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1409.3897

r

this paper mainly treats hypothesis testing in a bipartite quantum system and its @xmath4-copies extension . for this purpose , we firstly discuss hypothesis testing in a general quantum system @xmath9 and its @xmath4-copies extension . in quantum hypothesis testing , we consider two hypotheses , the null hypothesis and the alternative hypothesis . when a hypothesis consists of one element , it is called simple . otherwise , it is called composite . this paper mainly addresses simple hypotheses , but it discusses a composite hypothesis partially . here , we assume that the null hypothesis is a state @xmath10 and the alternative hypothesis is state @xmath11 . in the @xmath4-copies setting , the quantum system is given by @xmath12 . then , the null and alternative hypotheses are the states @xmath13 and @xmath14 . our decision is given by a two - valued povm consisting of two povm elements @xmath15 and @xmath16 , where @xmath17 is the identity operator on @xmath18 and @xmath15 is an positive - semi definite operator on @xmath18 . when the measurement outcome corresponds to @xmath15 , we judge an unknown state as @xmath14 , and when the measurement outcome is @xmath16 , we judge it as @xmath13 . thus , type-1 error is written as @xmath19 and type-2 error is written as @xmath20 the optimal type-2 error under the condition that the type-1 error is no more than a constant @xmath21 is written as @xmath22 now , we give the asymptotic properties of @xmath23 . for this purpose , we introduce the cumulative distribution function ( cdf ) of the standard normal distribution @xmath24 , the quantum relative entropy @xmath25 , and the quantities @xmath26 , and @xmath27 . then , we have the asymptotic expansions @xcite @xmath28 when @xmath29 . expansions ( [ 2 - 4 - 2 ] ) and ( [ 2 - 4 - 3 ] ) are called the stein - strassen and the hoeffding expansions , respectively . when @xmath10 and @xmath11 are commutative with each other , we have the more detailed expansion @xmath30 now , we proceed to the hypothesis testing on a bipartite quantum system and its @xmath4-copies extension , which is the main topic of this paper . a single copy of a bipartite hilbert space is written as @xmath31 , and its local dimensions are written as @xmath32 and @xmath33 . we use notations like @xmath34 , @xmath35 , @xmath36 , @xmath37 , @xmath38 , and @xmath39 for identity operations on @xmath40 , @xmath41 , @xmath42 , @xmath43 , @xmath44 , and @xmath45 , respectively . when it is easy to identify the domain of an identity operator , we abbreviate them to @xmath46 hereafter . in this paper , we define @xmath47 as @xmath48 and consider asymptotic hypothesis testing between @xmath4-copies of an arbitrary known pure - bipartite state @xmath0 with the schmidt decomposition as @xmath49 and @xmath4-copies of the completely mixed state ( or the white noise ) @xmath50 under the various restrictions on available povms : global povms , separable povms , one - way locc povms , and two - way locc povms @xcite . we choose the completely mixed state @xmath51 as a null hypothesis and the state @xmath52 as an alternative hypothesis . as variants of @xmath53 , the optimal type-2 error under the condition that the type-1 error is no more than a constant @xmath21 is written as @xmath54 where @xmath55 is either @xmath56 , @xmath57 , @xmath58 , and @xmath59 corresponding to classes of one - way locc , two - way locc , separable and global povms , respectively . here , we note that although @xmath56 , @xmath58 , and @xmath59 are compact sets , @xmath57 is not compact by its original definition @xcite . further , we denote the class of two - way loccs with @xmath1-round classical communication by @xmath60 . in this notation , @xmath61 is equivalent to @xmath56 . hence , in this paper , the class @xmath57 is defined as a closure of the set of all two - way locc povms , which involves infinite - step locc protocols as well @xcite . this definition of the class @xmath57 justifies the use of @xmath62 in eq.([eq def beta n c alpha rho sigma ] ) for @xmath63 . in the global povms @xmath59 , since @xmath64 as is shown in @xcite , we have @xmath65\\ \beta_{n , g}(e^{-nr}|\rho_{mix}\|\psi ) & = 1 \hbox { with } r \in ( \log d_a d_b , + \infty),\end{aligned}\ ] ] and the following expansions @xmath66 to discuss the remaining cases , we introduce the rnyi entropy @xmath67 of the reduced density of the entangled state @xmath0 and its derivative as follows . @xmath68 and @xmath69 is defined as the limit @xmath70 . by the rnyi entropy @xmath67 , the entropy of the entanglement @xmath71 , the schmidt rank @xmath72 @xcite , and the logarithmic robustness of entanglement @xmath73 @xcite are characterized as @xmath74 in the following , for the unified treatment , we only use the notation @xmath67 . we also prepare the quantity @xmath75 . then , our previous paper @xcite shows the following propositions . the stein bounds are given as follows . * theorem 2 ) for a given @xmath76 , there exists a sufficiently large number @xmath77 such that @xmath78 for @xmath79 . further , for a given @xmath76 , we have the following expansion . @xmath80 the hoeffding bounds are characterized as follows . * ( 40 ) and ( 110 ) ) we have the following relation . @xmath81 this relation implies the following equation for @xmath82 : @xmath83 further , when @xmath84 , we have @xmath85 in this subsection , we give a short description of the main results of this paper . as a refinement of proposition [ pro1 ] , we obtain the following theorem for stein - strassen bounds . define the function @xmath86 . let @xmath47 be the lattice span for the distribution given by the schmidt coefficient of @xmath87 . for a given @xmath76 , we have the following expansions . @xmath88 relations ( [ 2 - 5 - 7 ] ) and ( [ 2 - 5 - 8 ] ) show that the difference between @xmath89 and @xmath90 exists only on the order of @xmath5 . for the hoeffding bounds of two - way locc and separable cases , we obtain the following theorem . @xmath91 this theorem concludes that the chernoff bound for the two - way locc case equals that for the separable case , which was an open problem in the previous paper @xcite . since @xmath92 monotonically decreases for @xmath93 , the supremum @xmath94 is realized with @xmath95 when @xmath96 . in this case , the hoeffding bounds for two - way locc and separable cases coincide with the right hand side of . since the convexity of @xmath97 implies that @xmath98 this argument can be regarded as an extension of in proposition [ pro2 ] . the right hand sides of and are numerically calculated as shown in figs . [ g1 ] and [ g2 ] when the pure entangled state @xmath0 is given as a pure state @xmath99 : @xmath100 where @xmath101 satisfies @xmath102 . the graphs in figs . [ g1 ] and [ g2 ] show the typical points @xmath103 and @xmath104 on the horizontal line and @xmath105 , @xmath106 , and @xmath107 on the vertical line . note that @xmath108 is a product state and @xmath109 is a maximally entangled state . the results in figs . [ g1 ] and [ g2 ] show that two - way locc improves the hoeffding bound when @xmath110 is large .

we consider asymptotic hypothesis testing ( or state discrimination with asymmetric treatment of errors ) between an arbitrary fixed bipartite pure state and the completely mixed state under one - way locc ( local operations and classical communications ) , two - way locc , and separable povms . as a result

we consider asymptotic hypothesis testing ( or state discrimination with asymmetric treatment of errors ) between an arbitrary fixed bipartite pure state and the completely mixed state under one - way locc ( local operations and classical communications ) , two - way locc , and separable povms . as a result , we derive the hoeffding bounds under two - way locc povms and separable povms . further , we derive a stein s lemma type of optimal error exponents under one - way locc , two - way locc , and separable povms up to the third order , which clarifies the difference between one - way and two - way locc povm . our study gives a very rare example in which the optimal performance under the infinite - round two - way locc is also equal to that under separable operations and can be attained with two - round communication , but not attained with the one - way locc .

