochrones with extinction at of up to 6 mag are also presented . we find that care is needed when comparing extinction values that are estimated using different filter sets in the-band , in particular when comparing those between atmospheric and space filter sets : extinction values for space filters can be in error by up to 0.3 mag . to reduce this error , we introduce an `` effective extinction slope '' for each filter set and isochrone model , which describes the extinction behaviour of isochrones in the color - magnitude diagram more correctly than the actual extinction law . our calculation also suggests that the extinction law implied by the observations of rieke , rieke , & paul for wavelengths between and bands is better described by a power - law function with an exponent of 1.61 , instead of 1.55 , which is commonly used with an assumption that the transmission functions of and filters are dirac delta functions .

1109.0235

i

the evolution of galaxies involves the birth and death of stars , therefore , galaxies unavoidably produce metals as they live . thus , galaxies with very low metallic content are probably unevolved objects , and if we find them nearby , they provide a readily accessible fossil record from the early universe . these objects are to be expected according to the paradigm of hierarchical galaxy formation , where large galaxies arise through the assembly of smaller ones in an inefficient process leaving many dwarf galaxies as remnant ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? they seem to be materialized as the extremely metal - poor ( xmp ) dwarf galaxies observed today which , consequently , would be the closest examples we can find of these elementary primordial units from which larger galaxies assembled ( e.g. , * ? ? ? * ; * ? ? ? those units must have been extremely common in the past , but they can not be directly observed at high redshift . nearby low metallicity galaxies offer a chance for detailed studies otherwise impossible . studies of their interstellar medium ( ism ) can shed light on the properties of the primordial ism at the time of galaxy formation @xcite . for example , even the most metal - deficient galaxies in the local universe formed from matter already enriched by an early star formation episode , and the determination of the minimum galactic metallicity seems to be the best constraint available on these first stars ( e.g. , * ? ? ? * ; * ? ? ? because they have not undergone much chemical evolution , these galaxies are also the best objects for the determination of the primordial he abundance that constrains cosmological models ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . the class of blue compact dwarf galaxies ( bcds ; e.g. , * ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) contains the galaxies with the lowest known gas - phase metallicity . it is so far unclear whether such preference for xmp galaxies to be bcds is genuine or if the association results from an observational bias that systematically disfavors low surface brightness objects . the best xmp candidates in the local universe are bcds , but metal poor galaxies are found among other types of dwarf galaxies as well ( see * ? ? ? * ) . unfortunately , xmp galaxies are rare . the review by @xcite cites only 31 targets with metallicity below one tenth the solar value , which is the threshold customary used to define xmp galaxies . for decades izw18 held the record of lowest metallicity @xcite , and although a few other examples have been recently found ( e.g. , * ? ? ? * ; * ? ? ? * ) , there is a minimum metallicity close to that of i zw 18 , which corresponds to a few hundredths the solar value . the existence of such metallicity threshold is suggestive of the pre - galactic origin of metals as it happens with halo stars ( e.g. , * ? ? ? * ) , but it may also be due to other effects like the early self contamination of the ongoing starburst that rises any original level to a minimum metallicity ( e.g. , * ? ? ? * ) , or even the technical difficulty of metallicity determinations below a threshold . the number of low metallicity galaxies has significantly increased since the work by @xcite , but they are still rare objects . the thorough bibliographic compilation described in [ biblio_search ] shows only 129 such targets . the shortage of low metallicity galaxies is partly a consequence of their low luminosity as expected from the luminosity - metallicity relationship ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? . they must be faint and so detectable only within a very local volume . in order to enlarge the list of this rare yet interesting objects , we have carried out an automatic search for low metallicity galaxies in the seventh sloan digital sky survey data release ( sdss / dr7 ) . the work is reported here . so far as we are aware of , this is the first systematic search of this kind on sdss / dr7 , even though extensive searches in earlier sdss data releases have been reported . the advantage of an orderly search rather than the more traditional serendipitous discovery is twofold . first , it maximizes the number of potential candidates . second , the bias of the selection is quantifiable , allowing us to estimate for the first time the volume number density of xmp galaxies in the local universe . low metallicity galaxies are characterized by having a [ nii]@xmath56583 line negligibly small as compared to h@xmath0 . thus , the ratio between [ nii]@xmath56583 and h@xmath0 is used to measure metallicities through the appropriate calibration ( e.g. , * ? ? ? * ; * ? ? ? a low value of this ratio has been imposed as a necessary condition in classical works seeking for xmp galaxies . building on this classical approach , we address the problem in an original way by automatically classifying the galaxies according to the shape of their spectra in a region around h@xmath0 . we expected the classification to automatically separate classes of galaxies whose spectra present this property , and those targets would be regarded as metal poor candidates . note that our approach does not require the detailed knowledge of the spectral properties of the xmp galaxies , e.g. , we do not have to specify a particular ratio [ nii]@xmath56583 over h@xmath0 for a galaxy to be included . they are determined by the classification algorithm in view of the existing spectra . this minimum need of prior knowledge makes the search novel and robust against uncertainties in the selection criteria . the above conjecture turned out to work , and the result of the study is presented here . we employ a robust classification algorithm called _ k - means _ , commonly used in data - mining ( e.g. , * ? ? ? * ) , and which we have already successfully applied to sort out different types of astronomical spectra spanning from polarization profiles in the sun to galaxy spectra @xcite . the paper is organized as follows . first , we describe the systematic search for low metallicity galaxies ( [ kmeans ] ) . sdss / dr7 renders 32 xmp candidates . the physical properties of the galaxies thus selected are analyzed in [ properties ] . these candidates , together with the rest of sdss / dr7 galaxies , allow us to compute the volume number density of low metallicity galaxies in the local universe ( [ number_density ] ) . in order to contextualize our work , we carried out a comprehensive search for xmp in the literature . the results are given in [ biblio_search ] . a summary with conclusions and follow up work is provided in [ conclusions ] .

the xmp candidates are found by classifying all the galaxies according to the form of their spectra in a region 80 wide around h . due to the data size , the method requires an automatic classification algorithm . our systematic search renders 32 galaxies having negligible [ nii ] lines , as expected in xmp galaxy spectra .

we carry out a systematic search for extremely metal poor ( xmp ) galaxies in the spectroscopic sample of sloan digital sky survey ( sdss ) data release 7 ( dr7 ) . the xmp candidates are found by classifying all the galaxies according to the form of their spectra in a region 80 wide around h . due to the data size , the method requires an automatic classification algorithm . we use k - means . our systematic search renders 32 galaxies having negligible [ nii ] lines , as expected in xmp galaxy spectra . twenty one of them have been previously identified as xmp galaxies in the literature the remaining eleven are new . this was established after a thorough bibliographic search that yielded only some 130 galaxies known to have an oxygen metallicity ten times smaller than the sun ( explicitly , with ) . xmp galaxies are rare ; they represent 0.01% of the galaxies with emission lines in sdss / dr7 . although the final metallicity estimate of all candidates remains pending , strong - line empirical calibrations indicate a metallicity about one - tenth solar , with the oxygen metallicity of the twenty one known targets being . since the sdss catalog is limited in apparent magnitude , we have been able to estimate the volume number density of xmp galaxies in the local universe , which turns out to be . the xmp galaxies constitute 0.1% of the galaxies in the local volume , or 0.2% considering only emission line galaxies . all but four of our candidates are blue compact dwarf galaxies ( bcds ) , and 24 of them have either cometary shape or are formed by chained knots .

1109.0235

c

we have carried out a systematic search for extremely metal poor ( xmp ) galaxies among the spectroscopic sample of sdss / dr7 . these objects are rare , and have a clear cosmological interest as unevolved galaxies probably tracing physical conditions in an early phase of the universe ( see [ intro ] ) . the search is based on the classification of a narrow spectral region around h@xmath0 , known to be particularly sensitive to the ( hii gas ) metallicity . obviously , the almost one million spectra in the database can not be inspected individually , and we resort to the use of a standard automatic method of classification : k - means . after two nested runs of the procedure , and a subsequent cleaning up for artifacts created by the sdss pipeline , we end up with 32 targets ( [ kmeans ] , table [ list1 ] ) . they represent only 0.01% of the observed galaxies with emission lines . the final metallicity estimate remains pending , however , strong - line empirical calibrations by @xcite imply their oxygen metallicity to be of the order of one - tenth solar . obviously , our candidates must be studied in detail through imaging and spectroscopy in following up work . in order to put the work into context , we carried out a bibliographic search for galaxies with metallicity smaller than one - tenth the solar value ( [ biblio_search ] ) . we find only 129 ( table [ revision ] ) , and only 21 of them overlap with our sample which , consequently , provides 11 new xmp candidates . the oxygen metallicity of the 21 known targets turns out to be @xmath71 . these metallicities are based on electron temperatures and , thus , they are more precise than the empirical calibrations we have been employing . assuming this subset to be representative of the full sample , it confirms the xmp character of our targets . our procedure is systematic , therefore , in principle , it should have identified all the spectra in sdss / dr7 where h@xmath24}\lambda$]6583 . this assumption , together with the fact that the sdss spectroscopic sample is limited in apparent magnitude , allows us to estimate the volume number density of xmp galaxies . using the @xmath72 approximation , we estimate it to be @xmath3 . so far as we are aware of , it provides the first estimate of this number density . the xmp galaxies represent 0.1% of the galaxies in the local volume , or @xmath4 0.2% considering only emission line galaxies . we analyze some of the physical properties of the candidates in [ properties ] . all but four of our xmp candidates turn out to be blue compact dwarfs ( bcds ) . note that this association is by no means trivial . we have selected our sample according to the shape of their spectra in an narrow spectral window around h@xmath0 , and this narrow bit of spectrum turns out to determine many global properties of the galaxy such as color , compactness , and star formation rate . we ignore what causes the association between xmps and bcds . the fact that most metal poor galaxies tend to be bcds is known . @xcite point it out , but warn against a trivial interpretation since it may reflect an observational bias that makes it easier to detect high surface brightness objects such as bcds . actually , there are xmp galaxies whose surface brightness does not suffice to call them bcds ( see [ biblio_search ] ) . however , the fact that our xmp candidates are also bcds is revealing . the surface brightness where sdss starts having problems of completeness is about @xmath73 @xcite , i.e. , one magnitude fainter than the faintest xmp candidate . consequently , if we do not find low surface brightness galaxies with @xmath26}\lambda 6583 \ll { \rm h}\alpha$ ] is because they do not exist in sdss / dr7 . among the 32 xmp candidates , 24 of them have either cometary shape or are formed by chains of knots . already noticed the trend for xmp bcds to reveal a cometary morphology due to the presence of intense star formation at one edge that gradually decreases . this shape is not unique to xmp galaxies , but it comprises only 10% of all bcds @xcite , whereas it is dominant when they are metal poor . the origin of the xmp shapes is also unclear . there are arguments for gravitational triggering due to mergers with low - mass stellar or gaseous companions , or for the self propagation of star formation activity within a pre - existing gas rich galaxy . recently @xcite and @xcite have found that all xmp galaxies have distorted hi morphologies , which may indicate the infall of external unenriched gas feeding the starburst and dropping the metallicity ( e.g. , * ? ? ? . it may also be the signature of gas stripping forced by the interaction with an external medium ( e.g. , * ? ? ? * ; * ? ? ? a concluding remark is in order . the methods for mining massive astronomical databases are still under development . the bases are simply too large for the traditional techniques to be efficient . in this sense , the current paper presents a new approach that may be of interest beyond our particular application . the standard method to find xmp galaxies ( or galaxies with any other property ) would have been to set , beforehand , the observational criteria the targets should fulfill . then those targets complying with the criteria would have been selected . unfortunately , the criteria are often crude and have large uncertainties , which propagate into the selection as false objects sneaking in or true objects leaking out . here the criteria have not been stipulated in advance . we classify the whole database , and only afterward we select those galaxies belonging the classes that have the intended property . the search is comprehensive , and the results are robust against uncertainties in the selection criteria . thanks are due to b. elmegreen for fruitful discussions on the origin of the cometary shapes in xmp galaxies . thanks are also due to an anonymous referee for helping us completing the bibliographic search , as well as for insightful comments that prompted an improvement of both the argumentation and the presentation . this work has been partly funded by the spanish micinn , projects aya 2007 - 67965 - 03 - 01 , aya 2007 - 67752-c03 - 01 , and aya 2010 - 21887-c04 - 04 . jsa , ala and cmt are members of the consolider - ingenio 2010 program , grant micinn csd2006 - 00070 : first science with gtc . funding for the sdss and sdss - ii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , the u.s . department of energy , the national aeronautics and space administration , the japanese monbukagakusho , the max planck society , and the higher education funding council for england . the sdss is managed by the astrophysical research consortium for the participating institutions ( for details , see the sdss web site at http://www.sdss.org/ ) . _ facilities : _

we carry out a systematic search for extremely metal poor ( xmp ) galaxies in the spectroscopic sample of sloan digital sky survey ( sdss ) data release 7 ( dr7 ) . we use k - means . this was established after a thorough bibliographic search that yielded only some 130 galaxies known to have an oxygen metallicity ten times smaller than the sun ( explicitly , with ) . although the final metallicity estimate of all candidates remains pending , strong - line empirical calibrations indicate a metallicity about one - tenth solar , with the oxygen metallicity of the twenty one known targets being . since the sdss catalog is limited in apparent magnitude , we have been able to estimate the volume number density of xmp galaxies in the local universe , which turns out to be . the xmp galaxies constitute 0.1% of the galaxies in the local volume , or 0.2% considering only emission line galaxies .

we carry out a systematic search for extremely metal poor ( xmp ) galaxies in the spectroscopic sample of sloan digital sky survey ( sdss ) data release 7 ( dr7 ) . the xmp candidates are found by classifying all the galaxies according to the form of their spectra in a region 80 wide around h . due to the data size , the method requires an automatic classification algorithm . we use k - means . our systematic search renders 32 galaxies having negligible [ nii ] lines , as expected in xmp galaxy spectra . twenty one of them have been previously identified as xmp galaxies in the literature the remaining eleven are new . this was established after a thorough bibliographic search that yielded only some 130 galaxies known to have an oxygen metallicity ten times smaller than the sun ( explicitly , with ) . xmp galaxies are rare ; they represent 0.01% of the galaxies with emission lines in sdss / dr7 . although the final metallicity estimate of all candidates remains pending , strong - line empirical calibrations indicate a metallicity about one - tenth solar , with the oxygen metallicity of the twenty one known targets being . since the sdss catalog is limited in apparent magnitude , we have been able to estimate the volume number density of xmp galaxies in the local universe , which turns out to be . the xmp galaxies constitute 0.1% of the galaxies in the local volume , or 0.2% considering only emission line galaxies . all but four of our candidates are blue compact dwarf galaxies ( bcds ) , and 24 of them have either cometary shape or are formed by chained knots .

astro-ph0212072

r

note that a full description of the c array results and relevant images have been given in paper i and we have reproduced the zeroth moment c array map in fig . [ carray ] . the remaining the zeroth and first moment maps from the combined data set are shown in fig . [ moments ] , both rotated so that the x axis is parallel to the major axis of the galaxy . vertical slices have been taken perpendicular to the major axis at positions numbered 1 through 10 in fig . [ moments]a and these are shown as position - velocity ( pv ) plots in fig . [ pv ] . the pv slices in the last two panels of fig . [ pv ] show averages over the receding and advancing sides of the galaxy . for the first time , we see that there is a tail of emission on the south - eastern ( left , fig . [ moments]a ) side of the galaxy which resembles tidal tails seen in galaxy interaction simulations . this tail is likely produced via an interaction with the companion , eso 495-g017 , to the north - west , whose systemic velocity is separated from that of ngc 2613 by only 143 km s@xmath7 . the tail is at negative velocities with respect to the receding side of the galaxy from which it originates and shows a strong velocity gradient along its length , becoming negative with respect to the galaxy s systemic velocity as well , i.e. the velocities become forbidden . this can occur in the case of interactions but is difficult to explain any other way . given this velocity structure , the tail must be trailing from the eastern , receding side of ngc 2613 and is therefore in front of the galaxy . the anomalous emission seen around -200 km s@xmath7 in slice 2 , as well as the average over the receding side of the galaxy ( second last panel ) of fig . [ pv ] belongs to this tail as well . there is excess emission on the north - west ( right , fig . [ moments]a ) side of the galaxy in the vicinity of the companion , but we have found no systematic velocities associated with that emission or any other sign of a corresponding redshifted feature . in paper i , using the c array data alone , we identified and characterized the properties of 6 , symmetrically placed extensions labelled f1 to f6 in fig . [ carray ] . [ moments]a , which includes the lower d array resolution data , now also reveal these same features on broader scales , some of which are blended with other features . since a single cutoff level must be applied over the whole galaxy to create this image , this moment map is best used to see a global view of the disk - halo features and identify where new features might be present . the full _ z _ extents and , of course , the velocities of the individual features are best measured from pv slices perpendicular to the major axis . we have inspected many pv slices over the map and show selected slices ( labelled 1 through 10 in fig . [ moments]a ) in fig . [ pv ] . in the new data , the previously seen features f1 through f6 occur at the same velocities and the same positions as shown in fig . [ carray ] , after taking into account the different beam sizes and the addition of broader scale emission . please refer to both figs . [ moments]a and [ pv ] for a more thorough discussion of these features , presented below . f1 appears similar to what has previously been seen ( fig . [ carray ] ) , but at lower resolution . the pv plot for f1 can be seen in slice 2 which reveals it as a distinct feature at a velocity of 250 km s@xmath7 but it can also be seen in slice 1 as well , extending to a projected _ z _ height of at least 100@xmath9 ( 12.6 kpc ) `` above '' ( i.e. positive _ z _ ) mid - plane . a newly seen extension immediately to the west of f1 , sampled by slice 3 , may actually be associated with or part of f1 , since it is seen in pv space as a small arc at about the same velocity as f1 . f2 ( see slice 1 ) shows several velocity components and is more complex than previously seen . like f1 , f2 extends to at least 100@xmath9 at a velocity of 210 km s@xmath7 . it is not clear whether the other components may be blended with emission from the tidal tail . f3 reveals more structure than the extension in fig . [ carray ] and is sampled by slice 4 which reveals it as a 2-pronged arc above the disk centered at a velocity of 100 km s@xmath7 . such double peaks in velocity space are typical of such features and have been seen in other galaxies ( see , e.g. lee & irwin 1997 , lee et al . 2001 ) . the extension to the left of the f4 label in fig . [ moments]a ) extends to a height 225@xmath9 ( 28 kpc ) below ( i.e. negative _ z _ ) mid - plane in this map . as can be seen in slice 3 of the pv map , this feature occurs at a velocity of 50 km s@xmath7 and shows no velocity gradient with height . f4 reaches the highest _ z _ of all the extensions and , to our knowledge , reaches higher latitudes than any previously seen in an edge - on galaxy , exceeding even the starburst galaxy , ngc 5775 , whose known hi features extend to @xmath4 7 kpc from the plane ( lee et al . this is remarkable , given that ngc 2613 ( log l@xmath10 = 10.00 ) has a massive ( 0.1 @xmath11 100 m@xmath3 ) star formation rate that is a factor of 3 lower than that of ngc 5775 and a supernova input energy rate per unit area that is a factor of 7 less than ngc 5775 ( irwin et al . 1999 ) . feature f5 is sampled by slices 8 and 9 and can most clearly be seen in slice 9 as a vertical feature above the plane in pv space at a velocity of -300 km s@xmath7 . whereas it appeared as a single extension in fig . [ carray ] , it can now be seen to have a counterpart 55@xmath9 ( 7 kpc ) in projection farther out along the disk which is sampled by slice 10 . the counterpart clearly occurs at the same velocity and also shows no velocity gradient with height . these two features may form the base of a large loop or cylinder , similar to what has been seen in galaxies like ngc 5775 ( lee et al . 2001 ) . the most interesting and well - defined feature , however , is associated with f6 . for example , slices 6 , 7 , 8 and 9 pass through a feature below the major axis which extends 22 kpc ( 175@xmath9 ) in projection , from the plane and centers at -307 km individual channel maps of this feature are shown in fig . [ channels ] . we will refer to this as the -307 km s@xmath7 feature , rather than f6 since , as revealed by the new data , the feature is more extensive than what was originally seen in fig . [ carray ] . this feature will be discussed extensively in sect . [ 307feature ] . this disk - halo emission is faint ( 3 - 4 @xmath12 typically , note contour spacings in fig . [ pv ] ) but we consider the above - discussed features to be real because , _ 1 ) _ their spatial morphology is typical of the kinds of extensions and loops seen in other edge - on systems , _ 2 ) _ even though the feature might be faint far from the disk , there is evidence for disturbed contours ` beneath them ' even at highly significant contour levels ( see the 5th and 6th contours of fig . [ moments]a , for example ) , _ 3 ) _ at least the 6 major features , f1 to f6 can be seen in both independent data sets , _ 4 ) _ the features generally occur over several independent beams and/or velocity channels , and _ 5 ) _ in pv space , the features are distinct , yet smooth and connect continuously to the disk , unlike artifacts produced by a badly cleaned beam ( see , e.g. the arc above the disk seen in slice 3 of fig . [ pv ] at @xmath4 270 km s@xmath7 or the larger structures in slices 9 and 10 ) . in addition , _ 6 ) _ the receding and advancing panels of panels of fig . [ pv ] ) show _ averages _ over the entire advancing and receding sides of the disk , rather than just selected individual slices as shown elsewhere in the figure . in these panels , therefore , we have basically averaged together signal with noise and weak extensions would be diluted ( i.e. `` beam - averaged '' , where the beam is the size of half the galaxy ) . yet these panels still show the extensions quite clearly , especially on the advancing side where the disk - halo emission is dominated almost entirely by the -307 km s@xmath7 feature . this feature is seen up to the 4th contour which is a 6@xmath12 detection in the diluted averaged panel . finally , _ 7 ) _ for at least 4 of the 6 features , there is evidence from independent observations that extraplanar emission is present . for example , our radio continuum image ( see fig . 9 of paper i ) shows extended emission at the positions of f3 , f4 , f5 , and f6 . also , an early hi image by bottema ( 1989 ) at lower resolution shows extended hi emission at roughly the same locations . the zeroth moment map of fig . [ moments]a also shows a number of low intensity disconnected " features at high latitudes ( for example , the emission around -300@xmath9 , -200@xmath9 ) . we do _ not _ claim that all of these are real , but we have chosen to display them for the sake of comparison with future observations and because some of the emission shown in independent lower resolution images ( e.g. bottema 1989 , irwin et al . 1999 ) is so extended . an example would be the ` knot ' of emission between f3 and f5 which is sampled by slice 6 . for this feature , the velocities are discordent with respect to the underlying disk ( see fig . [ pv ] ) and therefore do not satisfy the criteria listed above . particularly interesting about these very high latitude features is that there is little or no evidence for any lag in velocity with _ z _ , even to very high distances from the place . the features seen below the plane in slices 3 , 8 , and 9 and features seen above the plane in slices 9 and 10 show no velocity gradient . the early data of bottema ( 1989 ) also showed that the high latitude hi was co - rotating . there is some evidence , in our data , for curvature in the smaller features ( cf . slices 3 & 4 above the plane ) , but one could not make any case for a lag . the only slice which shows some evidence for lagging gas is slice 1 , but this slice is also closest to the tidal tail , confusing the interpretation . the averages of the advancing and receding sides of the galaxy also do not support the presence of a lagging halo . here , we see an asymmetry in the sense of many disk - halo features on the receding side , but the advancing side is dominated by the single -307 km s@xmath7 feature . none of the features , however , show a decline with _ z_. we investigate this further in the next section . we have modeled the global hi density and velocity distributions for ngc 2613 following irwin & seaquist ( 1991 ) and irwin ( 1994 ) . this approach models all spectra in the hi cube by adopting a volume density distribution in and perpendicular to the plane , a rotation curve and velocity dispersion ( if required ) , and a position and orientation on the sky . given trial input parameters describing these distributions , the routine then varies the parameters , examining the residuals , until the best fit solution is found . various sections of the galaxy can be modeled , including galactocentric rings in the galaxy s plane . in the current version , we can also isolate slices parallel to the galaxy s plane . this permits modeling the halo , independent of the disk , which is important in this study in the event that a lagging hi halo might be present . while there is no evidence for lags in the discrete features shown in fig . [ pv ] , it is possible that the smooth , low intensity halo might be better fit with a lagging velocity distribution , similar to what has been found for ngc 2403 ( fraternali et al . the routine , called cubit , interfaces to classic aips ; potential users are requested to contact the first author for the code . for ngc 2613 , the adopted in - plane density distribution is a gaussian ring , described by : @xmath13 , where @xmath14 is the galactocentric radius , @xmath15 is the galactocentric distance of the center of the ring , @xmath16 is the in - plane density at the center of the ring , and @xmath17 is the scale length . @xmath17 can have different values for points @xmath18 ( @xmath19 ) and for points @xmath20 ( @xmath21 ) . the distribution perpendicular to the plane is given by the exponential , @xmath22 , where @xmath1 is the perpendicular distance from midplane and @xmath23 is the exponential scale height . the rotation curve is described by the brandt curve , @xmath24 , where @xmath25 is the galaxy s systemic velocity , @xmath26 is the peak of the rotation curve occurring at a galactocentric radius of @xmath27 and @xmath28 is the brandt index which is a shape parameter . a gaussian velocity dispersion , @xmath29 can also be applied , if needed . note that a velocity dispersion will result from all contributions to line widening along the entire line - of - sight direction , for example , any non - circular motions along the plane , streaming motions due to spiral arms and local turbulence . thus , @xmath29 may be larger than what might be expected from a local value . the above distributions result in 10 free parameters : @xmath16 , @xmath15 , @xmath19 , @xmath21 , @xmath23 , @xmath25 , @xmath26 , @xmath27 , @xmath28 , and @xmath29 . in addition , there are 4 more orientation parameters : the position of the galaxy center , ra(0 ) , dec(0 ) , the major axis position angle , pa , and the inclination , i. over the region of the cube occupied by ngc 2613 , there are 552 independent data points ( beam / velocity - channel resolution elements ) above a 2 @xmath12 intensity level in the combined c+d cube , so the 14 parameters are well constrained , over all . certain parameters may show a larger variation , however , depending on the nature of the distribution ; for example , @xmath27 tends to have a larger error since the point at which the rotation curve changes from rising to flat is not as well constrained by the data as some of the other parameters . table 2 lists the best fit modeled values for ngc 2613 for the combined c+d array data . we also modeled the c array data and d array data alone ; the error bars of table 2 reflect the variations in the parameters over the different arrays that result . given the range of resolution over these arrays , from 26.1@xmath9 @xmath30 20.2@xmath9 ( 3.3 @xmath30 2.5 kpc ) to 96.5@xmath9 @xmath30 42.9@xmath9 ( 12.1 @xmath30 5.4 kpc ) the error bars on the modeled parameters are very small . the best fit model is shown as dashed curves superimposed on the data in fig . [ pv ] . taking only residuals ( data cube - best fit model cube ) greater than 3@xmath12 , the root - mean - square value is 1.77 mjy beam@xmath7 and the average relative error is @xmath4 10% . a zeroth moment map made from the cube of the residuals of the best fit is shown in fig . [ residuals ] . to determine whether there are changes in i , pa , and @xmath23 with galactocentric radius , r , we also modeled the galaxy in concentric rings . for example , either a lower value of i with increasing r ( a warp ) or a higher value of @xmath23 with increasing r ( i.e. a flare ) could conspire to make the halo of a galaxy appear to lag . we find that the inclination does not decrease with radius ( there is a slight increase ) . there is indeed evidence for flaring such that , in each data set , @xmath23 systematically increases with r. the most significant change is measured for the d array data alone such that the mean scale height between a radius of 140@xmath9 and 300@xmath9 ( 17.6 to 38 kpc ) is 5.5@xmath9 ( 693 pc ) compared to a value of 1.7@xmath9 ( 214 pc ) over the whole galaxy . thus , the disk is quite thin with a modest flare at large galactocentric radii . in order to model the halo alone , a variety of lower and upper cutoffs to _ z _ were applied and these data were modeled in a similar fashion . ( note that _ z _ refers to the actual distance from the galaxy s midplane , not just the projected distance from the major axis . ) the number of independent data points is reduced typically by about a factor of 3 , depending on which _ z _ limits are chosen , but we have also held some of the parameters ( the central position , position angle and systemic velocity ) fixed . for the halo models , we find _ no _ evidence that @xmath26 could be lower at higher _ z_. the same conclusion is reached if the c array and d array data are modeled independently . the absence of a lagging hi halo in ngc 2613 will be discussed in sect . [ no - lag ] .

the global hi distribution is modeled in detail using a technique which can disentangle the effects of inclination from scale height and can also solve for the average volume density distribution in and perpendicular to the disk . one prominent feature in particular , of mass , m and height , 22 kpc , is seen on the advancing side of the galaxy at a projected galactocentric radius of 15.5 kpc . if this is correct , there should be an observable x - ray halo around ngc 2613 .

we combine new vla d array hi data of ngc 2613 with previous high resolution data to show new disk - halo features in this galaxy . the global hi distribution is modeled in detail using a technique which can disentangle the effects of inclination from scale height and can also solve for the average volume density distribution in and perpendicular to the disk . the model shows that the galaxy s inclination is on the low end of the range given by chaves & irwin ( 2001 ) and that the hi disk is thin ( = 188 pc ) , showing no evidence for halo . numerous discrete disk - halo features are observed , however , achieving heights up to 28 kpc from mid - plane . one prominent feature in particular , of mass , m and height , 22 kpc , is seen on the advancing side of the galaxy at a projected galactocentric radius of 15.5 kpc . if this feature achieves such high latitudes because of events in the disk alone , then input energies of order 10 ergs are required . we have instead investigated the feasibility of such a large feature being produced via buoyancy ( with drag ) within a hot , pre - existing x - ray corona . reasonable plume densities , temperatures , stall height ( 11 kpc ) , outflow velocities and ages can indeed be achieved in this way . the advantage of this scenario is that the input energy need only be sufficient to produce blow - out , a condition which requires a reduction of three orders of magnitude in energy . if this is correct , there should be an observable x - ray halo around ngc 2613 . # 1 # 1([eq:#1 ] )

astro-ph0212072

c

there are now several galaxies for which there is evidence for lagging halos . in ngc 891 ( i @xmath46 88.6@xmath38 ) , the rotation curve of the hi halo between _ z _ = 1.4 to 2.8 kpc reveals a peak velocity @xmath4 25 km s@xmath7 lower than in the disk ( swaters et al . 1997 ) . in ngc 5775 ( i = 86@xmath38 ) , the ionized gas velocities decrease with _ z _ to heights of 5 - 6 kpc above which the velocity remains roughly constant ( rand 2000 ) . the hi in this galaxy shows more complex structure , though lagging gas tends to dominate at _ z _ heights up to 5 to 6 kpc . above this region , the velocities are more nearly constant or the features break up into clumps which are seen over a wide range in velocity ( lee et al . models of ngc 2403 ( inclination of 61@xmath38 ) suggest that a lagging halo extends to _ z _ @xmath4 3 kpc ( schaap et al . 2000 ) . thus , from the sparse data available , the region of the lag extends to typically 3 to 6 kpc above the plane above which ( if gas is detected at all ) there is nt strong evidence for a global lag . given the presence of lagging halos in these other galaxies and also some theoretical expectation of lags ( cf . bregman 1980 , benjamin 2002 , collins et al . 2002 ) , the absence of a lagging velocity gradient along the discrete features ( sect . [ disk - halo ] ) and the absence of a global lag ( sect . [ models ] ) in ngc 2613 require comment . firstly , given the inclination of this galaxy ( 79@xmath38 , table 2 ) and its hi radius of @xmath4 35 kpc , the discrete features must reach a height of _ z _ @xmath47 6.5 kpc before they will be seen beyond the projection of the disk . if it is true that lags only exist up to 3 to 6 kpc and above this there is no longer a lag ( see above ) , then lags ( if they exist ) along the discrete features would be projected against the background disk . this would make a velocity gradient ( if present ) impossible to detect along the discrete features . the ` straightness ' of the -307 km s@xmath7 feature in velocity ( fig . [ pv ] ) to such high latitudes beyond the projection of the disk is , however , quite remarkable . if this feature emerges into a hot x - ray corona , as suggested in sect . [ buoyancy ] , then either the velocity of the broad - scale x - ray corona is not appreciably different from the underlying disk ( although the velocity dispersion is likely much higher ) , or the timescale over which it could appreciably affect this gas column is greater than the age of the feature . as for a globally lagging halo , our kinematical model is indeed capable of detecting such a lag , even if it is projected against the disk ( see sect . [ models ] ) provided there is sufficient high latitude emission that halo gas can be detected at all . what we have found , however , is that ngc 2613 does not have an hi thick disk or halo . the vertical exponential scale height ( 188 pc , table 2 ) indicates that the disk is , in fact , thin . if we create a model galaxy using the parameters of table 2 , it is straightforward to show that emission from all high latitude ( _ z _ @xmath47 1 kpc ) hi in fact falls below the map noise . thus , ngc 2613 does not have a detectable lagging halo because it does not have a halo at all . as a further comparative test , we consider the hi halo of another galaxy at the same distance , ngc 5775 ( i = 86@xmath38 , d = 25 mpc ) , for which we detected an hi halo with exponential scale height of 9.14@xmath9 ( 1.1 kpc ) using the same technique ( irwin 1994 ) . if we create a model for the lower inclination ( i = 79@xmath38 ) ngc 2613 in which the vertical density distribution declines exponentially from its in - disk value with the same scale height as ngc 5775 , we find that it could easily have been detected , even at the lower inclination of ngc 2613 . this result illustrates the importance of using a model , rather than pv slices alone , in drawing conclusions about the possible existence of lagging halos . for example , the model can disentangle inclination effects from the effects of a thick disk . for ngc 2613 , since the modeled inclination is now known to be on the low end of the range quoted in chaves & irwin ( 2000 ) , our earlier conclusion of a lag with _ z _ can now be largely explained by projection against the background disk . this is succintly illustrated via the dashed curves in fig . [ pv ] which show that our thin disk model provides an almost perfect fit to the data . we have argued elsewhere ( paper i ) , largely on the basis of above / below plane symmetry ( fig . [ carray ] ) , that the observed features are internally generated and represent outflows . while these new data show that the galaxy is indeed interacting , it is unlikely that most of the observed features are produced via cloud impacts since the cloud would have to pass completely through the disk , forming similar structures on both sides , in contrast to what is expected theoretically ( see santilln et al . anomalous velocities are also more likely in the case of impacts , whereas the velocities observed in ngc 2613 are typical of the underlying disk . thus , the new data are consistent with the outflow interpretation . we can not , however , rule out the possibility of some impacting clouds in this system and it is also possible that the interaction may assist in the process of disk - halo dynamics , for example via stimulating a starburst or instabilities such as the parker instability . if the features are internally generated , their very large sizes ( _ z _ up to 28 kpc , sect . [ disk - halo ] imply exceptional energies ( @xmath4 10@xmath5 ergs ) which are difficult to conceive of , especially at large distances from the nuclear vicinity and in a galaxy which is not a starburst . this energy problem has been known since the first detections of heiles shells in the milky way ( heiles 1979 , 1984 ) and has generated suggestions as far ranging as multiple supernovae and stellar winds ( heckman 2001 ) , gamma ray bursters ( efremov et al . 1998 , loeb & perna 1998 ) , and jet bubbles ( gopal - krishna & irwin 2000 ) to help explain the high energies . in the following section , we suggest that the exceptional heights achieved by the features in ngc 2613 may be as much a result of the environment into which the features emerge , as to the input source itself . the -307 km s@xmath7 feature ( fig . [ pv ] , advancing ) is remarkable in its well defined structure , in the very high latitude ( 22 kpc ) that it achieves , and in its sudden and dramatic widening and break up in velocity at a height of @xmath4 11 kpc . in individual slices ( see slices 8 and 9 , in particular ) , this velocity widening gives the feature a mushroom - like appearance and is reminiscent of buoyant gas rising through a higher density medium . a precedent for this kind of behaviour is the 350 pc galactic mushroom discovered in canadian galactic plane survey data and which has been interpreted in terms of buoyant outflow ( english et al . 2000 ) . given this similarity , we here consider whether buoyant outflow could explain the observed high latitude discrete hi features in ngc 2613 . we present the following as a feasibility study only to see whether the results provide a reasonable match to the data using realistic parameters . we consider a match to the -307 km s@xmath7 feature only , at this time , since it is the clearest case amongst the disk halo features in ngc 2613 ; however , if the model is correct , it must clearly apply to the other features as well . a similar development has been presented by avillez & mac low ( 2001 ) for smaller features like the galactic mushroom , but we here consider much larger scales ( many kpc ) , and also include the effects of drag . the scenario envisioned is one in which a hot , x - ray emitting corona already exists around the galaxy , possibly set up via venting through previous fountain or chimney activity . some event or events occur within the disk which are sufficiently energetic to produce blow - out . the hi is already entrained or swept up in some way by the time the outflow emerges into the halo . an initial velocity ( i.e. the velocity at blow - out ) could be present but is not included here . thus , the velocities achieved in the plume are a result only of buoyant forces . the attraction of this model is that , rather than requiring that all of the energy in the hi plume be supplied by the instigating event in the disk ( @xmath48 ergs , sect . [ 307feature ] ) , we require only enough energy to produce the blow - out condition ( e.g. @xmath49 ergs , tomisaka 1998 ) . the remaining energy is extracted from the pressure gradient in the hot coronal gas . ultimately , the galaxy s potential itself is providing the energy source . although we do not investigate the details of the entrainment or sweeping up of hi , we assume that the hot gas inside the plume carries the cool hi with it and that the density of the hi declines with _ z _ in a fashion similar to the hot buoyant plume material . in this feasibility study , we do not consider structure in the corona or outflow plume , other than the cylindrical geometry chosen for the plume , and also neglect the effects of shocks . the integrity of the hi in the presence of hot gas will be considered in the next section . the stellar / mass density distribution of the thin disk is described by : @xmath50 where @xmath51 is the scale height of the stellar disk , and @xmath52 is the stellar density at mid - plane . integration of poisson s equation : @xmath53 over the regime , @xmath54 , together with the above density distribution , results in a gravitational acceleration which is constant with @xmath1 and has a magnitude : g= 8g_*(0)z _ * the hot coronal gas ( subscripted , @xmath55 ) is taken to be isothermal at temperature , @xmath56 , with an exponential fall - off in both pressure and density , respectively : p_c(z)=p_c(z_*)e^-z / h _ c(z)=_c(z_*)e^-z / h where @xmath57 is the scale height . this hot coronal distribution starts at the top of the ( hi + stellar ) thin disk , i.e. at @xmath51 where the outflow just blows out of the thin layer . the scale height is given by h = kt_c/(gm_p ) where @xmath58 is boltzmann s constant , @xmath59 is the mean molecular weight and @xmath60 is the mass of the proton . we consider a pure hydrogen gas ( @xmath59 = 1 ) for simplicity . inside the plume ( subscripted , @xmath34 ) , we consider the gas to be adiabatic . the temperature gradient is : = ( 1 - 1 ) t_idp_i for a plume in pressure equilibrium with its surroundings , p_i(z)=p_c(z_*)e^-z / h where , again , we take the plume base to occur at @xmath51 . substituting eqn . and its derivative into eqn . yields : t_i(z)=t_i(z_*)e^((1-)zh ) and from eqn . , eqn . and the perfect gas law : _ i(z)=_i(z_*)e^ - ( z ) the equation of motion ( force per unit volume ) of the plume material is : _ i(z)dv = _ c(z ) g- _ i(z)g - c_d_c(z)v^2z - 2v the first term on the right hand side denotes the buoyancy force , the second term gives the weight of the plume material , the third term specifies the drag force against the upper surface ( assuming a case in which the effects of this force can propagate through the column ) where @xmath61 is the dimensionless drag coefficient , and the fourth term represents the viscous drag on the cylinder sides , where r is the cylinder radius and @xmath62 is the coefficient of viscosity ( @xmath63 ) . both @xmath61 and @xmath62 depend on the reynolds number : @xmath64 assuming a pure ionized hydrogen gas , where l is a scale length above which motion is damped by viscous effects and @xmath65 where @xmath66 is the coronal electron density . taking @xmath67 km s@xmath7 ( sect . [ 307feature ] ) and @xmath68 k , we find for size scales , @xmath69 , of order several kpc , @xmath70 is in the range @xmath71 . in this range of @xmath70 , @xmath72 for an incompressible fluid with cylindrical geometry . the viscosity coefficient includes both turbulent and molecular terms , i.e. @xmath73 , where @xmath74 = @xmath75 and @xmath76 , where @xmath77 is the critical reynolds number which designates the value of @xmath70 at which the flow becomes turbulent . @xmath78 is not known and depends on the geometry and nature of the interface , but typically has values between 1 and 100 . we can consider whether the drag force on the cylinder sides ( 4th term of eqn . ) is appreciable in comparison to the drag on the top of the cylinder ( 3rd term of eqn . ) . taking @xmath79 , the ratio of the 3rd to 4th drag terms becomes [ @xmath80 . since @xmath81 is of order @xmath1 , then for @xmath82 , even @xmath78 up to 100 ensures that the drag at the top will dominate over that at the sides . therefore the 4th term in eqn . is small and will be neglected . substituting @xmath83 , @xmath84 , and @xmath85 into eqn . and rearranging yields : = ( z _ * ) e^ -0.4zh gv- gv- ( z _ * ) e^-0.4zh vz this equation was integrated numerically for the input parameters shown in table 3 , yielding the curves of @xmath86 and @xmath87 shown in fig . [ vz ] and fig . [ zt ] , respectively . the stellar scale height , @xmath51 is set to 188 pc ( table 2 ) and we consider a coronal temperature , @xmath88 k ( models 1 to 4 ) which is comparable to that found from x - ray observations of ngc 253 ( pietsch et al . 2000 ) as well as a temperature which is a factor of 2 higher ( model 5 ) . since the midplane stellar density of 0.74 m@xmath3 pc@xmath45 is a value which has been scaled from galactic values , given the size and mass of ngc 2613 ( see sect . [ 307feature ] ) , we also consider a slightly lower value ( models 3 and 4 ) . the behaviour of the curves depends only on the density ratio at the base of the corona , @xmath89 , rather than the individual densities , but we can additionally fix the density at the bottom of the corona , @xmath90 to be equal to the hi density at the top of the thin disk at the position of the plume ( see table 2 ) , providing constraints upon the density within and outside of the plume . the peaks of the velocity curves ( fig . [ vz ] ) indicate where the acceleration of the plume material goes to zero ; we define the @xmath1 height at which this occurs to be @xmath91 . this position should correspond to the point at which the plume widens in velocity space , observationally determined to be @xmath4 11 kpc . models 1 and 2 ( fig . [ vz ] ) show the effect of changing the initial density ratio , such that the lower ratio ( model 2 ) results in a lower maximum velocity and a lower @xmath91 ( 7.4 kpc as compared to 11.9 kpc ) . a comparison of models 1 and 3 or of models 2 and 4 show the effect of decreasing the midplane mass density . this lowers the gravitational acceleration ( eqn . ) which lowers both the buoyancy and the weight of the plume material . it also increases the scale height ( eqn . ) which increases both the buoyancy and the drag . the net effect is higher @xmath91 at lower @xmath92 for the range of parameters given here . a comparison of models 1 and 5 shows the effect of increasing the coronal gas temperature . the higher temperature increases the scale height alone ( eqn . ) which , again , increases both buoyancy and drag . since drag is velocity dependent , the net effect is that the peak velocities achieved are lower for higher coronal temperatures . clearly , models 1 , 4 , and 5 provide an adequate match to the observed @xmath91 . model 1 , however , results in a mean plume density ( between @xmath51 and @xmath91 ) of only @xmath93 @xmath43 whereas the hi density alone is @xmath4 @xmath94 ( sect . [ 307feature ] ) , and is therefore not realistic . models 4 and 5 both result in reasonable fits to the known observational parameters , with model 5 slightly preferred because of its higher internal plume density ( higher than that of the hi alone ) and lower internal temperature . note that the mean internal temperature derived here ( @xmath95 k ) is comparable to the hot ( t = 1.2 kev = @xmath96 k ) component of the outflow in ngc 253 ( pietsch et al . the peak velocities derived here ( @xmath4 250 to 300 km s@xmath7 ) are lower than the gross estimate of 500 km s@xmath7 computed in sect . [ 307feature ] since we only model the feature up to the stall height ( 11 kpc ) rather than over its total length . the timescales of @xmath4 5 to 6 @xmath30 10@xmath39 yr ( fig . [ zt ] ) are in good agreement with the estimate found from the kinematical structure of the plume ( 4@xmath9710@xmath39 yrs ) . the mass outflow rate to the stall point is @xmath4 1 m@xmath3 yr@xmath7 . mass flow continuity requires that the plume of model 5 should increase in radius by a factor of 1.8 between _ z _ heights of 4.7 and 11.1 kpc . it is unlikely that the hi will be uniformly distributed at its mean density of @xmath4 @xmath98 @xmath43 but may exist in denser clouds or clumps whose sizes and distribution are not described by this simple model . in general , however , the situation will be not unlike that of those high velocity clouds ( hvcs ) which are in the hot halo of the milky way and the same issues regarding whether or not the clouds can remain neutral must be considered . photoionization of the hi by starlight should be negligible , considering the high galactic latitudes achieved . as pointed out by murali ( 2000 ) , the relevant interactions are hi - proton and hi - electron interactions for which the interaction cross - sections are in the range @xmath99 to @xmath100 @xmath101 for a relative velocity of order 200 km s@xmath7 as is appropriate here . the mean free path into the hi cloud is then l = 1/(@xmath102 ) = 0.3 to 3 pc or smaller if the hi is clumped . this is considerably smaller than the size scale of the plume and therefore these ionizing interactions should be minor . the most important interaction will be heating due to thermal conductivity leading to the evaporation of clouds . the classical mass evaporation rate , applicable to the case in which the mean free path is small in comparison to cloud size , is given , for approximately spherical clouds , by @xmath103 = 2.75 @xmath30 10@xmath104 t@xmath105 r@xmath106 @xmath107 g s@xmath7 , where t is the temperature of the external medium , r@xmath106 is 1/2 of the largest dimension of the cloud in parsecs , and @xmath107 is a parameter which measures the inhibition of heat flux due to the magnetic field and cloud geometry ( cowie & mckee 1979 , cowie et al . 1981 ) . we will assume @xmath107 = 1 ( no inhibition ) which maximizes the evaporation rate . using t = 2.5 @xmath30 10@xmath108 k and r = 5 @xmath30 10@xmath109 pc we find @xmath103 = 0.021 m@xmath110 yr@xmath7 ( to within factors of a few , given the different geometry ) . the timescale for complete evaporation of the 8@xmath9710@xmath39 m@xmath110 hi plume at a constant rate is then m/ @xmath103 = 4 @xmath30 10@xmath111 yr . since this is two orders of magnitude larger than the age of the plume , we expect that the plume will not evaporate over its lifetime . a caveat , however , is that since m/ @xmath103 @xmath112 r@xmath113 , if hi is distributed in many smaller clouds , then the evaporation time could approach the age of the plume . if the hi is indeed reaching such high values of _ z _ because of buoyancy , then hi disk - halo features probe the parameters of the halo gas , as suggested in sect . [ introduction ] . we have so far considered only whether buoyancy is feasible . there may be other dynamics at work as well ( for example , an initial velocity at blow - out or magnetic fields ) and the proposed hot corona is also unlikely to have the smooth distributions postulated here . nevertheless , in the context of the model , it is interesting to predict the x - ray luminosity of the corona in the vicinity of the plume . the results of table 3 show that it is feasible to transfer large masses to high galactic latitudes via buoyancy in a postulated x - ray corona . this drastically reduces the computed input energy requirements since it is no longer necessary to eject large masses to high altitudes . it is only necessary to achieve blow - out through the thin hi disk of ngc 2613 . the conditions required for blow - out have been investigated by a variety of authors ( see tomisaka 1998 , for example ) but energy requirements are typically of order 10@xmath127 ergs , rather than the 10@xmath5 ergs that would normally be required for the -307 km s@xmath7 feature . while the details of the interaction between the hi and hot outflowing gas are beyond the scope of this paper , it is important to ask whether there would originally have been sufficient hi in the disk from which the 8 @xmath30 10@xmath39 m@xmath3 in the -307 km s@xmath7 feature could have been swept up . assuming cylinderical geometry , a disk region of radius , 6.5 kpc ( sect . [ 307feature ] ) and using the modeled density and thickness of the disk ( table 2 ) , the available hi mass is @xmath4 3 @xmath30 10@xmath128 m@xmath3 suggesting that @xmath4 26% of the disk mass is swept up . this fraction would be higher for cone - like outflow . we should also consider whether the mass outflow rate is consistent with that of a galactic fountain . the estimated hi mass outflow rate ( sect . [ 307feature ] , sect . [ buoyancy ] ) is @xmath4 1 to 2 m@xmath3 yr@xmath7 . thus , the combined hi + hot gas outflow rate will be of order several m@xmath3 yr@xmath7 . collins et al . ( 2002 ) have estimated the mass flow rate for the diffuse ionized gas ( dig ) component in a galactic fountain , assuming a ballistic model of gas clouds . they find global values of @xmath129 = 22 @xmath130 m@xmath3 yr@xmath7 for ngc 891 and @xmath129 = 13 @xmath130 m@xmath3 yr@xmath7 for ngc 5775 , where @xmath131 is the filling factor . if these global values apply to a 20 kpc radius disk , taking @xmath131 = 0.2 and scaling to the disk area of the -370 km s@xmath7 feature yields mass outflow rates of 1.4 and 2.3 m@xmath3 yr@xmath7 which are comparable to what we estimate , above . it is not yet clear , however , whether these galactic fountain values can be directly scaled to the relevant regions of ngc 2613 . it may be that some additional source of pressure is still required , for example , magnetic fields in the form of a parker instability . if such fields continue to rise into the corona , the inclusion of this magnetic pressure would relax ( i.e. lower ) the density or temperature requirements internal to the plume ( table 3 ) .

numerous discrete disk - halo features are observed , however , achieving heights up to 28 kpc from mid - plane . we have instead investigated the feasibility of such a large feature being produced via buoyancy ( with drag ) within a hot , pre - existing x - ray corona . reasonable plume densities , temperatures , stall height ( 11 kpc ) , outflow velocities and ages can indeed be achieved in this way .