math0105111

i

let @xmath4 denote the space of ( ordered ) partitions of @xmath5 , that is @xmath6 by _ size - biased _ sampling according to a point @xmath7 we mean picking the @xmath8-th part @xmath9 with probability @xmath9 . the starting point for our study is the following markov chain on @xmath4 , which we call a _ coagulation - fragmentation _ process : size - bias sample ( with replacement ) two parts from @xmath10 . if the same part was picked twice , split it ( uniformly ) , and reorder the partition . if different parts were picked , merge them , and reorder the partition . we call this markov chain the _ basic chain_. we first bumped into it in the context of triangulation of random riemann surfaces @xcite . it turns out that it was already considered in @xcite , in connection with `` virtual permutations '' and the poisson - dirichlet process . recall that the poisson - dirichlet measure ( with parameter 1 ) can be described as the probability distribution of @xmath11 on @xmath4 obtained by setting @xmath12 , @xmath13 , and reordering the sequence @xmath14 , where @xmath15 is a sequence of i.i.d.uniform[0,1 ] random variables . tsilevich showed in @xcite that the poisson - dirichlet distribution is an invariant probability measure for the markov chain described above , and raised the question whether such an invariant probability measure is unique . while we do not completely resolve this question , a corollary of our results ( c.f . theorem [ theo - uniq ] ) is that the poisson - dirichlet law is the unique invariant measure for the basic chain which satisfies certain regularity conditions . of course , the question of invariant probability measure is only one among many concerning the large time behavior of the basic chain . also , it turns out that one may extend the definition of the basic chain to obtain a poisson - dirichlet measure with any parameter as an invariant probability measure , generalizing the result of @xcite . we thus consider a slightly more general model , as follows . for any nonnegative sequence @xmath16 , let @xmath17 , the @xmath18 norm of @xmath19 , and @xmath20 . set @xmath21 and @xmath22 and @xmath23 . unless otherwise stated , we equip all these spaces with the topology induced from the product topology on @xmath24 . in particular , @xmath25 is then a compact space . for a topological space @xmath26 with borel @xmath3-field @xmath27 we denote by @xmath28 the set of all probability measures on @xmath29 and equip it with the topology of weak convergence . @xmath30 denotes the space of all ( nonnegative ) measures on @xmath29 . define the following two operators , called the _ merge _ and _ split _ operators , on @xmath31 , as follows : @xmath32 note that the operators @xmath33 and @xmath34 preserve the @xmath18 norm . let @xmath35)$ ] be a probability measure on @xmath36 $ ] ( the _ splitting measure _ ) . for @xmath37 and @xmath38 $ ] , we then consider the markov process generated in @xmath25 by the kernel @xmath39 it is straightforward to check ( see lemma [ cont ] below ) that @xmath40 is feller continuous . the basic chain corresponds to @xmath41 $ ] , with @xmath42 . it is also not hard to check ( see theorem [ exists ] below ) that there always exists a @xmath43-invariant probability measure @xmath44 . basic properties of any such invariant probability measure are collected in lemma [ schteim ] and proposition [ prop ] . our first result is the following characterization of those kernels that yield invariant probability measures which are supported on finite ( respectively infinite ) partitions . to this end , let @xmath45 be the set of finite partitions . * ( support properties ) * [ theo - duo ] for any @xmath43-invariant @xmath44 , @xmath46=1&\mbox{\ if\ } & \int\frac{1}{x}\ d{\sigma}(x)\ < \ \infty\qquad\mbox{and}\\ \mu[s]=0&\mbox{\ if\ } & \int\frac{1}{x}\ d{\sigma}(x)\ = \ \infty.\end{aligned}\ ] ] transience and recurrence criteria ( which , unfortunately , do not settle the case @xmath41 $ ] ! ) are provided in the : * ( recurrence and transience ) * [ rectrans ] the state @xmath47 is positive recurrent for @xmath43 if and only if @xmath48 . if however @xmath49}\ dx<\infty\ ] ] then @xmath50 is a transient state for @xmath43 . we now turn to the case @xmath41 $ ] . in order to define invariant probability measures in this case , set @xmath51 for each @xmath52 consider the poisson process on @xmath53 with intensity measure @xmath54 which can be seen either as a poisson random measure @xmath55 on the positive real line or as a random variable @xmath56 taking values in @xmath57 whose distribution shall be denoted by @xmath58 , with expectation operator @xmath59 . ( indeed , @xmath60while @xmath61)=0 $ ] , and thus @xmath62 a.s . ) . a useful feature of such a poisson process is that for any borel subset @xmath63 of @xmath53 with @xmath64 , and conditioned on @xmath65 , the @xmath66 points in @xmath63 are distributed as @xmath66 independent variables chosen each according to the law @xmath67 . the poisson - dirichlet measure @xmath68 on @xmath4 is defined to be the distribution of @xmath69 . in other words , @xmath70 . in the case @xmath71 it coincides with the previously described poisson - dirichlet measure . see @xcite , @xcite and @xcite for more details and additional properties of poisson - dirichlet processes . we show in theorem [ theo - uniq ] below that , when @xmath41 $ ] , for each choice of @xmath72 there is a poisson dirichlet measure which is invariant for @xmath40 . we also show that it is , in this case , the unique invariant probability measure in a class @xmath73 , which we proceed to define . set @xmath74 and denote by @xmath75 the set of real valued functions on @xmath76 that coincide ( [email protected] . ) with a function which has a real analytic extension to some open neighborhood of @xmath78 . ( here and throughout , @xmath79 denotes the @xmath80-dimensional lebesgue measure ; all we shall use is that real analytic functions in a connected domain can be recovered from their derivatives at an internal point . ) for any @xmath81 and each integer @xmath80 , define the measure @xmath82 by @xmath83 \ , , \hspace{1cm}b\in{\mathcal b}_{\bar \omega_<^k}\ \,\ ] ] ( here @xmath84).an alternative description of @xmath85 is the following one : pick a random partition @xmath10 according to @xmath86 and then sample size - biased independently ( with replacement ) @xmath80 parts @xmath87 from @xmath10 . then , @xmath88 part of the proof of part ( b ) of theorem [ theo - uniq ] below will consist in verifying that these measures @xmath89 characterize @xmath86 ( see ( * ? ? ? 4 ) for a similar argument in a closely related context ) . set for @xmath90 , @xmath91 our main result is part ( b ) of the following : * ( poisson - dirichlet law ) * [ theo - uniq ] assume @xmath41 $ ] and fix @xmath92 . + ( a ) the poisson - dirichlet law of parameter @xmath93 belongs to @xmath94 , and is invariant ( in fact : reversing ) for the kernel @xmath40 . + ( b ) assume a probability measure @xmath95 is @xmath43-invariant . then @xmath86 is the poisson - dirichlet law of parameter @xmath93 . the structure of the paper is as follows : in section [ sec - pre ] , we prove the feller property of @xmath40 , the existence of invariant probability measures for it , and some of their basic properties . section [ sec - support ] and [ sec - trans ] are devoted to the proofs of theorems [ theo - duo ] and [ rectrans ] respectively , section [ sec - pois ] studies the poisson - dirichlet measures and provides the proof of theorem [ theo - uniq ] . we conclude in section [ concluding ] with a list of comments and open problems .

we consider markov chains on the space of ( countable ) partitions of the interval $ ] , obtained first by size biased sampling twice ( allowing repetitions ) and then merging the parts with probability ( if the sampled parts are distinct ) or splitting the part with probability according to a law ( if the same part was sampled twice ) . we characterize invariant probability measures for such chains . in particular , if is the uniform measure then the poisson - dirichlet law is an invariant probability measure , and it is unique within a suitably defined class of `` analytic '' invariant measures . we also derive transience and recurrence criteria for these chains .

we consider markov chains on the space of ( countable ) partitions of the interval $ ] , obtained first by size biased sampling twice ( allowing repetitions ) and then merging the parts with probability ( if the sampled parts are distinct ) or splitting the part with probability according to a law ( if the same part was sampled twice ) . we characterize invariant probability measures for such chains . in particular , if is the uniform measure then the poisson - dirichlet law is an invariant probability measure , and it is unique within a suitably defined class of `` analytic '' invariant measures . we also derive transience and recurrence criteria for these chains .

1602.00717

i

consider an open bounded domain @xmath1 ( @xmath2 ) . let @xmath3 be an operator defined as @xmath4 , where @xmath5 be a real @xmath6 matrix on @xmath7 that is bounded measurable and uniformly elliptic : that is , there exists a constant @xmath8 such that @xmath9 for all @xmath10 and @xmath11 . the matrix @xmath12 is not assumed to be symmetric . we say @xmath7 is regular for @xmath3 , if for any continuous function @xmath13 , the corresponding solution @xmath14 to the dirichlet problem @xmath15 is continuous in @xmath16 . in particular @xmath17 on the boundary in the classical sense . it was proved in @xcite that @xmath7 is regular for @xmath3 if and only if it is regular for the laplacian . assume @xmath7 is regular , then by the riesz representation theorem , for any @xmath11 there is a probability measure @xmath18 on @xmath19 such that @xmath20 for an arbitrary boundary value @xmath13 and its corresponding solution @xmath14 . the measure @xmath21 is called the elliptic measure ( harmonic measure if @xmath22 ) of @xmath7 at @xmath23 . from , we see that the information about the boundary behavior of solutions to dirichlet problem is encoded in the elliptic measure @xmath21 . if @xmath7 is connected , the elliptic measures @xmath21 and @xmath24 at different points @xmath25 are mutually absolute continuous , moreover they satisfy @xmath26 . thus for the problem we are concerned with , we just need to study the elliptic measure at a fixed point @xmath27 . denote @xmath28 . for lipschitz domains , by the work of @xcite , @xcite and @xcite , we know the elliptic measure @xmath29 and the solutions @xmath14 to enjoy numerous properties , most notably - ( see section [ sect : prelim ] ) . these pointwise estimates are important on their own , but they also serve as a toolkit to build global pde estimates for the solutions to the dirichlet problem . on the other hand , when the surface measure @xmath30 is well defined on @xmath19 , a natural question is : what is the relationship between the measures @xmath29 and @xmath30 ? in fact , the answer to this measure theoretic question is closely related to the boundary behavior of solutions to this pde problem . let @xmath7 be a regular domain such that the surface measure @xmath31 on the boundary is locally finite . here @xmath32 denotes the @xmath33-dimensional hausdorff measure restricted to @xmath19 . for @xmath34 , we say the problem is solvable in @xmath35 if there exists a universal constant @xmath36 such that for any boundary value @xmath13 and its corresponding solution @xmath14 , @xmath37 where @xmath38 is the maximal function of @xmath14 in the non - tangential cone @xmath39 ( the definition is specified in section [ sect : prelim ] ) . from we know @xmath40 is comparable to the hardy - littlewood maximal function @xmath41 with respect to @xmath29 . provided that @xmath30 is doubling , the theory of weights tells us that @xmath42 for the laplacian on lipschitz domains , dahlberg @xcite proved the harmonic measure @xmath43 ; therefore is solvable in @xmath35 for @xmath44 . when @xmath45 , follows trivially from the maximal principle . however , if @xmath22 and @xmath46 is the upper half plane , the problem is also solvable in the bmo space , that is , if @xmath47 , its harmonic extension @xmath14 has the property that @xmath48 is a carleson measure on @xmath7 ( see @xcite , and also section 4.4 theorem 3 of @xcite ) . in addition , the carleson measure norm of @xmath49 is equivalent to the bmo norm of @xmath50 . ( for the definition of carleson measure , see definition [ def : carl ] . ) this bmo solvability also holds for lipschitz domains , when @xmath49 is replaced by @xmath51 and @xmath52 ( see @xcite ) . recall @xmath53 is a quantitative version of absolute continuity with respect to @xmath30 , and that @xmath54 . ( see definition [ def : ainfty ] and its following paragraph . ) by the work of dahlberg , we know the elliptic measure @xmath55 if @xmath3 is a small perturbationof the laplacian ( see @xcite ) . later in @xcite , the smallness assumption was removed using harmonic analysis methods ( see also @xcite ) . more precisely , in @xcite the authors showed that if @xmath56 and @xmath57 is a perturbation of @xmath58 , then @xmath59 . assume the operator @xmath3 satisfies @xmath0 , then @xmath60 note that there is some ambiguity with @xmath61 : the fact that is not @xmath62 solvable does not necessarily imply @xmath63 . a natural question arises : is there a solvability criterion that directly characterizes @xmath0 ? in 2009 , dindos , kenig and pipher showed that for lipschitz domains , the elliptic measure @xmath64 if and only if the problem is bmo - solvable , i.e. for any continuous function @xmath13 , the carleson measure of @xmath65 is controlled by the bmo norm of @xmath50 ( see @xcite ) . the dirichlet problem has been studied on domains less regular than lipschitz ones , in particular @xmath66 domains , non - tangential accessible ( nta ) domains and uniform domains . these non - smooth domains arise naturally in free boundary problems and geometric analysis . roughly speaking , uniform domains are domains of which each ball centered at the boundary contains an interior ball comparable in size ( interior corkscrew condition , see definition [ def : icc ] ) and that satisfy a notion of quantified connectivity ( harnack chain condition , see definition [ def : hcc ] ) . nta domains are uniform domains whose exterior also satisfies the corkscrew condition . it is easy to see @xmath67 the notion of nta domain was introduced by jerison and kenig in the pioneer work @xcite , where they proved the set of properties - hold for the laplacian on nta domains . in @xcite the authors addressed the @xmath35 solvability of on chord - arc domains , i.e. nta domains with ahlfors regular boundary ( see definition [ def : adr ] ) . on the other hand , by the independent work of @xcite and @xcite , certain properties , notably the boundary comparison principle , are shown to hold for the laplacian on uniform domains ( the domains studied in the latter paper also require ahlfors regular boundary ) . in section [ sect : br ] we show that all the properties - hold for uniform domains with ahlfors regular boundary . moreover , we prove an equivalent characterization of the absolute continuity of elliptic measures by pde solvability condition : for uniform domains with ahlfors regular boundary , the elliptic measure @xmath0 if and only if the dirichlet problem is bmo solvable . in @xcite , the authors studied the geometric implication of the harmonic measure @xmath68 . for a uniform domain with ahlfors regular boundary , they showed @xmath69 which characterizes the absolute continuity of the harmonic measure from a geometric point of view . we should point out that some of the implications in had been proved earlier in @xcite , @xcite and @xcite . the complement of the four - corner cantor set inside a large ball @xmath70 is an example of a uniform domain with ahlfors regular boundary , whose boundary is purely unrectifiable . thus its harmonic measure @xmath71 by . our study of general elliptic operators raises the following question : if @xmath72 , is there a uniformly elliptic operator @xmath73 such that @xmath0 ? more generally , for a uniform domain with purely unrectifiable boundary , is there an @xmath3 such that @xmath0 ? if so , what geometric information does this carry , and can we characterize the corresponding matrix @xmath12 ? in this paper we assume quantified connectivity of the domain , in order to get a quantified characterization of the absolute continuity of @xmath29 with respect to @xmath30 , i.e. @xmath0 . recent work by several authors has addressed the question of the relation between @xmath29 and @xmath30 with no connectivity assumption on the domain . we refer interested readers to @xcite , @xcite and @xcite . the plan for this paper is as follows . we state the definitions and main theorem in section [ sect : prelim ] . in section [ sect : br ] we establish some preliminary lemmas for the elliptic measure and solutions to problem on uniform domains with ahlfors regular boundary . in section [ sect : showbmos ] we assume the elliptic measure is an @xmath74 weight with respect to the surface measure , and show the bmo solvability , i.e. the carleson measure of @xmath75 is bounded by the bmo norm of the boundary data . section [ sect : showainfty ] is devoted to the proof of @xmath0 under the assumption of the bmo solvability for . in section [ sect : converse ] we show that if @xmath0 , the converse to the carleson measure estimate holds .