we combine new vla d array hi data of ngc 2613 with previous high resolution data to show new disk - halo features in this galaxy . the global hi distribution is modeled in detail using a technique which can disentangle the effects of inclination from scale height and can also solve for the average volume density distribution in and perpendicular to the disk . the model shows that the galaxy s inclination is on the low end of the range given by chaves & irwin ( 2001 ) and that the hi disk is thin ( = 188 pc ) , showing no evidence for halo . numerous discrete disk - halo features are observed , however , achieving heights up to 28 kpc from mid - plane . one prominent feature in particular , of mass , m and height , 22 kpc , is seen on the advancing side of the galaxy at a projected galactocentric radius of 15.5 kpc . if this feature achieves such high latitudes because of events in the disk alone , then input energies of order 10 ergs are required . we have instead investigated the feasibility of such a large feature being produced via buoyancy ( with drag ) within a hot , pre - existing x - ray corona . reasonable plume densities , temperatures , stall height ( 11 kpc ) , outflow velocities and ages can indeed be achieved in this way . the advantage of this scenario is that the input energy need only be sufficient to produce blow - out , a condition which requires a reduction of three orders of magnitude in energy . if this is correct , there should be an observable x - ray halo around ngc 2613 . # 1 # 1([eq:#1 ] )

astro-ph0212072

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new vla d array data of ngc 2613 have been combined with previous higher resolution observations ( chaves & irwin 2001 ) to show a more extensive hi distribution than previously observed . the galaxy is now seen to have a tidal tail on its eastern side due to an interaction with its companion , eso 495-g017 , to the north - west . the three - dimensional hi distribution in ngc 2613 has been modeled following irwin & seaquist ( 1991 ) and irwin ( 1994 ) , a method which allows the volume density distribution to be determined as well as the scale height and inclination to be disentangled . we find that the inclination of the galaxy ( 79@xmath38 ) is on the low end of the range given in chaves & irwin ( 2001 ) and the model now shows that there is no hi halo in ngc 2613 . rather , the global hi distribution is well fit by a thin disk of exponential scale height , @xmath132 = 188 pc . the use of such a model is very important in drawing conclusions about the presence or absence of a global halo in a galaxy of this inclination . previous reports of a lagging halo from pv slices alone can largely be attributed to projection against the background disk . while there is no significant global hi halo in ngc 2613 , there are more discrete disk - halo hi features than previously detected and these hi features achieve extremely high latitudes . even though a tidal interaction is occurring , we suggest that most of the discrete kpc - scale features have been produced internally rather than from impacting clouds , although we do not rule out the possiblity of the companion galaxy having some indirect effect ( e.g. triggering instabilities ) . the presence of many discrete features may be related to the fact that the global hi disk is thin , favouring blow - out . the observed _ z _ heights are quite remarkable ( e.g. up to 28 kpc ) . the -307 km s@xmath7 feature , in particular , below the plane on the advancing side , reaching 22 kpc in @xmath133 height and of total mass , ( 8 @xmath32 2 ) @xmath30 10@xmath39 m@xmath3 , is very obvious and well - defined in pv space . its center is likely close to its projected radius of 15.5 kpc and it extends over a large ( @xmath32 7 kpc radius ) projected galactocentric radius . if this feature has achieved its @xmath133 height as a result of internal processes , then extremely large energies are required , @xmath4 10@xmath5 ergs . given the very high input energies required for the -307 km s@xmath7 feature , its resemblance to smaller buoyant features ( cf . the galactic mushroom , english et al . 2000 ) , and the fact that x - ray halos are being found around an increasing number of star forming spiral galaxies , we have carried out a feasibility study as to whether this feature can be interpreted as an adiabatic buoyant plume . the observed hi would be carried out by a hot , low density outflowing gas and , after having achieved blowout , would rise through a hot pre - existing x - ray corona . a reasonable example ( model 5 ) , has a mean plume temperature and density of @xmath134 k and 5.5 @xmath30 10@xmath45 @xmath43 rising into a hot isothermal corona of temperature and mean density , @xmath135 k and 0.035 @xmath43 , respectively . these conditions produce a stall height of 11 kpc which is where the observed plume widens in velocity and position space . the coronal density at the stall height is 2.8 @xmath30 10@xmath45 @xmath43 . the maximum outflow velocity in this model is 290 km s@xmath7 and it reaches the stall height in 5.4@xmath9710@xmath39 yrs . this model shows that , even with buoyancy alone ( and there may be additional sources of pressure such as magnetic fields ) , hi can reach these extreme _ z _ heights . the advantage of such a model is that the energy requirements from the initial event are drastically reduced to being only what is required for blowout , a reduction of several orders of magnitude . the energy is largely extracted from the gravitational potential of the galaxy rather than the initial event within the disk . the behaviour of the plume should sample the parameters of the x - ray corona . the predicted x - ray luminosity suggests that the corona should be observable at heights below the stall height although we expect that the distribution of x - ray emission may not be as smooth as assumed by the model . ji wishes to thank the natural sciences and engineering research council of canada for a research grant . we are grateful to dr . r. n. henriksen for fruitful and envigorating discussions . thanks also to mustapha ishak for assistance with maple . benjamin , r. 2002 , in seeing through the dust " , asp conf series , ed . a. r. taylor , t. l. landecker , & t. willis bottema r. 1989 , , 225 , 358 bregman j. n. 1980 , , 236 , 577 chaves t. a. , & irwin j. a. 2001 , , 557 , 646 ( paper i ) collins j. a. , rand r. j. , duric n. , & walterbos r. a. m. 2000 , , 536 , 645 collins j. a. , benjamin r. a. , & rand r. j. 2002 , in press cowie l. l. , & mckee c. f. 1977 , , 211 , 135 cowie l. l. , mckee c. f. , & ostriker j. p. 1981 , , 247 , 908 de avillez m. a. , & berry d. l. 2001 , , 328 , 708 duric n. , irwin j. , & bloemen h. 1998 , , 331 , 428 efremov y. n. , elmegreen b. g. , & hodge p. w. 1998 , , 501 , l163 english j. , taylor a. r. , mashchenko s. y. , irwin j. a. , basu s. , & johnstone d. 2000 , , 533 , l25 fraternali f. , oosterloo t. , sancisi r. , & van moorsel g. 2001 , astro - ph 0110369 gopal - krishna , & irwin j. a. 2000 , , 361 , 888 heckman t. 2001 , in gas and galaxy evolution , asp conf . series , vol . 240 , ( san francisco : asp ) , ed . j. e. hibbard , m. p. rupen , & j. h. van gorkom , 345 heiles c. 1979 , , 229 , 533 heiles c. 1984 , , 55,585 irwin j. a. 1994 , , 429 , 618 irwin j. a. , english j. , & sorathia b. 1999 , , 117 , 2102 irwin j. a. & seaquist e. r. 1991 , , 371 , 111 , erratum , 415,415 king d. l. , & irwin j. a. 1997 , newa , 2 , 251 lang k. 1999 , astrophysical formulae ( springer : berlin ) lee s .- w , & irwin j. a. 1997 , , 490 , 247 lee s .- w . , irwin j. a. , dettmar r .- j . , cunningham c. t. , golla g. , & wang q. d. 2001 , , 377 , 759 loeb a. , & perna r. 1998 , , 503 , l135 lotz w. 1967 , , 14 , 207 murali c. 2000 , , 529 , l81 olling r. , & merrifield m. r. 2000 , , 311 , 361 pietsch w. , vogler a. , klein u. , & zinnecker h. 2000 , , 360 , 24 rand r. j. 2000 , , 494 , l45 santilln a. , franco j. , martos m. , & kim j. 1999 , , 515 , 657 schaap w. e. , sancisi r. , & swaters r. a. 2000 , , 356 , l49 sofue y. & rubin v. 2001 , , 39 , 137 swaters r. a. , sancisi r. , & van der hulst j. m. 1997 , , 491 , 140 tomisaka k. 1998 , , 298 , 797 tllmann r. , dettmar r .- j . , soida m. , urbanik m. , & rossa j. 2000 , , 364 , l36 lcc no . velocity channels & 63 & 63 + velocity resolution ( km s@xmath7 ) & 20.84 & 20.84 + total bandwidth ( mhz ) & 6.25 & 6.25 + synthesized beam & & + major @xmath30 minor axis ( @xmath9 @xmath30 @xmath9 ) @ pa ( @xmath38 ) & 96.5 @xmath30 42.9 @ -21.6 & 47.1 @xmath30 32.1 @ -8.2 + rms noise / channel ( mjy beam@xmath7 ) & 0.93 & 0.45 + rms noise / channel ( k ) & 0.14 & 0.18 + ra ( j2000 ) ( h m s ) & 08 33 22.8 @xmath32 0.3 + dec ( j2000 ) ( @xmath38 @xmath136 @xmath9 ) & -22 58 29 @xmath137 + pa ( @xmath38 ) & 114.2 @xmath138 + i ( @xmath38 ) & 79.2 @xmath139 + v@xmath140 ( km s@xmath7 ) & 1663 @xmath141 + v@xmath142 ( km s@xmath7 ) & 304 @xmath32 4 + r@xmath142 ( @xmath9 ) & 112 @xmath143 + m & 0.51 @xmath144 + @xmath29 ( km s@xmath7 ) & 17 @xmath32 5 + n@xmath145 ( @xmath43)@xmath146 & 0.43 @xmath147 + r@xmath145 ( @xmath9 ) & 140 @xmath32 5 + d@xmath148 ( @xmath9 ) & 95 @xmath149 + d@xmath150 ( @xmath9 ) & 81 @xmath151 + h@xmath152 ( @xmath9 ) & 1.5 @xmath153 + 5 + @xmath56 ( @xmath154 k ) & 2.5 & 2.5 & 2.5 & 2.5 & 5.0 + @xmath52 ( @xmath155 ) & 0.74 & 0.74 & 0.50 & 0.50 & 0.74 + h@xmath156 & 1.4 & 1.4 & 2.1 & 2.1 & 2.8 + @xmath89 & 100 & 20 & 100 & 20 & 10 + @xmath157 ( @xmath43 ) & 0.15 & 0.15 & 0.15 & 0.15 & 0.15 + @xmath158 ( @xmath43 ) & 0.0015 & 0.0075 & 0.0015 & 0.0075 & 0.015 + @xmath91 ( kpc ) & 11.9 & 7.4 & 17.5 & 11.0 & 11.1 + @xmath159 ( @xmath43 ) & 0.015 & 0.025 & 0.016 & 0.026 & 0.035 + @xmath160 ( @xmath98 @xmath43 ) & 0.031 & 0.76 & 0.036 & 0.80 & 2.8 + @xmath161 ( @xmath98 @xmath43 ) & 0.27 & 2.1 & 0.28 & 2.2 & 5.5 + @xmath162 ( @xmath163 k ) & 6.8 & 2.0 & 6.9 & 2.0 & 1.2 +

we combine new vla d array hi data of ngc 2613 with previous high resolution data to show new disk - halo features in this galaxy . the model shows that the galaxy s inclination is on the low end of the range given by chaves & irwin ( 2001 ) and that the hi disk is thin ( = 188 pc ) , showing no evidence for halo . if this feature achieves such high latitudes because of events in the disk alone , then input energies of order 10 ergs are required . the advantage of this scenario is that the input energy need only be sufficient to produce blow - out , a condition which requires a reduction of three orders of magnitude in energy . # 1 # 1([eq:#1 ] )

we combine new vla d array hi data of ngc 2613 with previous high resolution data to show new disk - halo features in this galaxy . the global hi distribution is modeled in detail using a technique which can disentangle the effects of inclination from scale height and can also solve for the average volume density distribution in and perpendicular to the disk . the model shows that the galaxy s inclination is on the low end of the range given by chaves & irwin ( 2001 ) and that the hi disk is thin ( = 188 pc ) , showing no evidence for halo . numerous discrete disk - halo features are observed , however , achieving heights up to 28 kpc from mid - plane . one prominent feature in particular , of mass , m and height , 22 kpc , is seen on the advancing side of the galaxy at a projected galactocentric radius of 15.5 kpc . if this feature achieves such high latitudes because of events in the disk alone , then input energies of order 10 ergs are required . we have instead investigated the feasibility of such a large feature being produced via buoyancy ( with drag ) within a hot , pre - existing x - ray corona . reasonable plume densities , temperatures , stall height ( 11 kpc ) , outflow velocities and ages can indeed be achieved in this way . the advantage of this scenario is that the input energy need only be sufficient to produce blow - out , a condition which requires a reduction of three orders of magnitude in energy . if this is correct , there should be an observable x - ray halo around ngc 2613 . # 1 # 1([eq:#1 ] )

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active sterile neutrino oscillations in the early universe can generate large differences in the number densities of relic neutrinos and antineutrinos @xcite . ) and hence unimportant for all parameters of interest . this contrasts starkly with the later studies @xcite . ] the resulting `` lepton asymmetries '' have important phenomenological ramifications : the suppression of sterile neutrino production because of large matter effects @xcite , a modification to primordial helium synthesis if a sufficiently large asymmetry is created for the electron neutrino prior to or during the big bang nucleosynthesis epoch @xcite , with also the possibility to describe inhomogeneous bbn scenarios @xcite . we focus in this comment on two flavour active sterile oscillations . furthermore we restrict our discussion to that region of oscillation parameter space which induces large lepton asymmetry creation well before neutrino decoupling at @xmath4 mev . an important issue is the `` final value of the asymmetry '' , that is , the steady state value attained at the end of the dynamical evolution . the asymmetry is conveniently defined to be @xmath5 where @xmath6 is the number density of species @xmath7 , and @xmath8 is one of @xmath9 , @xmath10 or @xmath11 . in ref . @xcite it is argued that the final value for @xmath12 is of order @xmath0 for typical parameter choices . this claim is recently disputed by a. d. dolgov , s. h. hansen , s. pastor and d. v. semikoz ( dhps ) in ref . @xcite , who conclude that although the asymmetry can rise by five orders of magnitude above the baryon asymmetry level of @xmath13 , it can not reach the @xmath0 range found in ref . . the purpose of this comment is to explain the flaws in the dhps analysis . the basic reason turns out to be very simple : dhps neglect the pure mikheyev smirnov wolfenstein ( msw ) effect @xcite . as explained in ref.@xcite , pure msw transitions dominate lepton asymmetry evolution at lower temperatures , after the period of initial explosive @xmath12 growth . the approximate evolution equations derived by dhps have sufficient validity to describe the onset of asymmetry growth , but they are not a good approximation after the explosive amplification phase ends . their oversight of the role played by msw transitions also leads them to exaggerate the importance of a `` back - reaction term '' [ @xmath14 in eq . ( 51 ) of dhps ] . as we will explain , when this term is large , the msw effect is also dominant so that their eq.(51 ) is no longer valid . the size of the back - reaction is thus a moot point . we now clarify the structure of our paper , while simultaneously providing a summary of the main points to be made . these remarks will be of interest to those readers who want to know the gist of our argument but not the technical details . * section [ sec2 ] contains a quick survey of the quantum kinetic equations ( qkes ) governing active sterile neutrino evolution @xcite . these `` almost exact '' equations are not at issue ; the debate is on their correct solutions . the qkes simultaneously incorporate coherent matter - affected evolution , decoherence due to non - forward neutrino scattering , and repopulation of active neutrino distribution functions from the background plasma . * section [ sec3 ] reviews how the essential physics encoded in the qkes can be revealed . a fundamental issue is collision - dominated versus coherent matter - affected oscillation - driven amplification . the former pertains to conditions prior to and during the onset of asymmetry growth , in which case the evolution is well described by the static approximation of refs . @xcite , and by the closely related adiabatic limit approximation developed in refs.@xcite . equation ( 51 ) of dhps is identical to the leading order term of the static approximation if the @xmath14 term is neglected , and is thus able to correctly predict the existence of a critical temperature @xcite at which asymmetry evolution enters a brief explosive growth phase . subsequent evolution , however , ceases to be collision dominated . in addition , a significant asymmetry , typically @xmath15 when explosive growth stops , now exists in the plasma ; the antisymmetric wolfenstein term in the matter potential is sufficiently large to modify the neutrino and antineutrino oscillation patterns in noticeably dissimilar ways . a vitally important consequence of this is the separation of the neutrino and antineutrino msw resonance momenta @xcite . depending on the sign of @xmath12 , one resonance momentum remains in the body of the ( almost ) fermi dirac distribution , while the other is rapidly relegated to the tail . figures 1b and 2b depict this phenomenon for two different oscillation parameter choices . the separation means that the msw effect , now dominant over the collision mechanism , has very asymmetric consequences for neutrinos and antineutrinos @xcite . for @xmath16 , the resonance in the body is able to efficiently convert @xmath17 s into @xmath18 s , while the other is impotent in the scarcely populated tail . this important physics was not understood by dhps . indeed , when collisions are absent , neutrino density matrix evolution is driven only by matter - affected propagation ( and the expansion of the universe of course ) . equation ( 51 ) of dhps _ does not reduce _ to the coherent matter - affected evolution equations , so it does not contain the pure msw effect @xcite . the static approximation , which yields @xmath19 for zero collision rate , also neglects the msw effect . thus these equations are valid only in the collision dominated regime . figures 1a and 2a illustrate our arguments . the solid and dash - dotted lines represent respectively numerical solutions to the exact qkes and the static approximation equations . clearly , the latter describes the explosive growth phase excellently , but underestimates the subsequent growth of @xmath12 . at steady state , the discrepancy is significant . the dashed curve reveals the physics behind the qkes in a very amusing way . the generating code compares the decoherence or interaction length @xmath20 with the matter - affected oscillation length @xmath21 at every time step , with both lengths evaluated at resonance . if @xmath22 is less than one , the static approximation equations are used to forward the system in time . for @xmath23 , pure adiabatic msw evolution is employed . the quantity @xmath24 therefore measures the relative importance of collisions and msw transitions . in the event @xmath25 , the msw effect is damped since collisions seriously disrupt the coherence the opposite case has @xmath26 , implying that collisions are relatively negligible . the dashed curve in fig . 1a agrees with the qkes in both the high and low @xmath27 regimes extremely well . there is a slight discrepancy immediately after explosive growth , since neither effect dominates at this stage the very visible bump in fig . 2a is an artifact of this `` either / or '' approximation in this intermediate regime . * the dhps equations underestimate the asymmetry after explosive growth even more seriously than does the static approximation , because of their @xmath14 back - reaction term . section [ sec4 ] compares eq . ( 51 ) of dhps with the static approximation . as already noted , and acknowledged by dhps , these equations agree to leading order . we show , however , that the @xmath14 term is large only when the msw effect has taken over as the dominant driver of asymmetry evolution . since dhps eq . ( 51 ) and the static approximation both neglect this effect , they should not be used when msw transitions are important . ( we will also identify where the msw effect is unwittingly removed in their derivation . ) furthermore , the expansion parameter adopted by dhps in their approximation scheme is not in fact the correct choice at lower temperatures when there is a significant asymmetry in the plasma . this misunderstanding led dhps to erroneously claim validity for their equations at later stages in the evolution , especially the role of the back - reaction term which is but another casualty following from a faulty expansion parameter . in fact , the dramatic termination of the asymmetry growth due to this bogus term has its origin in the expression @xmath28 . the left hand side corresponds to the static approximation ( with a minor discrepancy ) , while the right hand side denotes the dhps result , with @xmath29 identified as the @xmath14 term . the artificially strong cut - off arises because the right hand side is used even when @xmath30 . * section [ sec5 ] contains comments on other less important errors and some misleading statements made by dhps , while sec.[sec6 ] is a conclusion . * the appendix provides a translation of dhps s notation into a more common _ lingua franca _ used by other authors . the rather obscure nomenclature of dhps proves to be the biggest obstacle to understanding their analysis .

we comment on the recent paper by a. d. dolgov , s. h. hansen , s. pastor and d. v. semikoz ( dhps ) [ astropart . phys . smirnov the msw effect is the dominant asymmetry amplifier . neither the static nor the dhps approach contains this important physics . however , for this regime the effective potential they employed is not valid . _

we comment on the recent paper by a. d. dolgov , s. h. hansen , s. pastor and d. v. semikoz ( dhps ) [ astropart . phys . * 14 * , 79 ( 2000 ) ] on the generation of neutrino asymmetries from active sterile neutrino oscillations . we demonstrate that the approximate asymmetry evolution equation obtained therein is an expansion , up to a minor discrepancy , of the well - established static approximation equation , valid only when the supposedly new higher order correction term is small . in the regime where this so - called `` back - reaction '' term is large and artificially terminates the asymmetry growth , their evolution equation ceases to be a faithful approximation to the quantum kinetic equations ( qkes ) simply because pure mikheyev smirnov wolfenstein ( msw ) transitions have been neglected . at low temperatures the msw effect is the dominant asymmetry amplifier . neither the static nor the dhps approach contains this important physics . therefore we conclude that the dhps results have sufficient veracity at the onset of explosive asymmetry generation , but are invalid in the ensuing low temperature epoch where msw conversions are able to enhance the asymmetry to values of order . dhps do claim to find a significant final asymmetry for very large values . however , for this regime the effective potential they employed is not valid . _ school of physics + research centre for high energy physics + the university of melbourne vic 3010 + australia + istituto nazionale di fisica nucleare ( infn ) + ( dibari , foot , r.volkas , [email protected])_

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in sec . [ sec4a ] we `` deconstruct '' the dhps equations , while we devote sec . [ fatal ] to pinpointing where in their derivation the msw effect is unknowingly neglected . for comparison with the static approximation , we rewrite dhps s evolution equations in the notation of this comment using the `` conversion relations '' given in the appendix . equation ( 42 ) of dhps describes sterile neutrino production . its translation is @xmath228 . \label{dhps42}\ ] ] comparing this with eq . ( [ eq : zpiu ] ) , one sees that it agrees with the latter s leading term , when ( i ) chemical potentials are neglected and thus @xmath229 , and ( ii ) the replacement @xmath230 is made . the neutrino asymmetry evolution equation [ eq . ( 51 ) of dhps ] is equivalently @xmath231 dy . \label{dhps51}\ ] ] the first term on the right hand side is again connected to the leading @xmath192 term of the static approximation [ eq.([eq : abc ] ) ] , with the substitution eq . ( [ substitution ] ) . the @xmath199 and @xmath200 terms are absent as expected , since dhps neglect chemical potentials in the @xmath31 and @xmath17 distribution functions . the second term in the square brackets is dhps s back - reaction term @xmath14 . this supposedly new term has , in fact , an interesting interpretation . consider the function @xmath232 . one can perform the expansion @xmath233 \nonumber \\ & & \quad+ { \cal o}\left({s^2\over d^2+(c - b+a)^2},{s^2\over d^2+(c - b - a)^2}\right)^2 . \label{expansion}\end{aligned}\ ] ] thus the back - reaction term is but the first order correction in an expansion of @xmath232 . but we have already discussed in sec . [ sec3b ] this sort of expansion , in the context of the @xmath191 term in the denominator of the eigenvalue @xmath181 , where the _ full decoupling _ and the _ instantaneous repopulation _ limits yielded @xmath234 and @xmath235 respectively . we argued that this distinction was of no practical importance , because the numerical difference between these two cases was only significant when the collision dominance assumption used in their derivation broke down . in a nutshell : ( i ) the first order terms are only large when the msw effect is important . ( ii ) when the msw effect is important , equations such as obtained from the static approximation , and dhps ( 51 ) , are no longer a good approximation to the qkes . let us now evaluate eq . ( [ expansion ] ) for the antineutrino ( @xmath236 ) resonance : @xmath237.\ ] ] when the asymmetry grows at the critical temperature @xmath141 , the resonance condition passes from a regime in which @xmath238 when @xmath91 is negligible , to @xmath239 . in this second regime the term @xmath240 and the last expression becomes simply , @xmath241 .\ ] ] so we see that the expansion parameter on resonance is @xmath242 , i.e. , the square of the ratio between the local interaction and matter - affected oscillation lengths @xmath243 . as explained earlier , a small @xmath244 denotes that collisions are frequent enough to interrupt coherent evolution and thus to prevent the msw effect , while a large @xmath245 means msw conversion can occur as the collisional mechanism switches off . of course this transition is gradual . moreover , using the equality @xmath246 , one can also see , using eqs . ( [ eq : b ] ) and ( [ eq : yres ] ) , that @xmath247 where @xmath125 is the resonant momentum when the asymmetry is negligible . recall that @xmath125 is very small at high @xmath27 , but grows as the temperature decreases , reaching @xmath248 at @xmath141 . the quantity @xmath249 is the general resonance momentum , which attains a minimum value depending on @xmath1 ( smaller for low @xmath1 ) when the asymmetry grows ( see figs . 1b and 2b ) . it is thus clear from eq . ( [ whatever ] ) that if one continues to use @xmath14 in the evolution equation when the asymmetry is large and @xmath250 , the rise of the asymmetry will be artificially made slower . from that moment its evolution will be approximately @xmath251 and from the equations eq.([eq : lt ] ) and eq.([eq : yres ] ) this implies that @xmath252 , a behaviour observed by dhps in their results . in this way the solution can grow just one order of magnitude since the onset of the instability . in summary , the back - reaction term @xmath14 is generated by an expansion in @xmath253 , and not simply @xmath254 as dhps believe . _ their evolution equation is therefore invalid for temperatures at which @xmath255 . _ as emphasised before @xcite , both the static approximation and the dhps equations belong to a family of collision dominated idealisations which require @xmath256 ( plus other conditions ) for their validity . when @xmath257 , the msw effect is missed in both cases . clearly dhps did not properly appreciate the constraints on the real expansion parameter adopted in their derivation , and hence trusted their equations validity for all temperatures . for very large @xmath1 , dhps do actually observe a large final value . this is because @xmath258 where @xmath259 is the freezing temperature corresponding to a resonant momentum ( of antineutrinos if @xmath91 is positive , of neutrinos if @xmath91 is negative ) well in the tail of the distribution ( @xmath260 ) and is very weakly dependent on the exact choice of @xmath261 . thus for @xmath262 they find @xmath263 , and are therefore still able to state that active sterile neutrino oscillations can yield large asymmetries . _ however , this high @xmath1 asymmetry rise is spurious . for @xmath264 , the effective potential as given by eq . ( [ eq : effp ] ) is meaningless , since the critical temperature is now much larger than @xmath265 mev . the conditions of the plasma are different , especially at temperatures above the quark hadron phase transition . the dynamics of neutrino oscillations in this regime is actually an open problem . _ in extracting their simplified evolution equations from the qkes , dhps make use of two small expansion parameters : ( i ) @xmath266 , and ( ii ) @xmath267 . we now examine their merits . \1 . _ small @xmath268 expansion_. the derivation begins with an attempt to solve analytically two out of a system of eight coupled differential equations , namely , eqs . ( 27 ) and ( 28 ) in dhps : @xmath269 where prime denotes differentiation with respect to @xmath11 . these expressions are equivalent to @xmath270 in our language , with @xmath271 . solutions to eq.([lhdes ] ) are generically oscillatory . to this end , dhps devise an oscillation averaging procedure that consists of setting all terms containing @xmath268 ( i.e. , the @xmath11-derivatives ) to zero , from which they obtain what are actually `` steady state '' solutions to the variables @xmath272 and @xmath273 . we now explain why this method is flawed . firstly , the variable @xmath274 enters the big picture as the `` driving force '' for @xmath157 production @xmath275 [ see eqs . ( [ formaldldt ] ) and ( [ bingo ] ) ] . in the context of solving differential equations , one may ignore contributions from oscillatory components in the driving force @xmath274 _ only _ if the oscillation amplitude is much smaller than the size of its steady `` main term '' . otherwise , oscillations propel the evolution , producing a marked change in the _ integrated _ variable @xmath276 ( i.e. , the msw effect ) when the oscillation frequency is a minimum at resonance , in the same way that @xmath277 . in their derivation , dhps do not consider at all the magnitudes of these oscillatory terms , and discard them on the basis that they impair computational efficiency , when in fact even the adiabatic solution to @xmath274 ( and @xmath278 ) is purely oscillatory at resonance in the post explosive growth environment where a relatively large @xmath279 ratio prevails @xcite . _ their equations can not describe the sharp change in @xmath276 at the low temperature resonance because the dominant and strongly frequency - dependent term responsible for the msw effect has been removed . _ indeed , one can not know the sizes of the steady and oscillatory components in @xmath274 or @xmath273 without some input of the initial conditions ; to eliminate dynamical variables in the equation s differential form is premature and may be dangerous . moreover , the process of artificially factoring out a large quantity by redefining the integration variable and then exploiting its inverse as an expansion parameter is not in fact a well - justified manuvre to obtaining steady state solutions . to see this , one needs only to consider the case of exponential growth / decay , @xmath280 , where the approximation @xmath281 and thus the conclusion @xmath282 crumble for a positive @xmath192 . fortunately , steady state solutions to @xmath272 and @xmath273 are indeed valid for some oscillation parameters @xmath283 when collisions are frequent enough to quickly damp the oscillations , even at resonance , provided that the adiabatic condition is also satisfied @xcite . thus dhps have managed to reproduce results ( albeit from a somewhat dubious procedure ) that are consistent with the static approximation , in the manner that the latter may also be derived in the @xmath284 limit by setting @xmath285 . but , like the static approximation , their equations do not apply to the low temperature region after explosive growth where steady state solutions do not hold at resonance . _ small @xmath267 expansion_. this approximation is used on two occasions , first as a pretext for disregarding the variable @xmath286 ( or @xmath287 ) in eq . ( [ lhdes ] ) [ eq . ( 28 ) in dhps ] , and then in evaluating the eigenvalues and other properties of the matrix @xmath288 in their eq . ( 33 ) . the first exploit is precarious from the perspective of solving differential equations , since @xmath289 ( and therefore @xmath290 ) are _ interdependent dynamical variables _ and one has no prior knowledge on their sizes . indeed , it is far more seemly to assume _ a priori _ the @xmath286 term to be of some substance at resonance when the msw effect kicks in at low temperatures , given that only antineutrinos ( for @xmath128 ) can be converted into sterile states in this epoch by the said mechanism . the neglect of this term is also related to dhps s observation of the asymmetry reaching arbitrarily small values prior to explosive growth , to be discussed later in sec . [ sec5 ] . in the second instance , the expansion procedure employed to diagonalise the matrix @xmath291 where @xmath292 , @xmath293 , @xmath294 and @xmath295 , is not itself at flaw . however , it does have its own limitations which dhps did not notice . equation ( [ matrix ] ) suggests that the term @xmath296 ( or @xmath297 ) should be compared with @xmath298 , @xmath299 , @xmath300 and @xmath301 if it is to be treated as a perturbation . dhps consider only @xmath297 and @xmath302 , presumably because @xmath303 at resonance , which they define as occurring at @xmath304 such that @xmath305 ( or @xmath306 ) . however , this resonance condition assumes a small asymmetry , i.e. , @xmath307 . _ thus it is able to describe the high temperature regime where the term @xmath94 dominates , but not after a sizeable asymmetry has been created , where the now separated neutrino and antineutrino resonances occur at any two @xmath11 s other than @xmath308 . the ratio @xmath254 is meaningless in this second regime . _ lastly , it must be stressed that msw flavour conversion is _ not _ a perturbative effect . _ small @xmath267 expansion equals no msw effect _ , in the spirit that treating the off - diagonal @xmath267 in the schrdinger equation for a two - flavour collisionless system as a perturbation will not yield the correct behaviour at resonance .

we demonstrate that the approximate asymmetry evolution equation obtained therein is an expansion , up to a minor discrepancy , of the well - established static approximation equation , valid only when the supposedly new higher order correction term is small . in the regime where this so - called `` back - reaction '' term is large and artificially terminates the asymmetry growth , their evolution equation ceases to be a faithful approximation to the quantum kinetic equations ( qkes ) simply because pure mikheyev

we comment on the recent paper by a. d. dolgov , s. h. hansen , s. pastor and d. v. semikoz ( dhps ) [ astropart . phys . * 14 * , 79 ( 2000 ) ] on the generation of neutrino asymmetries from active sterile neutrino oscillations . we demonstrate that the approximate asymmetry evolution equation obtained therein is an expansion , up to a minor discrepancy , of the well - established static approximation equation , valid only when the supposedly new higher order correction term is small . in the regime where this so - called `` back - reaction '' term is large and artificially terminates the asymmetry growth , their evolution equation ceases to be a faithful approximation to the quantum kinetic equations ( qkes ) simply because pure mikheyev smirnov wolfenstein ( msw ) transitions have been neglected . at low temperatures the msw effect is the dominant asymmetry amplifier . neither the static nor the dhps approach contains this important physics . therefore we conclude that the dhps results have sufficient veracity at the onset of explosive asymmetry generation , but are invalid in the ensuing low temperature epoch where msw conversions are able to enhance the asymmetry to values of order . dhps do claim to find a significant final asymmetry for very large values . however , for this regime the effective potential they employed is not valid . _ school of physics + research centre for high energy physics + the university of melbourne vic 3010 + australia + istituto nazionale di fisica nucleare ( infn ) + ( dibari , foot , r.volkas , [email protected])_

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one of the oldest challenges in galaxy formation theory is to explain its overall inefficiency , specifically how to prevent too much gas from cooling onto the central galaxies of dark matter halos and forming stars , resulting in higher - mass galaxies at a given number density than observed ( e.g. * ? ? ? a second , related challenge is to explain the bimodality in galactic properties , where massive galaxies are typically red , elliptical and have very little star formation , while lower mass objects are blue , disky , star - forming galaxies ( e.g. @xcite ) . early work on these problems emphasised the need for efficient feedback in low mass galaxies , to stop very early star formation and to be able to match the low mass end of the galaxy mass function @xcite . the mechanism most often invoked at the low - mass end is supernova - driven winds @xcite . these winds not only suppress galaxy masses in low - mass halos , but are also necessary to enrich the intergalactic medium with metals as observed . there has been substantial progress in understanding the basic scaling relations required for supernova - driven outflows : for example , the models most successful in explaining the igm metal distribution rely on scaling relations appropriate for momentum - driven winds @xcite . however , it is not yet clear under which conditions these winds operate in general . if the feedback at low masses is a supernova - driven wind , it is more likely to be efficient at high redshifts , when galaxies had star formation rates that are an order of magnitude or more higher than they are today . at lower redshifts , efficient feedback is also needed in low mass objects , but winds are less likely to be sufficient to remove gas from galaxies @xcite owing to their lower star formation rates . much of the recent focus has been on the properties of massive galaxies . some recent semi - analytic models ( sams ) of galaxy formation ( e.g. @xcite ) are able to reproduce the global properties of massive ellipticals , which appeared too blue and too massive in earlier theoretical models . all these models suppress star formation in massive halos by means of feedback from active galactic nuclei ( agn ) . in several models , supermassive black holes accreting gas that has cooled from the surrounding hot halo atmosphere provide strong feedback to the hot halo gas , which prevents or slows the gas cooling . this type of feedback from agn is often called `` radio mode '' feedback , since it is believed to operate in massive radio galaxies . however , such feedback can not directly change the galaxy morphology , which is believed to be changed by major mergers @xcite , i.e. mergers of galaxies with similar masses . during major mergers the rapid inflow of gas into the central parts can feed the black hole in the galactic centre , which in turn can ionise , heat , and expel the surrounding cold gas . in idealised simulations of such major mergers , this `` quasar mode '' feedback was also successful in preventing the accretion of gas after the merger @xcite . however , these simulations are typically evolved outside of their cosmological environment and do not model the subsequent evolution of halos , so it is still unclear how long this `` quasar mode '' feedback effect lasts before gas can fall in from the intergalactic medium and once again start cooling onto the galaxy . in our previous work ( * k05 , hereafter ) and in the first paper in this series ( * ? ? ? * k09 , hereafter ) , we followed the buildup of galaxies and halo gas in a @xmath1cdm universe ( inflationary cold dark matter with a cosmological constant ) , using hydrodynamic simulations _ without _ any of the strong feedback processes just mentioned . we showed that it is the smooth accretion of intergalactic gas that dominates the global galactic gas supply , not accretion by merging , and that it proceeds via two stages . first , gas is accreted through filamentary streams , where it remains relatively cold before it reaches the galaxy ( * ? ? ? this accretion mode , which we call cold mode accretion , is very efficient because the gas does not need to cool and hence it falls in on approximately a free - fall time . this means that the baryonic growth closely mimics the growth of the dark matter halo , albeit with a slight time delay . cold mode accretion dominates the global growth of galaxies at high redshifts and the growth of lower mass objects at late times . as the dark matter halo grows larger , a larger fraction of the infalling material shock heats to temperatures close to the virial temperature . in the denser , central regions a fraction of this hot gas is able to cool . this latter process is the `` classical '' scenario by which galaxies gain gas ( e.g. * ? ? ? * ; * ? ? ? * ) , and to differentiate it from the previous mode we call it hot mode accretion . the dominant accretion mode depends on halo mass , and the transition between these two regimes occurs at a mass of @xmath2@xmath3 . a similar ( albeit slightly lower ) transition mass between shock heated and non - shock heated halo gas is found in spherically symmetric calculations @xcite , and the physics behind this transition is apparently related to the ratio of post - shock compression and cooling times . in halos with masses near the transition mass , cold filamentary flows still supply the central galaxy with gas even though some of the infalling gas shock heats to near the virial temperature . at higher redshifts cold filaments are even able to survive within halos above this transition mass , i.e. halos dominated by hot halo gas ( k05 , @xcite , k09 ) . overall , the bulk of the baryonic mass in galaxies is accreted through the cold accretion mode and on average no galaxy of any mass acquires more than about 30% of its mass through hot mode accretion ( k09 ) . we can sort the galaxy feedback processes discussed above into two classes : those that prevent gas from entering a galaxy in the first place , `` preventive '' feedback , and those that expel a fraction of the gas that does manage to enter the galaxy , `` ejective '' feedback . agn radio mode heating and photoionisation are examples of preventive feedback , while winds driven by supernovae or agn `` quasar mode '' are examples of ejective feedback . ( the same feedback process could in principle be both ejective and preventive for example if the energy released in a quasar - driven wind heats the surrounding halo gas and thereby prevents it from cooling . ) the effectiveness of these two feedback types should vary depending on the dominant accretion mode in the halo hosting the galaxy . because cold mode halos have very little halo gas outside of the cold dense filaments , it is doubtful whether ejective feedback can drastically affect the accretion of gas . however , ejective feedback could lower the masses of galaxies in these halos by expelling already accreted material . in this case , whether or not the winds escaped into the igm would only be determined by energetics ( assuming winds can not destroy dense filamentary streams of gas ) , since the halos are mostly devoid of gas . such winds , however , might be stopped by the quasi - spherical , hot halos that surround hot mode galaxies , making them ineffective . conversely , preventive feedback like the `` radio mode '' of agn is likely most effective in hot mode halos , where it can prevent the hot , dilute gas that is in quasi - static equilibrium from cooling ( as discussed in k05 ) . the exceptions may be at very low masses , where photoionisation and preheating could prevent gas from getting into the halos in the first place by strongly reducing the gas cooling rates . to understand the role of feedback during galaxy formation and evolution , one also has to understand how galaxies are supplied with baryons and in particular with the gas that provides the fuel for star formation . this is difficult with current sams , as they do not yet accurately track cold mode accretion . on the other hand , simulations currently lack the resolution necessary to accurately simulate either preventive or ejective feedback processes directly within a cosmological environment . therefore , it is important to gain understanding of when and where feedback is necessary to explain the observed properties of galaxies . in this paper we do this from the vantage point of our own cosmological simulations , which do not include _ any _ strong feedback mechanisms . by comparing the observed properties of galaxies with the galaxies that form in our simulations , we confirm the conventional wisdom that one or more strong feedback mechanisms are needed to prevent the excessive accumulation of baryons into galaxies . we draw inferences about where in redshift and galaxy / halo mass gas accretion must be suppressed and what feedback mechanisms are likely to be successful . to mimic an extreme version of preventive feedback , e.g. , a perfectly efficient agn `` radio mode '' , we remove all the gas accreted through hot mode from all galaxies . we show that this extreme feedback scenario only slightly improves the match between simulated and observed galaxy masses , which still disagree at the faint and bright ends . therefore ejective feedback from starburst winds is required . in addition , a selective feedback mechanism , like one that occurs primarily during major mergers , is probably required to explain the bimodality of the galaxy population . a large fraction of the results presented in this paper are presented in slightly different form as a part of d. kere s phd thesis at university of massachusetts , amherst @xcite . in [ sec : simulations ] we describe our new simulations , and the specifics of our procedure for removing hot mode accretion , as well as the `` cold drizzle '' in massive galaxies which we suspect to be numerically enhanced . in [ sec : massfn ] we compare the observed stellar mass function of galaxies to that of simulated galaxies both with and without hot mode accretion . we discuss in [ sec : buildup ] the accumulation of galaxy mass and the stellar component , and in [ sec : ssfr ] we compare the observed star formation rates with the simulations , again with and without hot mode accretion . we discuss the feedback mechanisms needed to bring the masses and specific star formation rates of the simulated galaxies into better agreement with the observations in [ sec : discussion ] and conclude in [ sec : conclusions ] .

we compare the properties of galaxies that form in a cosmological simulation without strong feedback to observations of the galaxy population . we confirm previous findings that models without strong feedback overproduce the observed galaxy baryonic mass function , especially at the low and high mass extremes . through post - processing we investigate what kinds of feedback would be required to reproduce the statistics of observed galaxy masses and star formation rates . to mimic an extreme form of `` preventive '' feedback , such as a highly efficient agn `` radio mode , '' we remove all baryonic mass that was originally accreted from shock - heated gas ( `` hot mode '' accretion ) . feedback cluster galaxies : evolution galaxies : formation models : semi - analytic models : numerical

we compare the properties of galaxies that form in a cosmological simulation without strong feedback to observations of the galaxy population . we confirm previous findings that models without strong feedback overproduce the observed galaxy baryonic mass function , especially at the low and high mass extremes . through post - processing we investigate what kinds of feedback would be required to reproduce the statistics of observed galaxy masses and star formation rates . to mimic an extreme form of `` preventive '' feedback , such as a highly efficient agn `` radio mode , '' we remove all baryonic mass that was originally accreted from shock - heated gas ( `` hot mode '' accretion ) . this removal does not bring the high mass end of the galaxy mass function into agreement with observations because much of the stellar mass in these systems formed at high redshift from baryons that originally accreted via `` cold mode '' onto lower mass progenitors . an efficient `` ejective '' feedback mechanism , such as supernova - driven galactic winds , must reduce the masses of these progenitors before they merge to form today s massive galaxies . feedback must also reduce the masses of lower mass galaxies , which assemble at lower redshifts and have much lower star formation rates . if we monotonically remap galaxy masses to reproduce the observed mass function , but retain the simulation - predicted star formation rates , we obtain fairly good agreement with the observed sequence of star - forming galaxies . however , we fail to recover the observed population of passive , low star formation rate galaxies , especially at the high mass end . suppressing all hot mode accretion improves the agreement for high mass galaxies , but it worsens the agreement at intermediate masses . reproducing these observations requires a feedback mechanism that dramatically suppresses star formation in a _ fraction _ of galaxies , increasing with mass , while leaving star formation rates of other galaxies essentially unchanged . cooling flows feedback cluster galaxies : evolution galaxies : formation models : semi - analytic models : numerical