we consider the dirichlet boundary value problem for divergence form elliptic operators with bounded measurable coefficients . we prove that for uniform domains with ahlfors regular boundary , the bmo solvability of such problems is equivalent to a quantitative absolute continuity of the elliptic measure with respect to the surface measure , i.e. . this generalizes a previous result on lipschitz domains by dindos , kenig and pipher ( see ) .

we consider the dirichlet boundary value problem for divergence form elliptic operators with bounded measurable coefficients . we prove that for uniform domains with ahlfors regular boundary , the bmo solvability of such problems is equivalent to a quantitative absolute continuity of the elliptic measure with respect to the surface measure , i.e. . this generalizes a previous result on lipschitz domains by dindos , kenig and pipher ( see ) .

1411.6284

i

the mean field theory provides in principle a fair approximation of time evolved quantum states by many - body schrdinger dynamics in the mean field scaling ; namely when the number of particles is large and the pair interaction potential is proportionally weak . during the last decade , a strong activity around the mean - field problem has occurred within the community of mathematical physics . this in particular have led to a rigorous justification of the mean field approximation for singular potentials including coulomb interaction as well as the derivation of the gross - pitaevskii equation from many - body quantum dynamics ( see for instance @xcite and also @xcite for older results ) . more recently , emphasis has been placed on the speed of convergence of the mean - field approximation . this seems to be motivated by providing useful quantitative bounds and understanding higher order corrections ( see @xcite ) . the aim of our article , is to give at the level of a simple model more insight on the aforementioned problem . actually , the rate of convergence is essentially understood in the case of coherent or factorized type states with a particular structure . so , we can ask the following natural questions : * what should we expect if we start from another prepared state which is more correlated ? * is the specific coherent structure of the known examples important ? * can we determine the optimal rate of convergence in some examples ? * does the rate of convergence improves under the effect of the quantum dynamics ? we will show that the rate of convergence at a given time depends essentially on the rate of convergence of all reduced density matrices of the prepared state at time @xmath2 . in fact , we are able to give a general condition on the prepared state that guaranties a given speed of convergence at any time . the assumption we require at time zero , which is rather easy to check in initial states , is true at any time if it holds at @xmath2 . this allows in particular to consider the question of improvement of the convergence over time while the question of optimality will be addressed through numerical analysis . consider for instance the many - body schrdinger hamiltonian of an @xmath0-boson system [ schrod ] _ n=_i=1^n-_x_i+ _ 1i < jn v(x_i - x_j ) , where @xmath3 and @xmath4 is a real bounded potential satisfying @xmath5 . the self - adjoint operator @xmath6 acts on the space @xmath7 of symmetric square integrable functions . a function @xmath8 is symmetric if @xmath9 for any permutation @xmath10 on the symmetric group @xmath11 . suppose that the system is in a prepared quantum state @xmath12 at initial time @xmath2 ( that is @xmath12 is a non - negative trace class operator with @xmath13=1 $ ] ) . so , under the action of the schrdinger dynamics the system at time @xmath14 evolves into the state @xmath15 the mean field approximation at the dynamical level is usually understood as the following picture : if the system is in an uncorrelated state @xmath16 , with @xmath17 , at initial time @xmath2 then it will evolve into a state close in some sense to an uncorrelated one @xmath18 when @xmath0 is large and @xmath19 is the solution of the nonlinear hartree equation @xmath20{l } i\partial_t \varphi_t=-\delta \varphi_t+(v*\left|\varphi_t\right|^{2})\varphi_t\,,\\ \varphi_{t=0}=\varphi\ , . \end{array } \right.\end{aligned}\ ] ] the above convergence is neither a strong nor a weak one but rather in the sense of reduced density matrices . more precisely , the convergence is understood as _ n= _ t^p , a _ t^p_l^2(^dp ) , for any bounded ( or compact ) operator @xmath21 on @xmath22 and any @xmath23 ( @xmath24 is kept fixed while @xmath25 ) . + in some sense , the mean field approximation says essentially that the measurements [ correl ] , np , for any observable @xmath21 on @xmath26 converge , when @xmath0 goes to infinity while @xmath24 is kept fixed , to some classical or one particle quantities to be determined . hence , the main quantities to be analyzed are the reduced density matrices of the time evolved states @xmath27 . recall that for each @xmath28 , the @xmath24-reduced density matrix of @xmath27 is the unique non - negative trace class operator @xmath29 on @xmath30 satisfying [ eq.1 ] = , for any bounded operator @xmath21 on @xmath26 . therefore , the point is to determine for each @xmath28 the limit and the rate of convergence of these quantities when the number of particles @xmath0 goes to infinity . it turns out that the limit at @xmath2 may not exist and actually there is a difference between requiring convergence in for all bounded operators @xmath21 on @xmath26 , or convergence for compact operators only , since the weak and weak-@xmath31 topologies differ on the space of trace - class operators . however , one can characterize all the limit points of @xmath32 with respect to the weak-@xmath31 topology in the space of trace - class operators ( which is the dual space of compact operators ) and also describe their structure . indeed , at time @xmath2 , we can show that there exists always a subsequence @xmath33 such that for each @xmath34 , @xmath35 , the reduced density matrices @xmath36 converge to non - negative trace - class operators @xmath37 in the weak-@xmath31 topology . moreover , there exists a borel probability measure @xmath38 on @xmath39 such that @xmath40 in this way we have characterized all the possible limit points via subsequences of the reduced density matrices @xmath32 and identified their structure . more details are given in subsection [ sub.wigner ] while here we summarize the main result in the proposition below . we will use often the notation @xmath41 , @xmath42 , to refer to the schatten classes with @xmath43 denoting their norms . [ definetti ] let @xmath44 be a sequence of density matrices with @xmath45 for each @xmath46 . suppose that for any @xmath23 and each compact operator @xmath47 the sequence @xmath48)_{n\in{{\mathbb{n}}}^*}$ ] converges . then there exists a unique borel probability measure @xmath49 on @xmath39 invariant with respect to the unitary group @xmath50 and such that for any @xmath23 and any @xmath47 , _ ^(p)=_l^2(^d ) |z^pz^p| d_0(z ) . moreover , the measure @xmath49 is concentrated on the unit ball @xmath51 of @xmath39 centered at the origin and of radius one ( i.e. : @xmath52 . actually , the measure @xmath49 is the unique wigner measure of the sequence @xmath53 ( see subsection [ sub.wigner ] for definition and details ) . once this is understood we can consider the problem of rate of convergence for more general correlated states . [ main - th ] let @xmath54 be a sequence of positive numbers with @xmath55 and such that @xmath56 is bounded . let @xmath44 and @xmath57 be two sequences of density matrices with @xmath45 and @xmath58 for each @xmath59 . assume that there exist @xmath60 , @xmath61 and @xmath62 such that for all @xmath59 with @xmath63 : [ init - ineq ] ^(p)_n-_^(p)_1 c_0 . then for any @xmath64 there exists @xmath65 such that for all @xmath66 $ ] and all @xmath67 with @xmath63 , [ main - ineq ] ^(p)_n(t)-_^(p)(t)_1 c_t , where _ ^(p)(t)=_l^2(^d ) |z^pz^p| d_t(z ) , with @xmath68 is the push - forward of the initial measure @xmath49 ( given in proposition [ definetti ] ) by the well defined and continuous hartree flow @xmath69 on @xmath39 of the equation ( given in subsection [ sec.classical-quantum ] ) . * our result holds true in a more general framework . we can replace @xmath39 by any separable hilbert space @xmath70 , @xmath71 by any self - adjoint operator @xmath72 , and @xmath4 by any two - particle bounded interaction ( see subsection [ sec.classical-quantum ] ) . so from now on we will consider this setting , which has the advantage of covering several situations : e.g. either finite or infinite dimensional systems , as well as semi or non relativistic ones . * the assumption implies that we can apply proposition [ definetti ] and hence obtain the existence of the initial measure @xmath49 at @xmath2 . * the condition @xmath61 in the main assumption of theorem [ main - th ] can be replaced by @xmath73 at the cost of slightly changing the conclusion , by replacing @xmath74 in by @xmath75 . * we can apply theorem [ main - th ] backward in time . so , if the estimates hold true at a given time @xmath14 , then should also hold at time @xmath2 . this answers the question of improvement of the rate of convergence under the action of the quantum evolution . indeed , if we suppose that inequalities hold with a faster rate of convergence @xmath76 , @xmath77 , then the `` initial '' estimate should also hold with @xmath76 instead of @xmath78 by backward evolution . * the proof of theorem [ main - th ] allows to start with a rate of convergence @xmath78 faster than @xmath1 at time @xmath2 . however , we ca nt recover a better convergence at time @xmath79 . this is why we have restricted @xmath78 to be of order @xmath0 or less . however , this feature do not seem to be an artefact of the proof : numerical simulations on product states indicate a @xmath1 order of convergence even when at time @xmath2 the reduced density matrices coincide with their limit . the mathematical analysis of the mean field limit is quite rich and indeed there are several approaches and techniques applicable to this problem . for example coherent states analysis @xcite , bbgky hierarchy method @xcite , egorov type theorem @xcite , wigner measures approach @xcite or deviation estimates @xcite . hence the combination of these different techniques may lead to interesting results . the proof of our main theorem [ main - th ] relies on two ingredients : an egorov type theorem proved in @xcite and a wigner measures characterization of the limit points of reduced density matrices studied in @xcite . so the first step is to use second quantization formalism and wick observables , then the result in @xcite provides the asymptotics of time - evolved wick observables as [ int - expa ] e^it _ n b^wick e^-it _ n _ |l^2_s(^dn)=b(t)^wick _ |l^2_s(^dn)+r(n ) , where @xmath80 in some specific sense and where @xmath81 is an infinite sum of wick operators with time - dependent kernels or symbols ( see subsections [ sub.wick ] and [ sub.expansion ] ) . the mean field expansion gives actually the convergence of the correlation functions ( [ eq.1 ] ) . so that , if we use the idea of wigner measures extended to this framework in @xcite , we can obtain the rate of convergence for the quantities ( [ eq.1 ] ) . once this is proved , one can get the announced trace norm estimates for the difference between reduced density matrices . the article is organized as follows . the second quantization formalism and wick symbolic calculs is recalled in subsection [ sub.wick ] . the mean field expansion is explained in subsection [ sub.expansion ] while the the quantum and classical dynamics are introduced in subsection [ sec.classical-quantum ] . in section [ sec : rdm ] , we analyse the relationship between reduced density matrices ( rdm ) and wigner measures and provide the proof of proposition [ definetti ] . our main result is proved in section [ sec.rate ] with some preliminary lemmas . examples and numerical simulations are discussed in the last section [ sec.ens ] .

we consider the time evolution of quantum states by many - body schrdinger dynamics and study the rate of convergence of their reduced density matrices in the mean field limit . if the prepared state at initial time is of coherent or factorized type and the number of particles is large enough then it is known that is the correct rate of convergence at any time . we show in the simple case of bounded pair potentials that the previous rate of convergence holds in more general situations with possibly correlated prepared states . in particular , it turns out that the coherent structure at initial time is unessential and the important fact is rather the speed of convergence of all reduced density matrices of the prepared states . we illustrate our result with several numerical simulations and examples of multi - partite entangled quantum states borrowed from quantum information . : 81s30 , 81s05 , 81t10 , 35q55 , 81p40 + : mean field limit , reduced density matrices , wigner measures , entangled quantum states .

we consider the time evolution of quantum states by many - body schrdinger dynamics and study the rate of convergence of their reduced density matrices in the mean field limit . if the prepared state at initial time is of coherent or factorized type and the number of particles is large enough then it is known that is the correct rate of convergence at any time . we show in the simple case of bounded pair potentials that the previous rate of convergence holds in more general situations with possibly correlated prepared states . in particular , it turns out that the coherent structure at initial time is unessential and the important fact is rather the speed of convergence of all reduced density matrices of the prepared states . we illustrate our result with several numerical simulations and examples of multi - partite entangled quantum states borrowed from quantum information . : 81s30 , 81s05 , 81t10 , 35q55 , 81p40 + : mean field limit , reduced density matrices , wigner measures , entangled quantum states .

0903.3108

i

the observation @xcite of a fractional quantum hall ( fqh ) state at @xmath0 and suggestion @xcite that the moore - read pfaffian ( mr ) state @xcite might occur at this filling fraction gave the first real indication that non - abelian topological phases of matter might actually occur in nature . the striking feature of such new phases is that they possess quasiparticle excitations with exotic non - abelian braiding statistics @xcite . this property makes non - abelian topological phases appealing for their potential use as intrinsically fault - tolerant media for quantum information processing @xcite . recent experimental studies of transport through a point contact in fqh systems at @xmath0 gave evidence that there are charge @xmath4 quasiparticles in this state @xcite and found that the dependence of the current on voltage and temperature is most consistent @xcite with two particular non - abelian models : the anti - pfaffian ( @xmath6 ) state @xcite and the su@xmath1 naf ( non - abelian fqh ) state @xcite . however , these results are not conclusive because the @xmath3 state @xcite , which is abelian , also supports charge @xmath4 quasiparticles . it is also roughly consistent with the voltage and temperature dependence of tunneling found in ref . and , in any case , one might expect non - universal physics to have a significant effect on the observed dependence . thus , there is a glaring need for experiments which directly probe the braiding statistics of quasiparticles . in order to probe braiding statistics in fqh systems , one can use a double point - contact interferometer , as proposed in ref . for abelian states and later considered for the @xmath0 state in refs . . such interferometers can play a crucial role in properly identifying which phase a fqh state is in by providing information about the topological @xmath7-matrix , a mathematical quantity related to the braiding statistics that is strongly characteristic of the topological order ( for more details , see ref . ) . interferometers are also important for the implementation of topological quantum computation @xcite because they can be used for the topological charge measurements necessary for readout of qubits @xcite and , through adroit manipulation , can even be used to implement computational gates @xcite . fortunately , there have been recent advances in realizing quantum hall interferometers at integer filling @xcite and fractional filling in the lowest landau level @xcite . even more recently , double point - contact interferometers have been experimentally implemented for the @xmath0 fqh state @xcite . in this paper , we study the signatures of non - abelian statistics which can be seen in a double point - contact interferometer and discuss other effects which can mimic these signatures . we propose further experiments which can help disentangle the effects of non - abelian statistics from coulomb blockade and disorder physics . the paper is structured as follows : in section [ sec : experiment ] , we describe the basic features of the experiment of willett _ et al . _ @xcite . in section [ sec : interpretations ] , we explain three different interpretations of this experiment : ( a ) non - abelian interferometry , ( b ) coulomb blockade , and ( c ) possible explanations loosely grouped together because they depend on non - linear dependence of the interferometer area on the side gate voltage @xmath8 . in section [ sec : critical ] , we criticize each of these three interpretations . we argue that , while all three interpretations have problems , the problems with ( b ) and ( c ) are more serious and these explanations are less likely to be correct . in section [ sec : proposals ] , we propose further experiments which might further strengthen or rule out interpretation ( a ) . in section [ sec : discussion ] , we comment on the implications of this experiment for topological quantum computation , assuming that the non - abelian interference interpretation is correct . in the two appendices , we give predictions for interference experiments at other suspected non - abelian fractions and we argue that the bare backscattering amplitude for @xmath4 quasiparticles should be much larger than that for @xmath5 quasiparticles .

we compare the predictions of several different models of the state of the electrons at this plateau : the moore - read , anti - pfaffian , su naf , strong pairing , and states . et al . we suggest further experiments which could help rule out some possible scenarios .

we consider the tunneling current through a double point - contact fabry - prot interferometer such as used in recent experimental studies of the fractional quantum hall plateau at filling fraction . we compare the predictions of several different models of the state of the electrons at this plateau : the moore - read , anti - pfaffian , su naf , strong pairing , and states . all of these predict the existence of charge quasiparticles , but the first three are non - abelian while the last two are abelian . we give explicit formulas for the scaling of charge and charge quasiparticle contributions to the current as a function of temperature , gate voltage and distance between the two point contacts for all three models . based on these , we analyze several possible explanations of two phenomena reported for recent experiments by willett _ et al . _ , namely halving of the period of the observed resistance oscillations with rising temperature and alternation between the same two observed periods at low temperatures as the area of the interference loop is varied with a side gate . we conclude that the most likely explanation is that the observed alternation is due to switching between even and odd numbers of charge quasiparticles enclosed within the loop as a function of side gate voltage , which is a clear signature of the presence of non - abelian anyons . however , there are important features of the data which do not have a simple explanation within this picture . we suggest further experiments which could help rule out some possible scenarios . we make the corresponding predictions for future tunneling and interference experiments at the other observed second landau level fractional quantum hall states . `` with luck , we might see a non - abelian interferometer within a year . '' attributed to kirill shtengel , april 16 , 2008 in _ quantum computation : the dreamweaver s abacus _ .

0903.3108

c

we close this discussion by assuming , for a moment , that the experiments of refs . are , in fact , performing interferometry on the @xmath0 state of the sort envisioned in refs . and are detecting non - abelian quasiparticles . what forecast would these results give for topological quantum computation @xcite ? certainly , it would be encouraging that a non - abelian topological state , the _ sine qua non _ for topological quantum computing , would be found . one potential source of concern is the appearance of some seemingly unpredictable phase disruptions , which would make it difficult to distinguish the two states of a topological qubit , which differ by a @xmath35 phase shift in their ( @xmath4 oscillation ) interference patterns . however , if further investigation shows that they are @xmath141 phase shifts ( in the type i regions ) , then they may be attributable to @xmath5 quasiparticles or pairs of @xmath4 quasiparticles simultaneously entering or exiting the interference loop , and it would be a manageable problem . on the other hand , if they turn out to be @xmath35 phase shifts in the @xmath4 oscillations , then they could be attributed to either tunneling of a @xmath4 quasiparticle from one edge to the other between bulk quasiparticles within the interferometry region , or tunneling of an electrically neutral fermion between the edge and a bulk quasiparticle within the interferometry region . either of these @xmath35 phase shifting processes would cause errors in topological qubits , so if we attribute all the observed phase disruptions to such processes , this gives a crude estimate of about an hour for the time scale for such errors , or a contribution to the topological qubit error rate of @xmath153 . to better determine the rate of such errors , one could simply tune the voltage to a local @xmath4 oscillation maximum / minimum of the tunneling current in a type i region and time average duration it takes for the current to jump to a lower / higher value ( i.e. experiencing a @xmath35 phase shift to a minimum / maximum of the current ) . if the phase disruptions are neither @xmath141 nor @xmath35 phase shifts , then they would be a serious concern , as they would have no obvious explanation . finally , the apparent stability of the type i and type ii regions implies that thermally - activated charge @xmath4 quasiparticles do not move in and out of the interferometry region over the time scales of this experiment . indeed , these regions are stable on a time scale of a week , which would imply a topological qubit error rate from mobile bulk quasiparticles of @xmath154 . `` with luck , we might see a topological qubit within a year . '' attributed to kirill shtengel , january 9 , 2009 @xcite . we would like to thank r. willett for many important discussions and access to unpublished work , m. heiblum for a discussion of unpublished work , and s. das sarma , m. freedman , and y. gefen for helpful comments . wb , ks , and jks would like to acknowledge the support and hospitality of microsoft station q. pb , cn , and ks would like to acknowledge the hospitality of the aspen center for physics . cn and ks are supported in part by the darpa - quest program . ks is supported in part by the nsf under grants dmr-0748925 and phy05 - 51164 , and would like to acknowledge the hospitality of the kitp . jks is supported in part by the science foundation of ireland principal investigator grant 08/in.1/i1961 .

we make the corresponding predictions for future tunneling and interference experiments at the other observed second landau level fractional quantum hall states . `` with luck , we might see a non - abelian interferometer within a year . '' attributed to kirill shtengel , april 16 , 2008 in _ quantum computation : the dreamweaver s abacus _ .

we consider the tunneling current through a double point - contact fabry - prot interferometer such as used in recent experimental studies of the fractional quantum hall plateau at filling fraction . we compare the predictions of several different models of the state of the electrons at this plateau : the moore - read , anti - pfaffian , su naf , strong pairing , and states . all of these predict the existence of charge quasiparticles , but the first three are non - abelian while the last two are abelian . we give explicit formulas for the scaling of charge and charge quasiparticle contributions to the current as a function of temperature , gate voltage and distance between the two point contacts for all three models . based on these , we analyze several possible explanations of two phenomena reported for recent experiments by willett _ et al . _ , namely halving of the period of the observed resistance oscillations with rising temperature and alternation between the same two observed periods at low temperatures as the area of the interference loop is varied with a side gate . we conclude that the most likely explanation is that the observed alternation is due to switching between even and odd numbers of charge quasiparticles enclosed within the loop as a function of side gate voltage , which is a clear signature of the presence of non - abelian anyons . however , there are important features of the data which do not have a simple explanation within this picture . we suggest further experiments which could help rule out some possible scenarios . we make the corresponding predictions for future tunneling and interference experiments at the other observed second landau level fractional quantum hall states . `` with luck , we might see a non - abelian interferometer within a year . '' attributed to kirill shtengel , april 16 , 2008 in _ quantum computation : the dreamweaver s abacus _ .