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= 5.5 in we begin the comparison of simulated and observed galaxy properties with the @xmath21 stellar mass functions ( smf ) . in figure [ fig : mf ] we compare the observed ( _ g_-band derived ) smf from @xcite to the smf from our l50/288 simulation . we plot the smf starting from our adopted resolution limit . the stellar masses in @xcite are based on data from the sdds survey @xcite and the diet salpeter imf , and are shown to be consistent with the masses derived from the near infrared 2mass survey @xcite . the simulated galaxies are overabundant at all galaxy masses , with the largest disagreements occurring at the low and high mass ends . by matching the integrated number density of galaxies above a certain mass in the simulation with the observations , we estimate the difference in mass between the observed and simulated galaxies ( assuming the same rank ordering of galaxies by mass in the simulation and observations ) . we show this difference as a correction factor @xmath22 in the lower panel of figure [ fig : mf ] . the masses of the most massive simulated galaxies are about a factor of 35 higher than those observed . one can immediately conclude that strong feedback , which is not included in our simulations , is needed to decrease the masses of these simulated massive galaxies . the differences decrease at intermediate masses , around the `` knee '' of the observed mass function , where the simulated masses are only high by a factor of 1.52 . at masses lower than several times @xmath23 the differences between the observed and simulated stellar mass function are enormous . to match the number density of observed galaxies requires suppressing the masses of the simulated galaxies by more than an order of magnitude . these differences suggest that a very efficient mechanism must prevent the formation of the majority of low mass galaxies with masses up to several times @xmath24 or that it must drastically lower their masses to bring the simulated galaxies into agreement with the observations . another possibility is that the observed galaxies contain significantly more gas and less stars at similar galaxy masses . of course these conclusion are not new or unique to our work , and we will discuss the required properties of this mechanism in more detail in the discussion section . the total amount of baryons locked in the stellar component in our simulation is 18 percent , which is about a factor of 3 higher than the observed value ( e.g. * ? ? ? * ) . while the differences between the simulated and observed galaxies are large at the high and low mass ends , the stellar masses of galaxies are in relatively good agreement around the `` knee '' of the mass function where a large fraction of the global stellar mass is concentrated , making this disagreement more moderate globally . the galaxy masses in figure [ fig : mf ] do not account for stars dispersed into the intracluster medium from the hierarchically built remnants . observationally , in clusters of @xmath25 , about 2030% of all stars in a halo are part of the icm+central galaxy system , which is dominated by intracluster stars ( ics ) ( e.g. * ? ? ? * ) . in fractional terms this is not far from what we find in our simulated massive halos , which have 2035% of their stars in the ics at halo masses of about @xmath26 . the fraction of ics stars is also subject to the exact definition of where the light of the central ( brightest ) cluster galaxy ends and becomes ics and , therefore , any comparison of this aspect of our simulation to the observations is quite uncertain . however , the _ combined _ mass of the central galaxy and the ics is already higher in our simulations than what is observed . furthermore , most of the massive galaxies in our simulation are in halos of even lower mass , where ics is likely an even less important stellar component . given these facts , it appears unlikely that a large fraction of the factor of @xmath27 larger galaxy mass in the simulations could be explained by having more ics in the simulation . in [ sec : hotremoval ] we discussed removing the hot mode to mimic the extreme case of preventive feedback . we plot the smf with hot mode accretion removed in figure [ fig : mf ] ( dashed line ) . we see that the decrease in galaxy masses caused by this extreme feedback does bring the simulations into better agreement with the observations at high masses , but the change in mass is only modest . the change is largest at intermediate masses , around the `` knee '' in the observed mass function . the typical change is several tens of percent at masses of around @xmath20 and is even smaller at higher masses . the removal of hot mode accretion even changes galaxy masses in objects with masses as small as several times @xmath24 , because there are still some galaxies at these small masses with significant hot mode accretion at low redshifts . at even lower masses , however , there is almost no change in mass after hot mode removal , which is not unexpected since all low mass galaxies are built exclusively through cold mode accretion . the most surprising feature of this curve is the almost negligible change at the high - mass end . we conclude from this plot that the removal of hot mode accretion , to mimic an extreme case of preventive feedback such as an agn radio mode , _ can not _ explain the observed steep drop in the smf at the high mass end . the removal of hot mode accretion only partially succeeds at intermediate masses , where the simulated mass function is indeed quite close to the observed one , but only over a small range of masses . previously , in k09 , we saw that the accretion of many galaxies at low redshift is completely dominated by hot mode accretion and yet their masses are not greatly affected by hot mode removal . we provide an explanation for this seeming contradiction in the next section and later , where we discuss the processes needed to bring the simulated galaxy masses into better agreement with the observations . in [ sec : coldremoval ] we discussed the removal of the cold gas infall in massive galaxies in addition to removing all hot mode , since we suspect this infall to be a numerical artifact . we show the results of this in figure [ fig : mf ] as the dot - dashed line . the effect on massive galaxies is again rather small and , by construction , it only affects the most massive objects . typically , most galaxies of around @xmath28 have their masses lowered by only @xmath29 percent when the cold drizzle is removed . therefore , even without cold mode accretion in massive galaxies , preventive feedback alone ( such as an extreme agn radio mode ) is not sufficient to bring the high mass end of the observed and simulated smfs into agreement . = 3.4 in -15pt = 3.4 in -15pt in figure [ fig : formhist ] ( left ) , we plot lines showing the median redshift at which galaxies formed 25 , 50 , and 75 percent of their @xmath0 stellar mass as a function of the stellar mass of the galaxies . to indicate the scatter from one galaxy to another , we also show the mass weighted stellar formation redshift ( the redshift when 50 percent of the @xmath0 stellar mass was formed ) for each individual galaxy . the rising trend with mass has been described as the `` downsizing '' of galaxy formation . sometimes this trend has been explained as a consequence of particular feedback models , but here we see that it is present in our sph simulations _ without _ strong feedback , and therefore is a natural consequence of hierarchical models of galaxy formation ( see also @xcite ) . even the build - up of dark matter halos proceeds in a similar way , where the bulk of the present halo mass of massive halos was already assembled in lower mass progenitors ( above a given minimum mass ) at earlier times than the bulk of the mass in low mass halos @xcite . for comparison , we also present in figure [ fig : formhist ] ( right ) observational estimates of the stellar formation redshifts from the spectral analysis galaxies from the sloan digital sky survey by @xcite ( triangles ) . to generate these lines , we have taken the sfr as a function of redshift in each of five mass bins from their figure 4 , assumed the sfr to be constant within each redshift bin , extended the minimum redshift to @xmath0 , and interpolated the cumulative stars formed to get the 25 percent , 50 percent , and 75 percent redshifts . the analysis of @xcite , made purely from the integrated spectra of the local galaxy population , is clearly difficult and subject to systematic errors ( from the dust model , surface brightness biases , spectroscopic fibre coverage , or imperfections in the spectral modelling among others ) . the errors increase rapidly with the redshift , so the 25 percent curve is more reliable than the 75 percent one . however , the global behaviour of star formation and stellar mass as a function of redshift is in reasonable agreement with direct observations , and the overall `` downsizing '' picture inferred from this dataset has been confirmed by many previous studies . we also show the observationally inferred mass weighted stellar age from @xcite . their analysis differs in detail from @xcite , and it results in significantly younger stellar ages at all masses , but especially at the low mass end . we show the formation redshift of 50 percent of the galaxy stellar component ( diamonds ) from their figure 9 ( they do not provide 25th and 75th percentiles ) . to compare the simulated galaxies to these observations we correct the simulated galaxy stellar masses by the correction factor from figure [ fig : mf ] . by comparing the stellar formation redshift in the simulations to the observed values , one can infer whether the bulk of such a mass correction , which in nature would happen through some feedback mechanism , needs to occur below the observationally inferred formation redshift , in the case where the observed formation redshifts are higher than those simulated or above the observational redshift in the opposite case . both the observational results and our simulation show that stars in the progenitors of massive galaxies form very early . however , at the high mass end the simulated stellar ages are in rough agreement with the results of @xcite but are much higher than those of @xcite . it is beyond the scope of this paper to track the differences in the observationally inferred stellar ages , but it is clear that the systematic uncertainties in these estimates are still very significant . while the differences between the observed datasets are large at the low mass end , both observational estimates indicate that the simulated galaxies form too early , implying that their formation should be more suppressed at early times ( we discuss this in more detail in [ sec : discussion.masses ] ) . in figure [ fig : cold_fractions ] , we show the contribution of gas initially accreted through cold mode to the final masses of galaxies at @xmath30 and @xmath0 ( the second panel is similar to figure 7 in k09 ) . the dispersion in the cold mode fractions is large at all masses , but the overall trends with galaxy mass ( indicated with the median line ) are clear . we demonstrated in k09 that at @xmath31 , cold mode accretion completely dominates the smooth gas accretion rates at all masses . around @xmath30 , hot mode starts to be an important source of gas in a limited mass range , around few times @xmath23 . however , from figure [ fig : cold_fractions ] one can see that typical high - redshift galaxies at any mass build up 90100 percent of their mass through cold mode accretion , making the hot mode contribution insignificant at these early times . = 5.5 in the situation is a bit more complicated at @xmath0 . as expected , a typical low mass galaxy forms almost completely through cold mode accretion . the contribution of hot mode accretion increases with mass up to a maximum of 2530 percent for galaxies with masses of around @xmath32@xmath33 , but then the trend reverses and the median hot mode contribution decreases in more massive galaxies . ( we emphasise that this hot mode contribution is measured over the entire history of the baryons that make up the galaxy , whereas a plot of the _ current _ accretion would show much larger hot mode fractions . ) the increase in the cold mode contribution at higher masses owes to the increased contribution of mergers , which mostly adds material that was originally accreted through cold mode . this occurs because the merging progenitor galaxies accrete the bulk of their mass at much earlier times when cold mode accretion dominates the buildup of galaxies at all masses . this trend is reinforced by the lack of substantial hot mode accretion in massive halos at @xmath34 . the mass dependence of the cold mode fractions also explains why the simulated mass function is most affected by hot mode removal at masses of @xmath35@xmath36 , since these are the galaxies that had the largest fractions of their total mass accreted through hot mode . in figure [ fig : cold_fractions ] we also plot the median fraction of mass initially accreted in cold mode after the cold mode accretion is removed from massive galaxies as described in [ sec : coldremoval ] . the residual cold drizzle contributes around 20 percent to the galaxy mass , so removing it increases the ratio of hot to cold mode by around 20 percent ; since this ratio is itself small , this change raises the cold mode contribution by several percentage points at most . from figure [ fig : formhist ] , it is clear that bulk of the stellar mass in massive galaxies forms prior to @xmath30 , in much smaller objects whose formation is completely dominated by cold mode accretion . the most massive progenitors of these galaxies at @xmath31 contain typically only @xmath372025 percent of their present mass . these objects later merge to form even more massive galaxies . since in high - redshift galaxies only a small fraction of the baryonic mass is gained through the cooling of hot halo gas , the removal of hot mode accretion can not significantly affect the masses of these galaxies . therefore , any feedback mechanism that aims to lower the masses of the most massive galaxies must actually affect the masses of their lower - mass , high - redshift progenitors as we discuss in [ sec : discussion.masses ] . -40pt = 3.5 in -15pt = 3.5 in the final observable we shall consider is the current star formation rate of individual galaxies , which is most usefully presented relative to its mass as the specific star formation rate ( ssfr ) . quite frequently galaxy colour is used as a proxy for ssfr , although of course a galaxy s colour depends on its current star formation rate , the previous star formation history , and the amount of dust attenuation . colour - magnitude plots incorporating observations of many thousands of galaxies have become commonplace , and the main features of these plots are by now familiar ( e.g. @xcite ) : there is a red sequence of galaxies , mostly populated by massive , early types with low ssfrs , distinctly offset from a blue cloud of late type , lower mass galaxies with high ssfrs . while part of this division can be caused by dust attenuation , most of the differences are clearly caused by varying amounts of recent star formation . however , for comparison to the simulations , a plot of log(ssfr ) versus galaxy stellar mass is more useful . obtaining this requires modelling each observed galaxy s spectral energy distribution to obtain transformations from magnitude to mass and from colours to log(ssfr ) ; the latter transformation in particular is highly non - linear . just such a plot of the low redshift galaxy population was recently obtained by @xcite , using uv data from the galex satellite @xcite combined with _ ugriz _ photometric data from the sloan digital sky survey ( sdss ) @xcite . their analysis builds upon and supersedes earlier optical - only work by @xcite and @xcite . the authors consider a wide range of star formation histories for every observed galaxy and assign each a likelihood , leading to a two - dimensional probability distribution of ssfr and stellar mass for each individual galaxy ( where the ssfr is averaged over the last 100 myr ) . if one simply plots the mean value of this distribution for individual galaxies in the observed sample , it shows an obvious bimodality , as one can see in the left panel of figure [ fig : ssfr_data ] . the `` blue cloud '' galaxies identified in a colour - magnitude diagram now correspond to a tight star - forming sequence in the upper part of the plot , partly because scatter caused by variations in metallicity and dust have been removed by the sed fitting . the tight `` red sequence '' of the colour - magnitude diagram now corresponds to a low - ssfr sequence , broadened by the nonlinear transformation between colour and log(ssfr ) , and there is a significant bridge population between the two sequences . ( the relative prominence of the low - ssfr sequence in the left panel of figure [ fig : ssfr_data ] is partly an artifact : there is a lower limit of @xmath38 allowed in the models of ssfr history used in @xcite causing the mean log(ssfr ) of individual low - ssfr galaxies to cluster around a value somewhat higher than this . ) a fairer representation of observed galaxies in this plot smears each individual galaxy over its full two - dimensional probability distribution in ssfrs and mass , and normalises it by the effective survey volume at each mass , i.e. @xmath39 . we show this result , which is the only one that should be compared with simulations , as the solid contours in the right panels of figure [ fig : ssfr_data ] . this figure is equivalent to the grayscale image shown as the lower panel of figure 15 in @xcite . we generate the contours from a grid with a spacing of 0.05 in log(m ) and 0.1 in log(ssfr ) , and plot contours encompassing 25 , 50 , 75 , and 90 percent of the maximum probability density ( from darkest to lightest shading ) . with these changes , the lower - mass galaxies become more prominent , and the low - ssfr sequence smears out into a flat ledge covering a very wide range of ssfrs that extends downward from the star - forming sequence in contrast to the colour - magnitude diagram , one might now describe the features as a `` blue sequence '' and a `` red cloud '' . the star - forming sequence persists as a tight ssfr vs. galaxy mass relation at relatively high ssfrs , around @xmath40 at stellar masses of @xmath41 . ssfrs in this sequence decrease toward higher masses . the sequence dominates the number density over several orders of magnitude in galaxy mass , up to @xmath42 , although some galaxies have low ssfrs even at intermediate and low galaxy masses . the tightness and weak dependence on mass of this relation was discussed extensively in the literature ( e.g. * ? ? ? * ) . in the same plot , we also show the properties of the simulated galaxies . as we discussed previously , the masses of the simulated galaxies are much higher than those of observed galaxies . hence , even if the present star formation rate in a simulated galaxy were to correspond to the observed values , the ssfrs would be much lower than those observed . to avoid this problem we correct the masses of the simulated galaxies using the correction factors @xmath43 in figure [ fig : mf ] , assuming that the mass rank order of the simulated galaxies is preserved this is similar in spirit to halo and subhalo matching models that try to connect the observed properties of galaxies to the dark matter halos and sub - halos from n - body simulations ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , except in our case we are connecting observed and simulated galaxies . furthermore , to account for the different initial mass function ( imf ) used in @xcite , a diet @xcite imf , and that used in @xcite , a @xcite imf , we lower these corrected masses by @xmath44 . we leave the sfrs of individual galaxies unchanged in this plot , so that the ssfrs increase by a factor @xmath45 . our reasoning is that here we are essentially examining the star formation rates as a function of halo mass , and the adjustment to the mass should just enable a fair comparison of galaxies residing in similar halos . in k09 , we showed that the sfrs of individual galaxies closely follow the smooth gas accretion rates . as we discuss in [ sec : discussion.masses ] , if the mechanism that is responsible for producing the correct mass function is ejective feedback from sn - driven winds , it should not significantly affect the accretion of intergalactic gas at low redshift , when such feedback is inefficient , and hence it would also not likely affect the tight relation between gas accretion and star formation . therefore , the long term mass accumulation of galaxies ( that we are trying to correct with the mass re - normalisation ) should not affect the low - redshift sfrs . since the simulated galaxies have exact values for both their ssfrs and their masses , to compare them with the observational data we add two - dimensional gaussian uncertainties . we choose the mass uncertainties to have @xmath46 and the ssfr uncertainties to have @xmath47 linearly decreasing from 0.6 for the lowest ssfrs to 0.2 for the highest ssfrs , both in rough agreement with the errors present in @xcite . most of the simulated galaxies also reside in a well defined star forming sequence with properties that are similar to the observed star forming sequence . there is , however , a sizeable population of simulated galaxies with zero ssfr , which possibly corresponds to part of the observed red sequence . owing to our limited mass and time resolution , the transition between zero sfr galaxies and star forming galaxies suffers from discretisation effects , with the lowest possible nonzero simulated star formation rate being around @xmath48 . when we plot these zero ssfr simulated galaxies we assign them a very low ssfr of @xmath49 , before adding gaussian uncertainties . while most of the observed red sequence galaxies reside at the high mass end , most of the simulated zero ssfr galaxies reside at the low mass end . interestingly , the mass dependence and scatter of the simulated star forming sequence at @xmath0 is consistent with the observed trends . the median ssfrs of simulated galaxies at a given mass are very close to the observed sequence except around @xmath24 , where it is several tenths of a dex lower . however , as noted in [ sec : simulations ] , the current simulations do not include mass feedback from intermediate - mass stars . on average at least , this effect might boost the typical sfr by up to 0.3 dex , bringing the low - mass star - forming sequence back into agreement with the observed one , but if the same effect operates at high masses it would make their simulated ssfrs too high . to quantify any differences in the way galaxies populate the high and low ssfr regions , approximately corresponding to `` red '' and `` blue '' galaxies , we determine the fraction of galaxies with ssfrs lower and higher than @xmath50 . we plot the fraction of low ssfr galaxies in the lower - right panel of figure [ fig : ssfr_data ] for both observed ( solid line ) and simulated ( dashed line ) galaxies . the observed galaxy sample has about 20 percent of its galaxies in the red sequence for @xmath51 . in the simulation the fraction of low ssfr galaxies is about 2530 percent , which is slightly higher than the observed fraction . however , the differences begin to increase towards higher masses and by around @xmath52 about 60 percent of the observed galaxies have very low ssfrs while all but 15 percent of the simulated galaxies reside on the star forming sequence . the discrepancies get even larger at higher masses . this illustrates a generic problem that occurs for massive galaxies in simulations and sams without feedback : they form too many stars at late times and hence are too blue on average . the differences between the simulated and observed galaxies in figure [ fig : ssfr_data ] thus show some different symptoms than those in the mass function plot ( fig . [ fig : mf ] ) . at low masses the current star formation rates agree well with the observations , whereas the simulation masses are much higher . alternatively , whereas the masses should be reduced at high redshift by ejective feedback from sn - driven winds , perhaps it should not significantly affect the gas supply and star formation rates at low redshift when such feedback is inefficient ( as we discuss in [ sec : discussion.masses ] ) . starting at @xmath53 where the simulated masses are in the best agreement , however , the fraction of star - forming galaxies starts to diverge strongly from the observed fractions , even though the actual star formation rates of those galaxies still on the star - forming sequence are in reasonable agreement . -30pt = 3.5 in -15pt = 3.5 in as we did with the mass function , to mimic an extreme version of preventive feedback in hot halos , we completely remove all the hot mode accretion and plot the resulting galactic properties in the left panels of figure [ fig : ssfr_cleaned ] . we again re - normalise the galaxy masses to match the observed mass function after the removal of the hot mode in the same way as in figure [ fig : ssfr_data ] . this hot mode removal does not change any of the properties at the low mass end because these galaxies accrete their gas almost exclusively through cold mode accretion . as we showed before , even the highest mass galaxies do not significantly change their masses when hot mode accretion is removed , but they do significantly change their ssfrs . up to masses of @xmath54 , the average ssfrs of simulated galaxies change enough to be roughly consistent with the observed galaxies . however , if one looks more closely this leaves too few galaxies to correspond to the observed star forming sequence . even at intermediate masses of around @xmath24 , the removal of the hot mode ruins the relatively good agreement between the observed and simulated star forming sequence . although the fraction of galaxies below our adopted `` red sequence threshold '' is similar to the observed fraction , the typical ssfr of a star forming galaxy is now factor of 35 lower than those observed . even if one were to include mass feedback from intermediate - mass stars as in [ sec : simulations ] , the ssfr would still be low by a factor of about two . this suggests the need for a selective feedback mechanism , which only significantly affects star formation in a fraction of the galaxies at a given mass to preserve the star forming sequence . finally , at masses greater than @xmath55 the discrepancies persist and are as large as when the hot mode is not removed . in the right panels of figure [ fig : ssfr_cleaned ] , we remove both the hot mode accretion and the cold mode accretion in galaxies more massive than @xmath20 ( before the mass re - normalisation ) , i.e. the possibly spurious cold drizzle . we again renormalise the stellar masses of galaxies using the corrections from figure [ fig : mf ] to match to observed mass function . the ssfrs of the galaxies at the massive end are reduced even further and are more similar on average to the observed massive galaxies than when we only remove the hot mode accretion . the rough agreement in the red fraction now extends up to galaxy masses of about @xmath56 with the more massive galaxies remaining discrepant . however , once again there are not enough galaxies on the star forming sequence owing to the nature of our mock feedback that affects approximately all galaxies above a given mass ( in the case of cold drizzle removal ) and above a given halo mass ( in the case of hot mode removal ) . again , the need for a more selective feedback mechanism is obvious from the observed ssfr distribution alone , as a significant fraction of galaxies even at the largest masses appear to be part of a normal star forming sequence . to summarise , removing all the hot mode accretion and the potentially spurious cold mode accretion from massive galaxies , yields a fraction of simulated `` red '' galaxies that is similar to but actually slightly higher than the observed sample around @xmath20 , suggesting that this recipe removes too much late time accretion . furthermore , this procedure moves all galaxies away from the star - forming sequence and therefore is not supported by observations . however , the problem at the very massive end ( above @xmath56 ) remains the same , where only a small fraction of the simulated galaxies have low enough ssfrs . the removal of hot mode accretion and `` cold drizzle '' significantly lowers their ssfrs , but they are still higher than those observed . therefore , preventive feedback mechanisms like radio mode agn alone are probably not sufficient to make the most massive galaxies , those with @xmath57 , red enough . these massive galaxies are typically the central galaxy of a group or cluster and their ssfrs remain too high because fresh gas for star formation arrives through minor mergers . therefore , to keep the central galaxies red enough , an efficient feedback mechanism needs to lower the gas content of the satellite galaxies before they merge , or to prevent star formation from the gas that arrives with the satellites . another possibility is that a fraction of the gas identified as coming from mergers actually comes from stripped galactic disks ( similar to the `` cold drizzle '' ) but which we can not identify as such . because of our limited time spacing between the simulation outputs ( and possibly the numerically enhanced infall of such cold clumps ) , some of the gas stripped between two outputs can end up in the central galaxy of a massive halo by the next simulation output and , therefore , be identified as coming from merger .

an efficient `` ejective '' feedback mechanism , such as supernova - driven galactic winds , must reduce the masses of these progenitors before they merge to form today s massive galaxies . feedback must also reduce the masses of lower mass galaxies , which assemble at lower redshifts and have much lower star formation rates . if we monotonically remap galaxy masses to reproduce the observed mass function , but retain the simulation - predicted star formation rates , we obtain fairly good agreement with the observed sequence of star - forming galaxies .

we compare the properties of galaxies that form in a cosmological simulation without strong feedback to observations of the galaxy population . we confirm previous findings that models without strong feedback overproduce the observed galaxy baryonic mass function , especially at the low and high mass extremes . through post - processing we investigate what kinds of feedback would be required to reproduce the statistics of observed galaxy masses and star formation rates . to mimic an extreme form of `` preventive '' feedback , such as a highly efficient agn `` radio mode , '' we remove all baryonic mass that was originally accreted from shock - heated gas ( `` hot mode '' accretion ) . this removal does not bring the high mass end of the galaxy mass function into agreement with observations because much of the stellar mass in these systems formed at high redshift from baryons that originally accreted via `` cold mode '' onto lower mass progenitors . an efficient `` ejective '' feedback mechanism , such as supernova - driven galactic winds , must reduce the masses of these progenitors before they merge to form today s massive galaxies . feedback must also reduce the masses of lower mass galaxies , which assemble at lower redshifts and have much lower star formation rates . if we monotonically remap galaxy masses to reproduce the observed mass function , but retain the simulation - predicted star formation rates , we obtain fairly good agreement with the observed sequence of star - forming galaxies . however , we fail to recover the observed population of passive , low star formation rate galaxies , especially at the high mass end . suppressing all hot mode accretion improves the agreement for high mass galaxies , but it worsens the agreement at intermediate masses . reproducing these observations requires a feedback mechanism that dramatically suppresses star formation in a _ fraction _ of galaxies , increasing with mass , while leaving star formation rates of other galaxies essentially unchanged . cooling flows feedback cluster galaxies : evolution galaxies : formation models : semi - analytic models : numerical

0901.1880

c

many authors emphasise the overabundance of massive galaxies and their lack of red colours in simulations and sams ( e.g. k05 , @xcite ) and usually blame excessive gas cooling onto central galaxies in massive halos , i.e. hot mode accretion , for this failure . however , in k09 we demonstrated that many galaxies in massive halos have almost stopped accreting gas from their hot virialised atmospheres and their masses are still a factor of @xmath27 too large compared to the observations , indicating that the problem of massive galaxy formation is more complex . most of the material currently present in the most massive galaxies was originally acquired by smaller galaxies at very early times , as shown in figure [ fig : formhist ] , through cold mode accretion , which dominates gas accretion in all galaxies at early times . the time by which a significant fraction of a current galaxy s mass is already accreted into its progenitors is a strong function of galaxy mass . the most massive galaxies today have their mass accreted into their progenitors , and hence most of their stars form , before @xmath58 . such a scenario is a natural consequence of hierarchical halo and galaxy formation and this `` downsizing '' effect is ubiquitous in both cosmological simulations @xcite and sams of galaxy formation @xcite . this is the reason why preventive feedback alone , e.g. agn activity , can not significantly lower the masses of the most massive galaxies , contrary to the assumptions in some popular current models . this finding also helps us to elucidate the nature of the feedback mechanism needed to fix the problems at the high mass end in the simulated galaxy mass function . feedback in low and intermediate mass objects that form at early times , which subsequently hierarchically merge to make the massive galaxies today , must be very efficient at high redshifts to reduce their masses before they transform that mass into stars . since these galaxies gain most of their mass through cold mode accretion , it is natural that it should be an ejective feedback mechanism like some form of galactic winds . standard ejective feedback mechanisms have little or no effect on cold mode accretion since the gas is already cold and has a high momentum flux . however , since cold mode dominated halos do not possess a hot halo of gas , the winds are free to leave the galaxy unimpeded as long as they have enough energy . in fact , many high redshift galaxies show evidence of very strong , high velocity outflows of gas @xcite . strong feedback in high redshift galaxies could be the consequence of momentum driven winds , which could operate in starburst galaxies @xcite . in this model , driving galactic outflows requires a very efficient starburst with a high star formation rate per unit surface area . at redshifts @xmath59 almost all galaxies have sufficiently high star formation rates to enable this efficient feedback mechanism ( see the discussion in @xcite ) . to match the observed mass function it is probably still necessary to have some preventive feedback , especially to prevent the re - accretion of the necessarily large amounts of ejected gas . once a galaxy s halo grows massive enough , it will gain a hot halo of gas that will impede the winds , quenching the feedback . this could lead to a natural upper mass cutoff to the ejective feedback mechanism at approximately the dividing mass between hot and cold mode halos , @xmath60@xmath3 ( in reality this mass could be up to factor of 3 higher in simulations with strong outflows and metal line cooling ) . another alternative is to somehow keep the high redshift galaxies gas rich , with only a small fraction of their mass converted into stars , then remove the gas during some violent process occurring during galaxy mergers . however , this requires a significantly different star formation algorithm than we use in our simulations , which does not produce such gas - rich massive galaxies . even then , it is not clear if quasar - driven winds or some other mechanism would be sufficient to remove enough of the gas before the progenitors merge into a massive galaxy and convert the gas into stars . the largest differences between the observed and simulated mass functions occur at stellar masses around and below @xmath24 ( simulated mass ) . obviously , the comparison of theoretical and observational stellar mass functions highlights the need for very efficient feedback at the low mass end , but it is far from clear what mechanism actually reduces the masses of these galaxies . it is possible that a mechanism similar to the starburst driven winds that operate at high redshift , which are necessary to lower the mass function at the high mass end , are also able to lower the @xmath0 galaxy masses at the low mass end . however , we demonstrated that most of these galaxies acquire a large fraction of their stellar mass at late times ( after [email protected] ) and , therefore , such feedback needs to be active at late times . in general , feedback from supernova - driven winds @xcite is the most popular candidate and is often used in sams @xcite . simple calculations indicate that such feedback should be effective in halos with circular velocities up to @xmath61 @xcite , which is enough to significantly affect this problematic mass range . however , realistic hydrodynamic simulations show that such feedback has difficulty significantly reducing galaxy masses in galaxies with @xmath62 @xcite , unless the star formation rates are extremely high as at high redshifts @xcite . in some models the winds exhibit a thresholding behaviour : for example , in the momentum driven wind models discussed above the star formation rate surface density in most spiral galaxies at late times is not high enough to drive outflows at all after @xmath63 , except in a small number of starburst galaxies ( see @xcite and references therein ) . therefore , an additional efficient feedback mechanism appears necessary at the low mass end that can affect galaxies forming at much later times . these findings place strong requirements on cosmological simulations that model galaxy formation . the smallest objects that are often poorly resolved need to be resolved in detail at all times to understand the way feedback mechanisms interact with the infalling and galactic gas . uv background heating can affect the formation of galaxies that would form in halos with @xmath64@xmath36 at @xmath0 but it is efficient for only much lower mass galaxies at higher redshifts ( e.g. @xcite ) . other alternatives include pre - heating by gravitational pancaking . in hierarchical galaxy formation models like @xmath1cdm , at low redshifts many intermediate mass halos form in much more massive , flattened structures . in this pre - heating scenario , one assumes that the gas in these structures is shock heated to @xmath65 , a temperature equivalent to the expected infall velocities onto these structures , thus preventing the gas from collapsing into halos of lower virial temperature @xcite . however , some n - body simulations suggest that this scenario does not work in practice because halos in the problematic mass range actually form in pancakes of much lower mass and , therefore , in regions with temperatures lower than previously thought @xcite . the least likely possibility we consider is that a large fraction of the baryons in late forming galaxies are locked in a gaseous component . if the observed gas fraction were substantially higher than in the simulations this would lead to a very different stellar mass function for galaxies with similar total mass . however , we checked this directly and found that our simulated baryonic mass function is no more discrepant with the observed baryonic mass function from @xcite than with the stellar mass function . in addition , the observed mass functions of hi gas @xcite and of the molecular gas @xcite show a smaller number density of objects with gas masses comparable to the stellar masses in the most problematic mass range we analyse , @xmath66 , suggesting that stellar mass dominates a galaxy s baryonic mass in this mass range . only at lower masses does the gas begin to dominate the baryonic mass of galaxies ( e.g. * ? ? ? * ) and hence begin to alleviate the differences between the observed and simulated stellar mass functions . however , even if the baryons in these lower mass objects remained mostly gaseous , they would greatly overproduce the observed hi mass function @xcite . while the need for an ejective feedback mechanism is clear , the effect of such ejecta on the subsequent gas accretion are unknown at the present . depending on the halo mass , wind energy , structure , metallicity and ability to diffuse metals , ejected material can have both `` positive '' and `` negative '' feedback : i.e. while it removes the gas from galaxies and adds the entropy to the surrounding gas @xcite it also increases the amount of available gas in halos and pollutes halos with metals , which could increase the amount of gas that gets accreted at later times . significant feedback at the low mass end at early times could raise the gas fractions in massive halos at later times because a smaller amount of the halo gas will be locked up in galaxies , making this effect an _ intergalactic fountain_. some fraction of the mass that is ejected from low mass galaxies could be reaccreted by higher mass galaxies at later times when such feedback might be less efficient ( e.g. * ? ? ? this could lead to higher halo gas fractions , which in turn could supply more gas , thus leading to higher star formation rates in higher mass galaxies . this would increase the need for efficient preventive feedback in massive halos to remove this added late time accretion . in this sense , both ejective feedback ( e.g. supernova driven winds ) and preventive feedback ( e.g. agn radio mode ) might be needed to yield correct galaxy masses in massive halos . however , in k09 we showed that a large fraction of massive halos naturally develop a gas density core , which might persist even in the case of higher halo gas fractions , possibly alleviating the need for additional feedback . in the previous section we showed that the observed and simulated star forming sequence of galaxies share similar properties . however , the simulations are missing a large fraction of the passively evolving galaxies with very low star formation rates , which dominate the massive end in the observations . removing all the hot mode accretion and the ( potentially spurious ) cold drizzle produces a larger population of passive galaxies , but it makes the fraction of star - forming galaxies too low , especially at intermediate masses . reproducing the observations requires a mechanism that suppresses accretion in a _ fraction _ of galaxies but not in all galaxies , with the fraction itself increasing from intermediate to high masses . in addition , observed red sequence galaxies are preferentially early type ( morphologically ) relative to galaxies on the star forming sequence ( e.g. * ? ? ? * ) and suppressing accretion will not in itself change a galaxy s morphology , though it can help preserve early types by preventing the regrowth of disks . a promising candidate mechanism for moving galaxies to the red sequence is quasar and starburst driven winds , occurring during the mergers of gas rich galaxies @xcite . using the halo occupation distribution and the evolution of a type - separated galaxy mass function , ( * ? ? * a , b ) show that such a model , which assumes that star formation stops after the major mergers of gas rich galaxies , can explain the buildup of the red sequence over time as well as the fraction of red galaxies as a function of galaxy mass . the transformation from the blue to the red sequence during these events is aided by several processes : the development of a shocked hot virialised medium that slows the cooling of gas , quasar mode agn feedback from the growing black holes , and starburst driven winds , which all occur nearly simultaneously . the fraction of galaxies at a given mass that has undergone such a transition is an increasing fraction with increasing galaxy mass , a trend that is required to be consistent with the observations . this model requires that most galaxies do not return to a star forming phase after the star formation initially stops , so a long term preventive feedback mechanism is still necessary to prevent further gas accretion , perhaps `` radio mode '' agn feedback @xcite . even the need for this `` maintenance '' feedback could be avoided in a large fraction of massive halos owing to the natural development of constant density cores that prevent cooling from the hot atmosphere , as we found in k09 . however , if the accretion of cold gaseous clumps also occurs in massive halos ( i.e. if `` cold drizzle '' is not a numerical artifact ) , then this maintenance feedback must also be able to prevent the bulk of this form of accretion . in addition , accounting for metal cooling can enhance the cooling in massive halos where it can dominate at temperatures typical of halo gas . this could make the problem of preventing the accretion and re - accretion of gas in massive halos even more severe . of course the major mergers of late type galaxies have the additional advantage that they result in remnants with early type morphologies @xcite , as required for the majority of galaxies on the red sequence . therefore , most red sequence galaxies in such models would undergo colour and morphological transformations as a consequence of the same astrophysical process . in addition , this violent feedback combination could contribute to a faster termination of the cold accretion mode in massive halos , especially at low redshift . at high redshift this might happen only in very massive halos hosting massive galaxies with modest gas fractions , because the high gas fraction of lower mass galaxies make merger driven central gas flows and therefore starburst and quasar winds less efficient @xcite . in conclusion , agn radio mode feedback in very massive objects , mimicked by hot mode removal , can dramatically lower the ssfrs of massive galaxies but it should not affect every object with hot mode accretion and it should have a galaxy mass dependence . the total removal of hot mode accretion removes too much recent star formation . as a consequence , semi - analytic models that completely remove this accretion in massive halos must adopt a hot mode suppression threshold mass , i.e. the mass above which hot mode is suppressed , that is higher than the mass where hot virialised halos dominate @xcite . however , this approach , without additional assumptions , might have difficulty matching the evolution of the red sequence over time , as shown by ( * ? ?

however , we fail to recover the observed population of passive , low star formation rate galaxies , especially at the high mass end . suppressing all hot mode accretion improves the agreement for high mass galaxies , but it worsens the agreement at intermediate masses . reproducing these observations requires a feedback mechanism that dramatically suppresses star formation in a _ fraction _ of galaxies , increasing with mass , while leaving star formation rates of other galaxies essentially unchanged . cooling flows

we compare the properties of galaxies that form in a cosmological simulation without strong feedback to observations of the galaxy population . we confirm previous findings that models without strong feedback overproduce the observed galaxy baryonic mass function , especially at the low and high mass extremes . through post - processing we investigate what kinds of feedback would be required to reproduce the statistics of observed galaxy masses and star formation rates . to mimic an extreme form of `` preventive '' feedback , such as a highly efficient agn `` radio mode , '' we remove all baryonic mass that was originally accreted from shock - heated gas ( `` hot mode '' accretion ) . this removal does not bring the high mass end of the galaxy mass function into agreement with observations because much of the stellar mass in these systems formed at high redshift from baryons that originally accreted via `` cold mode '' onto lower mass progenitors . an efficient `` ejective '' feedback mechanism , such as supernova - driven galactic winds , must reduce the masses of these progenitors before they merge to form today s massive galaxies . feedback must also reduce the masses of lower mass galaxies , which assemble at lower redshifts and have much lower star formation rates . if we monotonically remap galaxy masses to reproduce the observed mass function , but retain the simulation - predicted star formation rates , we obtain fairly good agreement with the observed sequence of star - forming galaxies . however , we fail to recover the observed population of passive , low star formation rate galaxies , especially at the high mass end . suppressing all hot mode accretion improves the agreement for high mass galaxies , but it worsens the agreement at intermediate masses . reproducing these observations requires a feedback mechanism that dramatically suppresses star formation in a _ fraction _ of galaxies , increasing with mass , while leaving star formation rates of other galaxies essentially unchanged . cooling flows feedback cluster galaxies : evolution galaxies : formation models : semi - analytic models : numerical

quant-ph0205177

i

in 1921 , kaluza @xcite proposed a five dimensional ( 5d ) geometrical framework for the unification of the gravitational and the electromagnetic interactions . following the model of the 4d general relativity , kaluza discussed both the field equations and the particle propagation along 5d time - like geodesics , trying to establish the role of the fifth dimension for the traditional 4d physics . kaluza @xcite proposed that the fifth dimension be proportional to electric charge . several years later , klein studied quantum aspects of the 5d propagation @xcite , and noticed that the assumption of a compact and planckian fifth dimension leads to the quantization of electric charge , while addressing the question of why the fifth dimension is not experimentally observable @xcite . the kaluza - klein approach to the field theory has later been devoted an extensive amount of literature @xcite ; not the same has happened to the theory of the 5d particle propagation , in spite of its fundamental importance . in fact , kaluza @xcite immediately recognized that his 5d particle propagation theory can not apply to the electron and other elementary particles @xcite . in 1984 , gegenberg and kunstatter @xcite were led to the conclusion that , indeed , it is seemingly impossible to naturally describe the propagation of charged light particles ( i.e. , with rest mass less than the planck mass ) within a classical or quantum 5d kaluza - klein framework . in string theory this problem seems solved by giving up the concept of point particle . here we ask ourselves whether this problem is deeply rooted in the kaluza - klein interpretation of the 5d geometry , and search for alternatives . in the attempt to construct a _ scale - invariant gravity _ , wesson @xcite proposed an interpretation of a 5d geometry where the fifth dimension , not necessarily compact , is proportional to mass ( i.e. , @xmath0 , where @xmath1 is the newton constant , and @xmath2 is the velocity of light ) . this idea is known in the literature as _ kaluza - klein gravity_. investigating 5d time - like geodesics in this new framework , wesson was led to predict the existence of an exotic fifth force , yet to be discovered experimentally . recently , seahra and wesson @xcite approached the problem of the anomalous fifth force for null geodesics . their study is limited to 5d manifolds with metrics conformally conjugated to that of the kaluza - klein theory in the absence of electromagnetic fields . [ however , they do not require the fifth dimension be compact . ] furthermore , the metric depends on the fifth coordinate _ exclusively _ through the conformal factor @xcite which is required to depend _ only _ on the fifth coordinate . then , writing the 4d _ on - shell _ constraint @xmath3 [ @xmath4 , and the 4d metric is @xmath5 as @xmath6 ( @xmath7 ) , where @xmath8 , inspired seahra and wesson to pursue and demonstrate the idea that a 5d massless particle propagating along a 5d null geodesic can be seen as a 4d massive particle propagating along a 4d time - like geodesic . then , they show that for the 5d null geodesic propagation , the anomalous fifth force can be removed by a reparametrization , which in turn introduces ambiguities in defining the 4d proper time of the corresponding 4d time - like geodesic . thus , it seems that seahra and wesson have found an appropriate , anomaly - free 4d interpretation of the 5d null geodesics in the absence of electromagnetic fields ( and imposing other constraints mentioned above ) . however , a close look to their theory , reveals several consistency problems . first , the fact that the fifth dimension is proportional to mass is inconsistent with the 5d interpretation of the on - shell constraint . consider the simple case of a 5d massless particle following a null geodesic in a flat , minkovski - like 5d metric . assume that the particle has constant 4d mass . by the interpretation of the fifth dimension , the particle is moving in a hyperplane of constant @xmath9 . by the interpretation of the 4d on - shell constraint , the particle has constant momentum along the fifth dimension , and thus , unless @xmath10 ( i.e. , @xmath11 , or the particle is a 4d photon ) , the fifth coordinate changes with time . second , choosing a particular proper time for the 5d null geodesics as seen in four dimensions breaks 5d covariance , and this is inconsistent with the claim of a 5d gravity . while it is remarkable that 5d null geodesics can be regarded as 4d time - like geodesics , it is not clear _ why _ an observer would use such an interpretation . + in the attempt to find the proper relation between the 4d and the 5d particle propagation , this paper discusses a new interpretation of the 5d space - time geometry . we give a new 4d interpretation to 5d null propagation , and we apply it to the case of weak fields . to address the propagation problem in the presence of electromagnetic fields , in both classical and quantum regimes , we equip the 5d geometry with a quantum principle for 5d spinless and massless particle propagation . the geodesic propagation is then obtained by taking the classical limit . an important idea for our work is the distinction between _ active _ , _ pasive _ and _ inertial _ mass @xcite . in short , active mass is the source of gravitational field , and passive mass is the object the gravitational field acts upon @xcite . we adopt the equivalence principle of general relativity which identifies the inertial and the passive mass . the equivalence between the passive and the active mass is required by the action - reaction principle of newtonian mechanics . in general relativity , we may consider the active and the passive mass as distinct concepts , whose comparison is not necessarily meaningful @xcite . we also distinguish active and passive electric charge . another important concept for our work is that of path integral introduced to physics by feynman @xcite in 1948 . here we consider path integrals to be coordinate - free quantities . given two points 1 and 2 in a space - time manifold , a sum over all paths from 1 to 2 depends on the choice of the points 1 and 2 , but it is independent of coordinates . however , in the practice of calculating path integrals , global coordinates as a consistent labeling of all points in the space - time manifold are extremely useful . in 4d quantum physics , path integrals are now very powerful tools . feynman @xcite rewrote the quantum principles of 4d quantum and statistical mechanics in the same language of path integrals . in this paper , we implement a 5d path integral quantum principle to describe the massless and spinless 5d propagation . we then show that 4d quantum and statistical mechanics can emerge as different particular interpretations of the 5d geometry endowed with this feynman quantum principle . thus , in five dimensions , we obtain not only the unification of electromagnetic and gravitational interactions , but also a unification of 4d quantum and 4d statistical mechanics . perhaps , this is not surprising given that 4d mechanics and 4d statistics have been developing now for many decades side by side , borrowing each other ideas and formalism both in the quantum mechanical and in the quantum field theoretical frameworks , and being just a wick rotation away . + we start with a 5d space - time having a space - like fifth dimension . we do not request the fifth dimension be compact , and , in 5d context , we do not restrict the transformations of coordinates to be cylindrical [ i.e. , @xmath12 , @xmath13 , and @xmath14 . thus , in principle , the fifth dimension is observable both in the field equations and particle propagation . it is the purpose of this paper to discuss how the fifth dimension is revealed to an electrically uncharged 4d observer that perceives geometrically only the first four dimensions , but not the fifth . in four dimensions , the fifth dimension is not manifested as a geometrical entity , but rather through its consequences . consider the situation where a 5d spinless and massless quantum particle , called a _ 5d photon _ , propagates in a 5d curved space - time . we formulate the setup of the propagation problem introducing a path integral quantum principle . _ a zero rest mass particle is created at a point 1 of a 5d space - time with fixed metric , and then annihilated at a point 2 in the future cone of 1 . we assume that the existence of this particle does not alter the space - time geometry . maximal information on the particle s quantum propagation is obtained from the number of all null paths between points 1 and 2 . _ we call this setup _ 5d quantum optics_. we discuss breaking of 5d covariance when a 4d observer measures a 5d photon and assigns it a 4d physical picture for 5d metrics independent of some coordinates . in the case of translational symmetry along the fifth coordinate , our procedure has formal similarities to the traditional kaluza - klein dimensional reduction . in contrast , the spontaneous compactification of string theory is a proper physical phenomenon ; a macroscopic observer detects all 11 ( or 10 ) dimensions of the space - time up to quantum effects due to the small diameters of the compact dimensions . the outline of the paper is as follows . we proceed with presenting the general case of the 5d quantum optics ( sec . [ sec : qoptics ] ) . in section [ sec : qm ] , we introduce the particular situation where the 5d metric is independent of the fifth space - like coordinate . we first shortly discuss the field equations . then , in sec . [ sec : mcanqm ] , we show that the 5d null path integral is equivalent to a 4d path integral over time - like paths with specified length . thus , we construct a microcanonical ensemble for our 4d quantum mechanics from the microcanonical ensemble of the 5d quantum optics . in sec . [ sec : canqm ] we introduce the corresponding 4d canonical ensemble @xcite . then , we make the connection between the nonrelativistic limit of our formulation of quantum mechanics and feynman s . we conclude that our quantum mechanics is anomaly - free and equivalent to the traditional feyman formulation . in sec . [ sec : sm ] , we investigate another particular case of the 5d quantum optics which we interpret as a formulation of statistical mechanics . the state of thermal equilibrium implies that macroscopic observables do not change in time . presumably , this can be achieved for a 5d metric which is time - independent . in this case , we reformulate the 5d quantum optics as a statistical mechanics for a single spinless particle which belongs to an ensemble of non - interacting particles . it seems unavoidable that our path integral formulation of statistical mechanics needs the ergodic principle in order to establish relations with experiment . also , our statistical mechanics describes only ensembles of discernable particles , unless correction factors are introduced ` by hand ' . if the 5d metric is independent of both time and the fifth coordinate , quantum and statistical mechanics make different pictures of the same 5d reality . in sec . [ sec : kg ] , we present how the klein - gordon equation appears from the 5d formalism . section [ sec:5dst ] discusses the main aspects of the 5d special relativity , and makes further connections with traditional 4d physics . in sec . [ sec : x3 ] we discuss the case where the 5d metric is independent on a proper space dimension ( i.e. , @xmath15 ) and then conclude our work .

if the 5d metric is independent of the fifth coordinate , then the propagation problem can be reduced to four dimensions by foliation along the fifth coordinate , and we obtain a formulation of 4d quantum mechanics . if the 5d metric is independent of time , we foliate along the time coordinate , and obtain a formulation of 4d statistical mechanics . if the 5d metric is independent of both time and the fifth coordinate , then quantum and statistical mechanics are pictures of the same 5d reality . pacs : 03.65.-w , 05.30.-d , 04.50.+h , 31.15.kb keywords : quantum mechanics , quantum statistical mechanics , kaluza - klein gravity , path integrals

we consider a five dimensional ( 5d ) space - time with a space - like fifth dimension . we implement a quantum formalism by path integrals , and postulate that all the physical information on a 5d massless particle propagation is provided by the statistics over null paths in this 5d space - time . if the 5d metric is independent of the fifth coordinate , then the propagation problem can be reduced to four dimensions by foliation along the fifth coordinate , and we obtain a formulation of 4d quantum mechanics . if the 5d metric is independent of time , we foliate along the time coordinate , and obtain a formulation of 4d statistical mechanics . if the 5d metric is independent of both time and the fifth coordinate , then quantum and statistical mechanics are pictures of the same 5d reality . we also discuss the foliation of a proper space dimension , the klein - gordon equation , and a 5d special relativity , completing our interpretation of the 5d geometry . * interpretation of the five dimensional quantum propagation of a spinless massless particle * .25 in romulus breban _ institute for research in electronics and applied physics and department of physics , university of maryland , college park , maryland 20740 . _ pacs : 03.65.-w , 05.30.-d , 04.50.+h , 31.15.kb keywords : quantum mechanics , quantum statistical mechanics , kaluza - klein gravity , path integrals

nlin0608015

i

in recent work , we presented experimental and simulation results for two mutually coupled lasers @xcite with time - delayed asymmetric coupling . the light emitted from one laser propagates through fiber - optic cables to a photodetector that generates an electronic signal proportional to the light - intensity deviations from steady state . the electronic signal may be attenuated or amplified before it modulates the pump current of the other laser . the propagation time of the signal in the optoelectronic path introduces a significant time delay , and the coupling strength in each direction can be controlled separately . our work in @xcite investigated how the time delay and asymmetric coupling led to oscillatory and pulsating laser output . in this paper , we present a more theoretical exploration of the dynamics that result from this coupling configuration . in @xcite we investigated this same configuration ( asymmetric pump coupling ) but without including the effect of delay . in addition , the coupling constant from laser-2 to laser-1 was negative , while the coupling constant from laser-1 to laser-2 was positive . that is , we assumed that the electronic coupling signal from laser-2 was inverted before applying it to the pump of laser-1 . for purely harmonic signals , having opposite - sign coupling constants is equivalent to time - delayed coupling when the delay is half of the period . we found that as the coupling constant from laser-2 to laser-1 is increased in magnitude : ( i ) there is a hopf bifurcation to oscillatory output . ( ii ) for certain parameter values there exists a small - coupling resonance such that the amplitudes of both lasers are pulsating . ( iii ) for large coupling , laser-2 acts as a small - amplitude , nearly harmonic modulation to laser-1 . laser-1 exhibits period - doubling bifurcations to chaos and complex subharmonic resonances . in this paper we include the effect of the delayed - coupling , which results in a coupled set of delay - differential equations ( ddes ) . with delay there is again a hopf bifurcation to oscillatory output . however , the delay allows for periodic oscillations not just at the laser s relaxation period as in @xcite , but at periods that are integer multiples of the delay ; we refer to the former oscillatory solutions as internal modes , " and the latter as external modes . " we show that as the coupling strength is increased , the first instability is a hopf bifurcation to the internal mode . our nonlinear analysis then shows that the amplitude of the internal mode varies as the one - fourth root of the bifurcation parameter s deviation from the hopf bifurcation point . however , in the experiments of @xcite the output was not the internal mode but an external mode . the period of the oscillatory output was a multiple of the delay , and the amplitude of the oscillations varied as the square root of the bifurcation parameter . the discrepancy is due to the fact that the optoelectronic coupling contains an intrinsic low - pass filter that attenuates the internal mode . we show that the filter selects the external mode with the greatest possible frequency passed by the low - pass filter . a nonlinear analysis then shows that the amplitude of the external modes does indeed vary with a square - root power law . for the coupled lasers without delay in @xcite , we found that the parameters could be tuned to cause a resonance - type effect with respect to the coupling ; more specifically , the coupling could be tuned to maximize the amplitude of the oscillatory output . we find that this resonance effect also occurs with the inclusion of the delay . however , there are some dramatic qualitative differences as the coupling parameters are varied . in the system with delay , the branch of periodic solutions in the bifurcation diagram can be smoothly folded to form parameter intervals of bi - stability . then there is a critical value of the same coupling parameter beyond which the bi - stability disappears suddenly and non - smoothly . our coupling scheme is an example of `` incoherent coupling '' @xcite because it depends only on the laser s intensity and not on the complex electric field . this is because the intensity of one laser affects the other only indirectly ; in our case , the intensity of one laser modulates the pump current of the other . in contrast , `` coherent coupling '' refers to when the optical field of one laser is directly injected into the cavity of the other laser . analogously , a single laser with delayed and re - injected self - feedback would be called `` coherent '' feedback . semiconductor lasers with delayed coherent feedback have been extensively studied because of the their widespread application in electronics and communication systems ; there the laser s output signal may be reflected off external surfaces back into the laser . the lang - kobayashi ddes @xcite are the canonical model for semiconductor lasers with delayed self - feedback and have been used to investigate phenomena ranging from the onset of instabilities to the development of chaotic output referred to as `` coherence collapse '' ( see @xcite for a review ) . coupled sets of lang - kobayashi or related ddes are most often used to described coherently - coupled semiconductor lasers with delay two recent studies @xcite are in the same spirit as this paper as they track the number of and properties of oscillatory solutions that appear as the coupling strength is increased . the main simplification that results from considering incoherent coupling between the lasers is that neither the laser - frequency detuning nor the electric - field phase differences affect the dynamics of the coupled system @xcite . pieroux et al . @xcite have shown that the electrooptical coupling we consider in this paper leads to an equivalent dynamical model as incoherent coupling . there have recently been a number of other investigations of lasers with incoherent coupling . the main focus of many of these works was on chaotic synchronization ( see @xcite and included references).two recent papers by vicente et al . @xcite consider a similar implementation of optoelectronic coupling to that we consider here , i.e. , the intensity of one laser modulates the pump current of the other . their investigation of the oscillatory solutions is mainly numerical and they discuss interesting phenomena such as amplitude quenching , frequency locking and routes to chaos . delay - coupled relaxation and limit - cycle oscillators have been the subject of many investigations ( see @xcite and their included references ) . these systems are self - oscillatory and the amplitude is often fixed by the intrinsic properties of the oscillator . in many cases the system may be reduced to a phase equation , or a system of phase equations if the oscillators are coupled @xcite . in contrast , for laser systems the amplitude is an important dynamical variable . this is because the lasers we consider are weakly damped , nearly conservative systems such that the steady state is the only asymptotically stable solution . oscillations must be induced by external mechanisms such as modulation , injection or coupling @xcite . thus , the amplitude of the oscillations is highly dependent upon the external mechanism , in our case the coupling , rather than the individual laser . we should mention that for coupled limit - cycle oscillators there is the amplitude instability referred to as `` amplitude death , '' where for specific values of the coupling ( and oscillator parameter values ) the amplitude becomes zero . after presenting our model , we show that the linear - stability analysis predicts a critical value of the coupling constant ( that depends upon the delay time ) such that there is hopf bifurcation to the internal mode , i.e. , oscillations with the intrinsic relaxation period . we then use multiple - scale perturbation methods , modified to account for time delays @xcite , to analyze the long - time evolution of the internal mode . the results are a pair of complex stuart - landau ddes for the oscillation amplitudes that include a slow - time delay term . we analyze the amplitude equations to determine the bifurcation properties of the internal mode . of particular note is that we allow for independent control of the coupling constants ; most other studies of coupled lasers and oscillators consider symmetric coupling , where the coupling is the same across all of the elements . the independent control is important because , as we will show , it allows for a singularity in the bifurcation equations that marks the resonance " of large amplitude solutions . the hopf bifurcation to the internal mode occurs for small coupling . however , as the coupling is increased , the external modes appear via hopf bifurcations . we have extended our multiple - scale analysis to be able to describe the bifurcation of the external modes that occur for @xmath0 coupling . the analytical challenge is that the delay terms remain a part of the leading - order problem . describing the bifurcation of the external modes is important for comparing our results to those in experiments @xcite , because the experimental system contains low - pass filters that attenuate the internal mode originating from the first hopf bifurcation . an alternative to our multiple - scale method for deriving slow - time amplitude equations is to apply center - manifold theory with averaging @xcite . however , the averaging method does not retain the delay in the slow time ; that is , the amplitude equations are ordinary - differential equations , not ddes . the distinction is not important for their or our investigation because we look for steady - state solutions of the amplitude equations . however , time - varying amplitudes may require consideration of the slow - time delay . reddy et al . @xcite considered delay - coupled stuart - landau ddes similar to the amplitude equations we derive here . however , the complex coefficients they use are appropriate for limit - cycle oscillators and not the lasers that we consider . they focus their work on the properties of synchronization and amplitude death . in the next section , we nondimensionalize the model for two - coupled lasers , with the result being the focus of the rest of the paper . we perform the linear - stability analysis in sec . [ s : linstab ] . slow - time evolution equations for small and @xmath0 coupling are derived in sec . [ s : intmodes ] and sec . [ s : extmodes ] , respectively . we close with a discussion of the results .

we consider a model for two lasers that are mutually coupled optoelectronically by modulating the pump of one laser with the intensity deviations of the other . multiscale perturbation methods are used to describe the amplitude and period of oscillations as a function of the coupling strength and delay time . for weak coupling the oscillations have the laser s relaxation period , and the amplitude varies as the one - fourth power of the parameter deviations from the bifurcation point . for order - one coupling strength the period is determined as multiples of the delay time , and the amplitude varies with a square - root power law . because we allow for independent control of the individual coupling constants , for certain parameter values there is an atypical amplitude - resonance phenomena . finally , our theoretical results are consistent with recent experimental observations when the inclusion of a low - pass filter in the coupling loop is taken into account .

we consider a model for two lasers that are mutually coupled optoelectronically by modulating the pump of one laser with the intensity deviations of the other . signal propagation time in the optoelectronic loop causes a significant delay leading to the onset of oscillatory output . multiscale perturbation methods are used to describe the amplitude and period of oscillations as a function of the coupling strength and delay time . for weak coupling the oscillations have the laser s relaxation period , and the amplitude varies as the one - fourth power of the parameter deviations from the bifurcation point . for order - one coupling strength the period is determined as multiples of the delay time , and the amplitude varies with a square - root power law . because we allow for independent control of the individual coupling constants , for certain parameter values there is an atypical amplitude - resonance phenomena . finally , our theoretical results are consistent with recent experimental observations when the inclusion of a low - pass filter in the coupling loop is taken into account . coupled lasers , delay , hopf bifurcation , resonance 34d15 , 37g15 , 39a11 , 78a60

0811.1458

i

as a summary , we have considered an exact @xmath0 reflection symmetry in neutrino sector realized at the gut scale in the context of the seesaw model . the exact @xmath0 reflection symmetry has been imposed in the basis where both the charged lepton mass and heavy majorana neutrino mass matrices are real and diagonal . we have assumed that the two lighter heavy majorana neutrinos are degenerate at the gut scale . it has been shown that the rg evolution from the gut scale to the seesaw scale gives rise to breaking of the @xmath1 symmetry and a tiny splitting between two degenerate heavy majorana neutrino masses as well as small variations of the cp phases in @xmath2 , which are essential to achieve a successful leptogenesis . such small rg effects lead to tiny deviations of @xmath3 from the maximal value and the cp phase @xmath4 from @xmath5 imposed at the gut scale due to @xmath1 reflection symmetry . in our scenario , the required amount of the baryon asymmetry @xmath6 could be generated via so - called resonant @xmath7-leptogenesis , in which the wash - out factor concerned with electron flavor plays a crucial role in reproducing a successful leptogenesis . and we have found that the magnitude of the electron leptogenesis is enhanced by @xmath185 orders due to the flavor effects in the sm , and enhanced further by a factor of @xmath273 for the ssm . a point deserved to notice is that cp violation responsible for the generation of baryon asymmetry of our universe comes from the breaking of both the two degenerate heavy majorana neutrinos and the cp phases @xmath53 in @xmath2 by rg evolutions , which corresponds to the tiny breakdown of @xmath1 reflection symmetry , and such small rg effects cause leptogenesis to directly be linked with the cp violation measurable through neutrino oscillation as well as neutrino mixing angles @xmath8 and @xmath9 . we expect that in addition to the reactor and long baseline neutrino experiments for precise measurements of neutrino mixing angles and cp violation , the measurements for the supersymmetric parameter @xmath10 at future collider experiments would serve as an indirect test of our scenario of baryogenesis based on the @xmath1 reflection symmetry .

we consider an exact reflection symmetry in neutrino sector realized at the gut scale in the context of the seesaw model with and without supersymmetry . assuming the two lighter heavy majorana neutrinos are degenerate at the gut scale , it is shown that the renormalization group ( rg ) evolution from the gut scale to the seesaw scale gives rise to breaking of the symmetry and a tiny splitting between two degenerate heavy majorana neutrino masses as well as small variations of the cp phases in , which are essential to achieve a successful leptogenesis . such small rg effects lead to tiny deviations of from the maximal value and the cp phase from imposed at the gut scale due to reflection symmetry . in our scenario , the required amount of the baryon asymmetry can be generated via so - called resonant-leptogenesis , in which the wash - out factor concerned with electron flavor plays a crucial role in reproducing a successful leptogenesis . we show that cp violation responsible for the generation of baryon asymmetry of our universe can be directly linked with cp violation measurable through neutrino oscillation as well as neutrino mixing angles and . we expect that , in addition to the reactor and long baseline neutrino experiments , the measurements for the supersymmetric parameter at future collider experiments would serve as an indirect test of our scenario of baryogenesis based on the reflection symmetry . + pacs : 14.60.pq , 11.30.fs , 11.10.hi , 98.80.cq , 13.35.hb

we consider an exact reflection symmetry in neutrino sector realized at the gut scale in the context of the seesaw model with and without supersymmetry . assuming the two lighter heavy majorana neutrinos are degenerate at the gut scale , it is shown that the renormalization group ( rg ) evolution from the gut scale to the seesaw scale gives rise to breaking of the symmetry and a tiny splitting between two degenerate heavy majorana neutrino masses as well as small variations of the cp phases in , which are essential to achieve a successful leptogenesis . such small rg effects lead to tiny deviations of from the maximal value and the cp phase from imposed at the gut scale due to reflection symmetry . in our scenario , the required amount of the baryon asymmetry can be generated via so - called resonant-leptogenesis , in which the wash - out factor concerned with electron flavor plays a crucial role in reproducing a successful leptogenesis . we show that cp violation responsible for the generation of baryon asymmetry of our universe can be directly linked with cp violation measurable through neutrino oscillation as well as neutrino mixing angles and . we expect that , in addition to the reactor and long baseline neutrino experiments , the measurements for the supersymmetric parameter at future collider experiments would serve as an indirect test of our scenario of baryogenesis based on the reflection symmetry . + pacs : 14.60.pq , 11.30.fs , 11.10.hi , 98.80.cq , 13.35.hb

1312.6486

c

we considered @xmath0 photoproduction in ion ion upcs at the lhc and rhic in the coherent and incoherent channels with and without accompanying forward neutron emission and analyzed the role of nuclear gluon shadowing at small @xmath1 , @xmath2 , in these processes . we extended the formalism of leading twist nuclear shadowing characterized by large nuclear gluon shadowing to the incoherent @xmath13 cross section . we found that despite a good agreement between the approaches predicting large nuclear gluon shadowing at @xmath5 and the large nuclear suppression factor extracted from the alice data on coherent @xmath0 photoproduction in pb - pb upcs at the lhc @xcite , in the incoherent channel , the leading twist approximation predicts the amount of nuclear suppression due to gluon shadowing which exceeds that seen in the data by approximately a factor of @xmath3 ( fig . [ cirapalice ] ) . we hypothesize that one source of the discrepancy could be the contribution of incoherent nucleon dissociation , @xmath223 , which could potentially contribute to the alice data @xcite and which is not taken into account in our theoretical analysis . in coherent @xmath0 photoproduction in ion ion upcs , it is problematic ( except for @xmath147 and large @xmath179 ) to separate the contributions of high - energy and low - energy photons to the @xmath4 cross section , which reduces the range of @xmath1 for the studies of small-@xmath1 nuclear gluon shadowing . this problem can be circumvented by considering @xmath0 photoproduction in ion ion upcs accompanied by neutron emission due to electromagnetic excitation of one or both colliding nuclei . using the leading twist approximation for nuclear gluon shadowing , we made predictions for coherent and incoherent nuclear @xmath0 photoproduction in pb - pb upcs accompanied by neutron emission in various channels at the lhc ( fig . [ cms ] ) . in particular , we discuss the strategy allowing one to separate the low - photon - energy and the high - photon - energy contributions to coherent @xmath0 photoproduction performing a joint analysis of the data in the 0nxn and xnxn - channels . this gives an opportunity to shift the study of nuclear gluon shadowing to the lower @xmath1 region of @xmath6 . in addition , in the incoherent case accompanied by neutron emission , we show that the separation between the low - photon - energy and high - photon - energy contributions can be efficiently performed by measuring the correlation between the directions of @xmath0 and the emitted neutrons ( fig . [ ptdist ] ) . in the kinematics where nuclear shadowing is small , we showed ( fig . [ phenix ] ) that theoretical predictions based on the dipole model agree with the phenix data on @xmath0 photoproduction in au - au upcs at @xmath224 gev in the xnxn - channel ( both colliding nuclei emit neutrons detected in the zdcs ) .

we consider photoproduction in ion ion ultraperipheral collisions ( upcs ) at the lhc and rhic in the coherent and incoherent quasielastic channels with and without accompanying forward neutron emission and analyze the role of nuclear gluon shadowing at small , , in these processes . we find that despite the good agreement between large nuclear gluon shadowing and the alice data in the coherent channel , in the incoherent channel , the leading twist approximation predicts the amount of nuclear suppression which is by approximately a factor of exceeds that seen in the data . we hypothesize that part of the discrepancy can be accounted for by the incoherent inelastic process of photoproduction with nucleon dissociation . in addition , in the incoherent quasielastic case , we show that the separation between the low - photon - energy and high - photon - energy contributions can be efficiently performed by measuring the correlation between the directions of and the emitted neutrons .

we consider photoproduction in ion ion ultraperipheral collisions ( upcs ) at the lhc and rhic in the coherent and incoherent quasielastic channels with and without accompanying forward neutron emission and analyze the role of nuclear gluon shadowing at small , , in these processes . we find that despite the good agreement between large nuclear gluon shadowing and the alice data in the coherent channel , in the incoherent channel , the leading twist approximation predicts the amount of nuclear suppression which is by approximately a factor of exceeds that seen in the data . we hypothesize that part of the discrepancy can be accounted for by the incoherent inelastic process of photoproduction with nucleon dissociation . to separate the high - photon - energy and low - photon - energy contributions to the cross section , we consider ion ion upcs accompanied by neutron emission due to electromagnetic excitation of one or both colliding nuclei . we describe the corresponding phenix data and make predictions for the lhc kinematics . in addition , in the incoherent quasielastic case , we show that the separation between the low - photon - energy and high - photon - energy contributions can be efficiently performed by measuring the correlation between the directions of and the emitted neutrons .

1010.5651

i

due to the diverse features and applications of interconnection networks , it is possible to find many interpretations about network `` optimality '' in the literature . here we are concerned with the following ; see @xcite , @xcite , and ( * ? ? ? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ an optimal network contains the maximum possible number of nodes , given a limit on the number of connections attached to a node and a limit on the distance between any two nodes of the network . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ this interpretation has attracted network designers and the research community in general due to its implications in the design of large interconnection networks . in graph - theoretical terms , this interpretation leads to the _ degree / diameter problem _ ( the problem of finding the largest possible number of vertices in a graph with given maximum degree and diameter ) . if the graphs in question are subject to further restrictions such as being bipartite , planarity and/or transitivity , we can state the degree / diameter problem for the classes of graphs under consideration . in this paper we will consider only bipartite graphs , and in this case , the degree / diameter problem can be stated as follows . * _ degree / diameter problem for bipartite graphs _ : given natural numbers @xmath0 and @xmath1 , find the largest possible number @xmath27 of vertices in a bipartite graph of maximum degree @xmath3 and diameter @xmath4 . note that @xmath27 is well defined for @xmath28 and @xmath1 . an upper bound for @xmath27 is given by the _ moore bipartite bound _ @xmath29 , defined below : @xmath30 bipartite graphs of degree @xmath31 , diameter @xmath4 and order @xmath32 are called _ graphs_. moore bipartite graphs are rare ; for @xmath33 they are the cycles of length @xmath34 , while for @xmath35 moore bipartite graphs exist only for diameters 2 , 3 , 4 and 6 ; see @xcite . therefore , we are interested in studying the existence or otherwise of bipartite graphs of given maximum degree @xmath3 , diameter @xmath4 and order @xmath36 for @xmath37 ; that is , bipartite @xmath8-graphs , where the parameter @xmath9 is called the _ defect_. for notational convenience , we consider moore bipartite graphs as having defect @xmath38 . only a few values of @xmath27 are known at present . with the exception of @xmath39 , settled in @xcite , the other known values of @xmath27 are those for which there is a moore bipartite graph . the paper @xcite combined with @xcite almost settled the case of bipartite graphs of defect 2 ; if @xmath40 and @xmath13 , then such graphs may only exist for @xmath14 and certain values of @xmath31 . bipartite @xmath8-graphs with @xmath41 have been rarely considered in the literature so far . in this paper we consider bipartite @xmath42-graphs with @xmath43 and @xmath44 . by using combinatorial approaches we obtain several important results about bipartite graphs of defect 4 , including several necessary conditions for the existence of bipartite @xmath16-graphs ; the complete catalogue of bipartite @xmath17-graphs with @xmath18 and @xmath19 ; the complete catalogue of bipartite @xmath45-graphs with @xmath43 , @xmath21 ( @xmath22 ) and @xmath19 ; and a non - existence proof of all bipartite @xmath42-graphs with @xmath40 and odd @xmath25 . finally , we conjecture that there are no bipartite graphs of defect @xmath10 for @xmath35 and @xmath26 . the main results in this paper do not apply to bipartite @xmath42-graphs with @xmath46 and @xmath47 . some of our assertions , however , do offer a partial characterisation of all bipartite @xmath42-graphs with @xmath40 and @xmath13 . at the time of writing the paper we do not foresee a conclusive way to take on the diameters @xmath48 and @xmath10 . to deal with such graphs it would be necessary to either find different ideas or complement some of the ones presented here . section [ sub : diameters34 ] contains further comments on such diameters .

we consider the bipartite version of the _ degree / diameter problem _ , namely , given natural numbers and , find the maximum number of vertices in a bipartite graph of maximum degree and diameter . in this context , the moore bipartite bound represents an upper bound for . bipartite graphs of maximum degree , diameter and order called _ moore bipartite graphs _ turned out to be very rare . therefore , it is very interesting to investigate bipartite graphs of maximum degree , diameter and order with small ; that is , bipartite-graphs . the parameter is called the _ defect_. this paper considers bipartite graphs of defect at most , and presents all the known such graphs . bipartite graphs of defect have been studied in the past ; if and , they may only exist for . the main results of the paper include several necessary conditions for the existence of bipartite-graphs ; the complete catalogue of bipartite-graphs with and ; the complete catalogue of bipartite-graphs with , ( ) and ; and a non - existence proof of all bipartite-graphs with and odd . finally , we conjecture that there are no bipartite graphs of defect for and , and comment on some implications of our results for the upper bounds of . * keywords : * moore bipartite bound ; moore bipartite graph ; degree / diameter problem for bipartite graphs ; defect ; repeat . * ams subject classification : * 05c35 , 05c75 .

we consider the bipartite version of the _ degree / diameter problem _ , namely , given natural numbers and , find the maximum number of vertices in a bipartite graph of maximum degree and diameter . in this context , the moore bipartite bound represents an upper bound for . bipartite graphs of maximum degree , diameter and order called _ moore bipartite graphs _ turned out to be very rare . therefore , it is very interesting to investigate bipartite graphs of maximum degree , diameter and order with small ; that is , bipartite-graphs . the parameter is called the _ defect_. this paper considers bipartite graphs of defect at most , and presents all the known such graphs . bipartite graphs of defect have been studied in the past ; if and , they may only exist for . however , when bipartite-graphs represent a wide unexplored area . the main results of the paper include several necessary conditions for the existence of bipartite-graphs ; the complete catalogue of bipartite-graphs with and ; the complete catalogue of bipartite-graphs with , ( ) and ; and a non - existence proof of all bipartite-graphs with and odd . finally , we conjecture that there are no bipartite graphs of defect for and , and comment on some implications of our results for the upper bounds of . * keywords : * moore bipartite bound ; moore bipartite graph ; degree / diameter problem for bipartite graphs ; defect ; repeat . * ams subject classification : * 05c35 , 05c75 .

math0703377

i

solving a general nonlinear optimal control problem ( ocp ) is a difficult challenge , despite powerful theoretical tools are available , e.g. the maximum principle and hamilton - jacobi - bellman ( hjb ) optimality equation . the problem is even more difficult in the presence of state and/or control constraints . state constraints are particularly difficult to handle , and the interested reader is referred to capuzzo - dolcetta and lions @xcite and soner @xcite for a detailed account of hjb theory in the case of state constraints . there exist many numerical methods to compute the solution of a given optimal control problem ; for instance , _ multiple shooting _ techniques which solve two - point boundary value problems as described , e.g. , in @xcite , or _ direct methods _ , as , e.g. , in @xcite , which use , among others , descent or gradient - like algorithms . to deal with optimal control problems with state constraints , some adapted versions of the maximum principle have been developed ( see @xcite , and see @xcite for a survey of this theory ) , but happen to be very hard to implement in general . on the other hand , the ocp can be written as an infinite - dimensional linear program ( lp ) over two spaces of measures . this is called the _ weak _ formulation of the ocp in vinter @xcite ( stated in the more general context of differential inclusions ) . the two unknown measures are the state - action _ occupation measure _ ( o.m . ) _ up to _ the final time @xmath0 , and the state o.m . _ at _ time @xmath0 . the optimal value of the resulting lp always provides a lower bound on the optimal value of the ocp , and under some convexity assumptions , both values coincide ; see vinter @xcite and hernandez - hernandez et al . @xcite as well . the dual of the original infinite dimensional lp has an interpretation in terms of `` subsolutions '' of related hjb - like optimality conditions , as for the unconstrained case . the only difference with the unconstrained case is the underlying function space involved , which directly incorporate the state constraints . namely , the functions are only defined on the state constraint set . an interesting feature of this lp approach with o.m.s is that state constraints , as well as state and/or action constraints are all easy to handle ; indeed they simply translate into constraints on the supports of the unknown o.m.s . it thus provides an alternative to the use of maximum principles with state constraints . however , although this lp approach is valid for any ocp , solving the corresponding ( infinite - dimensional ) lp is difficult in general ; however , general lp approximation schemes based on grids have been proposed in e.g. hernandez and lasserre @xcite . this lp approach has also been used in the context of discrete - time markov control processes , and is dual to bellman s optimality principle . for more details the interested reader is referred to borkar @xcite , hernandez - lerma and lasserre @xcite and many references therein . for some continuous - time stochastic control problems ( e.g. , modeled by diffusions ) and optimal stopping problems , the lp approach has also been used with success to prove existence of stationary optimal policies ; see for instance cho and stockbridge @xcite , helmes and stockbridge @xcite , helmes et al . @xcite , kurtz and stockbridge @xcite , and also fleming and vermes @xcite . in some of these works , the moment approach is also used to approximate the resulting infinite - dimensional lp . * contribution . * in this paper , we consider the particular class of nonlinear ocp s with state and/or control constraints , for which all data describing the problem ( dynamics , state and control constraints ) are _ polynomials_. the approach also extends to the case of problems with _ smooth _ data and compact sets , because polynomials are dense in the space of functions considered ; this point of view is detailed in [ smooth ] . in this restricted polynomial framework , the lp approach has interesting additional features that can be exploited for effective numerical computation . indeed , what makes this lp approach attractive is that for the class of ocps considered : @xmath1 only the _ moments _ of the o.m.s appear in the lp formulation , so that we already end up with countably many variables , a significant progress . @xmath1 constraints on the support of the o.m.s translate easily into either lp or sdp ( semi definite programming ) _ necessary _ constraints on their moments . even more , for ( semi - algebraic ) compact supports , relatively recent powerful results from real algebraic geometry make these constraints also _ sufficient_. @xmath1 when truncating to finitely many moments , the resulting lp or sdp s are solvable and their optimal values form a monotone nondecreasing sequence ( indexed by the number of moments considered ) of lower bounds on the optimal value of the lp ( and thus of the ocp ) . therefore , based on the above observations , we propose an approximation of the optimal value of the ocp via solving a hierarchy of sdps ( or linear matrix inequalities , lmis)that provides a monotone nondecreasing sequence of lower bounds on the optimal value of the weak lp formulation of the ocp . in adddition , under some compactness assumption of the state and control constraint sets , the sequence of lower bounds is shown to converge to the optimal value of the lp , and thus the optimal value of the ocp when the former and latter are equal . as such , it could be seen as a complement to the above shooting or direct methods , and when the sequence of lower bounds converges to the optimal value , a test of their efficiency . finally this approach can also be used to provide a _ certificate _ of unfeasibility . indeed , if in the hierarchy of lmi - relaxations of the minimum time ocp , one is infeasible then the ocp itself is infeasible . it turns out that sometimes this certificate is provided at an early stage in the hierarchy , i.e. with very few moments . this is illustrated on two simple examples . in a pioneering paper , dawson @xcite had suggested the use of _ moments _ in the lp approach with o.m.s , but results on the @xmath2-moment problem by schmdgen @xcite and putinar @xcite were either not available at that time . later , helmes and stockbridge @xcite and helmes , rhl and stockbridge @xcite have used lp moment conditions for computing some exit time moments in some diffusion model , whereas for the same models , lasserre and prieto - rumeau @xcite have shown that sdp moment conditions are superior in terms of precision and number of moments to consider ; in @xcite , they have extended the moment approach for options pricing problems in some mathematical finance models . more recently , lasserre , prieur and henrion @xcite have used the o.m . approach for minimum time ocp without state constraint . preliminary experimental results on brockett s integrator example , and the double integrator show fast convergence with few moments .

we consider the class of nonlinear optimal control problems ( ocp ) with polynomial data , i.e. , the differential equation , state and control constraints and cost are all described by polynomials , and more generally for ocps with smooth data . in addition , state constraints as well as state and/or action constraints are allowed . we provide a simple hierarchy of lmi ( linear matrix inequality)-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value . under some convexity assumptions , the sequence converges to the optimal value of the ocp . preliminary results show that good approximations are obtained with few moments .

we consider the class of nonlinear optimal control problems ( ocp ) with polynomial data , i.e. , the differential equation , state and control constraints and cost are all described by polynomials , and more generally for ocps with smooth data . in addition , state constraints as well as state and/or action constraints are allowed . we provide a simple hierarchy of lmi ( linear matrix inequality)-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value . under some convexity assumptions , the sequence converges to the optimal value of the ocp . preliminary results show that good approximations are obtained with few moments .

cond-mat0001036

i

the interplay between the electron s spin degree of freedom and the inter - electron interaction has been of interest in the condensed matter physics , in particular in the jellium model where the neutralizing background is taken to be rigid and uniform . the relative strength of the interaction is conventionally measured through the parameter @xmath3 which is the interparticle distance measured in units of the bohr radius @xmath4 , @xmath5 being the dielectric constant and @xmath6 the band mass of electron . for electrons confined to two dimensions , which will be our focus in this paper , we have @xmath7 where @xmath8 is the two - dimensional density of electrons . the interaction strength is enhanced relative to the kinetic energy as the system becomes more dilute , i.e. , as @xmath3 increases . it has been predicted that as @xmath3 is increased , the electron liquid eventually becomes spontaneously spin polarized to gain in the exchange energy , ultimately going into a wigner crystal at @xmath9 @xcite . the two - dimensional electron systems , obtained experimentally at the interface of two semiconductors , constitute an almost ideal realization of the jellium model for several reasons . samples with mobility in access of 10 million @xmath10/vs are available @xcite , minizing the effect of disorder . furthermore , the density of electrons , which controls the strength of the interaction relative to the kinetic energy , can be varied by a factor of 20 @xcite . we will consider electrons in the presence of a magnetic field , specifically , at filling factor @xmath0 , which is a particularly clean test case for the kind of physics in which we are interested . there are three relevant energy scales here : @xmath11 is the cyclotron energy , @xmath12 is the typical coulomb energy , @xmath13 being the magnetic length , and @xmath14 is the zeeman splitting energy which is the zeeman energy cost necessary for a single spin flip . ( to an extent , the zeeman and the cyclotron energies can be varied independently by application of the magnetic field at an angle ; while the former depends on the total magnetic field , the latter is determined by the normal component only . ) the ground state is known in two limits . when @xmath15 dominates , the ground state is a spin singlet , with 0@xmath16 and 0@xmath17 landau levels fully occupied . on the other hand , when @xmath14 is the largest energy , the ground state is fully polarized ; when the coulomb interaction is not strong enough to cause substantial landau level mixing ( i.e. , in the limit of @xmath18 ) , the ground state has 0@xmath16 and 1@xmath16 landau levels occupied . when the ground state is described in terms of filled landau levels , we will denote it by @xmath19@xmath20@xmath21 , where @xmath22@xmath16 and @xmath22@xmath17 are the numbers of occupied landau levels for up and down spin electrons . the possible filled landau level states at @xmath0 are then @xmath23 and @xmath24 , the unpolarized and the fully polarized states , respectively . our interest will be in situations when @xmath25 becomes comparable to or greater than the cyclotron energy . this again corresponds to @xmath26 , where at @xmath0 , @xmath3 can be seen to be given by @xmath27 and is clearly a measure of the strength of the interaction relative to the cyclotron energy . here , landau level mixing becomes crucial and may destabilize the above states . our principal goal will be to determine the phase diagram of the fully polarized and the unpolarized states @xmath24 and @xmath23 . our work has been motivated by the recent experiments of eriksson _ et al . _ @xcite where they investigate by inelastic light scattering both the spin and the charge density collective modes at @xmath0 for samples with @xmath3 as large as 6 , corresponding to densities as low as @xmath28 @xmath29 . they find a qualitative change in the number and the character of collective modes at approximately @xmath30 . this was interpreted in a landau fermi liquid approach , where the magnetic field was treated as a perturbation on the zero field fermi liquid . however , the fermi liquid approach , which is suitable at small magnetic field , is not an obviously valid starting point for the problem at hand , and other approaches are desirable . a comparison between the ground state energies of the unpolarized and the fully polarized hartree fock state shows that a transition between them takes place at @xmath31 for @xmath32 , as we will see in . this raises the question : is the ground state at large @xmath3 fully polarized ? if true , this would indeed be an interesting example of an interaction driven ferromagnetism . if it is indeed fully polarized , is the @xmath24 state a reasonable starting point for its study ? besides being fully polarized , @xmath24 incorporates the effect of landau level mixing , albeit in a very special manner , through promoting all electrons in 0@xmath17 to 1@xmath16 . a reliable treatment of landau level mixing lies at the crux of the problem . we shall incorporate landau level mixing in a perturbative time - dependent hartree - fock scheme , i.e. , by incorporating vertex corrections through ladder diagrams in the random phase approximation ( rpa ) . the most crucial approximation in our calculations will be a restriction to the subspace of a single - particle hole pair ; within this subspace , however , the landau level mixing is treated accurately . clearly , this approach is not quantitatively valid except at small @xmath3 , but we believe that it gives an insight into the physics even when @xmath3 is not small . for a better quantitative description at large @xmath3 , it would be important to deal with screening by more than one particle - hole pair , but that is outside the scope of the present paper . as mentioned above , there certainly are parameters for which the fully polarized @xmath24 state describes the actual ground state ; in particular , it may occur even when @xmath3 is large provided that the zeeman energy is sufficiently strong . our approach here will be to take it as the starting point and investigate the regime of its stability by calculating the dispersion of the charge and the spin density collective modes . the collective modes have a simple interpretation when the landau level mixing is negligible ( @xmath33 ) . the lowest charge density excitation mode corresponds to the excitation of one electron from 1@xmath16 to 2@xmath16 landau level . the kinetic energy change of any collective mode is well defined when the landau level mixing is weak , and will be used to label the various modes ( this notation will be used even when the landau level mixing is significant , by looking at the evolution of the modes from small to large @xmath3 ) . the 1@xmath16@xmath342@xmath16 mode will be referred to as the @xmath35 mode . for spin - density excitation , there are three modes of primary interest , corresponding to excitations 0@xmath16@xmath340@xmath17 , 1@xmath16@xmath341@xmath17 , and 1@xmath16@xmath340@xmath17 which are depicted schematically in ( a ) , ( b ) , and ( c ) in fig.[sdediagram ] respectively . the first two are @xmath36 modes and the last one is @xmath37 mode . these are of course coupled , and a diagonalization of the problem produces the usual spin - wave excitation mode , with the energy approaching the zeeman splitting in the long wave length limit , in accordance with the goldstone theorem , as well as two massive spin - density modes . our principal result is that while the charge density collective mode shows no instability , the spin - density collective mode develops a deep roton minimum in the presence of substantial landau level mixing and becomes soft in certain parameter regimes . ( indeed , as @xmath3 is increased , there will eventually also be an instability in the charge density channel , indicating the formation of a wigner crystal , but we have not explored this question since our perturbation theory is not valid at very large @xmath3 . ) both the existence of the roton minimum and its softening as the zeeman energy is reduced are experimentally testable predictions of our theory . the phase diagram thus obtained later is shown in fig.[phase ] . it is instructive to compare it with the phase diagram in the absence of interactions , which consists of the fully polarized state @xmath24 for @xmath38 and the unpolarized state @xmath23 for @xmath39 with a transition taking place at precisely @xmath40 . at small @xmath3 , interactions make the @xmath24 state more stable , indicated by the fact that it survives even for @xmath41 . however , at large @xmath3 , @xmath38 is required to stabilize the fully polarized state . it is noteworthy that at small @xmath14 , the fully polarized state is found to be unstable at arbitrary @xmath3 . we also consider the collective modes of @xmath23 , expected to be valid at small @xmath14 and @xmath3 . it becomes unstable as @xmath3 is increased , consistent with an earlier conclusion of macdonald @xcite . what about the state at large @xmath3 but small zeeman energy ? as discovered in our study , here the @xmath0 state is not described by either of the two aforementioned hartree fock states . the finite wave vector spin - wave instability of the fully polarized state suggests that it is some kind of spin density wave state . it is not possible to be more definitive about it based on our present study . of course , at extremely large @xmath3 , when @xmath25 is much larger than the cyclotron energy , our calculation is unreliable , but indicates that even if a fully polarized state occurs , as expected based on the zero field result , it will most likely not be described by the @xmath24 hartree fock state . there have been many theoretical studies of the collective excitations of integer quantum hall effect ( iqhe ) states in the past , but , to our knowledge , the spin - density wave excitations of the fully polarized @xmath24 state have not been considered previously . for other collective modes , our results reduce to the earlier results in appropriate limits . if possible transitions of the electron and hole between different landau levels are ignored and if self - energy corrections are omitted , the problem of collective excitation is reduced to determining the binding energy of two oppositely charged particles strictly confined in their respective landau levels@xcite . in this case the wave function for the bound state is independent of interaction potential , and is uniquely determined by the wave vector @xmath42 . the transition of the electron and hole or the recombination of the particle - hole pair has been considered in the random phase approximation(rpa)@xcite . later the rpa was incorporated with the self - energy correction and the binding energy term by kallin and halperin @xcite where a number of interesting collective excitations from the unpolarized and the partially polarized ground state were considered in the absence of landau level mixing ( valid when @xmath43 ) . the landau level mixing was considered by macdonald in , treating the mixing matrix elements between various modes as small parameters and applying a second order perturbation theory . our calculation will be formulated in terms of diagrams , following kallin and halperin in , and will be performed with a full treatment of the mixing matrix elements within the subspace of a single particle - hole pair at any given instant . the diagrammatic formulation of the problem is presented in detail in sec.[sec - diagram ] below . in sec.[sec - fullypol ] we describe the diagrammatic formalism used to compute dispersion curves of the collective excitation from the fully polarized ground state at @xmath0 . we will concentrate on the spin density excitation which will be responsible for an instability of the iqhe state in the parameter regime under consideration . similarly , is devoted to the collective excitations of the unpolarized ground state at @xmath0 . dispersion curves of the spin density excitation is computed for various values of @xmath3 and zeeman splitting energy , @xmath14 . the phase diagram as a function of @xmath3 and @xmath14 is obtained in by determining the critical @xmath14 at which the energy of the spin density excitation vanishes . from the phase diagram we will learn that for large @xmath3 and small @xmath14 neither the fully polarized nor the unpolarized state is stable against a spin - density wave state . the paper is concluded in , where we also discuss the implications of our study for the fractional quantum hall effect ( fqhe ) .

we calculate the charge and the spin density collective modes in random phase approximation ( rpa ) including vertex corrections ( also known as time dependent hartree fock ) , and treating the landau level mixing accurately within the subspace of a single particle hole pair . the feasibility of the experimental observation of the roton minimum in the spin wave mode and its softening will be discussed .

we consider the effect of interactions on electrons confined to two dimensions at landau level filling , with the specific aim to determine the range of parameters where the fully polarized state is stable . we calculate the charge and the spin density collective modes in random phase approximation ( rpa ) including vertex corrections ( also known as time dependent hartree fock ) , and treating the landau level mixing accurately within the subspace of a single particle hole pair . it is found that the spin wave excitation mode of the fully polarized state has a roton minimum which deepens as a result of the interaction induced landau level mixing , and the energy of the roton vanishes at a critical zeeman energy signaling an instability of the fully polarized state at still lower zeeman energies . the feasibility of the experimental observation of the roton minimum in the spin wave mode and its softening will be discussed . the spin and charge density collective modes of the unpolarized state are also considered , and a phase diagram for the state as a function of and the zeeman energy is obtained .

1211.1806

i

the fermi - bose model under study here forms the underlying basis for a range of phenomena in condensed matter and ultra - cold atomic physics . it was proposed in the context of high - temperature superconductivity by friedberg and lee @xcite , and in ultracold gases it corresponds to the theory of resonance superfluidity with feshbach molecules @xcite . the latter forms the basis of a model for describing the physics of the bcs - bec crossover @xcite . more recently , the fermion - boson model has been used for analyzing the decay of double occupancies ( doublons ) @xcite in a driven fermi - hubbard system @xcite . the particular situation that we concentrate on in this article corresponds to spontaneous dissociation of a bose - einstein condensate of molecular dimers into fermionic atoms @xcite . this process represents a fermionic counterpart of parametric down - conversion in quantum optics . after recent experimental achivements of molecular dissociation @xcite , our aim here is to take the theory for numerical modeling of dissociation into fermionic atoms from the state of principally possible to the state of being useful in practice . let us here in brief present the three - wave interaction type hamiltonian of interest in this work @xcite . @xmath3 here all the quadratic terms are collected in @xmath4 and contains kinetic- and potential energy terms , @xmath5 stands for a bosonic field operator , whereas @xmath6 ( @xmath7 ) describe two particle fields that can be two fermions ( bosons ) in different spin states , finally @xmath8 is the strength of the fermion - boson ( boson - boson ) coupling term . in modern condensed matter physics the fermi - bose model have two major areas of applicability . first the so called `` s - channel '' model in high - temperature superconductivity @xcite . in this context it model the formation dynamics of bosonic cooper - pairs , ( 400,60 ) ( 185,32)(1,0)60 ( 135,32)(-1,0)60 ( 245,28)(-1,0)60 ( 75,28)(1,0)60 ( 60,30 ) ( 260,30 ) ( 149,30 ) ( 171,30 ) ( 157,24)~ ( 60,13)(0,1)34 ( 260,47)(0,-1)34 ( 149,13)(0,1)34 ( 171,47)(0,-1)34 ( 130,1)cooper - pair ( 55,1)@xmath9 ( 255,1)@xmath10 where the two atomic particles , the electrons , are fermions . in the field of ultra - cold atomic physics , it can model the dissociation of ultra - cold bosonic molecules @xcite , ( 400,60 ) ( 180,32)(1,0)65 ( 140,32)(-1,0)65 ( 245,28)(-1,0)65 ( 75,28)(1,0)65 ( 60,30 ) ( 260,30 ) ( 155,30 ) ( 165,30 ) ( 160,30 ) ( 60,13)(0,1)34 ( 260,47)(0,-1)34 ( 155,13)(0,1)34 ( 165,47)(0,-1)34 ( 135,1)molecule ( 42,1)atom 1 ( 242,1)atom 2 and hence we allow here for the atomic particles to be either two fermions or two bosons . various generalizations of time - dependent dmrg @xcite to higher dimensional systems is a topic of large present interest in the computational physics community @xcite , but have not yet reached a useful status for large higher dimensional systems as of interest here . methods for bosonic evolution based on stochastic differential equations ( sdes ) , with the ability for independent stochastic trajectories to be carried out on computer clusters for large systems , are succesful in many situations @xcite but are restricted to simulations of molecules dissociating into bosonic atoms . in this article we outline a method to study the fermionic time evolution for effective heisenberg equations that are linear in creation and annihilation operators . we apply the method to the evaluation of analytic short - time asymptots for the glauber s second order correlation functions @xcite , for a non - isotropic three - dimensional molecular condensate dissociating into fermionic atoms , against numerical data . we focus first on a general formulation in a @xmath0-dimensional cartesian momentum base , such that convenient numerical solutions can be directly obtained for an arbitrary shaped bosonic field . however , for a specific application the numerical performance may be further increased by using additional geometrical symmetries or by formulating the equations in a different basis . except for generating valuable results in certain physical regimes , the method presented here can also be useful as a reference for validation of approximate analytic results or to evaluate more advanced numerical methods , such as for example the gaussian fermionic phase - space representation ( gpsr ) that have recently been applied to the fermi - bose model with a uniform bosonic field @xcite and an implementation of gpsr for dissociation from a non - uniform molecular bec is in progress . turning off stochastic terms in the sdes of the gpsr , one obtain in effect the so called pairing mean - field theory ( pmft ) @xcite . furthermore , keeping the molecular variables in pmft undepleted will be equivalent to the formulation in the present article but is numerically less suitable . * * there is an obvious computational advantage to solve for the single operator dynamics , instead of solving for pairs of operators , the latter is done e.g. in the pmft ( and gpsr ) discussed above . to give one relevant example , to simulate a three - dimensional non - uniform field on a cartesian momentum grid of size @xmath11 requires in effect , as we will show in this paper , only to be able to store part of a ( sparse ) @xmath12 @xmath0-block - hankel matrix of the size @xmath13 and to multiply this @xmath0-block - hankel matrix with vectors only for each final time - point of interest . on the other hand c - number based mean - field methods for fermi - bose systems like pmft , where the basic variables represents pairs of operators with two indices , requires in this case to propagate @xmath14 variables in time through sufficiently many small time - steps up to the final time - point of interest . the methods for stochastic evolution that represents single bosonic field operators with complex stochastic fields mentioned above , see @xcite for a recent review , do not have any direct corresponding useful method for fermions . for example the gpsr that can treat the quantum dynamics of the fermi - bose model exact @xcite , involves basis elements that represents pairs of single operators @xcite , hence it is generally more restrictive in the size of the computational grid . due to the existence of several related methods for bosonic dynamics , we focus in the present article in particular on applications to systems with fermionic atomic operators . however , the specific analogue theory of two distinguishable bosonic atomic operators is also presented for comparison , since its formulation differ only with a sign . advantages with the method presented here are _ i ) _ to be able to study effects of quantum statistics [ by chosing @xmath15 ( @xmath16 ) for fermionic ( bosonic ) atomic particles ] ; _ ii ) _ to obtain accurate correlation functions for short times i.e. for a small number of atomic particles , where stochastic evolution methods have a low signal to noise ratio ; and _ iii ) _ to conviniently treat systems with a moderate size ( relative to the ram memory ) of the computational grid ( e.g. lower dimensional systems ) , where deterministic values of the observables are obtained fast even on a single standard pc . the article is organized as follows . section [ sec : the - momentum - space - operator ] provides the heisenberg equation of motion to be treated within the concept of molecular dissociation into fermionic ( bosonic ) atoms and also briefly mention dissociation into two indistinguishable bosonic atoms and the related problem of condensate collision . in section [ sec : non - uniform - molecular - field ] we relate blocks in the system matrix responsible for atom - molecule coupling to the so called @xmath0-block - hankel matrices . in section [ sub : a - theorem - for ] we formulate and prove results for the structure of the solution of heisenberg equation of motion . section [ sub : obtaining - the - observables ] provides the reader with the practical details of how to use the mathematical results in obtaining physical observables . we apply the general method to a three - dimensional non - isotropic harmonically trapped bose - einstein condensate in section [ sec : results ] and present numerical results for atomic correlation functions that we compare to recently derived analytic short - time asymptotes . finally the article is summarised in section [ sec : summary ] .

the problem is solved in spatial dimensions by dividing the system matrix into blocks with generalizations of hankel matrices , here refered to as-block - hankel matrices . the method is practically useful for treating large systems , i.e. dense computational grids or higher spatial dimensions , either on a single standard computer or a cluster . in particular the results can be used for studies of three - dimensional physical systems of arbitrary geometry . we illustrate the generality of our approach by giving numerical results for the dynamics of glauber type atomic pair correlation functions for a non - isotropic three - dimensional harmonically trapped molecular bose - einstein condensate . department of mathematics , technical university of denmark , 2800 kgs . lyngby , denmark . +center for mathematical sciences , lund university , box 118 , 22100 lund , sweden .

we consider the exponential matrix representing the dynamics of the fermi - bose model in an undepleted bosonic field approximation . a recent application of this model is molecular dimers dissociating into its atomic compounds . the problem is solved in spatial dimensions by dividing the system matrix into blocks with generalizations of hankel matrices , here refered to as-block - hankel matrices . the method is practically useful for treating large systems , i.e. dense computational grids or higher spatial dimensions , either on a single standard computer or a cluster . in particular the results can be used for studies of three - dimensional physical systems of arbitrary geometry . we illustrate the generality of our approach by giving numerical results for the dynamics of glauber type atomic pair correlation functions for a non - isotropic three - dimensional harmonically trapped molecular bose - einstein condensate . department of mathematics , technical university of denmark , 2800 kgs . lyngby , denmark . +center for mathematical sciences , lund university , box 118 , 22100 lund , sweden .

1601.07167

i

we proposed a scenario where the spin - zero 750 gev state is coupled to a new heavy lepton which lives in the bulk of a higher - dimensional theory and interacts only with the photons of the standard model . we found that they allow for a minimal and compelling explanation of the di - photon resonance via photo - production and decay . the central role in this effect is played by the summation over the kaluza - klein modes of these leptons appearing in the loops of the @xmath1 production and decay subprocesses . the set - up requires only a minimal extension of the standard model in the sense that the same mechanism is used for the production and the decay of the @xmath0 resonance . with the new lepton being coupled only to the @xmath17 gauge sector in the standard model one can explain the absence of other resonances at 8 and 13 tev in the vicinity of the 750 gev di - photon invariant mass . the decay channel into @xmath158 is suppressed by @xmath159 , while other potential candidates , such as two jets , @xmath160 and 2 leptons are either absent or suppressed by powers of @xmath150 . this feature is particularly important for suppressing standard model jets which would otherwise accompany the di - photon production mediated by @xmath0 . since at the parton level the entire @xmath161 process is electromagnetic , any additional qcd jet activity would be suppressed by extra powers of @xmath150 or a combination of @xmath162 ( for the vbf process ) relative to the @xmath27 factor in our leading order photon fusion process . thus the relative absence of additional jets which would accompany the di - photon resonance if it was produced in gluon fusion relative to the case of pure photo - production considered here , is a distinguishing feature of our model . similarly , while mono - jet searches disfavour a large invisible width @xmath163 gev , this conclusion @xcite does not apply directly to our model , as the mono - jet would have to originate e.g. from a quark in one of the initial protons @xmath164 in addition to the photon which participates in the photon fusion . this is again suppressed by the fine structure constant times the corresponding ratio of pdfs . at the same time , the approach presented here can be easily applied to the case where the di - photon ( pseudo)-scalar @xmath0 is produced in the gluon fusion channel . in this case one would simply substitute the vector - like lepton by a single species of a new quark @xmath54 , @xmath165 in the bulk of an extra - dimensional theory . the di - photon rate in the gluon fusion process would of course be greater relative to the photon fusion , and will be even easier to fit in our kk model . the extension of the standard model by a new spin - zero singlet state @xmath0 also sits very well with other items on the bsm wish list : @xmath0 can play the role of the inflaton as the singlet degree of freedom which is non - minimally coupled to gravity see e.g. @xcite . it can also help to stabilise the sm higgs potential @xcite , assist the first order phase transition and provide additional sources of cp violation for baryogenesis . finally as was already noted in section * [ sec : dark ] * , a ( pseudo)-scalar @xmath0 is also an obvious candidate for being a mediator to the dark matter sector @xcite .

we propose that the spin - zero state is coupled to a heavy lepton that lives in the bulk of a higher - dimensional theory and interacts only with the photons of the standard model . we compute the di - photon rate in these models with two and more compact extra dimensions and demonstrate that they allow for a compelling explanation of the di - photon excess recently observed by the atlas and cms collaborations . the central role in our approach is played by the summation over the kaluza - klein modes of the new leptons , thus providing a significant enhancement of the loops for the production and decay subprocesses .

we consider the phenomenology of a 750 gev resonance which can be produced at the lhc by only photon fusion and subsequently decay into di - photons . we propose that the spin - zero state is coupled to a heavy lepton that lives in the bulk of a higher - dimensional theory and interacts only with the photons of the standard model . we compute the di - photon rate in these models with two and more compact extra dimensions and demonstrate that they allow for a compelling explanation of the di - photon excess recently observed by the atlas and cms collaborations . the central role in our approach is played by the summation over the kaluza - klein modes of the new leptons , thus providing a significant enhancement of the loops for the production and decay subprocesses . it is expected that the jet activity accompanying these purely electromagnetic ( at the partonic level ) processes is numerically suppressed by factors such as . = 1

1411.5275

i

given a discrete structure on a set of elements , a natural question is to be able to locate efficiently the elements using the structure . if the elements are the vertices of a graph , one can use the neighbourhoods of the elements to locate them . in this context , karpovsky , chakrabarty and levitin @xcite have introduced the notion of identifying codes in 1998 . an identifying code of a graph is a dominating set having the property that any two vertices of the graph have distinct neighbourhoods within the identifying code . hence any vertex of the graph is specified by its neighbourhood in the identifying code . initially , identifying codes have been introduced to model fault - diagnosis in multiprocessor systems but later other applications were discovered such as the design of emergency sensor networks in facilities @xcite . they are related to other concepts in graphs like locating - dominating sets @xcite and resolving sets @xcite . the problem of computing an identifying code of minimal size is np - complete in general @xcite but can be naturally expressed as an integer linear problem . also , one can ask how good the fractional relaxation of this problem can be . we focus on vertex - transitive graphs since for these graphs , we are able to compute the optimal size of a fractional identifying code . this value depends only on three parameters of the graph : the number and degree of vertices and the smallest size of the symmetric difference of two distinct closed neighbourhoods . moreover , the optimal cardinality of an integer identifying code is at most at a logarithmic factor ( in the number of vertices @xmath4 ) of the fractional optimal value . identifying codes have already been studied in different classes of vertex - transitive graphs , especially in cycles @xcite and hypercubes @xcite . in these examples , the order of the size of an optimal identifying code seems to always match its fractional value . however , the smallest size of symmetric differences of closed neighbourhoods is small compared to the number of vertices : either it is constant ( for cycles ) or it has logarithmic order in the number of vertices ( for hypercubes ) . therefore we focus in this paper on vertex - transitive strongly regular graphs that are vertex - transitive graphs with the property that two adjacent ( respectively non - adjacent ) vertices always have the same number of common neighbours . in particular , the size of symmetric differences can only take two values and is of order at least @xmath5 if the graph is not a trivial strongly regular graph . another interest of considering identifying codes in strongly regular graphs is that they are strongly related to resolving sets . a resolving set is a set @xmath6 of vertices such that each vertex is uniquely specified by its distances to @xmath6 . the minimum size of a resolving set is called the metric dimension of the graph . if a graph has diameter @xmath7 as is the case for non - trivial strongly regular graphs then a resolving set is the same as an identifying code except that the vertices of the resolving set are not identified . a consequence is that the optimal size of identifying codes and the metric dimension have the same order in strongly regular graphs . actually , babai @xcite introduced a notion equivalent to resolving sets in order to improve the complexity of the isomorphism problem for strongly regular graphs . he established an upper bound of order @xmath8 on the metric dimension of strongly regular graphs @xcite . he also gave a finer bound using the degree @xmath9 of vertices of order @xmath10 @xcite . thanks to this last bound , any family of strongly regular graphs for which @xmath4 is linear with @xmath9 have logarithmic metric dimension . this is for example the case of paley graphs that have also been studied by fijav and mohar @xcite who gave a finer bound . bailey and cameron @xcite proved that the metric dimension of some kneser and johnson graphs has order @xmath5 . values for small strongly regular graphs have been computed @xcite . recently , bailey @xcite used resolving sets in strongly regular graphs to compute the metric dimension of some distance - regular graphs . paley graphs give an example of an infinite family of graphs for which the optimal value of fractional identifying code is constant but the integer value is logarithmic , and so the gap between the two is also logarithmic . we consider another family of strongly regular graphs that have never been studied in the context of identifying codes nor resolving sets : the adjacency graphs of generalized quadrangles . these graphs are constructed using finite geometries . constructing identifying codes can be seen as a way to break the inherent symmetry of these graphs . we give constructions of identifying codes with size of optimal order . this order is of the form @xmath2 with @xmath11 and corresponds to the order of the fractional value . * outline . * in section [ sec : bas ] , we give formal definitions and classic results useful for the rest of the paper . in section [ sec : frac ] , we exhibit the linear program for identifying codes , compute the optimal value of the relaxation for vertex - transitive graphs and deduce a general bound . in section [ sec : previous ] , we review known results for identifying codes in vertex - transitive graphs and compare them to our general bound . finally in section [ sec : srg ] , we study strongly regular graphs and in particular adjacency graphs of generalized quadrangles .

we consider the problem of computing identifying codes of graphs and its fractional relaxation . we focus on vertex - transitive graphs for which we can compute the exact fractional solution . there are known examples of vertex - transitive graphs that reach both bounds . we exhibit infinite families of vertex - transitive graphs with integer and fractional identifying codes of order with . they also provide examples for metric dimension of graphs . * keywords : * identifying codes , metric dimension , vertex - transitive graphs , strongly regular graphs , finite geometry , generalized quadrangles

we consider the problem of computing identifying codes of graphs and its fractional relaxation . the ratio between the size of optimal integer and fractional solutions is between 1 and where is the set of vertices of the graph . we focus on vertex - transitive graphs for which we can compute the exact fractional solution . there are known examples of vertex - transitive graphs that reach both bounds . we exhibit infinite families of vertex - transitive graphs with integer and fractional identifying codes of order with . these families are generalized quadrangles ( strongly regular graphs based on finite geometries ) . they also provide examples for metric dimension of graphs . * keywords : * identifying codes , metric dimension , vertex - transitive graphs , strongly regular graphs , finite geometry , generalized quadrangles