1701.08367

c

in this work we have presented a systematic study of weakly interacting bosonic gases with local and non - local multi - body interactions in the bogoliubov approximation . we considered conservative multi - body interactions for which the number of particles is conserved : of course multi - body interactions are associated with the presence of particle losses @xcite , that we did not study , rather focusing on the determination of the stability conditions due to the competition between @xmath3- and higher - body interactions . a variety of interparticle potentials have been considered . we first considered contact interactions , studying the case in which the interparticle potential can be written as a general sum of @xmath0-body @xmath1-interactions , providing the quasi - particle spectrum , the ground - state energy and the stability conditions . results for general effective contact potentials are also presented . our findings show that the well - known results for the @xmath3-body @xmath1-interactions in the homogeneous case are generalized in the bogoliubov approximation by the substitution @xmath111 , where @xmath106 is a function of the condensate fraction @xmath114 given by eq . for potentials which are sums of @xmath0-body @xmath1-potentials and by eq . in the general case . since the bogoliubov approximation works well when @xmath118 , then one can make the substitution @xmath148 in @xmath106 , resulting for a sum of @xmath0-body contact interactions in the substitution @xmath358 . the case of higher - body non - local interactions is instead different from this respect and the final results depend on the specific form of the interactions . we explicitly considered two different cases of @xmath2-body non - local interactions . in the last part we discussed a few interaction potentials which are of interest for current experimental setups with ultracold atoms . implementations include systems with @xmath3- and @xmath2-body @xmath1-interactions , where we applied in the homogeneous limit our results with the values given in @xcite . we also considered the effect of ( conservative ) @xmath2-body terms in dipolar systems , e.g. magnetic atoms and polar molecules , and soft - core potentials that can be simulated with rydberg dressed atoms . for each of these cases we analysed the energy of the elementary excitations and derived for some interesting parameter regimes the stability diagram of the bogoliubov spectra . in the present paper we focused on higher - body interactions in the homogeneous limit , having in mind both @xmath2-body terms and general effective multi - body interactions of course ultracold experiments are done in confined traps , and we think that a systematic study of the bogoliubov equations in inhomogeneous potentials with general multi - body local and non - local interactions is an interesting direction of future research .

we consider weakly interacting bosonic gases with local and non - local multi - body interactions . by using the bogoliubov approximation , we first investigate contact interactions , studying the case in which the interparticle potential can be written as a sum of-body-interactions , and then considering general contact potentials . our results are used for systems with- and-body-interactions and applied in the homogeneous limit with the values given in . finally , the effect of conservative-body terms in dipolar systems and soft - core potentials ( that can be simulated with rydberg dressed atoms ) is also studied .

we consider weakly interacting bosonic gases with local and non - local multi - body interactions . by using the bogoliubov approximation , we first investigate contact interactions , studying the case in which the interparticle potential can be written as a sum of-body-interactions , and then considering general contact potentials . results for the quasi - particle spectrum and the stability are presented . we then examine non - local interactions , focusing on two different cases of-body non - local interactions . our results are used for systems with- and-body-interactions and applied in the homogeneous limit with the values given in . finally , the effect of conservative-body terms in dipolar systems and soft - core potentials ( that can be simulated with rydberg dressed atoms ) is also studied .

1509.07116

i

kac @xcite in 1956 to obtain a solution from a poisson of the telegraph equation @xmath3 with @xmath4 , introduced the processes @xmath5 where @xmath6 is a poisson process of intensity @xmath7 . he noticed that if in equation ( [ tele ] ) the parameters @xmath7 and @xmath8 tend to infinity with @xmath9 constant and equal to @xmath10 , then the equation converges to the heat equation : @xmath11 let @xmath12 be the processes considered by kac with @xmath13 , @xmath14 . these values satisfy that @xmath9 is constant and @xmath15 and we get in ( [ calor ] ) an equation whose solution is a standard brownian motion . stroock @xcite proved in 1982 that the processes @xmath16 converge in law to a standard brownian motion . that is , if we consider @xmath17 the image law of the process @xmath16 in the banach space @xmath18)$ ] of continuous functions on @xmath19 $ ] , then @xmath17 converges weakly , when @xmath20 tends to zero , towards the wiener measure . doing a change of variables , these processes can be written as @xmath21\right\},\ ] ] where @xmath22 is a standard poisson process . in the mathematical literature we find generalizations with regard to the stroock result which can be channeled in three directions : a. modifying the processes @xmath16 in order to obtain approximations of other gaussian processes , b. proving convergence in a stronger sense that the convergence in law in the space of continuous functions , c. weakening the conditions of the approximating processes . in direction ( i ) , a first generalization is also made by stroock @xcite who modified the processes @xmath16 to obtain approximations of stochastic differential equations . there are also generalizations , among others , to the fractional brownian motion ( fbm ) @xcite , to a general class of gaussian processes ( that includes fbm ) @xcite , to a fractional stochastic differential equation @xcite , to the stochastic heat equation driven by gaussian white noise @xcite or to the stratonovich heat equation @xcite . on the other hand , there is some literature where the authors present realizations of the processes that converge almost surely , uniformly on the unit time interval . these processes are usually called as uniform transport processes . since the approximations always start increasing , a modification of the processes as @xmath23 has to be considered where @xmath24 independent of the poisson process @xmath25 . griego , heath and ruiz - moncayo @xcite showed that these processes converge strongly and uniformly on bounded time intervals to brownian motion . in @xcite gorostiza and griego extended the result to diffusions . again gorostiza and griego @xcite and csrg and horvth @xcite obtained a rate of convergence . more precisely , in @xcite it is proved that there exist versions of the transport processes @xmath26 on the same probability space as a given brownian motion @xmath27 such that , for each @xmath28 , @xmath29 as @xmath30 and where @xmath31 is a positive constant depending on @xmath7 , @xmath32 and @xmath33 . garzn , gorostiza and len @xcite defined a sequence of processes that converges strongly to fractional brownian motion uniformly on bounded intervals , for any hurst parameter @xmath34 and computed the rate of convergence . in @xcite and @xcite the same authors deal with subfractional brownian motion and fractional stochastic differential equations . since @xmath35 the question that if the convergence is also true with other angles appears . bardina @xcite showed that if we consider @xmath36 where @xmath37 the laws of the processes converge weakly towards the law of a complex brownian motion , i.e. , the laws of the real and imaginary parts @xmath38 and @xmath39 converge weakly towards the law of two independent brownian motions . the approximating processes are functionally dependent because we use a single poisson process but , in the limit , we obtain two independent processes . later , in @xcite it is shown that for different angles @xmath40 the corresponding processes converge in law towards independent brownian motions despite using only one poisson process . finally , in @xcite , we prove that we can use a lvy process instead of a poisson process in the definition of the sequence of approximations . in this paper we present an extension of the kac - stroock result in the directions ( ii ) and ( iii ) . our aim is to define a modification of the processes @xmath41 used by stroock , similar to ( [ dedede ] ) proposed in @xcite . these complex processes , that we will denote by @xmath42 , will depend on a parameter @xmath43 and will be defined from an unique standard poisson process and a sequence of independent random variables with common distribution bernoulli(@xmath44 ) . we will check that if we consider @xmath45 such that for all @xmath46 , @xmath47 , @xmath48 , @xmath49 and @xmath50 , the law of the processes @xmath51 converges weakly in the space of the continuous functions towards the joint law of @xmath52 independent brownian motions . moreover , we also prove that there exist realizations of @xmath53 that converge almost surely to a complex brownian motion and we are able to obtain the rate of convergence that does not depend on @xmath54 . as a consequence , simulating a sequence of independent random variables with common distribution exponential(1 ) and a sequence of independent random variables with common distribution bernoulli(@xmath44 ) , we can get sequences of almost sure approximations of @xmath55 independent brownian motions for any @xmath55 . for simplicity s sake , we only consider @xmath56 for which it does not exist any @xmath57 such that @xmath58 or @xmath59 . as usual , the weak convergence is proved using tightness and the identification of the law of all possible weak limits ( see , for instance @xcite , @xcite ) . the almost sure converge is inspired in @xcite while the computation of the rate of convergence follows the method given in @xcite and @xcite . the paper is organized in the following way . section 2 is devoted to define the processes and to give the main results . in section 3 we prove the weak convergence theorems . in section 4 we prove the strong convergence theorem . the proof of the rate of convergence is given in section 5 . finally , there is an appendix with some technical results . throughout the paper @xmath60 will denote any positive constant , not depending on @xmath20 , which may change from one expression to another .

we construct a family of processes , from a single poisson process , that converges in law to a complex brownian motion . moreover , we find realizations of these processes that converge almost surely to the complex brownian motion , uniformly on the unit time interval . finally the rate of convergence is derived . departament de matemtiques , facultat de cincies , edifici c , universitat autnoma de barcelona , 08193 bellaterra . facultat de matemtiques , universitat de barcelona , gran via 585 , 08007 barcelona .

we construct a family of processes , from a single poisson process , that converges in law to a complex brownian motion . moreover , we find realizations of these processes that converge almost surely to the complex brownian motion , uniformly on the unit time interval . finally the rate of convergence is derived . departament de matemtiques , facultat de cincies , edifici c , universitat autnoma de barcelona , 08193 bellaterra . facultat de matemtiques , universitat de barcelona , gran via 585 , 08007 barcelona . [email protected] , [email protected]