0910.0478

r

[ sec : discussion ] we show the rest - frame frc for our model with @xmath85 , the b07 star - formation law , and no winds , in figure [ fig : lfirradiorest ] ( _ left panel _ ) as an example . the solid dark red line is the @xmath86 frc . all solid lines assume that starbursts are compact , with @xmath38 . it is clear from figure [ fig : lfirradiorest ] that compact starbursts show little evolution in the frc , while low surface density galaxies have lower radio luminosities at high redshift . this behavior is robust in all of the variants . the cause of evolution in the frc is inverse compton losses off the cmb for cr electrons and positrons . figure [ fig : frcevolution ] ( _ left panel _ ) shows that the frc should display relatively little evolution out to @xmath87 , except for the lowest surface brightness galaxies . however , normal galaxies have suppressed synchrotron radio emission at @xmath3 , a factor of @xmath19 for @xmath88 ( @xmath89 ) and of order 10 for @xmath90 ( @xmath91 ) . the radio luminosities continue to fall with redshift . at @xmath92 , ic off the cmb starts to matter even for the weaker starbursts ( @xmath61 ; @xmath93 ) . dense starbursts ( @xmath94 ; @xmath95 for the k98 law or @xmath96 for the b07 law ) remain on a linear frc even at @xmath97 . the strong cooling from bremsstrahlung , ionization , and ic off starlight implied by the high-@xmath16 conspiracy ( [ sec : theory ] ) acts as a buffer against ic losses off the cmb . similarly , diffusive escape provides a similar buffering effect in low-@xmath16 galaxies , so that the increased ic losses off the cmb does not suppress the radio emission quickly . in other words , most of the power from ic scattering of cmb photons does not come at the expense of synchrotron , but of other losses . the radio dimming can not be described by a simple competition between magnetic field energy density and the cmb energy density ; the cmb energy density must also compete with _ every other loss process_. the buffering actually serves as an important test for both conspiracies described in [ sec : theory ] . in high-@xmath16 galaxies and starbursts , we predict that bremsstrahlung , ionization , and inverse compton of starlight already take a large portion of a electron s energy budget ; hence , the high-@xmath16 conspiracy works to hold @xmath63 constant out to quite high redshift . the buffering essentially doubles the redshift that compact starbursts remain on the frc ; the weakest starbursts ( @xmath61 ; @xmath93 ) are radio - dim by a factor of @xmath98 at @xmath99 with buffering , instead of @xmath100 without the buffering . in low-@xmath16 galaxies , electrons and positrons can easily escape before they lose energy to inverse compton off the cmb at low enough @xmath1 ; thus , the low-@xmath16 conspiracy also works to hold @xmath63 constant . the suppression due to ic losses off the cmb seen in figure [ fig : lfirradiorest ] can be estimated by examining the ratios of the synchrotron cooling time to the total loss time , including both escape and cooling losses . in appendix [ sec : cmbradiodim ] , we derive the ratios of loss times and we show that for a given schmidt law , a critical redshift @xmath101 can be defined for each @xmath16 and @xmath8 at which radio emission is suppressed . we define @xmath101 to be the redshift when the rest - frame radio luminosity at @xmath75 is suppressed by a factor of 3 compared to @xmath86 . for our model with the b07 star - formation law , no winds , and @xmath85 , we find the critical redshifts are approximated as @xmath102 where @xmath8 is in units of @xmath42 . we refer the reader to appendix [ sec : cmbradiodim ] , where we present similar relations for our other models of the frc . we note that the radio suppression could , conceivably , be used to measure the temperature of the cmb at high redshift . in principle , this method could apply to any galaxy with a radio and fir detection . however , the conspiracies would have to be accounted for , and they are affected significantly by both the gas surface density @xmath16 and scale height @xmath39 ( see [ sec : puffy ] ) . any measurement of the cmb temperature would depend on assumptions of the galaxy properties and would be model - dependent . as figure [ fig : frcevolution ] ( _ right panel _ ) shows , the inferred rest - frame values of @xmath103 show additional apparent evolution , simply because the spectral slopes of the galaxies are not exactly @xmath104 . compact starbursts have flatter spectra and @xmath105 are instantaneous spectral slopes , not the measured spectral slopes between two observed frequencies , unless otherwise noted . [ ftnt : alphanotation ] ] with @xmath106 at 1.4 ghz , so by adopting @xmath107 they _ appear _ to become slightly radio brighter until @xmath87 , after which at higher frequencies their spectra steepen , and their radio emission appears to dim again at higher @xmath1 . normal galaxies have steeper spectra with @xmath108 at 1.4 ghz , so their apparent radio luminosity sinks below their true radio luminosity at high redshift . at higher redshifts , our models predict that galaxies have intrinsically steeper radio spectra , because of increased ic losses from the cmb . the rest - frame spectral slope @xmath109 of normal galaxies at 1.4 ghz and asymptotes at @xmath110 by @xmath111 , when losses are dominated by ic for our injection spectrum of crs with @xmath51 . there is much less intrinsic rest - frame evolution of starburst radio spectra ; even at @xmath92 , @xmath109 increases only by 0.1 for the weakest compact starbursts . the observable @xmath112 shows much more pronounced evolution with redshift for starbursts , increasing by @xmath113 to @xmath6 , and @xmath114 to @xmath115 . this effect arises simply because we predict the cr electron and positron spectra steepen with rest - frame frequency as synchrotron and ic losses become stronger ( e.g. , * ? ? ? * ltq ) : at higher redshift and fixed observing frequency , we are seeing higher energy electrons and positrons . an important effect that we do not consider is the thermal free - free radio emission . this will set a minimum total observed radio emission that is directly proportional to the star - formation luminosity . thus , the true total radio deficit at ghz will not be as big as the synchrotron - only deficits plotted in figures [ fig : lfirradiorest ] and [ fig : frcevolution ] . thermal free - free emission will also flatten the spectrum , especially at high frequencies . however , free - free emission is much fainter than the synchrotron luminosity at ghz frequencies , except in the faintest star - forming galaxies @xcite . [ sec : puffy ] as shown in figure [ fig : lfirradiorest ] , puffy starbursts fall on a linear fir - radio correlation of their own ( dotted lines ) , in line with observations of smgs @xcite . the radio luminosity of these galaxies is nonetheless the result of a conspiracy , between ic losses on starlight , which decrease the radio luminosity , and the enhanced radio emission from secondary electrons and positrons , and the @xmath20 effect ( [ sec : theory ] ) . the variation in @xmath63 for puffy starbursts alone is usually less than a factor of @xmath116 over the range @xmath117 ( see table [ table : models ] ; in most variants the variation is @xmath118 ) . like compact starbursts , escape plays essentially no role in most of the models , except that winds can slightly decrease the radio emission in relatively tenuous @xmath61 ( @xmath93 ) starbursts ( footnote [ ftnt : windvariant ] ) . it is plain from figure [ fig : lfirradiorest ] ( _ left panel _ ) that the normalization of the puffy starburst frc ( dotted lines ) is different than the frc of the compact starbursts and normal galaxies ( solid lines ) when @xmath85 . we show in table [ table : models ] that models with @xmath119 have radio - bright puffy starbursts compared to the observed local frc , by a factor of @xmath120 at @xmath86 . like the compact starbursts , puffy starbursts show little rest - frame evolution in @xmath63 , except at relatively low surface densities ( @xmath61 ; @xmath93 ) , where they become radio dim at high redshifts because of ic losses on cmb photons . therefore , we predict that puffy starbursts , which are mainly observed at high @xmath1 , have _ intrinsically _ different radio properties not caused by their redshift . we propose a natural explanation of this radio excess in the framework of ltq ( [ sec : theory ] ) . in dense starbursts , protons are efficiently converted into secondary electrons and positrons through inelastic proton - proton scattering , which contribute to the synchrotron emission . furthermore , the @xmath20 effect increases @xmath63 for starbursts which have larger @xmath12 . compact starbursts lying on the @xmath86 frc balance these effects with increased bremsstrahlung , ionization , and ic losses , which compete with the synchrotron losses and suppress the excess radio luminosity ( [ sec : theory ] ) . in puffy starbursts with relatively low volume densities compared to their compact cousins at fixed @xmath16 , however , bremsstrahlung and ionization are not strong enough to compensate for these effects . only synchrotron and ic losses remain , upsetting the conspiracy . the radio excess predicted by this picture is systematically greater when using the k98 star - formation relation , because the ic loss rate on starlight is smaller at fixed surface density by a factor of 2.5 to 11 from weak starbursts to the densest starbursts . this freedom to vary the radio - excess with @xmath12 does not exist in the standard calorimeter model , where all cr electron / positron energy goes into synchrotron emission , and the radio emission saturates . the balance between synchrotron and the other forms of cooling can be changed in starbursts to alter the normalization of the frc , even though escape is negligible . there is a reason to expect our allowed @xmath119 specifically : radiation pressure may drive turbulence and enhance the magnetic field until its energy density is comparable to radiation ( e.g. , * ? ? ? if the k98 relation holds , then since the magnetic energy density scales as @xmath121 , @xmath85 , and if the b08 relation holds , then @xmath122 . this explanation is more problematic for the b07 relation and @xmath85 . to the _ total _ milky way magnetic field strength of @xmath123 near the solar circle . if most of the magnetic field strength in starbursts is driven by turbulence , perhaps scaling to the disordered galactic magnetic field strength ( @xmath124 ; * ? ? ? * ) near the solar circle would make more sense , because the ordered magnetic field arises from a different process . the lower normalization for @xmath12 then would partly compensate for the steeper dependence on @xmath16 . ] however , while we assume that there is a parametrization for @xmath12 that applied to both compact starbursts and puffy starbursts , the radio excess should arise more generally . the radio excess arises simply because synchrotron cooling time is shorter than the bremsstrahlung and ionization cooling times in puffy starbursts , but longer in compact starbursts at fixed @xmath16 : at fixed @xmath125 , @xmath126 and @xmath127 . we therefore expect there to be a radio excess with respect to the frc in any puffy starburst with a strong enough magnetic field , with the exact enhancement depending on magnetic field strength because of the remaining competition , after ionization and bremsstrahlung are sub - dominant , from the ic losses on starlight . , however , there will be more scatter in @xmath103 for puffy starbursts at fixed @xmath39 and @xmath1 . smgs would not form their own frc if @xmath12 was the same for all smgs regardless of @xmath16 , or if @xmath12 increased _ very _ steeply with @xmath16 , because there still must be a conspiracy with ic losses off starlight . since smgs do appear to form their own frc ( e.g. , * ? ? ? * ; * ? ? ? * ) , this could be evidence specifically that their magnetic field strengths increase with @xmath16 ( or @xmath17 ) . ] our results imply that a moderate radio excess at the factor of @xmath5 level alone is not a safe indicator of the presence of a radio - loud agn , especially at high redshifts where smgs are observed . while radio excess with respect to the local frc has been suggested as a selection criterion for radio - loud agns ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , our models with @xmath128 imply that @xmath129 for puffy starbursts powered by star - formation alone . a radio excess is inexplicable in our models only when the source is an order of magnitude brighter ( @xmath130 ) in the radio than predicted from the fir emission . while smgs are relatively rare and may not be a problem in small samples , we recommend that other means be used to be sure that the radio - excess is caused by an agn , such as a flat radio spectrum , radio morphology , mid - ir colors , or the presence of strong x - ray emission ( see also * ? ? ? a magnetic field dependence of @xmath131 appears to hold for galactic molecular clouds ( e.g. , * ? ? ? * ) , and ltq found that the fir - radio correlation was consistent with this magnetic field dependence . the existence of galaxies with different scale heights allows us to distinguish the two possibilities for magnetic field scaling . if @xmath57 , then the magnetic field strength will be the same for all galaxies with the same @xmath16 , regardless of scale height . in models with @xmath14 , by contrast , the magnetic field strength is weaker in puffy starbursts than in compact starbursts with the same @xmath16 . as seen in figure [ fig : lfirradiorest ] ( _ right panel _ , dotted lines ) , puffy starbursts again form their own frc . in models with @xmath14 , they are radio dim compared to the @xmath2 frc . we show in table [ table : models ] that the normalization of the frc is radio - dim by a factor of @xmath132 . we can explain this in the ltq theory of the frc as well . the magnetic field strength must increase more slowly with @xmath17 than with @xmath16 to reproduce the @xmath2 frc , because @xmath133 is 10 times smaller in compact starbursts than normal galaxies and puffy starbursts . compact starbursts are highly compressed with respect to normal galaxies , so they have strong magnetic fields and synchrotron radio emission is strong enough to compete with the other losses . puffy starbursts are not compressed , so that their magnetic fields are weak and synchrotron losses can not keep up with ic losses , nor with bremsstrahlung and ionization as 1.4 ghz emission traces ever lower electron energies at higher magnetic field strengths . puffy starbursts therefore turn out to be radio dim compared to compact starbursts on the @xmath2 frc , if @xmath14 . as before , the b07 star - formation relation predicts greater ic losses and therefore weaker radio emission . because of the claims in the literature that smgs are radio bright , we do not favor these models . the suggested relative radio brightness of high-@xmath1 smgs therefore provides some evidence that , in fact , @xmath134 rather than @xmath14 . however , the matter of whether high-@xmath1 smgs are in fact radio bright is not yet settled . although ltq concluded that @xmath12 must increase dramatically from normal galaxies to dense starbursts ( [ sec : theory ] ) , they were unable to distinguish between these two possibilities with the @xmath2 frc alone . for this reason , high-@xmath1 starbursts and their qualitatively different morphologies compared to those at @xmath2 can distinguish theories of the frc . a prediction of all of our variants is that puffy starbursts like submillimeter galaxies should have steep non - thermal radio spectra , with @xmath135 ( see table [ table : models ] ) . the steep spectra are caused by strong synchrotron cooling in the @xmath119 case and the relatively stronger ic cooling off starlight in the @xmath14 case . in general , puffy starbursts should have roughly the same @xmath136 as normal galaxies in the local universe , which tends to be somewhat higher ( @xmath137 ) than in compact starbursts ( @xmath138 ) . the slope should hold even out to extremely high @xmath16 , as long as starbursts are puffy . in contrast , we find that @xmath139 in compact starbursts , because of efficient ionization and bremsstrahlung losses , which flatten the equilibrium cr spectrum because of their energy dependence . as we note in ltq , our predicted spectral index for normal galaxies is somewhat too high , and this difference in @xmath136 may carry over to the puffy starbursts . however , the significant difference in @xmath136 between compact and puffy starbursts should remain as a general prediction of our model : compact starbursts should have flatter spectra than puffy starbursts . the high spectral slopes can be observed either with direct measurements of multifrequency data of individual submillimeter galaxies , or with single frequency observations at a variety of redshifts . there are relatively few measurements of @xmath136 for submillimeter galaxies specifically ; faint radio sources have @xmath140 @xcite , though that sample includes both compact starbursts and agns . @xcite do find that @xmath141 for smgs , comparable to our predictions . they also find that submillimeter galaxies have a radio - excess , in agreement with figure [ fig : lfirradiorest ] . more recently , @xcite found an average @xmath142 , which is somewhat flatter than our models . these spectral slopes are not different from normal star - forming galaxies , but are noticeably steeper than local ulirgs @xcite . however , we do not account for free - free absorption , which probably flattens the spectra of local ulirgs like arp 220 at low frequency @xcite , and is not well understood in smgs . since puffy starbursts have steeper spectra than compact starbursts , we expect their inferred @xmath63 will increase with redshift : if the true radio spectral slopes of smgs are greater than the assumed @xmath136 by @xmath143 , they will appear to become radio dimmer by a factor @xmath144 , or up to @xmath145 at @xmath146 . in figure [ fig : starburstspectra ] , we show the expected radio synchrotron spectra of starburst galaxies , without correcting for thermal absorption or thermal emission . at a rest - frame frequency of 1 ghz , puffy starbursts ( dashed ) have steeper radio spectra than compact starbursts ( solid ) . note that at high frequencies ( @xmath147 ) , the ratio of the radio luminosities per unit star formation of the compact and puffy starbursts asymptotes to a value set by the ratio of @xmath148 and @xmath149 in these starbursts . at these high frequencies , only synchrotron and ic cooling are effective , and ic cooling would be the same for puffy and compact starbursts because of the schmidt law ( [ sec : theory ] ) . for @xmath57 , @xmath148 is the same for puffy and compact starbursts , but for @xmath58 , puffy starbursts have much smaller @xmath148 . thus , measurements of the synchrotron radio emission of smgs at high @xmath125 could determine the magnetic field strength of smgs and determine which scenario applies . of course , there are unlikely to be two perfectly distinct populations of compact starbursts and puffy starbursts . instead , there may be a continuum variation in scale heights from tens to thousands of parsecs . we would then expect to see a larger scatter , both in @xmath63 and @xmath136 , in a full sample of both the most compact and the most puffy starbursts . @xcite find that submillimeter galaxies do have a larger scatter in @xmath150 than other galaxies . however , @xcite find a relatively small scatter of @xmath151 in smg radio spectral index . importantly , for larger @xmath39 , both @xmath63 and @xmath109 asymptote as cr electron and positron losses are entirely determined by synchrotron and ic ; @xmath34 starbursts are already near this limit . in other words , for arbitrarily large @xmath39 , the radio excess with respect to the @xmath2 frc asymptotes to a value of @xmath152 , depending on the assumed schmidt law , and the radio spectral slope asymptotes to @xmath110 for @xmath51 . relying on the frc , a number of studies have used the ghz radio emission as a tracer of star - formation ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? radio emission has the advantage that it is unaffected by dust obscuration , making it potentially very useful in starbursts , and therefore for most of the star - formation at @xmath153 ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? our models let us evaluate the theoretical basis for radio as a sfr indicator at all redshifts . we show the predicted radio emissivity as a function of star formation in figure [ fig : sfrradio ] . at low surface densities ( @xmath154 ; @xmath25 ) , synchrotron radio has a non - linear dependence on star - formation at all redshifts . the weak radio emission is caused by electrons escaping their host galaxies , as inferred by @xcite and discussed in ltq . that is , normal galaxies are not perfect electron calorimeters , so the radio emission is not a reliable star - formation tracer at low @xmath8 . at higher redshift , synchrotron emission is diminished by inverse compton off the cmb . for a milky way - like galaxy , we find that radio is a good star - formation tracer at @xmath155 , but underestimates it significantly by @xmath156 ( eq . [ eqn : b07zcrit ] ) . already galaxies with star formation rates similar to galactic levels are beginning to be observed in the radio at high redshift @xcite , so that the ic suppression may soon be observed . however , ic losses off the cmb should not be important even in the weakest starbursts until @xmath157 , as is also visible by the redshift evolution of the frc in figure [ fig : frcevolution ] . radio emission does grow linearly with star - formation rate between normal galaxies with @xmath88 ( at @xmath158 ) and compact starbursts . therefore , it serves as an acceptable star - formation indicator for these galaxies . however , if @xmath119 , puffy starbursts like smgs have about @xmath120 times the radio emission at any given star - formation rate than compact starbursts . therefore , we expect that if @xmath119 , the usual radio emission estimate based on the @xmath2 frc will _ overestimate _ their star formation rates by a factor of @xmath159 . the excess is greatest at @xmath160 corresponding to @xmath161 , typical of observed smgs . among the puffy starbursts themselves , the radio emission grows linearly with star - formation rate . if instead @xmath14 , the radio emission will underestimate the star - formation rate . however , because the smgs lie on their own frc , there is little real redshift evolution in the radio emissivity of puffy starbursts , because of the buffering provided by ic losses off starlight ( see [ sec : frcevolution ] , appendix [ sec : cmbradiodim ] ) . assuming a spectral slope @xmath107 will also underestimate the radio emissivity , since these galaxies can have steep radio spectra . this explains the apparent evolution with @xmath1 of puffy starbursts in figure [ fig : sfrradio ] : we have applied a k - correction using a typically employed @xmath107 when , in fact , the true synchrotron spectra are steeper . if the radio star - formation tracer could be calibrated to the special conditions in puffy starbursts like smgs , taking into account their different scale height , radio emissivity , and spectral slopes , we predict that radio would be a more accurate star - formation tracer for them . we can also directly calculate the _ observed _ ghz radio flux density @xmath162 from synchrotron emission of star - forming galaxies . we show the predicted flux density per unit star - formation at observer - frame 1.4 ghz in figure [ fig : ghzradiofluxes ] . surveys with the expanded very large array ( evla ) will have a continuum sensitivity of @xmath163 at frequencies of 1 - 50 ghz , and it should be able to directly detect galaxies with @xmath164 and star - formation rates of @xmath165 out past @xmath166 . as stated in @xcite , a starburst like m82 with sfr @xmath167 will become undetectable past @xmath87 . however , the buffering effect we emphasize in this paper preserves the radio emission of dense starbursts at high @xmath1 , so that bright starbursts will be detectable further : starbursts with sfr @xmath168 will be detectable with evla at 1.4 ghz out to @xmath169 and the most intense starbursts ( sfr @xmath170 and @xmath171 ) will be detectable out past @xmath97 in synchrotron emission . @xcite predicts the square kilometer array ( ska ) will be sensitive to star - forming galaxies with flux densities of @xmath172 . if this sensitivity is attained , then milky way - like galaxies ( @xmath173 ; sfr @xmath174 ) will be directly detectable at 1.4 ghz in synchrotron emission out to @xmath3 , and starbursts with sfr @xmath174 will be detectable at 1 ghz beyond @xmath175 . even at @xmath97 , the synchrotron emission of dense , compact starbursts ( @xmath176 ) with sfr greater than @xmath177 should be detectable at 1.4 ghz with ska ( models with @xmath178 have radio - dim puffy starbursts , and these are detectable at @xmath99 with the ska only for sfr greater than @xmath179 ) . by contrast , @xcite found a sensitivity of @xmath180 , based on the free - free emission ; this limit will apply to normal galaxies and weak starbursts where the synchrotron emission is suppressed . these sensitivities assume that natural confusion , in which radio sources overlap , will not hamper the ska ; estimates for the natural confusion limit vary from njy to @xmath181 levels ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? ska and evla will also have good spectral coverage , which may help measurements of the spectral index . if a galaxy is detected at @xmath182 ( @xmath183 for evla and @xmath184 for ska ; @xcite ) at two different frequencies @xmath185 and @xmath186 with @xmath187 , then @xmath188 can be constrained to @xmath189 at the @xmath190 level . evla will be better at high observer - frame frequencies ( 1 - 50 ghz ) . a problem for the evla will be the increasing fraction of thermal emission , which is expected to dominate the emission of starbursts at @xmath191 . evla will therefore not easily measure the nonthermal spectral indices of galaxies at high z. on the other hand , the ska will face free - free absorption when observing low - z starbursts ; for example , arp 220 may be optically thick even at 1 ghz @xcite . at high redshift , however , the rest - frame frequencies ska will observe will be less affected by free - free absorption . star - formation in galaxies over cosmic time produces a diffuse radio synchrotron background . our models indicate that submillimeter galaxies and other puffy starbursts ought to have enhanced radio emission . in principle , this means that the synchrotron radio background could be up to @xmath159 times higher than usually predicted from the cosmic infrared background ( cib ) and a naive application of the @xmath2 frc . the magnitude of this implied radio excess is interesting , because arcade2 recently reported an excess radio background at 3 , about five times higher than expected from star formation @xcite . @xcite found that constraints on inverse compton emission require the excess to come from regions with galactic - level ( @xmath192 ) magnetic fields , and suggest an evolution of the frc as the source of the reported excess . however , while smgs are individually very bright and contribute much to the cosmic star - formation rate at @xmath193 , they are not typical starbursts @xcite . instead , they seem to represent a transient phase that can survive about 100 before their gas is depleted @xcite . we can estimate the total radio background enhancement by scaling to the contribution of smgs to the cib , which is largely reprocessed starlight from galaxies at @xmath153 ( e.g. , * ? ? ? * ; * ? ? ? * ) , and adjusting by the smg radio excess . submillimeter galaxies do provide the majority of light at @xmath194 , but this is only a small fraction of the total ir background . at the peak of the cib ( @xmath195 ) , submillimeter galaxies provide @xmath196 of the total power , and possibly only @xmath197 @xcite . optimistically , the radio excess from smgs would be @xmath198 . this is significant , but not enough to explain the very large arcade2 excess . more conservatively , the excess is more likely @xmath199 , and could be as little as a few percent . since the number of radio sources down to several @xmath181 is well known , we can estimate the fraction of the expected radio background comes from bright smgs . @xcite find a tir background of about @xmath200 ; from the normalization of the fir - radio correlation we expect a 1.4 ghz background of @xmath201 . @xcite found an average radio flux density of @xmath202 for bright smgs ( @xmath203 ) . the number counts of @xmath204 sources imply that they have a density of @xmath205 , contributing roughly @xmath206 to the 1.4 ghz radio background ( e.g. , * ? ? ? bright smgs have an approximate density of @xmath207 ( e.g. , * ? ? ? * ; * ? ? ? * ) , so they constitute about @xmath145 of the background from @xmath204 sources , or @xmath208 of the expected 1.4 ghz background from star - formation . this is roughly in line with our estimate of @xmath209 , although the uncertainties are large enough that it could be consistent with smgs lying on the frc . in any case , it is fairly clear that bright smgs are not the source of the arcade excess . the total excess could be greater if most starbursts at @xmath153 are puffy , and not just smgs . we do not expect this simply because most current studies show that the local frc _ does _ hold out to high redshift for most observed galaxies and starbursts ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the spectral slope would also be a problem : arcade2 inferred @xmath210 , while we predict a spectral slope @xmath211 , steeper than local compact starbursts . resolved radio sources in the range @xmath212 , which are expected to be star - forming galaxies @xcite , contribute about @xmath213 to the 1.4 ghz radio background @xcite , which is consistent with the total energetics expected from the frc . @xcite also find consistency between the frc and the observed radio source counts at @xmath214 . stacking studies of fainter radio sources have given somewhat ambiguous results on whether the frc applies @xcite , but @xcite find no large evolution in the frc down to @xmath215 . any large radio excess would have to come either from a new population of low luminosity galaxies or very high-@xmath1 galaxies ( see figure [ fig : ghzradiofluxes ] ) ; extrapolations of the higher flux source populations do not predict a large radio excess ( e.g. * ? ? ? * ) . nonetheless , our work indicates that a radio excess from smgs can be significant . conversely , if the luminosity function of galaxies was very steep , most galaxies could be intrinsically radio - dim with respect to the frc , because of ic losses off the cmb ( see [ sec : frcevolution ] and figures [ fig : lfirradiorest ] and [ fig : frcevolution ] ) . then the frc would overestimate the strength of the radio background . however , most star - formation at high @xmath1 is believed to have occurred in starbursts @xcite , so this possibility is unlikely .

normal galaxies with low star - formation rates become radio - faint at high , because inverse compton ( ic ) losses off the cmb cool cr electrons and positrons rapidly , suppressing their nonthermal radio emission . however , we find that this effect occurs at higher redshifts than previously expected , because escape , bremsstrahlung , ionization , and starlight ic losses act to counter this effect and preserve the radio luminosity of galaxies . the radio dimming of star - forming galaxies at high is not just a simple competition between magnetic field energy density and the cmb energy density ; the cmb must also compete with every other loss process . we predict relations for the critical redshift when radio emission is significantly suppressed compared to the frc as a function of star - formation rate per unit area . for example , a milky way - like spiral becomes radio - faint at , while an m82-like starburst does not become radio - faint until . additionally , we provide a quantitative explanation for the relative radio brightness of some high- submillimeter galaxies . we show that at fixed star formation rate surface density , galaxies with larger cr scale heights are radio bright with respect to the frc , because of weaker bremsstrahlung and ionization losses compared to compact starbursts .

we construct one - zone steady - state models of cosmic ray ( cr ) injection , cooling , and escape over the entire dynamic range of the fir - radio correlation ( frc ) , from normal galaxies to starbursts , over the redshift interval . normal galaxies with low star - formation rates become radio - faint at high , because inverse compton ( ic ) losses off the cmb cool cr electrons and positrons rapidly , suppressing their nonthermal radio emission . however , we find that this effect occurs at higher redshifts than previously expected , because escape , bremsstrahlung , ionization , and starlight ic losses act to counter this effect and preserve the radio luminosity of galaxies . the radio dimming of star - forming galaxies at high is not just a simple competition between magnetic field energy density and the cmb energy density ; the cmb must also compete with every other loss process . we predict relations for the critical redshift when radio emission is significantly suppressed compared to the frc as a function of star - formation rate per unit area . for example , a milky way - like spiral becomes radio - faint at , while an m82-like starburst does not become radio - faint until . we show that the `` buffering '' effect of non - synchrotron losses improves the detectability of star - forming galaxies in synchrotron radio emission with evla and ska . additionally , we provide a quantitative explanation for the relative radio brightness of some high- submillimeter galaxies . we show that at fixed star formation rate surface density , galaxies with larger cr scale heights are radio bright with respect to the frc , because of weaker bremsstrahlung and ionization losses compared to compact starbursts . we predict that these `` puffy starbursts '' should have steeper radio spectra than compact galaxies with the same star - formation rate surface density . we find that radio bright submillimeter galaxies alone can not explain the excess radio emission reported by arcade2 , but they may significantly enhance the diffuse radio background with respect to a naive application of the frc .

0910.0478

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we have applied the theory of ltq to predict the frc for redshifts @xmath0 . we use one - zone models of galaxies and starbursts with cr injection , cooling , and escape to predict the equilibrium , steady - state radio spectra of galaxies and starbursts over the entire range of the frc . our goals were to determine how and why the low- and high-@xmath16 conspiracies crucial to the @xmath2 frc ( [ sec : theory ] ) affect the frc at high redshift , and to provide a quantitative model for predicting the critical redshifts at which galaxies deviate from the @xmath2 frc . we find the following : 1 . for compact starbursts ( @xmath45 ) , we find relatively little evolution in the fir - radio correlation out to @xmath216 ( figure [ fig : lfirradiorest ] ) . this is partly because the magnetic energy density in galaxies is strong enough to dominate the cmb even at high redshifts . however , the high-@xmath16 conspiracy ( [ sec : theory ] ) also acts as a buffer against ic losses off the cmb ; the increased ic losses must compete with the already present bremsstrahlung , ionization , and ic off starlight in addition to synchrotron losses . the rest - frame radio spectral slope @xmath109 at fixed @xmath125 does not change with @xmath1 , but the observed @xmath136 at fixed @xmath217 increases because the non - thermal synchrotron radio spectrum steepens at higher rest - frame frequency . 2 . we derive in appendix [ sec : cmbradiodim ] the critical redshifts when inverse compton losses off the cmb suppress the radio luminosity of galaxies compared to the @xmath2 frc . these relations are given for our standard model in equation [ eqn : b07zcrit ] . the non - thermal radio luminosity is suppressed severely in milky way - like galaxies ( @xmath89 ) at @xmath3 and the weakest compact starbursts at @xmath218 . the spectrum at ghz steepens to @xmath219 because of these enhanced ic losses . nonetheless , the low-@xmath16 conspiracy ( [ sec : theory ] ) also acts to prevent the radio emission from steeply falling with redshift , since inverse compton losses off the cmb must be more efficient than diffusive escape , not just synchrotron losses ( see [ sec : frcevolution ] ) . ltq found that the @xmath86 frc demands that @xmath12 scales with @xmath17 or @xmath16 in galaxies lying on the schmidt law . in models with @xmath119 , we find that puffy starbursts with @xmath37 such as smgs are radio bright compared to the @xmath86 frc by a factor of @xmath159 . this follows from a breakdown of the high-@xmath16 conspiracy ( [ sec : theory ] ) : bremsstrahlung and ionization cooling are weak in puffy starbursts relative to the compact starbursts that predominate in the @xmath86 universe . in contrast , in models with @xmath14 , we find that puffy starbursts are radio dim compared to the observed frc , because of weak synchrotron cooling relative to the ic losses . since several studies have reported radio excesses for smgs , we favor the @xmath119 scaling ; however the issue of whether smgs are radio - bright is still not fully resolved . in either case , puffy starbursts show little true evolution with @xmath1 , though they may appear to have fainter rest - frame radio luminosities at high @xmath1 because of their steep spectra . puffy starbursts inevitably have high @xmath136 ( @xmath220 ) , since bremsstrahlung and ionization losses are weak with respect to synchrotron and ic . a key prediction of our scenario with @xmath119 is that the variations in @xmath63 will be correlated with scale height at fixed @xmath8 , since the radio - excess in our models is a direct consequence of the large cr scale height and the small bremsstrahlung and ionization losses it causes . radio - excess ( low @xmath221 ) puffy starbursts will have steeper radio spectral slopes ( bigger @xmath136 ) , larger velocity dispersions @xmath222 compared to their rotation speeds @xmath223 , and possibly moderately cooler dust temperatures ( smaller @xmath224 ) . 4 . as previously expected , radio emission can be a poor tracer of star formation in low surface density galaxies , because of electron escape and ic losses off the cmb . for our preferred @xmath119 scaling , radio emission overestimates star - formation rate by a factor of @xmath120 in puffy starbursts . star - formation rate is underestimated by synchrotron radio emission with the @xmath14 scaling . while smgs may be individually radio bright compared to the local frc , they contribute a relatively small fraction of the cosmic infrared background and the total star - formation luminosity of the universe . this means that they enhance the star - formation radio background by @xmath225 , and possibly around @xmath209 , with respect to a naive application of the @xmath86 frc . as in ltq , we did not exactly match the observed radio spectral slopes of galaxies , with @xmath108 in normal galaxies and @xmath106 in compact starbursts . this will have a slight effect on the k - correction . an error of @xmath226 in @xmath136 should only affect inferred radio luminosity by 30% at @xmath146 and 60% at @xmath100 . nevertheless , the prediction of steeper radio spectra in puffy starbursts with respect to compact starbursts at all relevant @xmath1 should be robust . our explanation for the small @xmath63 ratio in submillimeter galaxies as a breakdown of the high-@xmath16 conspiracy is based purely on the steady - state spatially - averaged synchrotron emission , but the details of the fir emission may also matter . throughout this paper , we have simply assumed that the bolometric fir luminosity could be correctly inferred from observations , and have assumed the same uv opacity for all galaxies at all redshifts . the total fir emission is also likely to depend on the metallicity , and may be lower at high @xmath1 for the lowest surface density galaxies . the exact far - infrared sed is important in determining the fir emission when observations have only been made at only a few wavelengths . the presence of agns , a different imf at high @xmath1 , and selection biases may also affect the inferred @xmath221 of smgs . we did not include the effects of galaxy evolution on the cr spectrum in our models . we argued in ltq that it should not matter for quiescent spirals or for extreme starbursts , because the cr lifetime is much shorter than the time dependence of stellar populations . however , galaxy evolution may play a role in weaker starbursts @xcite and in post - starburst galaxies @xcite . studies of merging normal galaxies and galaxies in clusters have indeed found that they are radio bright with respect to the frc , possibly because of compression of magnetic fields or shock acceleration @xcite . we also assumed that the magnetic field strength at a given density does not depend on redshift . it is not entirely clear how long normal galaxies take to build up their magnetic fields , or even what process is at work ( see the reviews in * ? ? ? * ; * ? ? ? * ) , though there are theoretical mechanisms that can rapidly generate strong magnetic fields . studies at @xmath3 indicate that normal milky way - like galaxies had magnetic fields with similar strengths to the present @xcite . at the very highest redshifts , magnetic field strengths might be weaker , because the seed fields were essentially zero compared to the present strengths . starbursts also may build their magnetic fields up in much shorter times than normal galaxies , and through a different process than normal galaxies @xcite . finally , we have used one - zone models , which are appropriate if the crs sample all of the gas phases in each galaxy s ism . however , the ism is known to be clumpy in the milky way , in compact starbursts like arp 220 ( e.g. , * ? ? ? * ) , and even in the smgs themselves @xcite . a full understanding of the frc will probably require models that take into account the inhomogeneity of star - forming galaxies . we thank eric murphy and michal michaowski for critical readings of the text , eliot quataert for many stimulating conversations , and the galprop team for making their code and its subroutines freely available . galprop is available at http://galprop.stanford.edu . we would like to thank igor moskalenko for sharing his group s estimates of the milky way s total @xmath29-ray luminosity for normalization of our models of the frc . t. a. t. is supported in part by an alfred p. sloan fellowship .

we construct one - zone steady - state models of cosmic ray ( cr ) injection , cooling , and escape over the entire dynamic range of the fir - radio correlation ( frc ) , from normal galaxies to starbursts , over the redshift interval . we find that radio bright submillimeter galaxies alone can not explain the excess radio emission reported by arcade2 , but they may significantly enhance the diffuse radio background with respect to a naive application of the frc .

we construct one - zone steady - state models of cosmic ray ( cr ) injection , cooling , and escape over the entire dynamic range of the fir - radio correlation ( frc ) , from normal galaxies to starbursts , over the redshift interval . normal galaxies with low star - formation rates become radio - faint at high , because inverse compton ( ic ) losses off the cmb cool cr electrons and positrons rapidly , suppressing their nonthermal radio emission . however , we find that this effect occurs at higher redshifts than previously expected , because escape , bremsstrahlung , ionization , and starlight ic losses act to counter this effect and preserve the radio luminosity of galaxies . the radio dimming of star - forming galaxies at high is not just a simple competition between magnetic field energy density and the cmb energy density ; the cmb must also compete with every other loss process . we predict relations for the critical redshift when radio emission is significantly suppressed compared to the frc as a function of star - formation rate per unit area . for example , a milky way - like spiral becomes radio - faint at , while an m82-like starburst does not become radio - faint until . we show that the `` buffering '' effect of non - synchrotron losses improves the detectability of star - forming galaxies in synchrotron radio emission with evla and ska . additionally , we provide a quantitative explanation for the relative radio brightness of some high- submillimeter galaxies . we show that at fixed star formation rate surface density , galaxies with larger cr scale heights are radio bright with respect to the frc , because of weaker bremsstrahlung and ionization losses compared to compact starbursts . we predict that these `` puffy starbursts '' should have steeper radio spectra than compact galaxies with the same star - formation rate surface density . we find that radio bright submillimeter galaxies alone can not explain the excess radio emission reported by arcade2 , but they may significantly enhance the diffuse radio background with respect to a naive application of the frc .

astro-ph0503435

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to quantify the extent of the departure of the local sample from a log - linear relation we have plotted the logarithmic derivatives @xmath14 and @xmath151 of the @xmath12 and @xmath127 relations as a function of @xmath1 and @xmath133 in figure [ fig8 ] . the solid lines show the slopes of the best fit relations . the dashed lines show the slope of relations at the edges of the 1-sigma error ellipsoids in @xmath152 ( left panel ) or @xmath153 ( right panel ) space , while the grey stripes show the 1-sigma range for the slope of the log - linear fits from t02 and haering & rix ( 2004 ) respectively . the figure shows that in both cases the logarithmic slope of the log - quadratic relation varies substantially more over the range of @xmath1 or @xmath154 in the smbh sample than the statistical uncertainty in the slope @xmath5 of a log - linear fit . this fact has contributed to statistical bias and inconsistent results when comparing the log - linear slopes of the @xmath12 relation between different samples of smbhs . in the remainder of this section we discuss various implications of a log - quadratic @xmath12 relation . the possibility of a log - quadratic @xmath0-@xmath1 relation leads to several interesting consequences . the first concerns the velocity dispersion of galaxies in which the most massive smbhs reside . the mass of the largest smbhs in the sloan digital sky survey ( sdss ) survey volume was discussed in wyithe & loeb ( 2003 ) . we repeat part of the discussion here . consider a smbh of mass @xmath155 . we can estimate the co - moving density of black - holes of this mass from the observed quasar luminosity function and an estimate of quasar lifetime . if we assume eddington accretion , then at the peak of quasar activity , quasars powered by @xmath156 smbhs had a comoving density of @xmath157gpc@xmath158 . wyithe & loeb ( 2003 ) found that the number of quasars relative to the number of dark - matter halos at @xmath159 implies a duty cycle for quasars of @xmath160 . the comoving density of smbhs with masses in excess of @xmath161 at @xmath159 was therefore @xmath162gpc@xmath158 . as this corresponds to the peak of smbh growth , the smbh density should match the value observed today . this density implies that the nearest smbh of @xmath163 should be at a distance @xmath164mpc which is comparable to the distance of m87 , a galaxy known to possess a smbh of this mass ( ford et al . 1994 ) . what is the most massive smbh that can be detected dynamically in the sdss ? the sdss probes a volume of @xmath125gpc@xmath165 out to a distance @xmath166 times that of m87 . at the peak of quasar activity , the density of the brightest quasars implies that there should be @xmath167 smbhs with masses greater than @xmath168 per gpc@xmath165 , the nearest of which will be at a distance @xmath169mpc , or 5 times the distance to m87 . the radius of gravitational influence of the smbh scales as @xmath170 . we therefore find that for the nearest @xmath171 and @xmath172 smbhs , the angular radius of influence should be similar . thus the dynamical signature of the nearest @xmath168 smbhs on their stellar host should be detectable . in order to find these most massive smbhs one needs to identify the galaxies in which they reside . we estimate the value of @xmath1 implied for smbhs of mass @xmath173 using the mean @xmath31 relation . if one adopts the mean log - linear relation ( t02 ) , then smbhs with masses in excess of @xmath174 should reside in galaxies with @xmath175km / s ( see figure [ fig11 ] ) . however no such galaxies exist is the sdss ( e.g. sheth et al . 2003 ) , where largest values of galaxy velocity dispersion are found to be @xmath176km@xmath39s@xmath41 . the mean log - quadratic relation reaches @xmath177 at a more modest but still unobserved velocity dispersion , @xmath178km / s . however the intrinsic scatter in the @xmath31 relation is @xmath179 dex . we find that smbhs of mass @xmath173 differ by @xmath180 from the mean log - quadratic relation at @xmath176km / s . the most massive smbhs with masses of @xmath173 inferred from quasars at @xmath159 should therefore exist in the sdss and would lie at @xmath181 above the extrapolated mean log - quadratic relation for galaxies with the largest measured velocity dispersions of @xmath182km / s . this helps to reconcile the number of luminous quasars observed at @xmath159 with both the local @xmath12 relation and the lack of super massive galaxies . a positive log - quadratic term has a significant effect on the upper end of the smbh mass - function . in figure [ fig9 ] we show the smbh mass - function computed by combining the @xmath12 relation with the velocity dispersion function of sheth et al . two mass functions are shown . the grey stripe and dashed lines represent the ranges of uncertainty in the estimate of the mass - function obtained assuming log - linear and log - quadratic @xmath12 relations respectively . the ranges at fixed @xmath0 in each case correspond to the 16th and 84th percentiles , and were computed taking into account gaussian uncertainties in both the parameters of the @xmath31 relation and the velocity - dispersion function . the solid line shows the most likely estimate for the mass - function corresponding to the log - quadratic @xmath12 relation . figure [ fig9 ] shows that inclusion of a log - quadratic term in the @xmath12 relation results in an estimate for the number density of smbhs with masses of @xmath173 that is several orders of magnitude larger than inferred from a log - linear relation . we have estimated the mass density ( for a hubbles constant of @xmath183km@xmath39s@xmath184mpc@xmath41 ) of smbhs in the local universe . for a log - linear @xmath12 relation we find a density of @xmath185mpc@xmath158 , while for a log - quadratic @xmath12 relation we obtain @xmath186mpc@xmath158 . hence the addition of a log quadratic term does not effect estimates of the total mass density which is dominated by smbhs in the range @xmath187 ( aller & richstone 2002 ) . the sample of kinematically detected smbhs will not grow by a large factor in the foreseeable future ( ferrarese 2003 ) . progress in understanding the statistical properties of the smbh population may instead come via estimates of smbh masses that are based on reverberation mapping studies ( gebhardt et al . 2000b ; ferrarese et al . 2001 ; onken et al . 2004 ; peterson et al . 2004 ; nelson et al 2004 ) . onken et al . ( 2004 ) have presented a sample of 14 smbhs with virial masses ( @xmath188 ) determined via reverberation mapping studies , in galaxies with measured velocity dispersions . reverberation masses are determined up to a geometric factor @xmath189 , hence the smbh mass is @xmath190 . onken et al . ( 2004 ) have determined the average value @xmath191 by comparing the reverberation masses of these 14 smbhs , to the masses of smbhs in the local sample using a log - linear @xmath12 relation . they found @xmath192 over a range of values for the slope @xmath5 that include @xmath193 ( ferrarese 2002 ) and @xmath57 ( t02 ) . assuming this scaling factor we can combine the 14 galaxies used to obtain @xmath191 in onken et al . ( 2004 ) with the local sample of smbhs to form a sample of 45 galaxies . the left panel of figure [ fig10 ] shows the @xmath12 relation for the local sample ( solid dots ) , and its comparison to the agn smbh masses and velocity dispersions ( open circles ) presented in onken et al . we have repeated the @xmath46 minimisation using equation ( [ fit_quad ] ) for the combined sample of @xmath194 smbhs . in the right - hand panel we show the 1 , 1.5 , 2 and 2.5-sigma ellipsoids for @xmath5 and @xmath6 . the most likely solution has @xmath195 and @xmath196 with 1-sigma uncertainties of 0.3 and 1.0 respectively . the resulting best - fit @xmath12 relation is over - plotted in the left panel ( solid line ) . this solution is very close to the one obtained using only smbhs in the local sample ( @xmath197 , @xmath198 ) . the intrinsic scatter required for a reduced @xmath46 of unity in this fit was @xmath68 dex , indicating that the addition of the agn smbhs does not increase the scatter of the @xmath12 relation . the addition of agn smbhs results in a fit with a log - quadratic term which is non - zero at around the 1.5-sigma level . the sample of agn smbhs with masses determined from reverberation mapping therefore strongly supports a log - quadratic @xmath12 relation . this is despite the fact that the normalization of the reverberation smbh masses was determined via the assumption of a log - linear relation . there are no smbhs in the local sample with masses below @xmath32 . attempts to extend the @xmath12 relation to lower masses through dynamical observations have centered on two cases , m33 ( merritt , ferrarese & joseph 2001 ; gebhardt et al . 2001 ) , and ngc205 ( valluri , ferrarese , merritt & joseph 2005 ) . only upper limits have been obtained in these systems . however we can compare the log - quadratic fit in the low-@xmath1 regime with smbh masses obtained from single epoch virial estimates based on observations of agn . the upper panel of figure [ fig11 ] shows the extrapolation of the best fit log - quadratic relation for the local sample , and its comparison to the agn smbh masses and velocity dispersions presented in barth , greene & ho ( 2004 ) , as well as the point for pox52 ( barth , ho , rutledge & sargent 2004 ) . the agn smbh masses in this sample were estimated using the single epoch virial mass calibration of onken et al . the log - quadratic fit derived using the local sample appears to describe the smbh masses in these agn much better than the log - linear fit ( see right - hand panel of figure [ fig11 ] ) . the residuals are symmetrically placed around the best fit log - quadratic relation . on the other hand the dashed line in the right hand panel of figure [ fig11 ] shows the additional residual of the log - quadratic relation relative to the log - linear relation . the residuals of the agn smbhs relative to the log - linear relation are systematically positive , indicating that the log - linear relation provides a poor description . the single epoch virial smbh masses for the agn have been estimated in a regime where the technique is not directly calibrated . one must therefore be cautious comparing the agn and local samples since the agn smbh mass estimates may contain some unknown systematic uncertainty relative to the dynamical estimates of the local sample ( barth , greene & ho 2005 did not perform a fit to the combined sample for this reason ) . moreover it is possible that the agn smbh sample is biased towards large smbh masses ( barth , greene & ho 2005 ) . never - the - less it is instructive to combine the local and agn smbh samples and investigate the resulting log - quadratic @xmath31 relation . we have repeated the @xmath46 minimisation using equation ( [ fit_quad ] ) for the combined sample of @xmath199 smbhs . in the lower - left panel of figure [ fig11 ] we show the combined sample with the resulting best - fit @xmath12 relation over - plotted ( solid line ) . the intrinsic scatter required for a reduced @xmath46 of unity in this fit was @xmath200 dex . in the lower - right panel of figure [ fig11 ] we show the 1 , 1.5 , 2 and 2.5-sigma ellipsoids for @xmath5 and @xmath6 . the most likely solution has @xmath201 and @xmath202 with 1-sigma uncertainties of 0.3 and 0.7 respectively . this solution is very close to the one obtained using only smbhs in the local sample ( @xmath197 , @xmath203 and @xmath204 dex ) , indicating that the agn smbhs follow the same log - quadratic @xmath12 relation as the local sample . however the addition of low - mass agn smbhs results in a fit with a log - quadratic term which is non - zero at greater than the 2-sigma level . the sample of agn smbhs therefore support a log - quadratic @xmath31 relation . the log - quadratic relation describes the masses of smbhs in galaxies with velocity dispersions ranging from 25 - 400km@xmath39s@xmath41 . if one extrapolates this to lower @xmath1 then the log - quadratic relation offers the tantalising prediction that there is a minimum smbh mass of @xmath205 , and that this minimum smbh mass resides in bulges with @xmath206km@xmath39s@xmath41 . interestingly , this velocity dispersion corresponds to the minimum value of the virial velocity for a dark - matter halo within which gas accreted from the igm can cool via atomic transitions in hydrogen . finally we would like to make the following point regarding the relationship between the power - law slope of the @xmath12 and @xmath127 relations . an estimate of the bulge mass may be made using the virial mass , @xmath207 , where @xmath45 is the scale radius of the bulge . the projection of the fundamental plane yields a relation between radius and velocity dispersion of @xmath208 ( bernardi et al . consider the power - law slope at the mean velocity of the galaxy sample ( @xmath209km / s ) . we have @xmath210 , which implies @xmath211 , or @xmath212 . this is in excellent agreement with the best fit parameters of @xmath213 and @xmath214 derived in this paper . furthermore , a value of @xmath215 for the @xmath12 relation is ruled out at @xmath121 significance . if it is to be consistent with the @xmath12 relation , the @xmath130 relation should therefore be steeper than linear for galaxies with @xmath209km / s . given the relation between @xmath1 and the virial mass , we would also expect the @xmath130 relation to have a positive quadratic component , given a positive quadratic component in the @xmath12 relation .

furthermore , assuming no systematic offset , single epoch virial smbh masses estimated for agn ( barth et al . 2005 ) follow the same log - quadratic relation as the local sample , but extend it downward in mass by an order of magnitude . the log - quadratic term in the relation has a significant effect on estimates of the local smbh mass function at , leading to densities of smbhs with that are several orders of magnitude larger than inferred from a log - linear relation .

we demonstrate that a log - linear relation does not provide an adequate description of the correlation between the masses of super - massive black - holes ( smbh , ) and the velocity dispersions of their host spheroid ( ) . an unknown relation between and may be expanded to second order to obtain a log - quadratic relation of the form ^ 2 $ ] . we perform a bayesian analysis using the local sample described in tremaine et al . ( 2002 ) , and solve for , and , in addition to the intrinsic scatter ( ) . we find unbiased parameter estimates of , and . at the 80% level the relation does not follow a uniform power - law . indeed , over the velocity range 70km / skm / s the logarithmic slope of the best fit relation varies between 2.7 and 5.1 , which should be compared with a power - law estimate of . the addition of the 14 galaxies with reverberation smbh masses and measured velocity dispersions ( onken et al . 2004 ) to the local smbh sample leads to a log - quadratic relation with the same best fit as the local sample . furthermore , assuming no systematic offset , single epoch virial smbh masses estimated for agn ( barth et al . 2005 ) follow the same log - quadratic relation as the local sample , but extend it downward in mass by an order of magnitude . the log - quadratic term in the relation has a significant effect on estimates of the local smbh mass function at , leading to densities of smbhs with that are several orders of magnitude larger than inferred from a log - linear relation . we also estimate unbiased parameters for the smbh - bulge mass relation using the sample assembled by haering & rix ( 2004 ) . with a parameterization ^ 2 $ ] , we find and . we determined an intrinsic scatter which is% larger than the scatter in the relation . = = = = = = = = # 1 # 1 # 1 # 1 @mathgroup@group @mathgroup@normal@groupeurmn @mathgroup@bold@groupeurbn @mathgroup@group @mathgroup@normal@groupmsamn @mathgroup@bold@groupmsamn = `` 019 = ' ' 016 = `` 040 = ' ' 336 = " 33e = = = = = = = = # 1 # 1 # 1 # 1 = = = = = = = = # 1 latexl-.36em.3ex-.15em t-.1667em.7ex-.125emx [ section ] [ firstpage ] black - holes - galaxies : formation

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using the local sample of smbhs we have demonstrated that the parameter describing a log - linear fit to the @xmath12 relation is sensitive to the inclusion of individual galaxies at a level larger than the statistical uncertainty . this indicates that a log - linear @xmath12 relation does not provide a good description of the local sample of smbhs . we expand a general relation between @xmath216 and @xmath217 to second order , and fit the data using the resulting log - quadratic relation instead . we find that a log - quadratic relation provides a substantially better fit to the local sample of smbh masses and velocity dispersions . moreover unlike the log - linear relation , the parameters describing the log - quadratic relation are not systematically dependent on the inclusion of individual galaxies in the sample . after allowing for a second - order term in the @xmath12 relation we find an unbiased estimate for the slope of the local sample at @xmath28km / s to be @xmath9 . this value is slightly ( 2/3-sigma ) larger than previous estimates for this sample . however the logarithmic slope @xmath218 of the best fit log - quadratic relation varies substantially , from 2.7 - 5.1 over the velocity range of the local sample . the coefficient of the second order term @xmath10 is greater than zero at the 90% level . this indicates that with 80% confidence the local sample describes an @xmath12 relation that does not follow a single powerlaw between @xmath33km / s and @xmath116km / s . we have tested the sensitivity of this conclusion to different sub - samples of smbh masses determined via different techniques , as well as smbhs with and without resolved spheres of influence . the log - quadratic fit implies a non - linear contribution to the @xmath31 relation in a sub - sample of galaxies that contain only smbhs whose spheres of influence were resolved , in a sub - sample containing only smbhs with masses determined through stellar dynamics , and in a sub - sample containing only smbhs with masses determined only by non stellar dynamical methods . moreover the non - linearity is present in each sub - sample whether the central or effective velocity dispersion is used as the independent variable . smbh masses in active galaxies estimated via reverberation mapping offer an avenue to increase the smbh sample for study of the @xmath31 relation . we find that the combination of the 14 galaxies with reverberation smbh masses and measured velocity dispersions ( onken et al . 2004 ) with the local smbh sample leads to a log - quadratic relation with the same best fit as the local sample alone . the @xmath12 relation can be extended to lower masses through the inclusion of single epoch virial estimates of smbh masses based on observations of agn ( barth , greene & ho 2004 ) . in a @xmath46 analysis the best - fit log - quadratic @xmath12 relation is unchanged by the addition of a sample of 16 low mass smbhs . however the uncertainty in @xmath6 is reduced . we find that in the absence of a systematic error in the normalisation of smbh masses between the local and agn samples , the @xmath12 relation described by the combined sample deviates from a power - law at greater than the 2-sigma level . the best - fit log - quadratic relation predicts a minimum mass for smbhs in galaxies of @xmath205 , which should reside in bulges with @xmath206km@xmath39s@xmath41 . a log - quadratic @xmath12 relation has important implications for smbh demography . in particular , estimates of the local smbh mass - function that utilise the log - quadratic @xmath31 relation describe densities of smbhs with @xmath219 that are orders of magnitude larger than expected for a log - linear @xmath12 relation . in addition the departure from a power - law should provide important clues regarding the astrophysics responsible for the @xmath12 relation . for example one recent model describing the effects of radiative feedback on smbh growth predicts departure from a power - law relation , including steepening of the relation at large @xmath1 ( saznov et al . 2005 ) . we have also applied our analysis to the relation between smbh and bulge mass using the sample described in haering & rix ( 2004 ) . we find evidence for a log - quadratic term in the @xmath129 relation ( at the 1-sigma level ) , with @xmath220 and @xmath20 . we find an intrinsic scatter of @xmath21 dex . since we find the intrinsic scatter in the @xmath12 relation to be @xmath113 dex , there is @xmath221 more scatter in the smbh mass at fixed bulge mass than at fixed velocity dispersion . the sample of kinematically detected smbhs will not grow by a large factor in the foreseeable future ( ferrarese 2003 ) . progress in understanding the statistical properties of the smbh population will instead come via estimates of smbh masses that are based on reverberation mapping studies . the increased sample of smbhs will offer the possibility of more clearly defining the local @xmath31 relation ( gebhardt et al . 2000b ; ferrarese et al . 2001 ; onken et al . 2004 ; peterson et al . 2004 ; nelson et al 2004 ) , and of extending its study to high redshift ( shields et al .

we demonstrate that a log - linear relation does not provide an adequate description of the correlation between the masses of super - massive black - holes ( smbh , ) and the velocity dispersions of their host spheroid ( ) . we find unbiased parameter estimates of , and . at the 80% level / skm / s the logarithmic slope of the best fit relation varies between 2.7 and 5.1 , which should be compared with a power - law estimate of . the addition of the 14 galaxies with reverberation smbh masses and measured velocity dispersions ( onken et al . 2004 ) to the local smbh sample leads to a log - quadratic relation with the same best fit as the local sample . we also estimate unbiased parameters for the smbh - bulge mass relation using the sample assembled by haering & rix ( 2004 ) . with a parameterization ^ 2 $ ] , we find and .

we demonstrate that a log - linear relation does not provide an adequate description of the correlation between the masses of super - massive black - holes ( smbh , ) and the velocity dispersions of their host spheroid ( ) . an unknown relation between and may be expanded to second order to obtain a log - quadratic relation of the form ^ 2 $ ] . we perform a bayesian analysis using the local sample described in tremaine et al . ( 2002 ) , and solve for , and , in addition to the intrinsic scatter ( ) . we find unbiased parameter estimates of , and . at the 80% level the relation does not follow a uniform power - law . indeed , over the velocity range 70km / skm / s the logarithmic slope of the best fit relation varies between 2.7 and 5.1 , which should be compared with a power - law estimate of . the addition of the 14 galaxies with reverberation smbh masses and measured velocity dispersions ( onken et al . 2004 ) to the local smbh sample leads to a log - quadratic relation with the same best fit as the local sample . furthermore , assuming no systematic offset , single epoch virial smbh masses estimated for agn ( barth et al . 2005 ) follow the same log - quadratic relation as the local sample , but extend it downward in mass by an order of magnitude . the log - quadratic term in the relation has a significant effect on estimates of the local smbh mass function at , leading to densities of smbhs with that are several orders of magnitude larger than inferred from a log - linear relation . we also estimate unbiased parameters for the smbh - bulge mass relation using the sample assembled by haering & rix ( 2004 ) . with a parameterization ^ 2 $ ] , we find and . we determined an intrinsic scatter which is% larger than the scatter in the relation . = = = = = = = = # 1 # 1 # 1 # 1 @mathgroup@group @mathgroup@normal@groupeurmn @mathgroup@bold@groupeurbn @mathgroup@group @mathgroup@normal@groupmsamn @mathgroup@bold@groupmsamn = `` 019 = ' ' 016 = `` 040 = ' ' 336 = " 33e = = = = = = = = # 1 # 1 # 1 # 1 = = = = = = = = # 1 latexl-.36em.3ex-.15em t-.1667em.7ex-.125emx [ section ] [ firstpage ] black - holes - galaxies : formation

1204.6532

i

relativistic plasmas at extremely high temperature @xmath1 such as electron and/or quark - gluon plasma are expected to be realized in the early universe and the experiments of heavy ion collisions at relativistic heavy ion collider and large hadron collider . these systems have multi - energy scale at weak coupling ( @xmath5 ) even at so high @xmath1 that all mass scale in the lagrangian is negligible ; e.g , typical energy of particles is of order @xmath1 , while the energy of the bosonic and fermionic collective excitations called plasmon @xcite and plasmino @xcite is of order @xmath6 , and the fermion damping rate in gauge theories is of order @xmath0 @xcite . these energy scales , @xmath1 , @xmath6 , and @xmath0 , are called hard , soft , and ultrasoft scales , respectively . unlike perturbation theory in the vacuum , the loop expansion at finite temperature does not correspond to the coupling nor @xmath7 expansions , and the scale dependent expansion is necessary ( fig . [ fig : intro ] ) . when the energy scale is @xmath6 , the one - loop approximation obtained by integrating out hard internal momenta , called hard thermal loop ( htl ) approximation @xcite , is reliable , and the approximation establishes the htl effective theory @xcite . if the energy is of order or much less than @xmath0 , some resummation is necessary @xcite . here let us focus on the analysis for the fermion propagator with an ultrasoft momentum . the resummation scheme used in the analysis of the fermion propagator consist of the following procedures @xcite : 1 . resumming the thermal mass and the decay width of the hard particles . 2 . summing all the ladder diagrams ( in gauge theory ) . by analyzing the fermion propagator using the resummed perturbation theory , a novel fermionic excitation was found @xcite . each perturbation scheme with soft and ultrasoft momenta can be interpreted as different kinetic equations . when the energy is soft , the effect of collisions is negligible and hence the collisionless kinetic equation called vlasov equation is valid @xcite . this equation corresponds to the htl approximation @xcite introduced above . when the energy is of order or less than @xmath0 , the effects of the interaction among the hard particles are no longer negligible in general , so it is necessary to take into account their effects . in fact , the analysis on the gluon self - energy with an ultrasoft momentum should be performed with the resummed perturbation theory including the effect of collisions , and it was done by constructing the linearized boltzmann equation @xcite . the computation of transport coefficients , whose energy scale is much smaller than @xmath0 , is also performed with the resummed perturbation theory @xcite , the linearized boltzmann equation @xcite , and the two - particle irreducible formalism @xcite . these methods produce the same result in the leading order of the coupling constant . using the correspondence between the perturbation theory and the linearized kinetic theory , the self - consistent equation in the resummed perturbation theory is interpreted with the language of the kinetic theory . in this paper , we derive a generalized and linearized kinetic equation for fermionic excitations with an ultrasoft momentum , which we will call `` off - diagonal '' kinetic equation later , in the yukawa model and qed , while the boltzmann equation discussed above is employed for bosonic excitations . our equation is systematically derived from the kadanoff - baym equation , and is equivalent to the self - consistent equation in the resummed perturbation theory @xcite used in the analysis of the fermion propagator . the derivation helps us to establish the foundation of the resummed perturbation scheme . the kinetic equation will also give us the kinetic interpretation of the resummation scheme . furthermore , we also discuss the procedure of analyzing the higher point functions not only two - point function of the fermion in qed . this paper is organized as follows : section [ sec : yukawa ] is devoted to the derivation of the generalized and linearized kinetic equation and the discussion on the kinetic interpretation of the self - consistent equation in the resummed perturbation theory in the yukawa model , which is the simplest fermion - boson system . in sec . [ sec : qed ] , a similar analyses in qed is done in the coulomb gauge . we make concluding remarks and summarize our results in sec . [ sec : summary ] . in appendix [ app : analyticity ] , we evaluate the structure of the induced source terms . we analyze the kadanoff - baym equation that would yield the linearized kinetic equation in the diagonal case in appendix [ app : diagonal ] . appendix [ app : k0 ] is devoted to showing that the temporal component of @xmath8 introduced in sec . [ sec : qed ] can be neglected . we show that the result obtained in sec . [ sec : qed ] is valid also in the temporal gauge , which is the gauge - fixing of the original paper @xcite of the resummed perturbation theory , in appendix [ app : temporal ] .

we derive a linearized kinetic equation for fermionic excitations with an ultrasoft momentum , , from the kadanoff - baym equation in a yukawa model and quantum electrodynamics ( qed ) at extremely high , where is the coupling constant . we show that this equation is equivalent to the self - consistent equation in the resummed perturbation theory used in the analysis of the fermion spectrum with the ultrasoft momentum .

we derive a linearized kinetic equation for fermionic excitations with an ultrasoft momentum , , from the kadanoff - baym equation in a yukawa model and quantum electrodynamics ( qed ) at extremely high , where is the coupling constant . we show that this equation is equivalent to the self - consistent equation in the resummed perturbation theory used in the analysis of the fermion spectrum with the ultrasoft momentum . furthermore , we derive the equation that determines the-point function with external lines for a pair of fermions and bosons with ultrasoft momenta in qed .

0804.2179

c

we have described an implementation of the nanomechanical quantum superposition generation and verification scheme presented in the companion reference @xcite . the implementation is based on the circuit qed set - up with the incorporation of a mechanical degree of freedom formed out of a suspended squid loop segment located opposite the centre conductor of a coplanar waveguide . two qubit realizations were investigated , namely the capacitively coupled charge qubit with voltage - biased qubit - mechanical resonator coupling , and the inductively coupled flux qubit with current - biased qubit - mechanical resonator coupling . both qubit realizations were found to have comparable and feasible resonator coupling strengths that are adequate for the quantum superposition generation scheme @xcite . ultimately , less predictable qubit properties such as their coherence times will decide which implementation is the more promising of the two . nevertheless , the present considerations suggest that both implementations are equally worth pursuing in experiment . we especially thank a. rimberg and also e. buks , j. hertzberg , and k. schwab for very helpful discussions . mpb was partly supported by the national science foundation ( nsf ) under nirt grant no . cms-040431 , the us - israel binational science foundation ( bsf ) and by the foundational questions institute ( fqxi ) . ada was supported by the epsrc under grant ep / e03442x/1 .

we describe a possible implementation of the nanomechanical quantum superposition generation and detection scheme described in the preceding , companion paper [ armour a d and blencowe m p 2008 _ new . the implementation is based on the circuit quantum electrodynamics ( qed ) set - up , with the addition of a mechanical degree of freedom formed out of a suspended , doubly - clamped segment of the superconducting loop of a dc squid located directly opposite the centre conductor of a coplanar waveguide ( cpw ) .

we describe a possible implementation of the nanomechanical quantum superposition generation and detection scheme described in the preceding , companion paper [ armour a d and blencowe m p 2008 _ new . j. phys . _ * xx * xxx ] . the implementation is based on the circuit quantum electrodynamics ( qed ) set - up , with the addition of a mechanical degree of freedom formed out of a suspended , doubly - clamped segment of the superconducting loop of a dc squid located directly opposite the centre conductor of a coplanar waveguide ( cpw ) . the relative merits of two squid based qubit realizations are addressed , in particular a capacitively coupled charge qubit and inductively coupled flux qubit . it is found that both realizations are equally promising , with comparable qubit - mechanical resonator mode as well as qubit - microwave resonator mode coupling strengths .

astro-ph0503119

c

we have described algorithms that identify and extract self - absorption ( hisa ) features in high - resolution 21 cm line data cubes . these algorithms were designed to carry out a hisa survey of cold in the initial @xmath239 phase of the arcminute - resolution canadian galactic plane survey ( cgps ) , but they should have more general applicability . our search algorithms use clean - based spatial and spectral filtering to remove large - scale emission structure and identify hisa as significant negative residuals . features identified in both spectral and spatial domains are flagged as hisa , and the unabsorbed brightness @xmath77 along the feature sightline is estimated from a 3-d interpolation of the off - feature brightness temperature @xmath78 . hisa detections in overly noisy regions are rejected , as are those for which @xmath101 k , lest significant false detections result from gaps between sharply - structured emission features with faint backgrounds . in order to capture features larger than the clean filter scale , identified hisa is removed and the search process is repeated ; a total of three such passes suffices for the cgps data . we performed detailed tests of our hisa - finding software with model data to determine its detection limits , false positive rates , and measurement biases as functions of feature size , amplitude , and background field brightness . the tests show that hisa is well detected within the software design criteria , with high detection rates for hisa significantly stronger than the noise level , larger than a few beams , narrower than a few , and with @xmath200 k. at the same time , the bulk of hisa detections are reliable , with very low false positive rates in most parts of the parameter space except those occupied by beam - scale noise fluctuations . measurement drifts are small in well - detected features , with @xmath77 underestimated by a few k due to contamination of @xmath78 by faint , undetected hisa near the feature . where detections are truncated by noise fluctuations or faint @xmath77 , the bias may be somewhat larger . incomplete detections also make features appear smaller in angular size and linewidth than in reality due to truncation . this paper is the third in an ongoing series investigating hisa at high resolution in the galactic plane . a companion paper ( paper ii ) presents hisa survey results for the cgps . subsequent papers will further analyze the cgps hisa and also examine hisa in cgps extensions and in the vla galactic plane survey . we thank w. mccutcheon , t. landecker , and j. stil for a number of useful discussions on this project , and the anonymous referee for constructive comments on the manuscript . j. stil helped with multipanel figure layout . we are very grateful to r. gooch for tireless computing support , including continued expansion of the capabilities of the karma visualization software package @xcite , which was used extensively for this work . the dominion radio astrophysical observatory is operated as a national facility by the national research council of canada . the canadian galactic plane survey ( cgps ) is a canadian project with international partners . the cgps is described in @xcite . the main cgps data set is available at the canadian astronomy data centre . the cgps is supported by a grant from the natural sciences and engineering research council of canada .

we describe algorithms that detect 21 cm line self - absorption ( hisa ) in large data sets and extract it for analysis . our search method identifies hisa as spatially and spectrally confined dark features that appear as negative residuals after removing larger - scale emission components with a modified clean algorithm . false detection rates are very low in all parts of the parameter space except at sizes and amplitudes approaching those of noise fluctuations . absorption measurement biases introduced by the method are generally small and appear to arise from cases of incomplete hisa detection . this paper is the third in a series examining hisa at high angular resolution . a companion paper ( paper ii ) uses our hisa search and extraction method to investigate the cold atomic gas distribution in the canadian galactic plane survey .

we describe algorithms that detect 21 cm line self - absorption ( hisa ) in large data sets and extract it for analysis . our search method identifies hisa as spatially and spectrally confined dark features that appear as negative residuals after removing larger - scale emission components with a modified clean algorithm . adjacent hisa volume - pixels ( voxels ) are grouped into features in space , and the brightness of voxels outside the 3-d feature boundaries is smoothly interpolated to estimate the absorption amplitude and the unabsorbed emission brightness . the reliability and completeness of our hisa detection scheme have been tested extensively with model data . we detect most features over a wide range of sizes , linewidths , amplitudes , and background levels , with poor detection only where the absorption brightness temperature amplitude is weak , the absorption scale approaches that of the correlated noise , or the background level is too faint for hisa to be distinguished reliably from emission gaps . false detection rates are very low in all parts of the parameter space except at sizes and amplitudes approaching those of noise fluctuations . absorption measurement biases introduced by the method are generally small and appear to arise from cases of incomplete hisa detection . this paper is the third in a series examining hisa at high angular resolution . a companion paper ( paper ii ) uses our hisa search and extraction method to investigate the cold atomic gas distribution in the canadian galactic plane survey .

1202.3997

i

type ia supernovae ( sne ia ) are among the most energetic explosions in the known universe , releasing @xmath1 ergs of kinetic energy in their ejecta , and synthesizing @xmath2 @xmath3 of radioactive @xmath0ni . the discovery of the phillips relation @xcite has enabled the use of sne ia as standardizable cosmological candles which greatly enhances the accurate determination of their distance . the discovery of the accelerated expansion of the universe using sne ia @xcite has stimulated a tremendous amount of interest in the use of sne ia events as standard cosmological candles , allowing them to serve as probes of the equation of state of dark energy , as parameterized by the eos parameter @xmath4 . the main challenge to the enterprise of measuring @xmath5 using sne iais reducing the systematic errors in the accuracy with which such supernovae can be used as standard candles @xcite . the accuracy must be improved from the current level of about 15% to about 1% in order for large surveys to determine the values of @xmath6 and its rate of change with @xmath7 to better than 10% @xcite . the best hope for improvements in distance modulus accuracy is more accurate modeling of sne ia explosions . evidence suggests that sne ia are the results of the thermonuclear explosion of a carbon - oxygen ( c - o ) white dwarf ( wd ) . the leading scenario for sne ia explosions is the single - degenerate model in which a progenitor wd accretes material from a non - degenerate companion star until the mass of the wd grows nearly equal to the chandrasekhar limit @xcite . the wd then manages to release enough nuclear energy by fusing c and o into radioactive ni and other lighter @xmath8-elements in the time span of a few seconds or less @xcite , such that it deposits approximately @xmath9 ergs of energy , unbinding the star and accelerating the stellar material to speeds of thousands of kilometers per second @xcite . this rapid fusion process must proceed in two phases @xcite . the first phase begins with the initiation of a subsonic nuclear burning front ( referred to as a deflagration or flame ) . as the wd accretes material from its companion , convective carbon burn begins in its core . when carbon burning becomes too vigorous for convective cooling to be effective , a thermonuclear flame ( or deflagration ) is born in local hot spots that form in the convective region . the deflagration burns and rises due to buoyancy as it makes its way from the core to the outer layers of the star . the second phase consists of a supersonic burning front a detonation that consumes the remainder of the wd . the transition from the deflagration phase to the detonation phase is poorly understood , and has been the subject of much modeling research . a variety of models incorporates the scenario of a deflagration followed by a detonation , such as the deflagration - to - detonation transition ( ddt ) , the pulsating reverse detonation ( prd ) @xcite , or the gravitationally confined detonation gcd @xcite . these models differ primarily in the method by which the deflagration leads to a detonation . an alternative scenario to the single - degenerate model is the double - degenerate model in which two wds forming a binary system undergo a merger process that leads to the detonation of one of the wds . the double - degenerate channel @xcite has recently received revived attention from both observation ( e.g. , @xcite ) and theory ( e.g. , @xcite ) . however , while computational models have explored prompt detonations in near - equal mass super - chandrasekhar mergers and head - on collisions of binary wd systems @xcite it remains unclear whether more commonplace mergers between two typical c - o wds of masses @xmath10 will result in a type ia explosion . previous one - dimensional theoretical models suggest that such mergers will result in deflagration wave that sets off an accretion - induced collapse to a neutron star @xcite . in this work we focus on the gcd scenario of the single - degenerate model of sne ia . we use the flash code @xcite to extend the set of 3d whole - star gcd models in @xcite ( hereafter j08 ) to include multiple ignition points as initial conditions . these initial conditions provide more burning , and hence more energy release during the deflagration phase . the purpose of this work is to examine the conditions produced in the wd resulting from a scenario where more energy is released during the deflagration phase than in the previous gcd models and to demonstrate that the scenario manifests the necessary conditions for a detonation . to distinguish between the two versions of gcd models we refer to the previous body of gcd models ( @xcite , j08 , @xcite , and references therein ) as `` classical '' gcd models and refer to models in this paper as `` pulsationally - assisted '' gcd models or simply `` pulsational '' gcd ( pgcd ) models . the origin of the name stems from the fact that the wds in the models undergo a pulsation where they first expand due to energy input from the deflagration phase and then contract from the pull of gravity . these models require the contraction of the wd to create the thermodynamic conditions necessary to initiate a detonation , hence the phrase `` pulsationally - assisted '' . in fact , the paradigm we put forth has characteristics of both the classical gcd models and the prd models . in section [ sec : gcdrev ] we review the classical gcd model , introduce the pgcd model , and discuss the ignition of the deflagration . in section [ sec : det ] we discuss the zeldovich gradient mechanism as a detonation trigger and its implications for the pgcd . we additionally discuss the numerical detonation trigger used in our simulations . we give an overview of the flash code and the relevant physics modules used for our sne ia simulations in section [ sec : methods ] . in section [ sec : sims ] we describe the results of our simulations . we compare the detonation mechanisms between the classical gcd and the pgcd models in section [ sec : compare ] . finally , in section [ sec : discussion ] we discuss properties of the simulations as well as possible observational features of the models .

we describe the detonation mechanism comprising the `` pulsationally assisted '' gravitationally confined detonation ( gcd ) model of type ia supernovae ( sne ia ) . this model is analogous to the previous gcd model reported in ; however , the chosen initial conditions produce a substantively different detonation mechanism , resulting from a larger energy release during the deflagration phase . the resulting final kinetic energy andni yields conform better to observational values than is the case for the `` classical '' gcd models . in the present class of models , the ignition of a deflagration phase leads to a rising , burning plume of ash . we demonstrate feasibility of this scenario with three 3-dimensional ( 3d ) , full star simulations of this model using the flash code .

we describe the detonation mechanism comprising the `` pulsationally assisted '' gravitationally confined detonation ( gcd ) model of type ia supernovae ( sne ia ) . this model is analogous to the previous gcd model reported in ; however , the chosen initial conditions produce a substantively different detonation mechanism , resulting from a larger energy release during the deflagration phase . the resulting final kinetic energy andni yields conform better to observational values than is the case for the `` classical '' gcd models . in the present class of models , the ignition of a deflagration phase leads to a rising , burning plume of ash . the ash breaks out of the surface of the white dwarf , flows laterally around the star , and converges on the collision region at the antipodal point from where it broke out . the amount of energy released during the deflagration phase is enough to cause the star to rapidly expand , so that when the ash reaches the antipodal point , the surface density is too low to initiate a detonation . instead , as the ash flows into the collision region ( while mixing with surface fuel ) , the star reaches its maximally expanded state and then contracts . the stellar contraction acts to increase the density of the star , including the density in the collision region . this both raises the temperature and density of the fuel - ash mixture in the collision region and ultimately leads to thermodynamic conditions that are necessary for the zeldovich gradient mechanism to produce a detonation . we demonstrate feasibility of this scenario with three 3-dimensional ( 3d ) , full star simulations of this model using the flash code . we characterized the simulations by the energy released during the deflagration phase , which ranged from 38% to 78% of the white dwarf s binding energy . we show that the necessary conditions for detonation are achieved in all three of the models .

1202.3997

r

we extended the study of the gcd model described in j08with two primary differences . first , we included detonation physics in the simulations ( as we described in sections [ subsec : numreal ] and [ sec : methods ] ) and followed the models from ignition , through the detonation phase , and to the free expansion phase . we terminated the simulations when the temperature decreases to the point that nuclear reactions ceased . second , we initiated these simulations with multiple ignition points ( as described in section [ subsec : ics ] ) instead of a single ignition point with the method used in j08 . for completeness we give the basic points here but refer the reader to j08 and references therein for more details . our simulations used flash s amr capabilities with a finest resolution of 8 km . each simulation contained a 1.365 @xmath3 wd in hydrostatic equilibrium composed of equal parts carbon and oxygen . the wd had a central density of @xmath59 g/@xmath60 , an ambient temperature of @xmath61 k , a radius of approximately @xmath62 km , and a binding energy of @xmath63 ergs . although the core of the star is most likely convective with a turbulent convective rms velocity @xmath64 km / s @xcite , the turbulent convective rms velocity is much less than the laminar flame speed , and so we have ignored the background convective turbulence , and initialized the star with zero velocity . we initiated this series of simulations with multiple ignition `` points '' , which are @xmath65 km spheres comprised of hot ash placed in the star at rest . we placed the ignition points in a spherical region whose center coincided with the z - axis . we parameterized the spherical region by its radius and z - offset ( the distance from the origin of the center of the spherical region along the z - axis ) . the radius of the spherical region was @xmath66 km and the z - offsets were @xmath67 km , @xmath68 km , and @xmath69 km - one z - offset for each of our three simulations . we randomly populated a @xmath66 km spherical region with @xmath70 ignition points . we placed ignition points so that they did not overlap with one another , and so that they were contained entirely within the spherical region . we used the same random distribution of ignition points for all three simulations ; they only differed by their relative location along the z - axis . table [ tab : sims ] contains labels for the simulations referred to in this work along with parameters for the initial conditions . in this section we describe the evolution of the pgcd model as demonstrated by the @xmath71 simulation . figures [ fig : gcdpbrads1 ] and [ fig : gcdpbrads2 ] show snapshots of the @xmath71 simulation starting with the initial conditions and ending with the passage of the detonation wave . the green contour in the figures approximates the location of the wd s surface . the orange regions are high temperature regions . these regions are primarily hot ash . the temperature ranges from @xmath72 k ( dark orange ) to @xmath73 k ( bright orange ) . each simulation begins with one of the above multiple ignition point configurations . panel ( @xmath74 ) of figure [ fig : gcdpbrads1 ] shows the initial conditions of the @xmath71 simulation . in the first few tenths of a second , each ignition point quickly burns radially outward from its center and merges with the other ignition points to form a large asymmetric bubble of ash . the ash in the bubble is less dense than the surrounding stellar material and is therefore buoyant . after 0.3 - 0.4 seconds , the bubble , which continues to grow in size , begins to quickly rise towards the wd s surface . during the rise , rayleigh - taylor instabilities grow on the flame surface , which further increases the surface s complexity and enhances the burning rate @xcite . panel ( @xmath75 ) of figure [ fig : gcdpbrads1 ] shows the simulation at 0.6s . this panel shows the ignition points after they have risen and merged to form a complex volume whose surface has been enhanced by fluid instabilities . after approximately 1.5 s , the rising ash bubble breaks through the stellar surface and begins spreading laterally across the star in all directions , converging on a region antipodal to the bubble breakout region . since the density of the surface layers of the star are too low to maintain thermonuclear combustion , the flame quenches and the deflagration subsides . as the ash flows over the surface of the star , cold fuel ( c and o ) mixes with the ash at the interface between the ash and the stellar surface , creating a fuel - ash mixture . panels ( @xmath76 ) , ( @xmath77 ) , and ( @xmath78 ) of figure [ fig : gcdpbrads1 ] are at 1.1 s , 1.4 s , and 1.9 s , respectively . these panels show the ash after it has broken out of the surface and has started to spread . in panel ( @xmath76 ) the ash has spread approximately half way around the star . by 1.4 s ( panel @xmath77 ) , the ash has made it three - fourths the way around the star , and at 1.9 s ( panel @xmath78 ) the ash has almost completely engulfed the wd . a significant amount of nuclear energy , @xmath79 ergs ( comparable to the binding energy of the wd ) , is released during the deflagration . this provides a kick to the star which causes it to expand . during the first few seconds , while the ash flows over the surface , the star expands to several times its original size . the expanding star slows the ash before it reaches the collision region . this shown in panels ( @xmath76 ) - ( @xmath80 ) of figure [ fig : gcdpbrads1 ] and panel ( @xmath74 ) of figure [ fig : gcdpbrads2 ] . panel ( @xmath80 ) of figure [ fig : gcdpbrads1 ] is at 2.2 s and panel ( @xmath74 ) of figure [ fig : gcdpbrads2 ] is at 2.5 s. the ash seems to disappear from the panels because the star has expanded and the ash has cooled to the point that it has fallen out of the color range . panel ( @xmath75 ) of figure [ fig : gcdpbrads2 ] is at 3.1 s. the wd is maximally expanded in this image . several seconds after the ash is ejected from the surface of the star , it converges at the opposite pole from where is broke out . the converging flow compresses the material in the collision region until the pressure is sufficient to stop the mixture from flowing laterally and to drive a plume of fuel and ash towards the interior of the star . additionally , after the star has reached its maximally expanded state , it begins to contract . the stellar contraction increases the global density structure of the star , and thus the local density of at the collision region , eventually resulting in explosive c and o burning . once the conditions for detonation are met ( as discussed in section [ subsec : theory ] ) and the detonation is triggered ( as discussed in section [ subsec : numreal ] ) the combustion immediately sweeps across the star in a few tenths of a second . panels ( @xmath76 ) and ( @xmath77 ) of figure [ fig : gcdpbrads2 ] , at 3.7 s and 4.2 s respectively , show the star as it contracts . a hot region can be seen forming at the `` bottom '' of the star . this hot region is the result of the compressional heating of the mixture in the collision region from the work done by the contracting star as well as the material flows themselves . panel ( @xmath78 ) of figure [ fig : gcdpbrads2 ] is at 4.3 s and shows the simulation just after the initiation of the detonation wave . panel ( @xmath80 ) of figure [ fig : gcdpbrads2 ] shows the simulation at 4.4 s. the detonation wave has consumed about half of the star in just over 0.1 s. the detonation wave transforms the wd into a super - heated remnant composed of material that has reached nuclear statistical equilibrium ( nse ) in the core ( which is dominated by iron - group elements , most of which is @xmath0ni ) surrounded by a layer of intermediate mass elements and topped of with the ash of partially burned c and o. this whole structure is shrouded by the products of the deflagration which consisted of iron - group elements , intermediate mass elements , carbon burning products , and unburned c and o. the super - heated structure quickly expands and cools , and is transitioning into a homologous structure when the simulations are stopped . in each of our simulations , we found the necessary conditions to trigger a detonation as discussed in section [ sec : det ] . the main properties of the three simulations are summarized in table [ tab : sims ] . the simulations differ in the location of the center of their sphere of ignition points , and are labeled @xmath81 ( ignition sphere centered 68 km from the center of the star ) , @xmath82 ( 88 km from the center of the star ) , and @xmath71 ( 168 km from the center of the star ) . the deflagration phase of the sn ia provides a kick to the wd which causes the wd to rapidly expand and then contract . it is the expansion and subsequent detonation on contraction that characterizes the pulsation gcd model . figure [ fig : enucvstime ] shows the amount of nuclear energy release as a fraction of the binding energy of the star as a function of time for the three simulations . the simulations trend together for the first 0.8s and then diverged . the deflagration continued to release nuclear energy until approximately 1.5s in each simulation , at which time the flame stopped burning . in general , the simulations whose ignition points were placed closer to the core of the wd burned more during the deflagration and thus imparted more energy to the star . the amount of energy released ranged from @xmath83 ergs to @xmath84 ergs , or between 38% and 78% of the binding energy of the star . by comparison , the single bubble initial conditions in j08 released between @xmath85 ergs gand @xmath86 ergs , or between 6% and 21% of the binding energy of the wd . the energy released during the deflagration phase was sufficient to cause the star to undergo an energetic pulsation . figure [ fig : rhocvstime ] shows the evolution of the maximum density found in the computational domain , which is equivalent to the central density of the wd ( prior to detonation ) for the three simulations and gives a measure of the strength and the period of the pulsation . in each simulation , the wd expanded to a maximum amplitude and then contracted before detonating . the simulation that expanded the least was @xmath71 which reached a minimum central density , @xmath87 , of @xmath88 g/@xmath19 . the star expanded for 3.1 s before it began to contract . by contrast , @xmath81 achieved @xmath89 g/@xmath19 , and the wd did not begin to contract until 4.71 s. thus the more energy released during the deflagration phase , the more the wd expands and the longer its pulsational period . the vertical lines in figure [ fig : rhocvstime ] mark the time at which the star detonates . as the wd expanded , ash was ejected from the surface and flowed laterally over the star , mixing with surface fuel as it flowed . figure [ fig : thetaashvstime ] plots the polar angle of the leading edge of the flow as a function of time . initially a small region of ash crossed the origin and was responsible for the large values of @xmath90 seen in the figure during the first second . after one second , the ash reached the surface and started to spread around the star . the ash , which mixes with fuel on the surface as it flows , quickly reached a polar angle of approximately @xmath91 and then stalled in each of the simulations . this was in part because the mixture pushed some material in front of it which compressed material in the collision region and increased the pressure there . also , the expansion of the star robbed kinetic energy from the flow which also contributed to the mixture stalling . once the star contracted , the mixture slowly pushed its way further around the star , as well as into the high density regions towards the core . as before , the lines on the graph highlight the time at which the star detonated . the mixture only stalled for a short period of time in the @xmath71 simulation whose wd had the shortest pulsational period . the opposite is true for the @xmath81 simulation in which the mixture stalled the longest and the wd had the longest pulsational period . even though the mixture encroached on the collision region within a few seconds from when the flow started , it was the contraction of the star that assisted the mixture in making the final move to higher densities . after the star began to contract , the fuel - ash mixture made its way into the high - density layers of the wd . figure [ fig : maxtempvstime ] shows the evolution of the thermodynamic conditions in the fuel - ash mixture as it pushed into the star . the top plot in figure [ fig : maxtempvstime ] shows the temperature of the computational cell with the maximum temperature in the mixture . the middle plot shows the density and the bottom plot shows the radius of the computational cell with the maximum temperature . both the temperature and density follow the trend of the central density , as the wd expanded and contracted . as the star expanded , the temperature and density of the mixture decreased . as the star contracted , the temperature and density of the mixture increased . the location of the hot spot followed the same pattern ; hence , as the star contracted , the radius of the hot spot moves closer to the core . this was due both to the stellar contraction and the continued flow of the mixture . once the temperature of the hot spot exceeded @xmath92 k and the density exceeded @xmath93 g/@xmath19 rapid combustion ensued , which transitioned into a detonation . we stress that the detonation is the result of the numerical scheme discussed in section [ subsec : numreal ] and is not the result of the zeldovich gradient mechanism . it merely indicates that the conditions in the computational cell surpass those that are necessary to produce a gradient - induced detonation . in the @xmath71 simulation , the deflagration phase released the least amount of energy of all the simulations and thus the wd expanded the least , it had a shortest pulsational period , it began contracting the earliest . as a result , the detonation occurred the soonest . the opposite is true for the @xmath81 simulation whose deflagration phase released the most amount of energy and whose detonation was triggered last . an important set of observables of an sn ia are the nucleosynthetic yields produced in the event . we have approximated the yields from the three models using the reaction progress variables from flash s burning module @xcite . table [ tab : det ] lists the post - explosion nucleosynthetic yields from our simulations in terms of the quasi - static equilibrium groups that are represented by the progress variables . note that the material that burned to nse is predominately iron - group elements , most of which is @xmath0ni . thus , the amount of nse material can be considered an upper limit on the amount of @xmath0ni produced during the explosion . the upper limit on the @xmath0ni produced during these simulations ranges from @xmath94 @xmath3 to @xmath2 @xmath3 . though yields of @xmath94 @xmath3 of @xmath0ni are associated with luminous sne ia , yields of @xmath2 @xmath3 of @xmath0ni are associated with sne ia of normal luminosity . the combined mass of the intermediate mass elements and nse material is @xmath95 @xmath3 and is consistent with observed sne ia @xcite . the deflagration phase of the pgcd models burns approximately 0.1 - 0.25 @xmath3 of material . this material is ejected into the outer regions of the system , surrounding the wd when it detonates . table [ tab : def ] lists the nucleosynthetic yields produced during the deflagration phase of the three simulations . the primary product of the deflagration phase is nse material with about a third of the material composed of carbon burning products and intermediate mass elements . these simulations show that through the course of an off - centered ignition , if a detonation is not triggered as the flame breaks down when it moves through the low density layers of the star on its way to the surface ( i.e. the first scenario in @xcite ) and if the energy release during the deflagration is sufficient to significantly disrupt the star and cause it to rapidly expand , ash will flow around the surface ( mixing with cold fuel as it flows ) , and stall in the collision region while the star is expanding . as the wd contracts , the conditions in the fuel - ash mixture are pushed to higher temperature and density until the values exceed that which are necessary to produce a gradient - triggered detonation . once the detonation is triggered in the mixture , it quickly consumes the star .

the amount of energy released during the deflagration phase is enough to cause the star to rapidly expand , so that when the ash reaches the antipodal point , the surface density is too low to initiate a detonation . the stellar contraction acts to increase the density of the star , including the density in the collision region . this both raises the temperature and density of the fuel - ash mixture in the collision region and ultimately leads to thermodynamic conditions that are necessary for the zeldovich gradient mechanism to produce a detonation .

we describe the detonation mechanism comprising the `` pulsationally assisted '' gravitationally confined detonation ( gcd ) model of type ia supernovae ( sne ia ) . this model is analogous to the previous gcd model reported in ; however , the chosen initial conditions produce a substantively different detonation mechanism , resulting from a larger energy release during the deflagration phase . the resulting final kinetic energy andni yields conform better to observational values than is the case for the `` classical '' gcd models . in the present class of models , the ignition of a deflagration phase leads to a rising , burning plume of ash . the ash breaks out of the surface of the white dwarf , flows laterally around the star , and converges on the collision region at the antipodal point from where it broke out . the amount of energy released during the deflagration phase is enough to cause the star to rapidly expand , so that when the ash reaches the antipodal point , the surface density is too low to initiate a detonation . instead , as the ash flows into the collision region ( while mixing with surface fuel ) , the star reaches its maximally expanded state and then contracts . the stellar contraction acts to increase the density of the star , including the density in the collision region . this both raises the temperature and density of the fuel - ash mixture in the collision region and ultimately leads to thermodynamic conditions that are necessary for the zeldovich gradient mechanism to produce a detonation . we demonstrate feasibility of this scenario with three 3-dimensional ( 3d ) , full star simulations of this model using the flash code . we characterized the simulations by the energy released during the deflagration phase , which ranged from 38% to 78% of the white dwarf s binding energy . we show that the necessary conditions for detonation are achieved in all three of the models .

1202.3997

c

we have conducted a series of numerical experiments simulating the evolution of a wd star in which we initiate a deflagration at off - center ignition points . the amount of energy released during the deflagration phase is enough to cause the star to undergo an energetic pulsation . as in the classical gcd model , the off - center ignition leads to a plume of material that is ejected from the star , flows laterally over the stellar surface , and converges on a collision region at the antipodal point from the ash breakout point . as the wd contracts , it creates thermodynamic conditions in the collision region such that it is possible for the zeldovich gradient mechanism to trigger a detonation . we find that these necessary ( but not sufficient ) conditions for detonation are reached in all three of our models . the energy deposition from the deflagration phase in these models ranges from 38% to 78% of the binding energy of the wd . we further comment that the detonation mechanism in the pgcd depends only on the bulk fluid motion of the system after the deflagration is ignited as opposed to a specific flow pattern , such as the focusing of the ash flows in the collision region in the classical gcd . this property confers a measure of robustness to the detonation mechanism . finally , the features of the pgcd qualitatively agree with the observations of sne ia , insofar as such comparisons can be made without subjecting the remnant to a radiation transfer treatment in order to compute actual light curves . the three models produced upper limits on the yields of @xmath0ni ranging from 0.72 @xmath3 to 0.98 @xmath3 . these @xmath0ni yields are less than those produced in the classical gcd models of j08 , primarily because the wd in our models is in a more expanded state at the time of detonation and contains a lower abundance of high - density , nse - producing matter . this class of models allows sne ia to evolve and detonate with characteristics similar to the classical gcd while producing supernovae of lower luminosity . the authors thank the flash code group , especially chris daley and anshu dubey for help with the development of and troubleshooting the code . we thank brad gallagher for creating figures [ fig : gcdpbrads1 ] and [ fig : gcdpbrads2 ] . we also thank katherine riley , mike papka , and the staff at the argonne leadership computing facility at argonne national laboratory for help running our large - scale simulations on intrepid at anl . this work was supported in part at the university of chicago by the u.s department of energy ( doe ) under contract b523820 to the asc alliances center for astrophysical nuclear flashes , and in part by the national science foundation under grant no . ast - 0909132 for the `` petascale computing of thermonuclear supernova explosions '' . this research used computational resources awarded under the incite program at alcf at anl , which is supported by the office of science of the us department of energy under contract no . de - ac02 - 06ch11357 . , a. , benzi , r. , berg , j. , biferale , l. , bodenschatz , e. , busse , a. , calzavarini , e. , castaing , b. , cencini , m. , chevillard , l. , fisher , r. t. , grauer , r. , homann , h. , lamb , d. , lanotte , a. s. , lvque , e. , lthi , b. , mann , j. , mordant , n. , mller , w. , ott , s. , ouellette , n. t. , pinton , j. , pope , s. b. , roux , s. g. , toschi , f. , xu , h. , & yeung , p. k. 2008 , physical review letters , 100 , 254504 , a. c. , fryxell , b. , plewa , t. , rosner , r. , dursi , l. j. , weirs , v. g. , dupont , t. , robey , h. f. , kane , j. o. , remington , b. a. , drake , r. p. , dimonte , g. , zingale , m. , timmes , f. x. , olson , k. , ricker , p. , macneice , p. , & tufo , h. m. 2002 , , 143 , 201 , g. c. , meakin , c. a. , hearn , n. , fisher , r. t. , townsley , d. m. , lamb , d. q. , & truran , j. w. 2009 , in astronomical society of the pacific conference series , vol . 406 , astronomical society of the pacific conference series , ed . n. v. pogorelov , e. audit , p. colella , & g. p. zank , 92+ , p. e. , sullivan , m. , cenko , s. b. , thomas , r. c. , kasen , d. , howell , d. a. , bersier , d. , bloom , j. s. , kulkarni , s. r. , kandrashoff , m. t. , filippenko , a. v. , silverman , j. m. , marcy , g. w. , howard , a. w. , isaacson , h. t. , maguire , k. , suzuki , n. , tarlton , j. e. , pan , y .- c . , bildsten , l. , fulton , b. j. , parrent , j. t. , sand , d. , podsiadlowski , p. , bianco , f. b. , dilday , b. , graham , m. l. , lyman , j. , james , p. , kasliwal , m. m. , law , n. m. , quimby , r. m. , hook , i. m. , walker , e. s. , mazzali , p. , pian , e. , ofek , e. o. , gal - yam , a. , & poznanski , d. 2011 , , 480 , 344 , s. , aldering , g. , goldhaber , g. , knop , r. a. , nugent , p. , castro , p. g. , deustua , s. , fabbro , s. , goobar , a. , groom , d. e. , hook , i. m. , kim , a. g. , kim , m. y. , lee , j. c. , nunes , n. j. , pain , r. , pennypacker , c. r. , quimby , r. , lidman , c. , ellis , r. s. , irwin , m. , mcmahon , r. g. , ruiz - lapuente , p. , walton , n. , schaefer , b. , boyle , b. j. , filippenko , a. v. , matheson , t. , fruchter , a. s. , panagia , n. , newberg , h. j. m. , couch , w. j. , & the supernova cosmology project . 1999 , , 517 , 565 , a. g. , filippenko , a. v. , challis , p. , clocchiatti , a. , diercks , a. , garnavich , p. m. , gilliland , r. l. , hogan , c. j. , jha , s. , kirshner , r. p. , leibundgut , b. , phillips , m. m. , reiss , d. , schmidt , b. p. , schommer , r. a. , smith , r. c. , spyromilio , j. , stubbs , c. , suntzeff , n. b. , & tonry , j. 1998 , , 116 , 1009 lccccccccccc @xmath71 & 8 & 63 & 128.0 & 168.0 & 18.9 & 0.38 & 3.51 & 3.10 & 4.20 & 1,630 & 1.23 + @xmath82 & 8 & 63 & 128.0 & 88.0 & 29.1 & 0.59 & 1.13 & 3.83 & 6.21 & 2,124 & 1.19 + @xmath81 & 8 & 63 & 128.0 & 68.0 & 38.6 & 0.78 & 0.43 & 4.71 & 8.67 & 2,660 & 1.05 +

the ash breaks out of the surface of the white dwarf , flows laterally around the star , and converges on the collision region at the antipodal point from where it broke out . we characterized the simulations by the energy released during the deflagration phase , which ranged from 38% to 78% of the white dwarf s binding energy . we show that the necessary conditions for detonation are achieved in all three of the models .

we describe the detonation mechanism comprising the `` pulsationally assisted '' gravitationally confined detonation ( gcd ) model of type ia supernovae ( sne ia ) . this model is analogous to the previous gcd model reported in ; however , the chosen initial conditions produce a substantively different detonation mechanism , resulting from a larger energy release during the deflagration phase . the resulting final kinetic energy andni yields conform better to observational values than is the case for the `` classical '' gcd models . in the present class of models , the ignition of a deflagration phase leads to a rising , burning plume of ash . the ash breaks out of the surface of the white dwarf , flows laterally around the star , and converges on the collision region at the antipodal point from where it broke out . the amount of energy released during the deflagration phase is enough to cause the star to rapidly expand , so that when the ash reaches the antipodal point , the surface density is too low to initiate a detonation . instead , as the ash flows into the collision region ( while mixing with surface fuel ) , the star reaches its maximally expanded state and then contracts . the stellar contraction acts to increase the density of the star , including the density in the collision region . this both raises the temperature and density of the fuel - ash mixture in the collision region and ultimately leads to thermodynamic conditions that are necessary for the zeldovich gradient mechanism to produce a detonation . we demonstrate feasibility of this scenario with three 3-dimensional ( 3d ) , full star simulations of this model using the flash code . we characterized the simulations by the energy released during the deflagration phase , which ranged from 38% to 78% of the white dwarf s binding energy . we show that the necessary conditions for detonation are achieved in all three of the models .