1607.02792

i

the entscheidungsproblem from mathematical logic led ramsey @xcite to the following combinatorial principle that became a cornerstone of an area now called ramsey theory . [ thm : ramsey ] for any positive integers @xmath1 , @xmath0 , and @xmath2 there exists a positive integer @xmath3 with @xmath4 i.e. , such that no matter how the @xmath0-element subsets of an @xmath3-element set @xmath5 are coloured with @xmath2 colours , there will always be an @xmath1-element subset @xmath6 of @xmath5 such that all @xmath0-element subsets of @xmath6 are the same colour . this result admits a standard reformulation in the language of hypergraphs : for a fixed integer @xmath7 , an _ @xmath0-uniform hypergraph _ , or _ @xmath0-graph _ for short , is a pair @xmath8 consisting of a vertex set @xmath9 and an edge set @xmath10 . if @xmath11 is an @xmath0-graph , we use the standard notation of writing @xmath12 , @xmath13 , @xmath14 , and @xmath15 . in case that @xmath16 has all possible edges , that is if @xmath17 , we say that @xmath16 is _ a clique _ and if additionally @xmath18 we say that @xmath16 is a @xmath19 . now theorem [ thm : ramsey ] informs us that if @xmath3 is large enough depending on @xmath1 , @xmath0 , and @xmath2 , then @xmath20 holds , meaning that in every edge - colouring of @xmath21 using @xmath2 colours there occurs a monochromatic copy of @xmath19 . this raises the question whether there is a similar result when the target hypergraph @xmath19 is replaced by an arbitrary @xmath0-graph @xmath16 . of course , when we just ask for a monochromatic appearance of @xmath16 as a subhypergraph we may apply ramsey s theorem with @xmath22 . but the problem becomes significantly more challenging when we ask for a monochromatic induced copy of @xmath16 . here , for two given @xmath0-graphs @xmath16 and @xmath23 , we say that @xmath16 is an _ induced subhypergraph _ of @xmath23 and write @xmath24 if @xmath25 and @xmath26 . by an _ induced copy _ of @xmath16 in @xmath23 we mean an induced subhypergraph @xmath27 of @xmath23 that is isomorphic to @xmath16 . [ thm : rind ] given any @xmath0-uniform hypergraph @xmath16 and any number @xmath28 of colours , there exists an @xmath0-uniform hypergraph @xmath23 with @xmath29 in the sense that for every colouring of the edges of @xmath23 with @xmath2 colours there exists a monochromatic induced copy of @xmath16 in @xmath23 . for @xmath30 this was proved independently by deuber @xcite , by erds , hajnal , and psa @xcite , and by rdl in his master thesis @xcite . for an alternative proof we refer to @xcite . that article introduces the so - called _ partite method _ on which much of the subsequent progress in this area is based , including the present work . there are even `` arithmetic '' applications of this method , see e.g. , the work of leader and russell @xcite . for general hypergraphs the proof of theorem [ thm : rind ] was obtained independently by abramson and harrington @xcite and by neetil and rdl @xcite . actually both of these articles prove considerably stronger results . shorter proofs of theorem [ thm : rind ] utilising partite structures may be found in @xcite and @xcite . the next level of generality is obtained by replacing the edge - symbol @xmath31 in formula by other @xmath0-graphs . such considerations may actually take place in a more abstract context that we are going to introduce next . [ dfn : rcl ] let @xmath32 be a class of objects endowed with an equivalence relation called _ isomorphism _ and with a transitive _ subobject _ relation . given two objects @xmath33 and @xmath16 from @xmath32 we write @xmath34 for the class of all subobjects of @xmath16 that are isomorphic to @xmath33 . for three objects @xmath35 and a positive integer @xmath2 the partition symbol @xmath36 means that no matter how @xmath37 gets coloured with @xmath2 colours , there is some @xmath38 for which @xmath39 is monochromatic . the class @xmath40 is said to have the _ @xmath33-ramsey property _ if for every @xmath41 and every @xmath2 there exists an @xmath42 with @xmath43 . finally , @xmath40 is a _ ramsey class _ if it has the @xmath33-ramsey property for every @xmath44 . for example , ramsey s theorem asserts that the class of finite sets with isomorphisms being bijections and subobjects being subsets is a ramsey class . moreover , the induced ramsey theorem tells us that the class @xmath45 of all @xmath0-uniform hypergraphs with the usual notion of isomorphism and whose subobjects are induced subhypergraphs has the @xmath31-ramsey property , where @xmath46 . it was proved in @xcite that @xmath45 has the @xmath33-ramsey property if @xmath33 is either a clique or discrete , i.e. , edgeless ( see also @xcite ) . that this condition on @xmath33 is also necessary was proved for @xmath30 in @xcite and it seems to belong to the folklore of the subject that the probabilistic approach of @xcite yields the same result for all @xmath7 ( see also theorem [ thm : main - b ] below ) . so @xmath45 is not a ramsey class , but it turns out that a slight variant of this class is ramsey : let @xmath47 be the class of all _ ordered @xmath0-uniform hypergraphs _ , that is , @xmath0-graphs endowed with a fixed linear ordering of their vertices . the isomorphisms of @xmath47 are required to respect these orderings . thus for @xmath48 with underlying ( unordered ) @xmath0-graphs @xmath33 and @xmath16 the set @xmath49 may in general correspond to a proper subset of @xmath34 . [ thm : hrc ] the class @xmath47 of all ordered @xmath0-uniform hypergraphs is a ramsey class . again this was proved in @xcite and @xcite . other known examples of ramsey classes include finite vector spaces over a fixed field @xmath33 ( see @xcite ) , and finite partially ordered sets with fixed linear extensions @xcite . the study of ramsey classes found its revival after several decades due to its connection with topological dynamics via ultrahomogeneous structures described by kechris , pestov , and todorcevic in their seminal paper ( see @xcite ) . further results in this direction were obtained in the recent work of van th @xcite and by hubika and neetril @xcite . a very readable account of the kechris - pestov - todorcevic correspondence has recently been given by solecki in his survey @xcite . for more information on structural ramsey theory in general we refer to bodirsky s survey chapter @xcite . throughout the rest of this article , we consider classes of @xmath0-graphs called steiner systems . for fixed integers @xmath50 , by a _ steiner @xmath51-system _ we mean an @xmath0-uniform hypergraph @xmath11 with the property that every @xmath52-element subset of @xmath9 is contained in at most one edge of @xmath16 . such objects are also called `` partial steiner systems '' in the design - theoretic literature , while the term `` steiner system '' is reserved there to what we will call `` complete steiner systems '' ( see definition [ dfn : cmpl ] below ) . we denote the class of all steiner @xmath51-systems with subobjects again being induced subhypergraphs by @xmath53 . for example , the members of @xmath54 are sometimes referred to as _ linear hypergraphs _ while @xmath55 . the following generalisation of the induced ramsey theorem was obtained by neetil and rdl in @xcite . [ thm : edgesteiner ] for any integers @xmath56 the class @xmath53 has the edge - ramsey property . as remarked in @xcite the proof described there does also show that the corresponding ordered class @xmath57 has the edge - ramsey property . the members of this class are , of course , steiner @xmath51-systems with fixed linear orderings of their vertex sets and the isomorphisms of @xmath57 are required to preserve these orderings . in the light of theorem [ thm : hrc ] it is natural to wonder whether these classes @xmath57 are ramsey classes as well , but it turns out that for @xmath58 they are not ( see also corollary [ cor : ind - st - ord ] below ) . the main result of this article , however , asserts that those classes can be made ramsey by changing the subobject relation as follows . [ dfn : strong ] given two steiner @xmath51-systems @xmath16 and @xmath23 , we say that @xmath16 is a _ strongly induced subsystem _ of @xmath23 and write @xmath59{{$\blacktriangleleft$}}}\hskip.4em}h$ ] if 1 . [ it : str - a ] @xmath24 , i.e. , @xmath16 is an induced subsystem of @xmath23 2 . [ it : str - b ] and moreover @xmath60 holds for all @xmath61 . the set of all strongly induced copies of @xmath16 in @xmath23 is denoted by @xmath62{{$\blacktriangleleft$}}}}$ ] . this concept leads to two further classes of steiner systems . [ dfn : str - cl ] let @xmath63{{$\blacktriangleleft$}}}}(r , t)$ ] be the class of all steiner @xmath51-systems with isomorphisms as usual and whose subobjects are strongly induced subsystems . similarly , @xmath63{{$\blacktriangleleft$}}}}_<(r , t)$ ] refers to the corresponding class of ordered steiner @xmath51-systems . we may now announce the first main result of this article . [ thm : main - a ] the class @xmath63{{$\blacktriangleleft$}}}}_<(r , t)$ ] is ramsey . in order to gain a better understanding as to why this is true , whilst in general the class @xmath53 fails to be ramsey , we will also determine for each of the four classes of steiner systems introduced so far for which objects @xmath33 they have the @xmath33-ramsey property . in this manner we can separately study the effects of ordering the vertices and of changing the definition of subobjects . the adjectives _ weak _ , _ strong _ , _ unordered _ , and _ ordered _ will be applied to these classes as indicated by the following table . [ cols="^,^,^",options="header " , ] it will turn out that the property of steiner systems relevant to unordered classes is that of homogeneity . [ dfn : rigid ] a steiner @xmath64-system @xmath33 is said to be _ homogeneous _ if every permutation of @xmath65 induces an automorphism of @xmath33 . thus a member of @xmath66 is homogeneous if either it is of the form @xmath67 for some @xmath68 or if it has no edges . it should be observed , however , that except for the edge @xmath31 the homogeneous @xmath0-graphs of the former type do not belong to @xmath69 as long as @xmath58 . similarly for @xmath58 the weak classes demand completeness . [ dfn : cmpl ] a steiner @xmath64-system @xmath33 is called _ complete _ if for every @xmath70 there is an edge @xmath71 with @xmath72 . trivial cases for this to happen are that @xmath33 consists of less than @xmath52 isolated vertices or that @xmath73 . non - trivial examples of complete steiner systems , also known as _ designs _ in the literature , are very hard to come up with ( at least for @xmath74 , say ) . but recently keevash @xcite established an important 160 year old conjecture of steiner regarding their existence . with this terminology the second main result of this article reads as follows . [ thm : main - b ] let @xmath56 , @xmath75{{$\blacktriangleleft$ } } } } , \ccs^{\,{\scalebox{1.1}[1.1]{{$\blacktriangleleft$}}}}_<\bigr\}$ ] , and @xmath76 . then @xmath77 has the @xmath33-ramsey property if both of the following conditions hold : 1 . [ it : main - uno ] if @xmath77 is unordered , then @xmath33 is homogeneous , 2 . [ it : main - weak ] if @xmath77 is weak and @xmath78 , then @xmath33 is a complete steiner system . if on the other hand [ it : main - uno ] or [ it : main - weak ] fails , then @xmath77 fails to have the @xmath33-ramsey property . notice that this generalises all other structural ramsey - theoretic theorems stated above . theorem [ thm : main - a ] follows , as the above clauses [ it : main - uno ] and [ it : main - weak ] hold vacuously for @xmath79{{$\blacktriangleleft$}}}}_<$ ] . the case @xmath80 and @xmath73 yields theorem [ thm : edgesteiner ] , and the induced ramsey theorem corresponds to the case @xmath81 , @xmath80 , and @xmath73 . for the readers convenience we would now like to state more explicitly what theorem [ thm : main - b ] says for @xmath75{{$\blacktriangleleft$}}}}\bigr\}$ ] . [ cor : ind - st ] the class @xmath53 has the @xmath33-ramsey property if and only if one of the following two cases holds : 1 . @xmath82 and either @xmath33 is an edge or @xmath83 , 2 . @xmath81 and @xmath33 is homogeneous . [ cor : ind - st - ord ] the class @xmath84 has the @xmath33-ramsey property if and only if @xmath81 or @xmath33 is a complete steiner @xmath64-system ( the cases @xmath85 and @xmath73 are included ) . [ cor : ind - st - str ] the class @xmath63{{$\blacktriangleleft$}}}}(r , t)$ ] has the @xmath33-ramsey property if and only if 1 . @xmath33 is an edge 2 . or @xmath33 is discrete , 3 . or if @xmath81 and @xmath33 is a clique

we construct a ramsey class whose objects are steiner systems . in contrast to the situation with general-uniform hypergraphs , it turns out that simply putting linear orders on their sets of vertices is not enough for this purpose : one also has to strengthen the notion of subobjects used from `` induced subsystems '' to something we call `` strongly induced subsystems '' . moreover we study the ramsey properties of other classes of steiner systems obtained from this class by either forgetting the order or by working with the usual notion of subsystems .

we construct a ramsey class whose objects are steiner systems . in contrast to the situation with general-uniform hypergraphs , it turns out that simply putting linear orders on their sets of vertices is not enough for this purpose : one also has to strengthen the notion of subobjects used from `` induced subsystems '' to something we call `` strongly induced subsystems '' . moreover we study the ramsey properties of other classes of steiner systems obtained from this class by either forgetting the order or by working with the usual notion of subsystems . this leads to a perhaps surprising induced ramsey theorem in which _ designs _ get coloured .