1501.05954

i

one of the most prominent characteristics of the ultraviolet ( uv ) , optical , and near - infrared ( nir ) spectra of active galactic nuclei ( agns ) is the presence of broad emission lines . while we know that these features arise on scales not much larger than the accretion disk , their physical nature remains one of the major unsolved mysteries in agn astrophysics . a particularly important feature of the broad emission lines is that they are , by definition , resolved in line - of - sight ( los ) velocity , and their large widths leave little doubt that the primary broadening mechanism is differential doppler shifts due to the motion of individual gas clouds , filaments , or more - or - less continuous flows around the central black hole . however , it is not possible to establish the broad - line region ( blr ) kinematics simply by inverting the line profiles because this inverse problem is degenerate , with a wide variety of simple velocity models providing satisfactory fits ( e.g. , * ? ? ? * ) . the existing evidence on the blr kinematics is ambiguous : some of this gas may flow inward , helping to feed the central black hole . extended , flattened , rotating disk - like structures seem to be important in at least some blrs , as shown statistically for radio - loud agns @xcite , by the pronounced double - peaked profiles observed in some sources ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and from spectropolarimetry @xcite . there is evidence of the importance of the black hole gravity in dominating the motion of the blr gas @xcite , although radiation pressure may also play a role @xcite . on the other hand , developments over the last two decades re - open the interesting possibility that much of the emitting blr gas is due to outflowing winds ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , perhaps connected to the outflows detected in absorption features ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ) , whose kinematics and energetics are also poorly understood . the unknown dynamics of the blr gas represents a serious gap in our understanding of agns and in the calibrations needed for the study of black - hole / host - galaxy co - evolution up to very high redshifts . there have been many attempts to model the physics of the blr . in general , photoionization equilibrium models can reproduce the line intensities , but self - consistent models that provide simultaneous solutions to the line intensities , profiles , and variability are lacking . the locally optimally emitting cloud model @xcite and the stratified cloud model @xcite explain most observed line intensities and some of the observed time lags between the continuum and emission lines . however , they lack the important kinematic ingredients required to explain the observed line profiles . in order to understand the structure and kinematics of the blr , we must break the degeneracy that comes from the study of the line profiles alone . we can do this by using reverberation mapping ( rm ) to determine how gas at various los velocities responds to continuum variations as a function of light travel - time delay @xcite . over the last quarter century , the rm technique has become a standard tool for investigating the blr . in its simplest form , rm is used to determine the mean time delay between continuum and emission - line variations , typically by cross - correlation of the respective light curves . it is assumed that this represents the mean light - travel time across the blr . by combining this with the emission - line width , which is assumed to reflect the velocity dispersion of gas whose motions are dominated by the mass of the central black hole , the black hole mass can be estimated . rm in this form has been used to measure the black hole masses in over 50 agns ( for a recent compilation , see * ? ? ? * ) to a typical accuracy of @xmath8dex . important findings that have arisen from these rm studies include the following : 1 . in a given agn , emission lines that are characteristic of higher - ionization gas respond more rapidly to continuum flux variations than those characteristic of lower - ionization gas , indicating ionization stratification within the blr @xcite . 2 . there is an inverse correlation between the time delay , or lag @xmath9 , for a particular emission line and the doppler width @xmath10 of that emission line . the relationship for a given agn is consistent with the virial prediction @xmath11 @xcite . without this relationship , rm masses would be highly dubious . there is an empirical relationship between the agn luminosity @xmath12 and the radius of the blr @xmath13 ( hereafter the @xmath13@xmath12 relationship ) that is well - established only for the h@xmath14 emission line @xcite . limited data on civ@xmath15 indicates a similar relationship applies to that line as well @xcite . the existence of @xmath13@xmath12 relationships for both low - ionization and high - ionization lines has been independently confirmed by gravitational microlensing observations @xcite . the @xmath13@xmath12 relationship is of particular interest as it allows estimation of the central black - hole mass based on a single spectrum from which the line width is measured and the blr radius is inferred from the agn luminosity . this neatly bypasses the need for a direct rm measurement of the emission - line time lag . rm is necessarily resource intensive : even to determine the mean time delay for an emission line typically requires some 3050 well - spaced high - quality spectrophotometric observations or a good measure of luck for fewer observations . the @xmath13@xmath12 relationship is very important as the rm - based mass determinations anchor empirical scaling relationships ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) that are used to estimate the masses of quasar black holes in large numbers ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? virtually all quasar mass estimates and their astrophysical uses are tied to rm . measurement of the mean lag and line width for a given emission line provides important , though limited , information about the blr and the central mass of the agn . we are only now beginning to realize the full power of rm through velocity - resolved investigations of the blr response . the first generation of successful rm programs provided sufficient understanding of agn variability and blr response times to design programs that could effectively extract velocity dependent information that would lead to an understanding of the structure and kinematics of the blr through recovery of `` velocity delay '' maps from rm data @xcite . the relationship between the continuum variations @xmath16 and velocity - resolved emission - line variations @xmath17 is usually described as @xmath18 where @xmath19 is the `` response function , '' or velocity delay map @xcite . as can be seen by inspection , @xmath19 is simply the observed emission - line response to a delta - function continuum outburst . the velocity delay map is simply the blr geometry and kinematics projected into the two observable quantities of los velocity and time delay relative to the continuum . this linearized echo model is justified by the fact that the continuum and emission - line variations are generally quite small ( 1020% ) on reverberation time scales ( see also * ? ? ? the technical goal of a reverberation program such as the one described here is to recover the velocity delay map @xmath19 from the data and thus infer the geometry and kinematics of the blr . time - resolved velocity delay maps have now been obtained for a handful of agns ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , but only for optical lines ( the balmer lines , hei@xmath20 , and heii@xmath21 ) . in general , these suggest flattened geometries at small to modest inclinations and some combination of virialized motion and infall . an outflow signature has been observed in only one case , ngc3227 @xcite . the lack of velocity delay maps for uv lines , on the other hand , leaves us with a very incomplete understanding of the blr . it is , in fact , the high - ionization level uv resonance lines ( e.g. , civ@xmath15 , siiv@xmath6 , ly@xmath3@xmath4 ) that might be expected to dominate any outflowing component of the blr . the optical lines , in contrast , generally seem to arise in disk - like structures with infall components ( e.g. , * ? ? ? rm studies in the uv have been limited . several observing campaigns were undertaken with the _ international ultraviolet explorer ( iue ) _ or _ hubble space telescope ( hst ) _ or both on ( i ) ngc5548 @xcite , ( ii ) ngc3783 @xcite , ( iii ) fairall9 @xcite , ( iv ) 3c390.3 @xcite , ( v ) ngc 7469 @xcite , ( vi ) ngc4151 @xcite , ( vii ) akn564 @xcite , and ( viii ) ngc4395 @xcite . with the exception of akn564 , which showed essentially no emission - line variability over a comparatively short campaign , all of these programs yielded emission - line lags , but only limited information about the detailed response of the uv emission lines ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the existing velocity - delay map for ngc4151 shows some incipient structure in civ@xmath15 and heii@xmath1 and a general shape that seems to be consistent with a virialized blr @xcite . given the importance of the uv emission lines in the photoionization equilibrium of the blr gas and the probable differences between the geometry and kinematics of the high and low - ionization gas in the blr , we have undertaken a large rm program in the uv using the cosmic origins spectrograph ( cos ; @xcite ) on _ hst _ ( _ hst _ program go-13330 ) , the agn space telescope and optical reverberation mapping ( agn storm ) project , in the first half of 2014 . the program was designed with certain specific goals in mind : 1 . determine the structure and kinematics of the high - ionization blr through observations of the variations in the civ@xmath15 , ly@xmath3@xmath4 , nv@xmath22 , siiv@xmath6 , and heii@xmath1 emission lines . , siiv@xmath23 , and civ@xmath24 . moreover , the heii feature is blended with oiii]@xmath25 , 1665 and siiv is blended with the quintuplet oiv]@xmath26 , 1399.8 , 1401.2 , 1404.8 , 1407.4 , where the second , third , and fifth transitions dominate . ] carry out simultaneous ground - based observations of ( a ) the high - ionization optical line heii@xmath21 for direct comparison with heii@xmath27 and ( b ) the balmer lines , particularly h@xmath14@xmath28 , to determine the structure and kinematics of the low - ionization blr . although the optical spectrum is extremely well - studied ( * ? ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) , simultaneous observations are necessary , as the dynamical timescale for the blr in ngc5548 is only a few years . 3 . compare in detail the continuum variations in the uv ( at @xmath29 ) with those at other wavelengths ( see * ? ? ? * hereafter paper ii ) and infer the structure of the continuum - emitting region . the motivation for the uv / optical continuum comparison is multifold : 1 . delays between continuum variations at longer versus shorter wavelengths have been detected or hinted at in a number of sources ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? such delays can provide insight into the structure , geometry , and physics of the continuum - emitting region . 2 . velocity delay maps recovered using the uv continuum as the driving light curve ( equation [ eq : trans ] ) are expected to be of higher fidelity than those obtained from the optical continuum because the observable uv is closer in wavelength to the ionizing continuum ( @xmath30 ) that powers the emission lines . the optical continuum is not only a slightly time - delayed version of the uv continuum , but it seems smoothed somewhat as well @xcite , which might make it difficult to recover detailed structure in the velocity delay maps . our _ hst _ program afforded a valuable opportunity for exploring agn behavior at high time resolution for an extended period at wavelengths beyond those covered by our _ hst _ cos spectra . the _ hst_program is the anchor of a much broader agn storm project to address broader issues through observations across the electromagnetic spectrum . this paper serves as the first in a series . of special interest is the possibility of using short - timescale lags between variations in different continuum bands to map the temperature structure of the accretion disk . the _ swift _ satellite @xcite is especially suitable for such a study because of its broad wavelength coverage ( hard x - ray through @xmath31-band ) and ability to execute high - cadence observations over an extended period of time . in paper ii , we present the results of a four - month program of high - cadence ( approximately twice per day ) multiwavelength observations with _ swift_. additional papers in this series will describe high - cadence ground - based photometry from the near uv through the nir . we will also present results from a program of ground - based spectroscopy that is similar in cadence to the _ hst_cos observations , but covers a somewhat longer temporal baseline . other additional papers will present results on the variable absorption features and on our efforts to decipher the broad emission - line variations and determine the structure and geometry of the blr . in section 2 , we describe the observations and data processing , including a discussion of the program design and a complete description of how the standard data reduction pipeline was modified to meet our stringent calibration requirements . we describe our initial data analysis and results in section 3 , and in section 4 , we briefly discuss the first results from our program and place these results in the context of previous monitoring campaigns on ngc 5548 . when necessary , we assume a @xmath32cdm cosmology with @xmath33 , @xmath34 , and @xmath35 @xcite .

the variations of all the strong emission lines lag behind those of the continuum , with heii lagging behind the continuum bydays and ly , civ , and siiv lagging bydays . the relationship between the continuum and emission lines is complex . in particular , during the second half of the campaign , all emission - line lags increased by a factor of 1.32 and differences appear in the detailed structure of the continuum and emission - line light curves . velocity - resolved cross - correlation analysis shows coherent structure in lag versus line - of - sight velocity for the emission lines ; the high - velocity wings of civrespond to continuum variations more rapidly than the line core , probably indicating higher velocity blr clouds at smaller distances from the central engine .

we describe the first results from a six - month long reverberation - mapping experiment in the ultraviolet based on 171 observations of the seyfert 1 galaxy ngc 5548 with the cosmic origins spectrograph on the _ hubble space telescope_. significant correlated variability is found in the continuum and broad emission lines , with amplitudes ranging from% to a factor of two in the emission lines and a factor of three in the continuum . the variations of all the strong emission lines lag behind those of the continuum , with heii lagging behind the continuum bydays and ly , civ , and siiv lagging bydays . the relationship between the continuum and emission lines is complex . in particular , during the second half of the campaign , all emission - line lags increased by a factor of 1.32 and differences appear in the detailed structure of the continuum and emission - line light curves . velocity - resolved cross - correlation analysis shows coherent structure in lag versus line - of - sight velocity for the emission lines ; the high - velocity wings of civrespond to continuum variations more rapidly than the line core , probably indicating higher velocity blr clouds at smaller distances from the central engine . the velocity - dependent response of ly , however , is more complex and will require further analysis .

1202.4372

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the thermal control of a spacecraft ensures that the temperatures of its various parts are kept within their appropriate ranges @xcite . the simulation and prediction of temperatures in a spacecraft during a mission are usually carried out by commercial software packages . these software packages employ `` lumped parameter '' models that describe the spacecraft as a discrete network of nodes , with one energy - balance equation per node . the equations for the thermal state evolution are coupled nonlinear first - order differential equations , which can be integrated numerically . given the thermal parameters of the model and its initial thermal state , the numerical integration of the differential equations yields the solution of the problem , namely , the evolution of the node temperatures . however , a detailed model with many nodes is difficult to handle , and its integration for a sufficiently long time of evolution can take considerable computer time and resources . therefore , it is very useful to study simplified models and approximate methods of integrating the differential equations . many spacecraft missions , in particular , satellite missions , consist of an initial transient part and then a stationary part , in which the spacecraft just goes around a closed orbit , in which the heat inputs are periodic . these periodic heat inputs are expected to induce periodic temperature variations , with a maximum and a minimum temperature in each orbit . this suggests a conservative approach that consists in computing only the temperatures for the _ hot _ and _ cold cases _ of the given orbit , defining them as the two steady cases with the maximum and minimum heat loads , respectively . naturally , the real temperature variations in the orbit are smaller , because there is not enough time for the hot and cold cases to establish themselves . in fact , the temperature variations can be considerably smaller , to such a degree that it is necessary to integrate the differential equations , at least approximately . the differential equations for energy balance are nonlinear due to the presence of radiation couplings , which follow the stefan - boltzmann quartic law . a common approach to these equations involves a linearization of the radiation terms that approximate them by heat conduction terms @xcite . this approach transforms the nonlinear equations into standard linear heat conduction equations . but this approach has not been sufficiently justified , is of a heuristic nature and does not constitute a systematic approximation . in fact , nonlinear equations are very different from linear equations and , in particular , a periodic driving may not induce periodic solutions but much more complex solutions , namely , _ chaotic _ solutions . therefore , we have carried out in preceding papers a full nonlinear analysis of spacecraft thermal models @xcite . the conclusion of the analysis is that the complexities of nonlinear dynamics , such as multiple equilibria and chaos , do not appear in these models . while the existence of only one equilibrium state can be proved in general , the absence of chaos under driving by variable external heat loads can only be proved for a limited range of magnitudes of the driving loads . this range presumably includes the magnitudes involved in typical spacecraft orbits . the proofs in refs . and are constructive and are based on a perturbation method that is expected to be sound when the _ linear _ equations corresponding to the first perturbative order constitute a good approximation of the nonlinear equations . this implies that the fully nonlinear solution describes a weakly nonlinear oscillator . since the perturbative approximation is mathematically rigorous and systematic , it is worthwhile to study in detail the scope of the perturbative linear equations and , furthermore , to compare them with previous linear approaches of a heuristic nature . the main purpose of this paper is to study the linear method of predicting the thermal behavior of spacecraft in stationary orbits ( sect . [ linear ] and [ fourier - anal ] ) and to test it on a minimally realistic thermal model of a satellite in a circular orbit . since the general one and two - node models analyzed in refs . and , respectively , are too simple , we define in this paper a ten - node thermal model of a small moon - orbiting satellite ( sect . [ ten - node ] ) . this model is simple enough to allow us to explicitly show all the quantities involved ( thermal couplings and capacities , heat inputs , etc . ) and it is sufficient for illustrating the main features of the linear approach . as realistic thermal models have many more nodes , we consider in sect . [ scale ] the important issue of scalability of the method and , hence , its practical applications . computational aspects of the steady - state problem have been studied by krishnaprakas @xcite and by milman and petrick @xcite , while computational aspects of the direct integration of the nonlinear equations for the unsteady problem have been studied by krishnaprakas @xcite . here we focus on the linear equations for the stationary but unsteady case and survey its computational aspects . a note on notation : in the equations that contain matrix or vector quantities , sometimes we use component notation ( with indices ) while other times we use compact matrix notation ( without indices ) , according to the nature of the equations .

we develop a linear method for solving the nonlinear differential equations of a lumped - parameter thermal model of a spacecraft moving in a closed orbit . our method , based on perturbation theory , is compared with heuristic linearizations of the same equations . we apply our method to a minimal thermal model of a satellite with ten isothermal parts ( nodes ) and we compare the method with direct numerical integration of the nonlinear equations .

we develop a linear method for solving the nonlinear differential equations of a lumped - parameter thermal model of a spacecraft moving in a closed orbit . our method , based on perturbation theory , is compared with heuristic linearizations of the same equations . the essential feature of the linear approach is that it provides a decomposition in thermal modes , like the decomposition of mechanical vibrations in normal modes . the stationary periodic solution of the linear equations can be alternately expressed as an explicit integral or as a fourier series . we apply our method to a minimal thermal model of a satellite with ten isothermal parts ( nodes ) and we compare the method with direct numerical integration of the nonlinear equations . we briefly study the computational complexity of our method for general thermal models of orbiting spacecraft and conclude that it is certainly useful for reduced models and conceptual design but it can also be more efficient than the direct integration of the equations for large models . the results of the fourier series computations for the ten - node satellite model show that the periodic solution at the second perturbative order is sufficiently accurate . lcl & = & outward - facing area of _ _ i__th - node , m + & = & thermal capacitance diagonal matrix , j / k + & = & thermal capacitance of _ _ i__th - node , j / k + & = & eigenvector of , k + & = & _ _ j__th - component of eigenvector , k + & = & driving function vector , k / s + & = &th fourier coefficient of , k / s + & = & complex conjugate of , k / s + & = & driving function forth - mode , k / s + & = & time derivative of , k / s + & = & driving function forth - node , k / s + & = &th fourier coefficient of , k / s + & = & driving function for second order temperature vector , k / s + & = & jacobian matrix , s + & = & jacobian matrix _ ij_-element , s + & = & number of steps in numerical integration of odes + & = & conduction coupling matrix , w / k + & = & matrix of conductances from linearized radiation coupling terms , w / k + & = &th - node conductance from linearized environment - radiation terms , w / k + & = & conduction coupling matrix _ ij_-element , w / k + & = & _ ij_-element of conductance matrix from linearized radiation terms , w / k + & = & number of samples for discrete fourier transform + & = & number of nodes + & = & eigenvector matrix for _ j _ , k + & = & _ _ i__th - component of-eigenvector forth - mode , k + & = & auxiliary heat input vector , k / s + & = & heat input to _ _ i__th - node , w + & = & mean value of over period , w + & = & _ _ i__th - node coefficient of radiation to the environment , w / k + & = & radiation coupling matrix , w / k + & = & time , s ( min in figures ) + & = & temperature vector , k + & = & vector of `` errors '' w.r.t . esatan solution , k + & = & steady - state temperature vector , k + & = & temperature of _ _ i-__node , k + & = & cosmic microwave background radiation temperature , k + & = & _ _ n__th order term in _ _ j__th - node temperature expansion , k + & = & stationary solution temperature vector , k + & = & _ _ n__th order of stationary solution temperature vector , k + & = & time derivative of _ _ i__th - node temperature , k / s + & = & steady - state temperature of _ _ i__th - node , k + & = & orbital period , s + & = & matrix of independent solutions to homogeneous equations , k + & = & solar absorptivity + & = & kronecker s delta + & = & antisymmetric part of , s + & = & _ ij_-element of , s + & = & infrared emissivity of _ _ i__th - node outward - facing surface + & = & perturbation parameter + & = & eigenvalue of _ j _ forth mode , s + & = & perturbation of _ j_-eigenvalue forth mode , s + & = & stefan - boltzmann constant , wmk +

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we have studied the evolution of the thermal state of an orbiting spacecraft and developed a linear approach to this problem that is based on a rigorous perturbative treatment of the exact nonlinear equations . the first - order perturbation equations , eqs . ( [ linode - pert ] ) , constitute the basic linear system , which can be applied to higher orders after calculating the corresponding driving terms . as the jacobian matrix of the nonlinear equations has negative eigenvalues , the linear equations describe the relaxation to a stationary thermal state , namely , a periodic solution that is independent of the initial conditions and only depends on the external heat input . this relaxation is similar to the relaxation to steady - state under constant external heat load . we have shown that the perturbative treatment reveals the scope of a common linearization procedure of a heuristic nature , in which the nonlinear equations are rendered linear by the definition of radiation conductances ( sect . [ heur ] ) . if one previously calculates , with the correct nonlinear eqs . ( [ bode - pert ] ) , the reference steady - state condition that corresponds to the average external heat input , the deviation from that steady - state is well approximated by the linear equations with radiation conductances . the jacobian matrix corresponding to radiation conductances , obtained in eqs . ( [ njij ] ) and ( [ njii ] ) , is related to a symmetric matrix and , therefore , is easier to diagonalize . furthermore , this relation implies that the thermal modes are normal , like the vibrational modes of a mechanical system . although the notion of radiation conductance is just an approximation , it serves nonetheless to show that the jacobian matrix is diagonalizable and has real eigenvalues . the diagonalization of the jacobian matrix is useful for the computation of the stationary thermal state and also provides information on the relaxation to that state , because the relaxation times of the thermal modes are the inverses of the eigenvalues . these times span a considerable range , but the longest times are much more significant than the shortest times , because the latter depend on the details of the lumped - parameter thermal model employed whereas the former are essentially independent of it . in fact , a thermal model that has more nodes and therefore more details also has more thermal modes ; but the slowest modes , which correspond to temperature changes in large parts of the spacecraft , are hardly affected by the details , whereas the fast modes can be significantly altered . the slowest mode , in particular , corresponds to a simultaneous but non - uniform increase ( or decrease ) of the temperature throughout the spacecraft and is hardly altered by small - scale changes . the computation of the stationary thermal state with the linear method relies on an explicit integral , eq . ( [ t_1_lim ] ) , or a fourier expansion , eq . ( [ d_fourier - sol ] ) . given a sampling of the thermal driving function at equal time intervals , the periodic solution can be obtained through two discrete fourier transforms : a direct transform to get the fourier coefficients of the driving function and an inverse transform of the coefficient vector multiplied by a suitable matrix ( sect . [ fourier - anal ] ) . of course , the discrete fourier transforms are best performed with a fft algorithm . this computation is more efficient than the numerical computation of the integral , eq . ( [ t_1_lim ] ) , if we need the values of the temperatures at all the given sampling times . however , the fourier transform presents the gibbs phenomenon , associated with sudden variations of the heat loads , as occur at eclipse times , for example . the gibbs phenomenon introduces errors , but these errors could be suppressed with special methods . the computation of the thermal modes and the stationary thermal state for a satellite ten - node thermal model confirms the validity of the linear method for a minimal but realistic model . the relaxation times span a considerable range , between 55 seconds and nearly one hundred minutes . of course , the latter time must be almost independent of the particular thermal model used , whereas the former has no intrinsic significance , and , if the number of nodes grew , that time would shrink ( thus further expanding the range of relaxation times ) . the slowest mode corresponds to node temperature increments with the same sign ( positive by convention ) , whereas the increments corresponding to other modes have both signs . the periodic variation in the external heat input ( fig . [ heat - in ] ) excites the thermal modes and produces a definite pattern of stationary temperature oscillations , well approximated by the first - order solution ( fig . [ tevol ] ) . the second - order correction is small compared to the first - order solution , but it is worth computing , as it reaches 1.7 k. higher order corrections are essentially negligible , but the error due to the gibbs phenomenon at the eclipse positions reaches 0.6 k ( at the most ) . focusing on the computational aspects of the linear approach , we have studied how it scales with the number @xmath30 of nodes and the number @xmath29 of sampling positions on the orbit . if the jacobian matrix is dense , the complexity of the corresponding matrix operations is of order @xmath265 . it is convenient to employ just one matrix operation , namely , the diagonalization of the jacobian matrix , because then only a few of the slowest modes are needed for the remaining operations , so these have negligible complexity . the complexity of a direct numerical integration of the nonlinear equations is of order @xmath259 , @xmath23 being the number of time steps necessary for relaxation . for a low - altitude orbit , @xmath23 is expected to be on the order of one thousand , as for our moon - orbiting satellite . therefore , the linear method would be computationally effective as just an integration method only for models with a few hundred nodes . at any rate , the jacobian matrix can be assumed to be sparse , and its conduction part can be assumed to be especially sparse , in addition to being the larger part of the jacobian matrix and also being independent of the orbit . as the orbit may be subjected to changes in the planning of a mission , a convenient strategy probably is to diagonalize the conduction part at the outset and , when needed , add the radiation part within some approximation scheme . this strategy can be far more efficient than integrating the nonlinear equations each time . moreover , the strength of the linear approach lies with the insight that it provides about the thermal behavior of the spacecraft , as embodied by the decomposition of its thermal modes , of which only the slowest ones are significant . these significant modes can actually be obtained with a reduced thermal model using few nodes . therefore , the linear approach is especially useful in the context of reduced models . furthermore , it provides a method for model reduction based on the mode decomposition : this decomposition can be used to group nodes . indeed , there is a technique for graph partitioning based on the eigenvalues and eigenvectors of the laplacian matrix of the graph @xcite . according to sect . [ heur ] , this technique is applicable to the jacobian matrix , but the details of this application are beyond the scope of the present paper and are left for future work . finally , our linear approach can surely be applied to other cyclic heating processes that involve radiation heat transfer . we thank isabel prez - grande for bringing ref . to our attention .

the essential feature of the linear approach is that it provides a decomposition in thermal modes , like the decomposition of mechanical vibrations in normal modes . the stationary periodic solution of the linear equations can be alternately expressed as an explicit integral or as a fourier series . we briefly study the computational complexity of our method for general thermal models of orbiting spacecraft and conclude that it is certainly useful for reduced models and conceptual design but it can also be more efficient than the direct integration of the equations for large models .

we develop a linear method for solving the nonlinear differential equations of a lumped - parameter thermal model of a spacecraft moving in a closed orbit . our method , based on perturbation theory , is compared with heuristic linearizations of the same equations . the essential feature of the linear approach is that it provides a decomposition in thermal modes , like the decomposition of mechanical vibrations in normal modes . the stationary periodic solution of the linear equations can be alternately expressed as an explicit integral or as a fourier series . we apply our method to a minimal thermal model of a satellite with ten isothermal parts ( nodes ) and we compare the method with direct numerical integration of the nonlinear equations . we briefly study the computational complexity of our method for general thermal models of orbiting spacecraft and conclude that it is certainly useful for reduced models and conceptual design but it can also be more efficient than the direct integration of the equations for large models . the results of the fourier series computations for the ten - node satellite model show that the periodic solution at the second perturbative order is sufficiently accurate . lcl & = & outward - facing area of _ _ i__th - node , m + & = & thermal capacitance diagonal matrix , j / k + & = & thermal capacitance of _ _ i__th - node , j / k + & = & eigenvector of , k + & = & _ _ j__th - component of eigenvector , k + & = & driving function vector , k / s + & = &th fourier coefficient of , k / s + & = & complex conjugate of , k / s + & = & driving function forth - mode , k / s + & = & time derivative of , k / s + & = & driving function forth - node , k / s + & = &th fourier coefficient of , k / s + & = & driving function for second order temperature vector , k / s + & = & jacobian matrix , s + & = & jacobian matrix _ ij_-element , s + & = & number of steps in numerical integration of odes + & = & conduction coupling matrix , w / k + & = & matrix of conductances from linearized radiation coupling terms , w / k + & = &th - node conductance from linearized environment - radiation terms , w / k + & = & conduction coupling matrix _ ij_-element , w / k + & = & _ ij_-element of conductance matrix from linearized radiation terms , w / k + & = & number of samples for discrete fourier transform + & = & number of nodes + & = & eigenvector matrix for _ j _ , k + & = & _ _ i__th - component of-eigenvector forth - mode , k + & = & auxiliary heat input vector , k / s + & = & heat input to _ _ i__th - node , w + & = & mean value of over period , w + & = & _ _ i__th - node coefficient of radiation to the environment , w / k + & = & radiation coupling matrix , w / k + & = & time , s ( min in figures ) + & = & temperature vector , k + & = & vector of `` errors '' w.r.t . esatan solution , k + & = & steady - state temperature vector , k + & = & temperature of _ _ i-__node , k + & = & cosmic microwave background radiation temperature , k + & = & _ _ n__th order term in _ _ j__th - node temperature expansion , k + & = & stationary solution temperature vector , k + & = & _ _ n__th order of stationary solution temperature vector , k + & = & time derivative of _ _ i__th - node temperature , k / s + & = & steady - state temperature of _ _ i__th - node , k + & = & orbital period , s + & = & matrix of independent solutions to homogeneous equations , k + & = & solar absorptivity + & = & kronecker s delta + & = & antisymmetric part of , s + & = & _ ij_-element of , s + & = & infrared emissivity of _ _ i__th - node outward - facing surface + & = & perturbation parameter + & = & eigenvalue of _ j _ forth mode , s + & = & perturbation of _ j_-eigenvalue forth mode , s + & = & stefan - boltzmann constant , wmk +

astro-ph0204055

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the masses of galaxies are traditionally estimated by dynamical methods from the kinematics of their stars and gas . ever since extended hi rotation curves were first measured for spirals , it has been clear that the implied masses include not only the observed material , but also substantial amounts of dark matter . indeed , it is now believed that most galaxies are surrounded by dark halos which extend to many times their optical radii and contain an order of magnitude more mass than the visible components . the properties of these halos can be inferred directly from tracers at large radii such as x - ray emitting atmospheres , systems of satellite galaxies , or weak gravitational distortion of background galaxy images . in practice , gaseous atmospheres are visible only around some bright elliptical galaxies , while the other two techniques are too noisy to apply to individual galaxies ; they are used to obtain average halo properties for stacked samples of similar galaxies ( zaritsky et al 1993 ; mckay et al 2002 ) . in order to understand how galaxies formed , we would like to map the relationship between the properties of the observed baryonic components of galaxies and those of their dark halos . this mapping should yield information about how the baryons cooled , condensed and turned into stars as the halo - galaxy systems were assembled , and should clarify the complex physical processes that regulated the efficiency and timing of galaxy formation . most studies of the halo - galaxy relation have used luminosity as a surrogate for total baryon content , and a kinematic measure peak rotation velocity , stellar velocity dispersion , x - ray atmosphere temperature as a surrogate for halo mass . both surrogates are far from ideal . kinematic measures are strongly affected by the visible components of the galaxy and so have an uncertain relation to halo mass ; only satellite and weak lensing studies can reliably estimate total halo masses , albeit as an average over all galaxies in a chosen class . galaxy luminosity may not correlate well with stellar mass ( the dominant baryonic component in all but a subset of the smallest systems ) . there are strong dependences on the fraction of young stars in the galaxy and on its dust content . thus a technique to correct for attenuation by dust and to estimate the mass - to - light ratio of the underlying stellar population is needed to estimate the stellar mass of a galaxy . it is well - known that luminosities are less affected by stellar population variations in the near - infrared than in the optical , and that extinction corrections are also smaller at longer wavelengths . recently verheijen ( 2001 ) studied the b , r , i and k-band tully - fisher relations of a volume - limited sample of 49 spiral galaxies in the ursa major cluster . he showed that the k-band relation exhibited the tightest correlation with rotation velocity , suggesting that the stellar masses of galaxies are linked closely with the masses of the dark matter halos in which they formed . the larger scatter in the shorter wavelength passbands was attributed to variations in star formation history and dust extinction between different galaxies in the sample . although near - infrared luminosities are less dependent on star formation history than optical luminosities , they nevertheless exhibit some sensitivity to stellar age . bell & de jong ( 2001 ) estimate that the near - infrared mass - to - light ratios of local spirals can vary by as much as a factor of two and propose a correction based on the optical colours of the galaxies . brinchmann & ellis ( 2000 ) also used colour - based methods to transform the near - infrared magnitudes of a sample of intermediate redshift galaxies into stellar masses . in both analyses , it was assumed that the star formation histories of galaxies could be described by simple exponential laws . if galaxies formed a major ( @xmath26% ) fraction of their stars in recent bursts , it was shown that this would introduce substantial errors into the estimated mass - to - light ratios . in this paper , we make use of spectral indicators as diagnostics of the past star formation histories of galaxies . in particular , two spectral features , the 4000 break and the h@xmath27 absorption line , provide important information about the ages of the stellar populations in galaxies and are able to distinguish recent star formation histories dominated by bursts from those that are more continuous . we develop a method based on these two indicators and on broad - band photometry that allows us to derive maximum likelihood estimates of the stellar mass of a galaxy , the attenuation of its starlight by dust , and the fraction of its stars formed in recent bursts . we apply our method to a sample of @xmath28 galaxies drawn from the sloan digital sky survey and show how the derived stellar mass - to - light ratios of galaxies in four sloan bandpasses ( @xmath29 , @xmath30 , @xmath31 and @xmath32 ; fukugita et al 1996 ) depend both on galaxy luminosity and on structural parameters such as concentration index . we also compute the fraction of the total stellar mass in the universe in galaxies of different masses , sizes , colours and concentrations . the dependence of galaxy properties on stellar mass is addressed in a separate paper ( kauffmann et al 2002 ; paper ii )

a comparison with broad band photometry then yields estimates of dust attenuation and of stellar mass . the distribution of d(4000 ) is strongly bimodal , showing a clear division between galaxies dominated by old stellar populations and galaxies with more recent star formation . -0.55 + _ box 208121 , new haven , ct 06520 _ + _ department of physics , eotvos lorand university , pf .

we develop a new method to constrain the star formation histories , dust attenuation and stellar masses of galaxies . it is based on two stellar absorption line indices , the 4000 break strength and the balmer absorption line index h . together , these indices allow us to constrain the mean stellar ages of galaxies and the fractional stellar mass formed in bursts over the past few gyr . a comparison with broad band photometry then yields estimates of dust attenuation and of stellar mass . we generate a large library of monte carlo realizations of different star formation histories , including starbursts of varying strength and a range of metallicities . we use this library to generate median likelihood estimates of burst mass fractions , dust attenuation strengths , stellar masses and stellar mass - to - light ratios for a sample of 122,808 galaxies drawn from the sloan digital sky survey . the typical 95% confidence range in our estimated stellar masses is 40 % . we study how the stellar mass - to - light ratios of galaxies vary as a function of absolute magnitude , concentration index and photometric pass - band and how dust attenuation varies as a function of absolute magnitude and 4000 break strength . we also calculate how the total stellar mass of the present universe is distributed over galaxies as a function of their mass , size , concentration , colour , burst mass fraction and surface mass density . we find that most of the stellar mass in the local universe resides in galaxies that have , to within a factor of about 2 , stellar masses , half - light radii kpc , and half - light surface mass densitieskpc . the distribution of d(4000 ) is strongly bimodal , showing a clear division between galaxies dominated by old stellar populations and galaxies with more recent star formation . -0.55 cm -0.55 cm 0.1 mm 16.75 cm 21.0 cm stellar masses and star formation histories for galaxies from the sloan digital sky survey + guinevere kauffmann , timothy m. heckman , simon d.m . white , stphane charlot , christy tremonti , jarle brinchmann , + gustavo bruzual , eric w. peng , mark seibert , + mariangela bernardi , michael blanton , jon brinkmann , francisco castander , istvan csbai , masataka fukugita , zeljko ivezic , jeffrey a. munn , robert c. nichol , nikhil padmanabhan , aniruddha r. thakar , david h. weinberg , donald york + + _department of physics and astronomy , johns hopkins university , baltimore , md 21218 _ + _ institut dastrophysique du cnrs , 98 bis boulevard arago , f-75014 paris , france _ + _ ( ae ) centro de investigaciones de astronomia , merida , venezuela _ + _ department of astronomy , university of chicago , 5640 south ellis ave , chicago , il 60637 _ + _ department of physics , new york university , 4 washington place , new york , ny 10003 _ + _ apache point observatory , p.o . box 59 , sunspot , nm 88349 _ + _ department of physics , yale university , p.o . box 208121 , new haven , ct 06520 _ + _ department of physics , eotvos lorand university , pf . 32 , h-1518 budapest , hungary _ + _ institute for cosmic ray research , university of tokyo , chiba 277 - 8582 , japan _ + _ princeton university observatory , peyton hall , princeton nj 08544 - 1001 _ + _ us naval observatory , flagstaff station , p.o . box 1149 , flagstaff , az 86002 _ + _ department of physics , carnegie mellon university , 5000 forbes ave , pittsburgh , pa 15232 _ + _ department of physics , princeton university , princeton nj 08544 _ + _ department of astronomy , ohio state university , 140 west 18th avenue , columbus , oh 43210 _ + keywords : galaxies : formation , evolution ; galaxies : stellar content

astro-ph0204055

i

we have developed a new method to constrain the past star formation histories of galaxies . it is based on two stellar absorption line indices , the 4000 break strength d@xmath6(4000 ) and the balmer absorption line index h@xmath0 . together these two indices allow us to place constraints on the mean age of the stellar population of a galaxy and the fraction of its stellar mass formed in recent bursts . we have generated a library of monte carlo realizations of different star formation histories , which includes bursting as well as continuous models and a wide range of metallicities . we use the library to generate estimates and confidence intervals for a variety of parameters for a sample of 122,808 galaxies drawn from the sloan digital sky survey , these include : 1 . @xmath77 the fraction of the stellar mass of the galaxy formed in bursts in the past two gyr . 2 . @xmath91 the attenuation of the rest - frame @xmath32-band light due to dust . 3 . stellar mass - to - light ratios in the @xmath29 , @xmath30 , @xmath31 and @xmath32 bands . 4 . stellar masses . note that the analysis can be extended to include other parameters describing the star formation history of a galaxy , but not all parameters are equally well - constrained . for example , the luminosity - weighted or mass - weighted mean stellar ages have large errors , because of the rather strong dependence of the 4000 break on metallicity at ages of more than 1 - 2 gyr ( see fig . in the first part of the paper , we have illustrated in detail how our methods can be applied to galaxies in the sdss and we have estimated the confidence with which we can constrain basic parameters such as stellar mass . in the second part of the paper , we have presented a number of astrophysically interesting applications of our methods . we have shown that the attenuation of the @xmath32-band light due to dust depends strongly on both the absolute magnitude and the mean stellar age of a galaxy . we have also studied the distribution of stellar mass - to - light ratios of galaxies as a function of absolute magnitude in the four sdss pass bands . we have shown that the distribution of @xmath111 is strongly dependent on galaxy luminosity in all photometric bands . almost all very luminous galaxies have high mass - to - light ratios . faint galaxies have lower mass - to - light ratios , but also span a wider range in @xmath111 . we have also shown that the scatter in @xmath111 at a given luminosity is a factor of @xmath109 smaller in the @xmath32-band than it is in the @xmath29-band . finally , we have computed how galaxies of different types contribute to the total stellar mass budget of the universe . in the standard paradigm for structure formation in the universe , galaxy formation occurs hierarchically through the merging of small protogalactic condensations to form more and more massive systems . in this picture , the contribution of different kinds of galaxies to the stellar mass budget is expected to evolve strongly with redshift . the rate and form of this evolution depend not only on the values of cosmological parameters such as @xmath149 and @xmath150 , but also on the physical processes that control the rate at which stars form in galaxies . for example , if star formation rates are enhanced during galaxy - galaxy mergers , the fraction of stars formed in recent bursts should rise strongly with redshift , simply because merging rates and gas fractions were higher in the past ( see for example kauffmann & haehnelt 2000 ) . although it is now clear that the integrated star formation rate density increases strongly to higher redshifts ( madau et al 1996 ) , it is still not understood which galaxies undergo the strongest evolution or which physical processes cause galaxies to form stars more rapidly in the past . in the next few years , there will be a number of new large redshift surveys of the faint galaxy population . these surveys will contain enough galaxies to carry out an inventory of the stellar mass at @xmath151 . when these results are compared with the distributions derived from the sdss , it will be possible to draw quantitative conclusions about how galaxies have evolved over the past two thirds of a hubble time and to begin disentangling the effects of the different processes that may have influenced this evolution . the sloan digital sky survey ( sdss ) is a joint project of the university of chicago , fermilab , the institute for advanced study , the japan participation group , the johns hopkins university , los alamos national laboratory , the max - planck - institute for astronomy ( mpia ) , the max - planck - institute for astrophysics ( mpa ) , new mexico state university , princeton university , the united states naval observatory , and the university of washington . apache point observatory , site of the sdss telescopes , is operated by the astrophysical research consortium ( arc ) . funding for the project has been provided by the alfred p. sloan foundation , the sdss member institutions , the national aeronautics and space administration , the national science foundation , the u.s . department of energy , the japanese monbukagakusho , and the max planck society . the sdss web site is http://www.sdss.org/. let us recall the basis of bayesian statistics for this kind of problem . an initial assumption is made that the data are randomly drawn from a distribution which is a member of a model family characterised by a parameter vector * p*. the dimension of * p * can , in principle , be arbitrarily large . in particular , it can be much larger than the number of points n in the dataset to be fitted . the goal is then to use the data to define a likelihood function on the space of all possible * p*. this function can be used to obtain a best estimate and confidence interval for any model property y(*p * ) . in bayesian statistics one has to specify a prior distribution on the space of all possible * p*. this is a probability density distribution @xmath152(*p * ) which encodes knowledge about the relative likelihood of various * p * values in the absence of any data . for example , the physically accessible range for each element of * p * may be limited . typically one takes a uniform prior in parameters with a small dynamic range and a uniform prior in the log of parameters with a large dynamic range . where a is a constant which is adjusted so that @xmath155(*p * @xmath156 normalises correctly to unity and @xmath157 is the probability of the observed dataset on the hypothesis that the underlying distribution is described by the particular parameter set * p*. the likelihood of the derived parameter y(*p * ) given the data is then @xmath158 where the integral extends over all * p * for which y lies in a specified bin @xmath1dy/2 . note that there is no regularity requirement on the function y(*p * ) other than piecewise continuity so it makes sense to define a probability density . the most likely value of y can then be taken as the peak of this distribution ; the most typical value as its median ; the 95% ( symmetric ) confidence interval for scalar y can be defined by excluding the 2.5% tails at each end of the distribution . when applied to the kinds of problems presented in this paper , the prior is taken to be the distribution of possible star formation histories in the comparison library , which can be viewed as a monte carlo sampling of @xmath159 . the integral in the above expression for the likelihood of y is then trivially evaluated through binning the integrand as a function of y. the expression for @xmath160 is also straightforward for our case , since we have a measure of each element of * d * and we can assume the errors are normal with known correlation matrix c. in this situation it is worth noting that this procedure makes no assumptions about the shapes of the distributions @xmath159 , @xmath164 or @xmath165 . the first can be assumed at will , and for small error bars and a well constrained problem should have little effect on the answer . the other two are then derived consistently . the important assumptions are that the model makes a well defined and specific prediction for the value of the observable in the absence of observational errors ( in practice there will be some degree of theoretical uncertainty and this could be included in c if it can be modelled as gaussian ) and that the observed data * d * have a known observational error which can be assumed gaussian with covariance matrix c.

we develop a new method to constrain the star formation histories , dust attenuation and stellar masses of galaxies . it is based on two stellar absorption line indices , the 4000 break strength and the balmer absorption line index h . together , these indices allow us to constrain the mean stellar ages of galaxies and the fractional stellar mass formed in bursts over the past few gyr . we generate a large library of monte carlo realizations of different star formation histories , including starbursts of varying strength and a range of metallicities . we use this library to generate median likelihood estimates of burst mass fractions , dust attenuation strengths , stellar masses and stellar mass - to - light ratios for a sample of 122,808 galaxies drawn from the sloan digital sky survey . we study how the stellar mass - to - light ratios of galaxies vary as a function of absolute magnitude , concentration index and photometric pass - band and how dust attenuation varies as a function of absolute magnitude and 4000 break strength . white , stphane charlot , christy tremonti , jarle brinchmann , + gustavo bruzual , eric w. peng , mark seibert , + mariangela bernardi , michael blanton , jon brinkmann , francisco castander , istvan csbai , masataka fukugita , zeljko ivezic , jeffrey a. munn , robert c. nichol , nikhil padmanabhan , aniruddha r. thakar , david h. weinberg , donald york + + _department of physics and astronomy , johns hopkins university , baltimore , md 21218 _ + _ institut dastrophysique du cnrs , 98 bis boulevard arago , f-75014 paris , france _ + _ ( ae ) centro de investigaciones de astronomia , merida , venezuela _ + _ department of astronomy , university of chicago , 5640 south ellis ave , chicago , il 60637 _ + _ department of physics , new york university , 4 washington place , new york , ny 10003 _ apache point observatory , p.o . box 59 , sunspot , nm 88349 _ + _ department of physics , yale university , p.o . 32 , h-1518 budapest , hungary _ + _ institute for cosmic ray research , university of tokyo , chiba 277 - 8582 , japan _ + _ princeton university observatory , peyton hall , princeton nj 08544 - 1001 _ + _ us naval observatory , flagstaff station , p.o . box 1149 , flagstaff , az 86002 _ + _ department of physics , carnegie mellon university , 5000 forbes ave , pittsburgh , pa 15232 _ + _ department of physics , princeton university , princeton nj 08544 _ + _ department of astronomy , ohio state university , 140 west 18th avenue , columbus , oh 43210 _ + keywords : galaxies : formation , evolution ; galaxies : stellar content

we develop a new method to constrain the star formation histories , dust attenuation and stellar masses of galaxies . it is based on two stellar absorption line indices , the 4000 break strength and the balmer absorption line index h . together , these indices allow us to constrain the mean stellar ages of galaxies and the fractional stellar mass formed in bursts over the past few gyr . a comparison with broad band photometry then yields estimates of dust attenuation and of stellar mass . we generate a large library of monte carlo realizations of different star formation histories , including starbursts of varying strength and a range of metallicities . we use this library to generate median likelihood estimates of burst mass fractions , dust attenuation strengths , stellar masses and stellar mass - to - light ratios for a sample of 122,808 galaxies drawn from the sloan digital sky survey . the typical 95% confidence range in our estimated stellar masses is 40 % . we study how the stellar mass - to - light ratios of galaxies vary as a function of absolute magnitude , concentration index and photometric pass - band and how dust attenuation varies as a function of absolute magnitude and 4000 break strength . we also calculate how the total stellar mass of the present universe is distributed over galaxies as a function of their mass , size , concentration , colour , burst mass fraction and surface mass density . we find that most of the stellar mass in the local universe resides in galaxies that have , to within a factor of about 2 , stellar masses , half - light radii kpc , and half - light surface mass densitieskpc . the distribution of d(4000 ) is strongly bimodal , showing a clear division between galaxies dominated by old stellar populations and galaxies with more recent star formation . -0.55 cm -0.55 cm 0.1 mm 16.75 cm 21.0 cm stellar masses and star formation histories for galaxies from the sloan digital sky survey + guinevere kauffmann , timothy m. heckman , simon d.m . white , stphane charlot , christy tremonti , jarle brinchmann , + gustavo bruzual , eric w. peng , mark seibert , + mariangela bernardi , michael blanton , jon brinkmann , francisco castander , istvan csbai , masataka fukugita , zeljko ivezic , jeffrey a. munn , robert c. nichol , nikhil padmanabhan , aniruddha r. thakar , david h. weinberg , donald york + + _department of physics and astronomy , johns hopkins university , baltimore , md 21218 _ + _ institut dastrophysique du cnrs , 98 bis boulevard arago , f-75014 paris , france _ + _ ( ae ) centro de investigaciones de astronomia , merida , venezuela _ + _ department of astronomy , university of chicago , 5640 south ellis ave , chicago , il 60637 _ + _ department of physics , new york university , 4 washington place , new york , ny 10003 _ + _ apache point observatory , p.o . box 59 , sunspot , nm 88349 _ + _ department of physics , yale university , p.o . box 208121 , new haven , ct 06520 _ + _ department of physics , eotvos lorand university , pf . 32 , h-1518 budapest , hungary _ + _ institute for cosmic ray research , university of tokyo , chiba 277 - 8582 , japan _ + _ princeton university observatory , peyton hall , princeton nj 08544 - 1001 _ + _ us naval observatory , flagstaff station , p.o . box 1149 , flagstaff , az 86002 _ + _ department of physics , carnegie mellon university , 5000 forbes ave , pittsburgh , pa 15232 _ + _ department of physics , princeton university , princeton nj 08544 _ + _ department of astronomy , ohio state university , 140 west 18th avenue , columbus , oh 43210 _ + keywords : galaxies : formation , evolution ; galaxies : stellar content

1010.1264

i

in a sense , ads / cft duality reduces the construction of quantum gravity to a solved problem . gravity is written in terms of a nongravitational quantum field theory @xcite , and the technology of wilson @xcite can then be applied . in its current form , this duality reports only the measurements made by an external observer studying gravity confined to an anti - de sitter box . still , this allows one to address many of the conceptual questions of quantum gravity , most notably the purity of black hole hawking radiation . this implies in turn an extreme nonlocality of quantum gravity @xcite . formulating a theory in which locality has been so radically abandoned is a great challenge . fortunately , we have the example of ads / cft duality , and so we should understand this example as fully as possible . in retrospect , what ads / cft describes are the simplest and most sharply defined observables possible in a theory of quantum gravity . one needs go beyond these , to describe local observers within ads space , and to understand gravity outside the ads box . in this paper we study a framework suggested by the discussion above , in which we pull the wilson renormalization group back through the duality , where it takes a holographic form . of course there is a wide literature that falls under the broad heading of _ holographic renormalization group ( hrg)_. however , the parallels between the wilson and holographic perspectives have not been fully developed , and there are some simple observations and exercises that we would like to add , although we will also leave many questions unanswered for now . many of the points that we make have already been made in various forms in the literature , but it is useful to bring together here a coherent point of view . although we have emphasized the use of the duality to understand quantum gravity , clarifying the relation between the rg s should also be useful in the applications to strongly coupled field theories . indeed , there is interesting overlap between some recent work in this area and ours . wilson separates the path integral into high- and low - energy modes , and integrates out the former , @xmath0 where we use @xmath1 for generic boundary fields . we are being impressionistic here : the precise form of the cutoff at scale @xmath2 is not specified . the progressive integration of momentum shells is then described by a differential equation , and by integrating out to @xmath3 one obtains the full path integral . the intermediate stages are quite complicated : @xmath4 is necessarily a quasilocal function of length scale @xmath5 , and so depends on an infinite number of parameters , but the flow is strongly convergent in almost all directions . in essence , this flow supplies the deltas and epsilons of path integration , reducing the construction of qft to dimensional analysis . in the spirit of full disclosure we should note that it is difficult to make the mode separation while preserving explicitly important structures such as gauge invariance , supersymmetry , and duality . ultimately this may point to the need for a new way to think about qft , but for now this is the only tool of broad applicability , enabling one to reduce arbitrary calculations to algorithms . in ads / cft duality , the radial coordinate @xmath6 of the ads bulk emerges from the energy scale of the boundary field theory @xcite . this suggests a correspondence between radial evolution in the bulk and wilson renormalization group flow in the field theory . in sec . 2 we develop this idea . our approach is to postulate a mapping between the radial cutoff on the bulk , and a wilsonian cutoff on the field theory . to make the form of this mapping precise is the deep and difficult problem that we would like to solve in the future , but for the present we are interested in the consequences of this postulate for the structures on the two sides . two somewhat unexpected results are the central role played by multi - trace operators , and the need to carry out the gravitational path integral in gauge - fixed rather than wheeler - dewitt form . in sec . 3 we work out some examples , in particular the flows induced by relevant single- and double - trace operators , and also flows involving bulk gauge fields and the metric . in sec . 4 we discuss various truncations of the full wilsonian flow and relations with the earlier literature . in sec . 5 we discuss the picture from the boundary field theory point of view , and are led to a possible , but rather unusual , regulator . in sec . 6 we discuss future directions and intended applications .

we develop parallels between the holographic renormalization group in the bulk and the wilsonian renormalization group in the dual field theory . our philosophy differs from most previous work on the holographic rg ; the most notable feature is the key role of multi - trace operators . we work out the forms of various single- and double - trace flows . the key question , ` what cutoff on the field theory corresponds to a radial cutoff in the bulk ? ' is left unanswered , but by sharpening the analogy between the two sides we identify possible directions . santa barbara , ca 93106 - 4030 _ = 16pt

we develop parallels between the holographic renormalization group in the bulk and the wilsonian renormalization group in the dual field theory . our philosophy differs from most previous work on the holographic rg ; the most notable feature is the key role of multi - trace operators . we work out the forms of various single- and double - trace flows . the key question , ` what cutoff on the field theory corresponds to a radial cutoff in the bulk ? ' is left unanswered , but by sharpening the analogy between the two sides we identify possible directions . holographic and wilsonian renormalization groups * idse heemskerk * _ department of physics _ _ university of california _ _ santa barbara , ca 93106 _ * joseph polchinski * _ kavli institute for theoretical physics _ _ university of california _ _ santa barbara , ca 93106 - 4030 _ = 16pt

gr-qc0604058

i

it is by now well established that the physics associated with classical and quantum fields in curved spacetimes can be reproduced , within certain approximations , in a variety of different physical systems the so - called `` analogue models of general relativity ( gr ) '' @xcite . the simplest example of such a system is provided by acoustic disturbances propagating in a barotropic , irrotational and viscosity - free fluid . in the context of analogue models it is natural to separate the kinematical aspects of gr from the dynamical ones . in general , within a sufficiently complex analogue model one can reproduce any pre - specified spacetime and the kinematics of fields evolving on it independently of whether or not it satisfies the classical ( or semiclassical ) einstein equations @xcite . indeed , to date there are no analogue models whose effective geometry is determined by einstein equations . in this sense we currently have both analogue spacetimes and analogues of quantum field theory in curved spacetimes , but ( strictly speaking ) no analogue model for gr itself @xcite . in order to reproduce a specific spacetime geometry within an analogue model , one would have to take advantage of the specific equations describing the latter ( for example , for fluid models , the euler and continuity equations , together with an equation of state ) , plus the possibility of manipulating the system by applying appropriate external forces . in the analysis of this paper we will think of the spacetime configuration as `` externally given '' , assuming that it has been set up as desired by external means any back - reaction on the geometry is neglected as in principle we can counter - balance its effects using the external forces . in the context of analogue models this is not merely a hypothesis introduced solely for theoretical simplicity , but rather a realistic situation that is in principle quite achievable . specifically , in this paper we analyze in simple terms the issue of quantum quasi - particle creation by several externally specified @xmath1-dimensional analogue geometries simulating the formation of black hole - like configurations . ( in a previous companion paper @xcite we investigated the causal structure of these , and other , spacetimes . ) in this analysis we have in mind , on the one hand , the possibility of setting up laboratory experiments exhibiting hawking - like radiation @xcite and , on the other hand , the acquisition of new insights into the physics of black hole evaporation in semiclassical gravity . all the discussion holds for a scalar field obeying the dalembert wave equation in a curved spacetime . this means that we are not ( for current purposes ) considering the deviations from the phononic dispersion relations that show up at high energies owing to the atomic structure underlying any condensed matter system . we shall briefly comment on these modifications at the end of the paper . for simplicity , throughout the paper we adopt a terminology based on acoustics in moving fluids ( we will use terms such as acoustic spacetimes , sonic points , fluid velocity , etc . ) , but our results are far more general and apply to many other analogue gravity models not based on acoustics . we summarise the main conclusions below . first of all , we recover the standard hawking result when considering fluid flows that generate a supersonic regime at finite time . ( that is , we recover a stationary creation of quasi - particles with a planckian spectrum . ) we then analyze the quasi - particle creation associated with other types of configurations . in particular , we shall discuss in detail a `` critical black hole '' a flow configuration that presents an acoustic horizon without an associated supersonic region . from this analysis we want to highlight two key results : * the existence of a supersonic regime ( sound velocity @xmath2 strictly smaller than fluid velocity @xmath3 ) is not needed in order to reproduce hawking s stationary particle creation . we demonstrate this fact by calculating the quantity of quasi - particle production in an evolving geometry which generates only an isolated sonic point ( @xmath0 ) , but without a supersonic region , in a finite amount of laboratory time . * moreover , in order to produce a hawking - like effect it is not even necessary to generate a sonic point at finite time . all one needs is that a sonic point develops in the asymptotic future ( that is , for @xmath4 ) _ with sufficient rapidity _ ( we shall explain in due course what we exactly mean by this ) . from the point of view of the reproducibility of a hawking - like effect in a laboratory , the latter result is particularly interesting . in general , the formation of a supersonic regime in a fluid flow normally considered to be the crucial requirement to produce hawking emission is associated with various different types of instability ( landau instability in superfluids , quantized vortex formation in bose einstein condensates , etc . ) that could mask the hawking effect . to reproduce a hawking - like effect without invoking a supersonic regime could alleviate this situation . from the point of view of gr , we believe that our result could also have some relevance , as it suggests a possible alternative scenario for the formation and semiclassical evaporation of black hole - like objects . the plan of the paper is the following : in the next section we introduce the various acoustic spacetimes on which we focus our attention , spacetimes that describe the formation of acoustic black holes of different types . in section [ sec : creation ] we present separately the specific calculations of redshift for sound rays that pass asymptotically close to the event horizon of these black holes . by invoking standard techniques of quantum field theory in curved spacetime , one can then immediately say when particle production with a planckian spectrum takes place . finally , in the last section of the paper we summarise and discuss the results obtained .

it is sufficient to set up a dynamically changing flow _ either _ eventually generating an arbitrarily small sonic region , but without any ergoregion , _ or _ even just asymptotically , in laboratory time , approaching a sonic regime with sufficient rapidity . pacs : 04.20.gz , 04.62.+v , 04.70.-s , 04.70.dy , 04.80.cc + keywords : analogue models , acoustic spacetime , hawking radiation

we discuss the issue of quasi - particle production by `` analogue black holes '' with particular attention to the possibility of reproducing hawking radiation in a laboratory . by constructing simple geometric acoustic models , we obtain a somewhat unexpected result : we show that in order to obtain a stationary and planckian emission of quasi - particles , it is _ not _ necessary to create an ergoregion in the acoustic spacetime ( corresponding to a supersonic regime in the flow ) . it is sufficient to set up a dynamically changing flow _ either _ eventually generating an arbitrarily small sonic region , but without any ergoregion , _ or _ even just asymptotically , in laboratory time , approaching a sonic regime with sufficient rapidity . pacs : 04.20.gz , 04.62.+v , 04.70.-s , 04.70.dy , 04.80.cc + keywords : analogue models , acoustic spacetime , hawking radiation

astro-ph0212205

i

it has long been realized that galaxies , and self - gravitating systems in general , follow a kind of organization despite the diversity of their initial conditions and their environement . this organization is illustrated by morphological classification schemes such as the hubble sequence and by simple rules which govern the structure of individual self - gravitating systems . for example , elliptical galaxies display a quasi - universal luminosity profile described by de vaucouleurs @xmath1 law and most of globular clusters are well fitted by the michie - king model @xcite . the question that naturally emerges is , what determines the particular configuration to which a self - gravitating system settles . it is possible that their present configuration crucially depends on the conditions that prevail at their birth and on the details of their evolution . however , in view of their apparent regularity , it is tempting to investigate whether their organization can be favoured by some fundamental physical principles like those of thermodynamics and statistical physics . we ask therefore if the actual states of self - gravitating systems are not simply more probable than any other possible configuration , i.e. if they can not be considered as maximum entropy states . this thermodynamical approach may be particularly relevant for globular clusters and elliptical galaxies which are described by a distribution function that is almost isothermal @xcite . in the case of globular clusters , the relaxation proceeds via two - body encounters and this collisional evolution is well - described by kinetic equations of a fokker - planck - landau type for which a h - theorem is available . by contrast , for elliptical galaxies , two - body encounters are completely negligible ( the corresponding relaxation time @xmath2 exceeds the age of the universe by many orders of magnitude ) and the galaxy dynamics is described by the _ vlasov equation _ , i.e. collisionless boltzmann equation @xcite . since the vlasov equation rigorously conserves entropy , a relaxation towards an isothermal distribution looks at first sight relatively surprising . yet , the inner regions of elliptical galaxies appear to be isothermal and this fact stemed as a mystery for a long time . in a seminal paper , lynden - bell @xcite argued that the violently changing gravitational field of a newly formed galaxy leads to a redistribution of energies between stars and provides a mechanism analogous to a relaxation in a gas . the importance of this form of relaxation had previously been stressed by a number of authors including hnon and king but lynden - bell showed for the first time the relevance of a statistical description . he argued that the vlasov - poisson system develops an intricate _ mixing process _ in phase space associated with the heavily damped oscillations of a protogalaxy initially far from mechanical equilibrium and collapsing under its own gravity . as a result , the solutions of the vlasov equation are not smooth but involve intermingled filaments at smaller and smaller scales . in this sense , there is no convergence towards equilibrium but rather the formation of a fractal - like structure in phase space . however , if we introduce a macroscopic level of description and make a local average of the distribution function over the filaments , the resulting `` coarse - grained '' distribution function is smooth and is expected to reach a maximum entropy state ( i.e. most mixed state ) on a very short time scale of the order of the dynamical time @xmath3 . this process is called _ violent relaxation _ and is acknowledged to account for the regularity of elliptical galaxies or other collisionless self - gravitating systems . lynden - bell predicted that the equilibrium state should be described by a fermi - dirac distribution function or a superposition of fermi - dirac distributions . here , degeneracy is due not to quantum mechanics but to the liouville theorem that prevents the smooth distribution function from exceeding the maximum of its initial value . in the non degenerate limit , the fermi - dirac distribution functions reduce to maxwellians . the prediction of an isothermal distribution for collisionless stellar systems was considered as a triumph in the 1960 s and laid the foundation of a new type of statistical mechanics . of course , the validity of the theory is conditioned by a hypothesis of ergodicity which may not be completely fulfilled . this is the complicated problem of `` incomplete relaxation '' which limitates the power of prediction of lynden - bell s approach . however , as we shall see , these difficulties should not throw doubt on the importance of this statistical description . a similar relaxation process is at work in two - dimensional turbulence ( described by the 2d euler equation ) and can explain the organization and maintenance of coherent vortices , such as the great red spot of jupiter , which are common features of large - scale geophysical or astrophysical flows @xcite . the mathematical relevance of this statistical description has been given by robert @xcite introducing the concept of young measures . the formal analogy between two - dimensional vortices and stellar systems has been discussed by chavanis @xcite . this paper is organized as follows . in section [ vp ] , we introduce the gravitational vlasov - poisson system and list its main properties . in section [ lb ] , we present the statistical approach of lynden - bell @xcite to the problem of violent relaxation . in section [ fd ] , we show that the fermi - dirac equilibrium distribution predicted by lynden - bell is not entirely satisfactory since it has an infinite mass . we must therefore invoke _ incomplete relaxation _ and introduce truncated models . in the artificial situation in which the system is enclosed within a spherical box , we can calculate the fermi - dirac spheres explicitly and prove the existence of a global entropy maximum for each value of energy . for low energies , this equilibrium state has a degenerate core surrounded by a dilute atmosphere , as calculated by chavanis & sommeria @xcite . more generally , we determine the complete equilibrium phase diagram and discuss the nature of phase transitions in self - gravitating systems . in section [ mepp ] , we describe the coarse - grained relaxation of collisionless stellar systems towards statistical equilibrium in terms of a generalized fokker - planck equation . this relaxation equation is derived from a phenomenological maximum entropy production principle ( mepp ) and involves a diffusion in velocity space compensated by a nonlinear friction . in section [ qt ] , we present a quasilinear theory of the vlasov - poisson system and show that it leads to a kinetic equation of a landau type . when the system is close to equilibrium ( so that a thermal bath approximation can be implemented ) this equation reduces to the fokker - planck equation of the thermodynamical approach and the diffusion coefficient can be explicitly evaluated . this provides a new , self - consistent , equation for the `` coarse - grained '' dynamics of stellar systems where small scales have been smoothed - out in an optimal way . in section [ tm ] , we use this kinetic model to derive the distribution function of a tidally truncated collisionless stellar system . this truncated model preserves the main features of lynden - bell s distribution ( including degeneracy ) but has a finite mass , avoiding the artifice of a spherical container . other truncated models attempting to take into account incomplete relaxation are discussed .

, the system is expected to reach an equilibrium state of a fermi - dirac type within a few dynamical times . we describe in detail the equilibrium phase diagram and the nature of phase transitions which occur in self - gravitating systems . these relaxation equations , of a generalized fokker - planck type , are derived from a maximum entropy production principle ( mepp ) .

we discuss the statistical mechanics of violent relaxation in stellar systems following the pioneering work of lynden - bell ( 1967 ) . the solutions of the gravitational vlasov - poisson system develop finer and finer filaments so that a statistical description is appropriate to smooth out the small - scales and describe the `` coarse - grained '' dynamics . in a coarse - grained sense , the system is expected to reach an equilibrium state of a fermi - dirac type within a few dynamical times . we describe in detail the equilibrium phase diagram and the nature of phase transitions which occur in self - gravitating systems . then , we introduce a small - scale parametrization of the vlasov equation and propose a set of relaxation equations for the coarse - grained dynamics . these relaxation equations , of a generalized fokker - planck type , are derived from a maximum entropy production principle ( mepp ) . we make a link with the quasilinear theory of the vlasov - poisson system and derive a truncated model appropriate to collisionless systems subject to tidal forces . with the aid of this kinetic theory , we qualitatively discuss the concept of `` incomplete relaxation '' and the limitations of lynden - bell s theory . # 1eq.#1 # 10=-.025em0 - 0 -0.05em0 - 0-.025em.0233em0

physics9910025

r

we have carried out a series of experiments to determine the statistical characteristics of the dark , maintained , and driven neural discharge in cat rgc and lgn cells . using the analysis techniques presented in sec . [ sec : analysis ] , we compare and contrast the neural activity for these three different stimulus modalities , devoting particular attention to their fractal features . the results we present all derive from on - center x - type cells . the experimental methods are similar to those used by kaplan and shapley @xcite and teich _ et al . experiments were carried out on adult cats . anesthesia was induced by intramuscular injection of xylazine ( rompun 2 mg / kg ) , followed 10 minutes later by intramuscular injection of ketamine hcl ( ketaset 10 mg / kg ) . anesthesia was maintained during surgery with intravenous injections of thiamylal ( surital 2.5% ) or thiopental ( pentothal 2.5% ) . during recording , anesthesia was maintained with pentothal ( 2.5% , 26 ( mg / kg)/hr ) . the local anesthetic novocain was administered , as required , during the surgical procedures . penicillin ( 750,000 units intramuscular ) was also administered to prevent infection , as was dexamethasone ( decadron , 6 mg intravenous ) to forestall cerebral edema . muscular paralysis was induced and maintained with gallium triethiodide ( flaxedil , 515 ( mg / kg)/hr ) or vecuronium bromide ( norcuron , 0.25 ( mg / kg)/hr ) . infusions of ringer s saline with 5% dextrose at 34 ( ml / kg)/hr were also administered . the two femoral veins and a femoral artery were cannulated for intravenous drug infusions . heart rate and blood pressure , along with expired co@xmath76 , were continuously monitored and maintained in physiological ranges . for male cats , the bladder was also cannulated to monitor fluid outflow . core body temperature was maintained at 37.5@xmath77 c throughout the experiment by wrapping the animal s torso in a dc heating pad controlled by feedback from a subscapular temperature probe . the cat s head was fixed in a stereotaxic apparatus . the trachea was cannulated to allow for artificial respiration . to minimize respiratory artifacts , the animal s body was suspended from a vertebral clamp and a pneumothorax was performed when needed . eyedrops of 10% phenylephrine hydrochloride ( neo - synephrine ) and 1% atropine were applied to dilate the pupils and retract the nictitating membranes . gas - permeable hard contact lenses protected the corneas from drying . artificial pupils of 3-mm diameter were placed in front of the contact lenses to maintain fixed retinal illumination . the optical quality of the animal s eyes was regularly examined by ophthalmoscopy . the optic discs were mapped onto a tangent screen , by back - projection , for use as a positional reference . the animal viewed a crt screen ( tektronix 608 , 270 frames / sec ; or conrac , 135 frames / sec ) that , depending on the stimulus condition , was either dark , uniformly illuminated with a fixed luminance level , or displayed a moving grating . a craniotomy was performed over the lgn ( center located 6.5 mm anterior to the earbars and 9 mm lateral to the midline of the skull ) , and the dura mater was resected . a tungsten - in - glass microelectrode ( 510-@xmath78 m tip length ) @xcite was lowered until spikes from a single lgn neuron were isolated . the microelectrode simultaneously recorded rgc activity , in the form of s potentials , and lgn spikes , with a timing accuracy of 0.1 msec . the output was amplified and monitored using conventional techniques . a cell was classified as y - type if it exhibited strong frequency doubling in response to contrast - reversing high - spatial - frequency gratings , and x - type otherwise @xcite . the experimental protocol was approved by the animal care and use committee of rockefeller university , and was in accord with the national institutes of health guidelines for the use of higher mammals in neuroscience experiments . results for simultaneously recorded rgc and target lgn spike trains of 4000-sec duration are presented in fig . 3 , when the retina is thoroughly adapted to the dark ( this is referred to as the `` dark discharge '' ) . the normalized rate functions ( a ) for both the rgc ( solid curve ) and lgn ( dashed curve ) recordings exhibit large fluctuations over the course of the recording ; each window corresponds to a counting time of @xmath79 sec . such large , slow fluctuations often indicate fractal rates @xcite . the two recordings bear a substantial resemblance to each other , suggesting that the fractal components of the rate fluctuations either have a common origin or pass from one of the cells to the other . the normalized interevent - interval histogram ( b ) of the rgc data follows a straight - line trend on a semi - logarithmic plot , indicating that the interevent - interval probability density function is close to an exponential form . the lgn data , however , yields a nonmonotonic ( bimodal ) interevent - interval histogram . this distribution favors longer and shorter intervals at the expense of those near half the mean interval , reflecting clustering in the event occurrences over the short term . various kinds of unusual clustering behavior have been previously observed in lgn discharges @xcite . r / s plots ( c ) for both the rgc and lgn recordings follow the @xmath80 line for sums less than 1000 intervals , but rise sharply thereafter in a roughly power - law fashion as @xmath81 , suggesting that the neural firing pattern exhibits fractal activity for times greater than about 1000 intervals ( about 120 sec for these two recordings ) . both smoothed periodograms ( d ) decay with frequency as @xmath82 for small frequencies , and the allan factors ( e ) increase with time as @xmath83 for large counting times , confirming the fractal behavior . the 0.3-hz component evident in the periodograms of both recordings is an artifact of the artificial respiration ; it does not affect the fractal analysis . as shown in table 1 , the fractal exponents calculated from the various measures bear rough similarity to each other , as expected @xcite ; further , the onset times also agree reasonably well , being in the neighborhood of 100 sec . the coherence among these statistics leaves little doubt that these rgc and lgn recordings exhibit fractal features with estimated fractal exponents of @xmath84 and @xmath85 ( mean @xmath86 standard deviation of the three estimated exponents ) , respectively . moreover , the close numerical agreement of the rgc and lgn estimated fractal exponents suggests a close connection between the fractal activity in the two spike trains under dark conditions @xcite . curves such as those presented in fig . 3 are readily simulated by using a fractal - rate stochastic point process , as described in @xcite . with the exception of the interevent - interval distribution , it is apparent from fig . 3 that the statistical properties of the dark discharges generated by the rgc and its target lgn cell prove to be remarkably similar . figure 4 presents analogous statistical results for simultaneously recorded maintained - dis/-charge rgc and target - lgn spike trains of 7000-sec duration when the stimulus presented by the crt screen was a 50 cd / m@xmath87 uniform luminance . the cell pair from which these recordings were obtained is different from the pair whose statistics are shown in fig . as is evident from table 1 , the imposition of a stimulus increases the rgc firing rate , though not that of the lgn . in contrast to the results for the dark discharge , the rgc and lgn action - potential sequences differ from each other in significant ways under maintained - discharge conditions . we previously investigated some of these statistical measures , and their roles in revealing fractal features , for maintained discharge @xcite . the rate fluctuations ( a ) of the rgc and the lgn no longer resemble each other . at these counting times , the normalized rgc rate fluctuations are suppressed , whereas those of the lgn are enhanced , relative to the dark discharge shown in fig . 3 . significant long - duration fluctuations are apparently imparted to the rgc s - potential sequence at the lgn , through the process of selective clustered passage @xcite . spike clustering is also imparted at the lgn over short time scales ; the rgc maintained discharge exhibits a coefficient of variation ( cv ) much less than unity , whereas that of the lgn significantly exceeds unity ( see table 1 ) . the normalized interevent - interval histogram ( b ) of the rgc data resembles that of a dead - time - modified poisson point process ( fit not shown ) , consistent with the presence of relative refractoriness which becomes more important at higher rates @xcite . dead - time effects in the lgn are secondary to the clustering that it imparts to the rgc s - potentials , in part because of its lower rate . the r / s ( c ) , periodogram ( d ) , and allan factor ( e ) plots yield results that are consistent with , but different from , those revealed by the dark discharge shown in fig . 3 . although both the rgc and lgn recordings exhibit evidence of fractal behavior , the two spike trains now behave quite differently in the presence of a steady - luminance stimulus . for the rgc recording , all three measures are consistent with a fractal onset time of about 1 sec , and a relatively small fractal exponent ( @xmath88 ) . for the lgn , the fractal behavior again appears in all three statistics , but begins at a larger onset time ( roughly 20 sec ) and exhibits a larger fractal exponent ( @xmath89 ) . again , all measures presented in fig . 4 are well described by a pair of fractal - rate stochastic point processes @xcite . figure 5 presents these same statistical measures for simultaneously recorded 7000-sec duration rgc and lgn spike trains in response to a sinusoidal stimulus ( drifting grating ) at 4.2 hz frequency , 40% contrast , and 50 cd / m@xmath87 mean luminance . the rgc / lgn cell pair from which these recordings were obtained is the same as the pair illustrated in fig . 4 . the results for this stimulus resemble those for the maintained discharge , but with added sinusoidal components associated with the restricted phases of the stimulus during which action potentials occur . using terminology from auditory neurophysiology , these spikes are said to be `` phase locked '' to the periodicity provided by the drifting - grating stimulus . the firing rate is greater than that observed with a steady - luminance stimulus , particularly for the lgn ( see table 1 ) . again , the rgc and lgn spike trains exhibit different behavior . the rate fluctuations ( a ) of the lgn still exceeds those of the rgc , but not to as great an extent as in fig . 4 . both action - potential sequences exhibit normalized interevent - interval histograms ( b ) with multiple maxima , but the form of the histogram is now dominated by the modulation imposed by the oscillatory stimulus . over long times and small frequencies , the r / s ( c ) , periodogram ( d ) , and allan factor ( e ) plots again yield results in rough agreement with each other , and also with the results presented in fig . the most obvious differences arise from the phase locking induced by the sinusoidal stimulus , which appears directly in the periodogram as a large spike at 4.2 hz , and in the allan factor as local minima near multiples of @xmath90 sec . the rgc results prove consistent with a fractal onset time of about 3 sec , and a relatively small fractal exponent ( @xmath91 ) , whereas for the lgn the onset time is about 20 sec and the fractal exponent is @xmath92 . for both spike trains fractal behavior persists in the presence of the oscillatory stimulus , though its magnitude is slightly attenuated . we previously examined information exchange among pairs of rgc and lgn spike trains using information - theoretic measures @xcite . while these approaches are very general , finite data length renders them incapable of revealing relationships between spike trains over time scales longer than about 1 sec . we now proceed to investigate various rgc and lgn spike - train pairs in terms of the correlation measures for pairs of point processes developed in sec . [ sec : corrmeas ] . pairs of rgc discharges are only weakly correlated over long counting times . this is readily illustrated in terms of normalized rate functions such as those presented in fig . 6a , in which the rate functions of two rgcs are computed over a counting time @xmath79 sec . calculation of the correlation coefficient ( @xmath93 ) shows that the fluctuations are only mildly correlated . unexpectedly , however , significant correlation turns out to be present in pairs of lgn discharges over long counting times . this is evident in fig . 6b , where the correlation coefficient @xmath94 ( @xmath95 ) for the rates of two lgn discharges computed over the same counting time @xmath79 sec . for shorter counting times , there is little cross correlation for either pairs of rgc or of lgn spike trains ( not shown ) . however , strong correlations are present in the spike rates of an rgc and its target lgn cell as long as the rate is computed over times shorter than 15 sec for this particular cell pair . the cross correlation can be quantified at all time and frequency scales by the normalized wavelet cross - correlation function ( see sec . [ sec : nwccf ] ) and the cross periodogram ( see sec . [ sec : cpg ] ) , respectively . figure 6c shows the normalized wavelet cross - correlation function , as a function of the duration of the counting window , between an rgc / lgn spike - train pair recorded under maintained - discharge conditions , as well as for two surrogate data sets ( shuffled and poisson ) . for this spike - train pair , it is evident that significant correlation exists over time scales less than 15 seconds . the constant magnitude of the normalized wavelet cross - correlation function for @xmath96 sec is likely associated with the selective transmission properties of the lgn @xcite . figure 6d presents the normalized wavelet cross - correlation function for the same rgc / lgn spike - train pair shown in fig . 6c ( solid curve ) , together with that between two rgc action - potential sequences ( long - dashed curve ) , and between their two associated lgn spike trains ( short - dashed curve ) . also shown is a dotted line representing the aggregate behavior of the normalized wavelet cross - correlation function absolute magnitude for all surrogate data sets , which resemble each other . while the two rgc spike trains exhibit a normalized wavelet cross - correlation function value which remains below 7 , the two lgn action - potential sequences yield a curve that steadily grows with increasing counting window @xmath0 , attaining a value in excess of 1000 . indeed , a logarithmic scale was chosen for the ordinate to facilitate the display of this wide range of values . it is of interest to note that the lgn / lgn curve begins its steep ascent just as the rgc / lgn curve abruptly descends . further , the normalized wavelet cross - correlation function between the two lgn recordings closely follows a power - law form , indicating that the two lgn action - potential rates are co - fractal . one possible origin of this phenomenon is a fractal form of correlated modulation of the random - transmission processes in the lgn that results in the two lgn spike trains . some evidence exists that global modulation of the lgn might originate in the parabrachial nucleus of the brain stem ; the results presented here are consistent with such a conclusion . analogous results for the cross - periodograms , which are shown in figs . 6e and f , provide results that corroborate , but are not as definitive as , those obtained with the normalized wavelet cross - correlation function . the behavior of the normalized wavelet cross - correlation functions for pairs of driven spike trains , shown in fig . 7 , closely follow those for pairs of maintained discharges , shown in fig . 6 , except for the presence of structure at the stimulus period imposed by the drifting grating .

a drifting - grating stimulus yields rgc and lgn driven spike trains similar in character to those observed in the maintained discharge , with two notable distinctions : action potentials are reorganized along the time axis so that they occur only during certain phases of the stimulus waveform , and fractal activity is suppressed . under both uniform - luminance and drifting - grating stimulus conditions ( but not in the dark )

we employ a number of statistical measures to characterize neural discharge activity in cat retinal ganglion cells ( rgcs ) and in their target lateral geniculate nucleus ( lgn ) neurons under various stimulus conditions , and we develop a new measure to examine correlations in fractal activity between spike - train pairs . in the absence of stimulation ( i.e. , in the dark ) , rgc and lgn discharges exhibit similar properties . the presentation of a constant , uniform luminance to the eye reduces the fractal fluctuations in the rgc maintained discharge but enhances them in the target lgn discharge , so that neural activity in the pair no longer mirror each other . a drifting - grating stimulus yields rgc and lgn driven spike trains similar in character to those observed in the maintained discharge , with two notable distinctions : action potentials are reorganized along the time axis so that they occur only during certain phases of the stimulus waveform , and fractal activity is suppressed . under both uniform - luminance and drifting - grating stimulus conditions ( but not in the dark ) , the discharges of pairs of lgn cells are highly correlated over long time scales ; in contrast discharges of rgcs are nearly uncorrelated with each other . this indicates that action - potential activity at the lgn is subject to a common fractal modulation to which the rgcs are not subjected .

physics9910025

c

the presence of a stimulus alters the manner in which spike trains in the visual system exhibit fractal behavior . in the absence of a stimulus , rgc and lgn dark discharges display similar fractal activity ( see fig . the normalized rate functions of the two recordings , when computed for long counting times , follow similar paths . the r / s , allan factor , and periodogram quantify this relationship , and these three measures yield values of the fractal exponents for the two spike trains that correspond reasonably well ( see table 1 ) . the normalized interevent - interval histogram , a measure which operates only over relatively short time scales , shows a significant difference between the rgc and lgn responses . such short - time behavior , however , does not affect the fractal activity , which manifests itself largely over longer time scales . the presence of a stimulus , either a constant luminance ( fig . 4 ) , or a drifting grating ( fig . 5 ) , causes the close linkage between the statistical character of the rgc and lgn discharges over long times to dissipate . the normalized rate functions of the lgn spike trains display large fluctuations about their mean , especially for the maintained discharge , while the rgc rate functions exhibit much smaller fluctuations that are minimally correlated with those of the lgn . again , the r / s , allan factor , and periodogram quantify this difference , indicating that fractal activity in the rgc consistently exhibits a smaller fractal exponent ( see also table 1 ) , and also a smaller fractal onset time ( higher onset frequency ) . both the r / s and allan - factor measures indicate that the lgn exhibits more fluctuations than the rgc at all scales ; the periodogram does not , apparently because it is the only one of the three constructed without normalization . in the driven case ( fig . 5 ) , the oscillatory nature of the stimulus phase - locks the rgc and lgn spike trains to each other at shorter time scales . the periodogram displays a peak at 4.2 hz , and the allan factor exhibits minima at multiples of @xmath90 sec , for both action - potential sequences . the normalized interevent - interval histogram also suggests a relationship between the two recordings mediated by the time - varying stimulus ; both rgc and lgn histograms achieve a number of maxima . although obscured by the normalization , the peaks do indeed coincide for an unnormalized plot ( not shown ) . in the presence of a stimulus , rgcs are not correlated with their target lgn cells over the long time scales at which fractal behavior becomes most important , but significant correlation does indeed exist between pairs of lgn spike trains for both the maintained and driven discharges ( see figs . 6 and 7 , respectively ) . these pairs of lgn discharges , exhibiting linked fractal behavior , may be called co - fractal . the normalized wavelet cross - correlation function and cross periodogram plots between rgc 1 and lgn 1 remain significantly above the surrogates for small times ( figs . 6c and 6e ) . the results for the two rgcs suggest some degree of co - fractal behavior , but no significant correlation over short time scales for the maintained discharge ( figs . 6d and 6f ) . since the two corresponding rgc spike trains do not appear co - fractal nearly to the degree shown by the lgn recordings , the co - fractal component must be imparted at the lgn itself . this suggests that the lgn discharges may experience a common fractal modulation , perhaps provided from the parabrachial nucleus in the brain stem , which engenders co - fractal behavior in the lgn spike trains . although similar data for the dark discharge are not available , the tight linkage between rgc and lgn firing patterns in that case ( fig . 3 ) suggests that a common fractal modulation may not be present in the absence of a stimulus , and therefore that discharges from nearby lgn cells would in fact not be co - fractal ; this remains to be experimentally demonstrated . correlations in the spike trains of relatively distant pairs of cat lgn cells have been previously observed in the short term for drifting - grating stimuli @xcite ; these correlations have been ascribed to low - threshold calcium channels and dual excitatory / inhibitory action in the corticogeniculate pathway @xcite . in the context of information transmission , the lgn may modulate the fractal character of the spike trains according to the nature of the stimulus present . under dark conditions , with no signal to be transmitted , the lgn appears to pass the fractal character of the individual rgcs on to more central stages of visual processing , which could serve to keep them alert and responsive to all possible input time scales . if , as appears to be the case , the responses from different rgcs do not exhibit significant correlation with each other , then the lgn spike trains also will not , and the ensemble average , comprising a collection of lgn spike trains , will display only small fluctuations . in the presence of a constant stimulus , however , the lgn spike trains develop significant degrees of co - fractal behavior , so that the ensemble average will exhibit large fluctuations @xcite . such correlated fractal behavior might serve to indicate the presence of correlation at the visual input , while still maintaining fluctuations over all time scales to ready neurons in later stages of visual processing for any stimulus changes that might arrive . finally , a similar behavior obtains for a drifting - grating stimulus , but with somewhat reduced fractal fluctuations ; perhaps the stimulus itself , though fairly simple , serves to keep more central processing stages alert . fractal behavior is present in all 50 of the rgc and lgn neural spike - train pairs that we have examined , under dark , maintained - discharge , and drifting - grating stimulus conditions , provided they are of sufficient length to manifest this behavior . indeed , fractal behavior is ubiquitous in sensory systems . its presence has been observed in cat striate - cortex neural spike trains @xcite ; and in the spike train of a locust visual interneuron , the descending contralateral movement detector @xcite . it is present in the auditory system @xcite of a number of species ; primary auditory ( viii - nerve ) nerve fibers in the cat @xcite , chinchilla , and chicken @xcite all exhibit fractal behavior . it is exhibited at many biological levels , from the microscopic to the macroscopic ; examples include ion - channel behavior @xcite , neurotransmitter exocytosis at the synapse @xcite , and spike trains in rabbit somatosensory - cortex neurons @xcite and mesencephalic reticular - formation neurons @xcite . in almost all cases , the upper limit of the observed time over which fractal correlations exist is imposed by the duration of the recording . the significance of the fractal behavior is not fully understood . its presence may serve as a stimulus to keep more central stages of the sensory system alert and responsive to all possible time scales , awaiting the arrival of a time - varying stimulus whose time scale is _ a priori _ unknown . it is also possible that fractal activity in spike trains provides an advantage in terms of matching the detection system to the expected signal @xcite since natural scenes have fractal spatial and temporal noise @xcite .

the presentation of a constant , uniform luminance to the eye reduces the fractal fluctuations in the rgc maintained discharge but enhances them in the target lgn discharge , so that neural activity in the pair no longer mirror each other . , the discharges of pairs of lgn cells are highly correlated over long time scales ; in contrast discharges of rgcs are nearly uncorrelated with each other . this indicates that action - potential activity at the lgn is subject to a common fractal modulation to which the rgcs are not subjected .

we employ a number of statistical measures to characterize neural discharge activity in cat retinal ganglion cells ( rgcs ) and in their target lateral geniculate nucleus ( lgn ) neurons under various stimulus conditions , and we develop a new measure to examine correlations in fractal activity between spike - train pairs . in the absence of stimulation ( i.e. , in the dark ) , rgc and lgn discharges exhibit similar properties . the presentation of a constant , uniform luminance to the eye reduces the fractal fluctuations in the rgc maintained discharge but enhances them in the target lgn discharge , so that neural activity in the pair no longer mirror each other . a drifting - grating stimulus yields rgc and lgn driven spike trains similar in character to those observed in the maintained discharge , with two notable distinctions : action potentials are reorganized along the time axis so that they occur only during certain phases of the stimulus waveform , and fractal activity is suppressed . under both uniform - luminance and drifting - grating stimulus conditions ( but not in the dark ) , the discharges of pairs of lgn cells are highly correlated over long time scales ; in contrast discharges of rgcs are nearly uncorrelated with each other . this indicates that action - potential activity at the lgn is subject to a common fractal modulation to which the rgcs are not subjected .

astro-ph0004309

i

galaxy clusters are the youngest and largest organized structures in the universe , and as such provide us with a wealth of cosmological information . the most massive clusters draw their substance from cosmologically significant volumes of linear scale @xmath7 mpc . these scales are large enough that no known coherent process competes against gravity , so rich cluster contents are thought to comprise a fair sample of the universe s ingredients ( white 1993 ) . because clusters are rare nonlinear excursions of the cosmic density field , the statistical properties of their population are quite sensitive to both cosmological model and slope of the primordial fluctuation spectrum . unfortunately , their relative youth can also make interesting physical properties difficult to measure : about 50% of the local population bears evidence of ongoing mergers , and the canonical `` relaxed '' cluster is a relatively rare beast . nearly all interesting cosmological tests depend on accurate measurement of cluster virial masses . observations of the intracluster medium ( icm ) have shown promise in this regard : the icm s high x - ray luminosity and large spatial extent make it possible to probe the content and structure of clusters in great detail . bulk properties of the icm such as luminosity , temperature , mass , and gas density profile shape have been found to display highly significant correlations with each other ( edge & stewart 1991 ; david 1993 ; mohr & evrard 1997 ; mushotzky & scharf 1997 ; markevitch 1998 ; allen & fabian 1998 ; mohr , mathiesen & evrard 1999 ; arnaud & evrard 1999 ) . in contrast to the noisy correlations of early x - ray data ( sarazin 1986 and references therein ) , many correlations now display scatter at the @xmath8 level , indicating that a high degree of physical uniformity exists even in this structurally diverse population . hydrodynamic simulations of cluster evolution predict tight relationships between observable quantities and between those quantities and the cluster binding mass ( evrard 1990 ; kang 1994 ; navarro , frenk & white 1995 ; evrard 1996 ; bryan & norman 1998 ) , even when some members of the sample are far from dynamical equilibrium . the existence of both observed and theoretical correlations implies that the prevalence of cluster substructure is not a fundamental barrier to interpreting the properties of the population . however , moderate biases caused by the presence of substructure are likely to be present , and we explore the role of substructure in temperature measurements of the icm in this paper . a previous paper ( mathiesen , evrard & mohr 1999 ) demonstrated that a icm clumping leads to a modest ( @xmath9 ) overestimate of icm masses derived under the typical assumptions of spherical symmetry and isothermality . as the x ray data improve , the limits of simplifying assumptions such as these become clearer . high - resolution x ray images reveal secondary peaks and strong asphericities in many clusters and x ray spectra indicate the presence of multiple temperature components within the cores of many clusters ( fabian 1994 , holzapfel 1997 , allen 2000 ) . chandra _ and _ xmm _ satellite missions will provide the most detailed maps of the icm emission and temperature structure yet obtained and will allow more precise definition of the limitations of the current models . three - dimensional hydrodynamical simulations of cluster formation can help bridge the gap between the new generation of data and traditional methods and results . while simulated clusters often do not include many processes thought to be important to icm evolution ( e.g. radiative cooling and galactic winds ) , they excel at the creation of populations with realistic merger histories ( mohr 1995 ; tsai & buote 1996 ) . ensembles of simulated clusters can therefore be used to investigate the effects of accretion events , major mergers , clumping , and substructure on measurements of the icm . in this paper , we analyze the spectral properties of an ensemble of 24 simulated clusters using a realistic plasma emission model and assuming a uniform metallicity @xmath10 times the solar abundance . we find that even minor accretion events can significantly bias our measurements of the mean , mass - weighted cluster temperature , and that clusters undergoing a major merger can sometimes be identified as extreme examples of this bias . section 2 of this paper describes the simulations , the cluster ensemble , and the process of creating our spectral images . section 3 discusses the various measures of cluster temperature which have seen frequent use and explores the relationships between them . in particular we explore the relationship between spectrally determined temperatures and the mass - weighted mean temperature . the latter is found in simulations to follow most closely the virial relationship . section 4 then delves into cluster dynamics , investigating the effects of a major merger on the icm and looking for observable signatures of the merging process . finally , section 5 summarizes our conclusions .

we employ an ensemble of 24 hydrodynamic cluster simulations to create spatially and spectrally resolved images of quality comparable to _ chandra _ s expected performance . emission from simulation mass elements is represented using the xspec ` m`ekal program assuming 0.3 solar metallicity and the resulting spectra are fit with a single - temperature model . despite significant departures from isothermality in the cluster gas , single - temperature models produce acceptable fits to 20,000 source photon spectra .

we employ an ensemble of 24 hydrodynamic cluster simulations to create spatially and spectrally resolved images of quality comparable to _ chandra _ s expected performance . emission from simulation mass elements is represented using the xspec ` m`ekal program assuming 0.3 solar metallicity and the resulting spectra are fit with a single - temperature model . despite significant departures from isothermality in the cluster gas , single - temperature models produce acceptable fits to 20,000 source photon spectra . the spectral fit temperature is generally lower than the mass weighted average temperature due to the influence of soft line emission from cooler gas being accreted as part of the hierarchical clustering process . the nature of this deviation depends on the bandpass used for spectral fitting . in a _ chandra_-like bandpass of 0.5 to 9.5 kev we find a nearly uniform fractional bias of , although smaller clusters sometimes demonstrate much greater deviations . if the minimum energy threshold is raised to 2 kev , however , the effect of line emission on the spectrum is greatly decreased and becomes a nearly unbiased estimator of for smaller clusters . the fractional deviation in relative to is scale - dependent in this bandpass and follows the approximate relation . this results in an observed relationship for the simulations with slope of about 1.6 , intermediate between the virial relation and the observed relation . tracking each cluster in the ensemble at 16 epochs in its evolutionary history , we catalogue merger events with mass ratios exceeding 10% in order to investigate the relationship between spectral temperature and proximity to a major merger event . clusters that are very cool relative to the mean mass - temperature relationship lie preferentially close to a major merger , suggesting a viable observational method to cull a subset of dynamically young clusters from the general population .

astro-ph0211175

i

in the absence of gradients of velocity and magnetic field in the resolution element , the polarization emerging from an atmosphere must be either symmetric or antisymmetric with respect to the central wavelength of each spectral line ( e.g. , @xcite @xcite ; @xcite @xcite ) . the polarization observed in the solar photosphere does not show such symmetries . asymmetric stokes profiles to represent the intensity , stokes @xmath2 and @xmath3 for the two independent types of linear polarization , and stokes @xmath0 for the degree of circular polarization . examples are given in figure [ full_vs_misma ] . ] arise from the quiet sun ( e.g. , @xcite @xcite ; @xcite @xcite ) , from plages and network regions ( e.g. , @xcite @xcite ; @xcite @xcite ) , as well as from sunspot penumbrae ( e.g. , @xcite @xcite ; @xcite @xcite ; @xcite @xcite ) . the fact that such asymmetries are found even when observing at the limit of present resolution suggests that a rich structuring remains unresolved to the current observations . because asymmetries carry information on the spatially unresolved properties of the photospheric plasma , their study and correct interpretation offers a chance to overcome the limitations imposed by the angular resolution , and to retrieve information inaccessible to direct imaging . indeed , such possibility has been exploited during the last decade , always relying on a considerable amount of modeling and assumptions . in broad terms , one can distinguish two approaches depending on the size of the unresolved structures that are responsible for the asymmetries . the first approach assumes that the unresolved photospheric structures are actually on the verge of being resolved in broad - band images taken with the current instrumentation . the smallest detectable features are of the order of 0.2(or 150 km on the sun ) ; a size set by technical limitations of the present solar telescopes ( e.g. , @xcite @xcite ) . several models of this kind have been proposed to explain asymmetries in special cases like penumbrae , plage and network regions , and in the quiet sun ( e.g. , @xcite @xcite ; @xcite @xcite ; @xcite @xcite ; @xcite @xcite ) . for example , @xcite ( @xcite ) invokes special thermal structures ( temperature inversion ) within magnetic regions in order to explain some extreme stokes @xmath0 shapes frequently observed in the quiet sun . the distinctive feature of this approach is that the proposed configurations ( thermal , magnetic or kinetic ) are specific to the case under study . the fact that asymmetries occur everywhere is therefore difficult to explain within this framework . the second approach is more consonant with the ubiquity of the asymmetries in the polarization of photospheric lines . it assumes that the photospheric plasma is in a turbulent state and that small - scale structures both in velocity and magnetic field are present . order of magnitude estimates for the magnetic and kinetic reynolds numbers in the granulation indicate that the magnetic field could be structured on spatial scales as small as a few kilometers ( e.g. , @xcite @xcite ) . this picture is consistent with recent progress in dynamo theory suggesting that a substantial part of the magnetic field in the quiet sun could be generated locally by dynamo action driven by the granular flows ( @xcite @xcite ; @xcite @xcite ; @xcite @xcite ; @xcite @xcite ) . this second approach is also supported by certain observations indicating that the magnetic field is structured on spatial scales below the resolution limit of current telescopes ( e.g. , @xcite @xcite ; @xcite @xcite ; @xcite @xcite ) . based on these premises , it is reasonable to think of the asymmetries as the result of observing magnetic fields that vary spatially on scales much smaller than the mean - free - path of the photons . interpretations of stokes profiles taking into account this very fine structuring of the atmosphere have been carried out for several years ( @xcite @xcite ) . the model atmospheres used to fit the observed profiles consist of a collection of magnetic and non - magnetic components , each containing mild gradients to comply with the height variations of the mean photosphere , but interleaved in such a way as to produce large gradients along the line - of - sight ( @xcite @xcite ) . the appealing aspect of this approach is that asymmetries emerge spontaneously , and independently of the details of the model ; arising from correlations between the magnetic and the velocity fields of the various components ( e.g. , asymmetries occur if , on average , downflowing elements have low magnetic field strength ) . it is known that atmospheres with micro - structure reproduce all kinds of stokes profiles observed in the quiet sun , including network and inter - network ( in ) regions ( @xcite @xcite ; @xcite @xcite ) . these micro - structured magnetic atmospheres ( mismas ) portray a quiet sun with large amounts of unsigned magnetic flux and very complex magnetic topology ( very often two magnetic polarities coincide in a resolution element ) . in the present paper we take advantage of recent developments in the numerical modeling of surface dynamos to understand the origin of asymmetries in the line polarization . we use the magnetic and velocity fields from a set of numerical data generated to study the interaction between thermally driven turbulent convection and magnetic fields ( @xcite @xcite ; @xcite @xcite ) . although these numerical simulations were not designed for a detailed description of the solar photosphere , the complexity and ubiquity of its fields recall in many respects the magnetic quiet sun inferred from the observed asymmetries . assuming a milne - eddington ( me ) atmosphere for the thermodynamic variables we produce synthetic stokes profiles . thus , the asymmetries in the resulting profiles are directly related to the correlations between the velocity and the magnetic field that exist in the numerical data , but they are decoupled from the thermodynamic variables of the simulation . the comparison between the synthetic profiles and solar data shows that the synthetic spectra are frequently similar to the observed ones . such agreement suggests that the simulation includes some of the ingredients that characterize the quiet sun magnetic fields ; in particular , the correlations between magnetic field and velocity at the smallest spatial scales . on the other hand , discrepancies between synthetic and observed stokes profiles allow to identify missing ingredients and , consequently , to devise strategies to improve the simulations and the inversions . finally , following @xcite ( @xcite ) , one can use the synthetic profiles to estimate the angular resolution required to determine the basic properties of the magnetic structures present in the numerical simulation . this angular resolution may be of relevance to decide the specifications of new solar instruments . the work is organized as follows . the numerical data is briefly described in [ sec_mhd ] . the synthesis procedure is detailed in [ sec_spectra ] and includes two subsections : in [ seeing ] we characterize the angular resolution of the model observations , and in [ calibration ] we calibrate the synthetic magnetograms . the main results of the synthesis are analyzed in [ sec_results ] : the variation of the apparent flux of the region depending on the sensitivity and spatial resolution of the observation ( [ flux_density ] ) , the asymmetries of the stokes @xmath0 profiles ( [ asym ] ) , and the magnetic broadening of the intensity profiles ( [ broadening ] ) . hanle depolarization signals to be expected for @xmath14607 are worked out in [ hanle ] . [ telescope ] discusses the diameter of the ideal telescope needed to spatially resolve the simulations . finally , the implications of the present work are discussed in [ conclusions ] .

we employ the magnetic and velocity fields from turbulent dynamo simulations to synthesize the polarization of a typical photospheric line . the simulated magnetograms present a level of signal similar to that of the inter - network regions . this deficit may reflect the fact that the reynolds numbers of the numerical data are still far from solar values . this scenario has several important consequences .

we employ the magnetic and velocity fields from turbulent dynamo simulations to synthesize the polarization of a typical photospheric line . the synthetic stokes profiles have properties in common with those observed in the quiet sun . the simulated magnetograms present a level of signal similar to that of the inter - network regions . asymmetric stokes profiles with two , three and more lobes appear in a natural way . the intensity profiles are broadened by the magnetic fields in fair agreement with observational limits . furthermore , the hanle depolarization signals of the line turn out to be within the solar values . differences between synthetic and observed polarized spectra can also be found . there is a shortage of stokes asymmetries , that we attribute to a deficit of structuring in the magnetic and velocity fields from the simulations as compared to the sun . this deficit may reflect the fact that the reynolds numbers of the numerical data are still far from solar values . we consider the possibility that intense and tangled magnetic fields , like those in the simulations , exist in the sun . this scenario has several important consequences . for example , less than 10% of the existing unsigned magnetic flux would be detected in present magnetograms . the existing flux would exceed by far that carried by active regions during the maximum of the solar cycle . detecting these magnetic fields would involve improving the angular resolution , the techniques to interpret the polarization signals , and to a less extent , the polarimetric sensitivity .