1304.0391

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by mostow rigidity , a hyperbolic structure on a closed -manifold @xmath2 is unique up to isometry . while the geometry of @xmath2 is thus completely determined by its underlying topology , it can be difficult to understand the qualitative and quantitative connections between these two facets of @xmath2 . here , we show that a geometric property involving injectivity radii can be varied independently of the homology of the manifold . to state our results , we first need some notation . the injectivity radius @xmath3 at @xmath4 is the largest radius for which the ball about @xmath5 is embedded , and the ( lower ) injectivity radius of @xmath2 itself is @xmath6 . on the topological side , an _ integer homology -sphere _ is a closed -manifold @xmath2 where @xmath7 , and the term _ rational homology 3-sphere _ is similarly defined . our main result here is : [ thm : ihs ] given positive constants @xmath8 and @xmath9 there exists a hyperbolic integer homology -sphere @xmath2 where @xmath10 in fact , we show that the homology of @xmath2 can be specified arbitrarily ( theorem [ thm : full ] ) . the proof is based on the modern theory of kleinian groups ; before sketching it , we motivate our result in several ways . starting with any closed hyperbolic -manifold , one can make the injectivity radius arbitrarily large everywhere by taking a suitable finite cover . in the context of the virtual haken conjecture , this motivated cooper to ask whether there are hyperbolic _ rational _ homology -spheres with arbitrarily large injectivity radius . in fact , such manifolds do exist by the work of calegari - dunfield and boston - ellenberg @xcite . however , if one instead considers _ integer _ homology -spheres , then the analogous question is open ; our theorem [ thm : ihs ] answers affirmatively a weakened version of this question . the manifolds of @xcite came from a tower of congruence covers of a fixed base manifold , and it seems unlikely this method would work for integer homology -spheres as we now describe . recently , number theorists have become interested in torsion in the homology of arithmetic groups @xcite . specifically , bergeron and venkatesh posited the following as part of an intriguing general conjecture for arithmetic lattices in semisimple lie groups ; in the present context of hyperbolic 3-manifolds , le independently formulated a closely related conjecture , see @xcite for details . [ conj : bv ] let @xmath2 be a closed congruence arithmetic hyperbolic -manifold , and @xmath11 a tower of congruence covers where @xmath12 . then the size of the torsion subgroup of @xmath13 grows exponentially in @xmath14 and moreover @xmath15 in particular , if this conjecture holds then the approach of @xcite which used exactly such a tower to answer cooper s question can not be modified to prove theorem [ thm : ihs ] . one of two key parts to conjecture [ conj : bv ] is the expected convergence of ray - singer analytic torsion in such a tower of covers . more precisely , the logarithm of the analytic torsion of a riemannian manifold @xmath2 is @xmath16 where @xmath17 is the laplacian on smooth @xmath18-forms and @xmath19 is the zeta - regularized product of nonzero eigenvalues ( see e.g. @xcite for details ) . then for covers @xmath20 as in conjecture [ conj : bv ] , part of ( [ eqn : l2tor ] ) is that one should have @xmath21 where @xmath22 is the @xmath1-analytic torsion of @xmath0 . a corollary of theorem [ thm : ihs ] is that one _ need not _ have ( [ eqn : torconv ] ) for a sequence @xmath20 of hyperbolic -manifolds which benjamini - schramm converge to @xmath0 , which is a natural geometric notion of convergence implied by the hypotheses of conjecture [ conj : bv ] . as this corollary was the primary motivation for this paper , we now discuss it and its context in detail . for a manifold @xmath2 , we define @xmath23 . following @xcite , we say that a sequence @xmath24 of closed hyperbolic -manifolds benjamini - schramm converge to @xmath0 if for all @xmath25 one has @xmath26 as @xmath27 . we emphasize here that the @xmath20 may have no relationship with each other beyond being hyperbolic ; in particular , they need not be covers of a fixed manifold . despite this , abert et . were able to show that this notion of geometric convergence also implies convergence of part of the topology : [ thm : localconv ] let @xmath20 be a sequence of closed hyperbolic -manifolds which benjamini - schramm converge to @xmath0 . then @xmath28 here , the @xmath29 in the right - hand side of ( [ eqn : l2betti ] ) should be interpreted as the first @xmath1betti number of @xmath0 , and the moral of theorem [ thm : localconv ] is that suitable local convergence of the geometry of the @xmath20 leads to convergence of their normalized betti numbers to the corresponding @xmath1betti number of their common universal cover . theorem [ thm : localconv ] generalizes results of lck and lott @xcite which apply only to @xmath20 coming from finite covers of a fixed manifold ( as in conjecture [ conj : bv ] ) . a key consequence of theorem [ thm : ihs ] is that theorem [ thm : localconv ] does not have an analog for analytic torsion : [ cor : tornonconverge ] there exist closed hyperbolic -manifolds @xmath20 which benjamini - schramm converge to @xmath0 where @xmath30 as @xmath27 . in particular , the limit is not @xmath31 . thus , while the geometric notion of benjamini - schramm convergence is enough to control the convergence of ( normalized ) betti - numbers to the corresponding @xmath1 invariant of the limit , the same is not true for torsion . corollary [ cor : tornonconverge ] limits how much one can broaden conjecture [ conj : bv ] , and in this narrow sense could be taken as evidence against conjecture [ conj : bv ] . however , we present here computational evidence which strongly supports conjecture [ conj : bv ] as well as certain generalizations to nonarithmetic manifolds . our experiments complement prior work of engn @xcite and page @xcite . to frame our results , we need to expand on the connection between conjecture [ conj : bv ] and analytic torsion . for a closed riemannian -manifold , the cheeger - mller theorem @xcite implies ( see e.g. @xcite ) that @xmath32 here the regulator of @xmath33 is the covolume of the lattice @xmath34 in @xmath35 , where the latter has the inner product coming from its identification with the set of harmonic forms . the first part of conjecture [ conj : bv ] is that @xmath36 and the second is that @xmath37 . in section [ sec : exp ] , we provide evidence in favor of a broadening of the first part conjecture [ conj : bv ] to _ all _ hyperbolic -manifolds : [ conj : gentor ] let @xmath20 be covers of a fixed closed hyperbolic -manifold @xmath2 which benjamini - schramm converge to @xmath0 . then @xmath38 . in contrast , it is not expected that @xmath39 for nonarithmetic manifolds ; we give data in support of this , see especially figure [ nonarithg ] . for arithmetic manifolds , experiments of engn @xcite identified the case of congruence covers of prime - power level as a place where such convergence appears to be slowest , to the point where one hits computational limits before getting convincing evidence for or against conjecture [ conj : bv ] . in section [ sec : exp ] , we investigate several families of examples of this type . while some of these remain ambiguous , overall they provide additional evidence that @xmath40 even in this case . given a homeomorphism @xmath41 of a surface @xmath42 there are two natural 3-manifolds we can build from it . one is the mapping torus @xmath43 , which fibers over the circle . alternatively , we can identify @xmath42 with the boundary of a handlebody @xmath44 and consider the associated heegaard splitting : @xmath45 . while the natural copies of @xmath42 in @xmath43 and @xmath46 are radically different topologically ( the first is incompressible and the other maximally compressible ) , the philosophy of kleinian groups , specifically @xcite , indicates that in favorable conditions on @xmath41 , and for large powers @xmath47 , there are large chunks of the geometry of @xmath48 and @xmath49 that are nearly isometric . here is the basic idea behind the manifolds in theorem [ thm : ihs ] . fixing @xmath25 , it is easy to construct @xmath50 so that @xmath43 has @xmath51 . now for @xmath43 we have @xmath52 , and in particular @xmath43 is not a homology sphere . however , we will `` photocopy '' its geometry onto a heegaard splitting whose homology we can independently control . specifically , choose homeomorphisms @xmath53 and @xmath54 of @xmath42 so that @xmath55 and @xmath54 acts trivially on @xmath56 . then define @xmath20 to be the heegaard splitting associated to @xmath57 . this @xmath20 is an integral homology sphere since the gluing map acts on @xmath58 precisely as @xmath53 does . we show that @xmath41 and @xmath54 can be chosen so that when @xmath47 is large , most of the geometry of @xmath20 is locally nearly isometric to @xmath43 and hence @xmath59 on most of @xmath20 . specifically , the volume of @xmath60 is uniformly bounded whereas @xmath61 ; hence we can make the ratio @xmath62 , as required by theorem [ thm : ihs ] . in realizing this outline , there are several different routes one could take through the machinery of kleinian groups . we choose one which only uses results about manifolds with incompressible boundary and bounded geometry . moreover , unlike the corresponding parts of @xcite , our argument does not rely on @xcite . one very natural question is whether there are integral homology 3-spheres where the injectivity radius is large everywhere . from the point of view in the discussion in sections [ sec : context ] and [ sec : bs ] , in fact it would be very interesting if one could add to theorem [ thm : ihs ] a _ uniform _ lower bound on @xmath63 independent of @xmath8 and @xmath9 . the current construction provides no control on @xmath63 as @xmath8 varies , basically because the genus of @xmath42 has to change with @xmath8 ; see remarks [ rmk : genusinj ] and [ rmk : injepsilon ] . the weaker version of theorem [ thm : ihs ] where one just requires that @xmath64 for _ some _ @xmath5 follows from @xcite by doing @xmath65 dehn filling on the knot complements constructed there which also have this property . a natural question is whether there are knots in @xmath66 where @xmath67 is big most places . we give a possible construction of such knots in remark [ rmk : knots ] . section [ sec : mainthm ] gives the precise construction of the manifolds in theorem [ thm : ihs ] and proves that result modulo the central lemma [ lem : geom - of - cusped ] . section [ sec : lemma ] reviews the needed background in kleinian groups and uses it to prove lemma [ lem : geom - of - cusped ] . finally , section [ sec : exp ] contains the details of the experimental results . the authors were partially supported by us nsf grants dms-0906229 , dms-0707136 , and dms-1105476 . we are very grateful to nicolas bergeron for suggesting this question and explaining its relation to @xcite , which happened at the conference `` geometry , analysis , and surfaces '' in autrans , france , in march 2011 . the computational part of this paper was motivated by a workshop on torsion in the homology of arithmetic groups held in banff in july 2012 . we thank the organizers of both of these excellent events . finally , we thank the referee for providing very helpful comments on the initial version of this paper .

we construct hyperbolic integer homology 3-spheres where the injectivity radius is arbitrarily large for nearly all points of the manifold . as a consequence , there exists a sequence of closed hyperbolic -manifolds which benjamini - schramm converge to whose normalized ray - singer analytic torsions do _ not _ converge to the-analytic torsion of . al . who showed that benjamini - schramm convergence forces convergence of normalized betti numbers . our results shed light on a conjecture of bergeron and venkatesh on the growth of torsion in the homology of arithmetic hyperbolic -manifolds , and we give experimental results which support this and related conjectures .

we construct hyperbolic integer homology 3-spheres where the injectivity radius is arbitrarily large for nearly all points of the manifold . as a consequence , there exists a sequence of closed hyperbolic -manifolds which benjamini - schramm converge to whose normalized ray - singer analytic torsions do _ not _ converge to the-analytic torsion of . this contrasts with the work of abert et . al . who showed that benjamini - schramm convergence forces convergence of normalized betti numbers . our results shed light on a conjecture of bergeron and venkatesh on the growth of torsion in the homology of arithmetic hyperbolic -manifolds , and we give experimental results which support this and related conjectures .

1504.03389

i

consider a sample @xmath5 we look for substitutes @xmath6 * * and * * @xmath7 of the sample mean vector and covariance matrix , that are resistant to atypical observations . we also want estimators that have a high efficiency for normal samples@xmath8 as a measure of robustness we consider not only the breakdown point but also the maximum expected kullback - leibler divergence between the estimator and the true value . under contamination . the most frequently employed estimators are not quite satisfactory in this respect . the minimum volume ellipsoid ( mve ) and the minimum covariance determinant ( mcd ) estimators ( rousseeuw 1985 ) are known to have a low efficiency . this efficiency can be increased by means of a one - step reweighting . croux and haesbroeck ( 1999 , tables vii and viii ) computed the finite - sample efficiencies of the reweighted mcd ; although they are much higher than for the raw estimator , they are still low if one wants a high breakdown point . s - estimators ( davies 1987 ) with a monotonic weight function like the bisquare have a low efficiency for small @xmath9 rocke ( 1996 ) showed that their efficiency tends to one with increasing @xmath0 ; unfortunately , this advantage is paid for with a serious loss of robustness for large @xmath0 . we restrict ourselves to equivariant estimators . there exist many non - equivariant proposals ; but the comparison between equivariant and non - equivariant estimators is difficult . in particular , a non - equivariant estimator is more difficult to tune for a given efficiency , since the latter depends on the correlations . among the published equivariant proposals , there are four families of estimators with controllable efficiencies : non - monotonic s - estimators ( rocke 1996 ) , mm - estimators ( tatsuoka and tyler 2000 ) , @xmath2-estimators ( lopuhaa 1991 ) and the estimator proposed independently by stahel ( 1981 ) and donoho ( 1982 ) but their behavior for large dimensions has not been explored to date . we compare their behaviors employing different weight functions . a simulation study shows that the rocke and mm estimators , with an adequate weight function and an adequate tuning , can simultaneously attain high efficiency and high robustness . it will be seen below that if we have a good @xmath10 it is easy to find a good equivariant @xmath11 but the converse is not true . for this reason we shall put more emphasis on the estimation of the scatter matrix . since all the considered estimators are based on the iterative minimization of a non - convex function , the starting values are crucial . subsampling is the standard way to compute starting values ; but we shall see that a semi - deterministic equivariant procedure proposed by pea and prieto ( 2007 ) may yield both shorter computing times and better statistical performances . in section [ secmesti ] we describe monotonic m - estimators ; section [ secminscale ] deals with estimators based on the minimization of a robust scale of mahalanobis distances . sections [ secmm ] and [ sec_stadono ] deal with mm and stahel - donoho estimators respectively . in section [ secrho ] we discuss the choice of the @xmath12function for mm- and @xmath13estimators . section [ seccomputing ] deals with computational details . in section [ secsimula ] the estimators are compared through a simulation study . in section [ secreal ] the estimators are applied to a real data set . finally section [ secconclu ] summarizes the results . section [ secappend ] is an appendix containing the full results of the simulations , the approximations for the tuning constants and some details on the rocke and the pea - prieto procedures .

the most frequently employed estimators are not quite satisfactory in this respect . the minimum volume ellipsoid ( mve ) and minimum covariance determinant ( mcd ) estimators are known to have a very low efficiency . s - estimators with a monotonic weight function like the bisquare have a low efficiency for small and their efficiency tends to one with increasing . unfortunately , this advantage is paid for by a serious loss of robustness for large . we consider four families of estimators with controllable efficiencies whose performance for moderate to large has not been explored to date : s - estimators with a non - monotonic weight function ( rocke 1996 ) , mm - estimators ,-estimators , and the stahel - donoho estimator . two types of starting estimators are employed : the mve computed through subsampling , and a semi - deterministic procedure proposed by pea and prieto ( 2007 ) for outlier detection . a simulation study shows that the rocke estimator starting from the pea - prieto estimator and with an adequate tuning , can simultaneously attain high efficiency and high robustness for and the mm estimator can be recommended for . keywords : mm - estimator , tau - estimator , s - estimator , stahel - donoho estimator , kullback - leibler divergence .

we deal with the equivariant estimation of scatter and location for-dimensional data , giving emphasis to scatter . it is important that the estimators possess both a high efficiency for normal data and a high resistance to outliers , that is , a low bias under contamination . the most frequently employed estimators are not quite satisfactory in this respect . the minimum volume ellipsoid ( mve ) and minimum covariance determinant ( mcd ) estimators are known to have a very low efficiency . s - estimators with a monotonic weight function like the bisquare have a low efficiency for small and their efficiency tends to one with increasing . unfortunately , this advantage is paid for by a serious loss of robustness for large . we consider four families of estimators with controllable efficiencies whose performance for moderate to large has not been explored to date : s - estimators with a non - monotonic weight function ( rocke 1996 ) , mm - estimators ,-estimators , and the stahel - donoho estimator . two types of starting estimators are employed : the mve computed through subsampling , and a semi - deterministic procedure proposed by pea and prieto ( 2007 ) for outlier detection . a simulation study shows that the rocke estimator starting from the pea - prieto estimator and with an adequate tuning , can simultaneously attain high efficiency and high robustness for and the mm estimator can be recommended for . keywords : mm - estimator , tau - estimator , s - estimator , stahel - donoho estimator , kullback - leibler divergence .

astro-ph0003220

i

a number of codes were built in the past to compute the structure and the emission of photoionized media . with time , these codes became more and more sophisticated , and able to treat a larger number of situations . in the sixties they were specially designed for planetary nebulae and hii regions , i.e. for dilute and optically thin media ( except in the lyman continuum ) ionized by the thermal radiation of a hot star , and were rapidly used also for ionization by a non thermal continua extending in the x - ray range , i.e. for the narrow line region of active galactic nuclei ( agn ) . at the same time another generation of codes was developed for optically thin hot collisionally ionized media , and used for the solar corona , for supernova remnants , and for the hot intergalactic gas . at the end of the seventies , observations of compact x - ray sources implying the presence of a thomson thick medium incited ross ( 1979 ) to develop a radiative transfer method for the continuum using a modified version of the kompaneets equation . in the same paper he introduced the so - called escape probability " approximation to take into account diffusion and absorption into the lines . this approximation was thereafter amply used for the broad line region : this was the beginning of the local escape probability era , with the fiducial paper of kwan & krolik ( 1981 ) aimed at studying the broad line region of agn ( blr ) , immediately followed by a similar computation for the atmospheres of x - ray binary stars ( kallman and mccray 1982 ) from which derived . the most popular of these codes is , designed by ferland ( cf . for instance ferland & rees 1988 ) and continuously updated since this time ( cf . ferland 1996 , ferland et al . 1998 ) . these codes are not only used for relatively cold " clouds like the blr , but also for warm photoionized media ( broad absorption line region in quasars and warm absorbers " in agn , shock heated media , etc ... ) . at the other extreme ( i.e. for dense , non irradiated , and semi - infinite media ) model atmosphere codes have been developed since the fifties with an emphasis put onto the computation of line transfer , which was treated completely , but with the lte approximation . non lte effects were introduced in the sixties , and extensively studied in the seventies , with the state of the art being beautifully exposed in mihalas book ( 1978 ) . since this time many improvments have been made in the numerical methods , in particular aiming at taking into account a large number of atoms and levels , cf . for introductory reviews rutten 1995 , hubeny 1997 . in the nineties appeared the urgent need for intermediate " codes , valid for thick or semi - infinite dense media , eventually hot , irradiated by a non thermal continuum extending in the hard x - rays , to cover the whole range of situations encompassed in agn and in binary stars . several codes were then built , mainly to compute the em - ission spectrum of accretion disks , irradiated or not by an x - ray continuum . for irradiated disks , they were either of photoionization type " , using the kompaneets equation ( ross & fabian , 1993 , based on the ross 1979 code ) , or coupling an existing photoionization code to a monte carlo computation ( zycki et al . 1994 ) , to take into account compton diffusions . on the other hand , sophisticated model atmosphere codes were transformed to be applied to accretion disk structure and emission ( hubeny , 1990 , hubeny & hubeny 1997 and 1998 ) , but without the external irradiation by an x - ray continuum . owing to the high optical thickness of the medium in several frequency ranges , such codes require that the transfer of both the continuum and the lines be solved in an exact " way , i.e. avoiding approximations such as local escape approximation ( for the lines ) or one stream approximation ( for the continuum ) . since the medium is generally dense and sometimes close to lte , they require that all processes and inverse processes be carefully handled . being irradiated by an x - ray continuum , the medium contains a large number of ionic species , from low to high ionization , which should all be introduced in the computation . finally , the medium being hot and thick , not only thomson , but also compton scattering , should be taken into account . we have undertaken to build a code in order to satisfy these requirements . precisely we have built several interconnected codes , which allow more flexibility . the ensemble is far from being perfect and still contains several approximations which restrict its use , but we intend to improve it in the future . we have presently four codes . one of them ( ) is designed to study the structure of a warm or hot thick photoionized gas , and to compute its emission - reflection - transmission spectrum from the infrared up to about 20 kev . it solves the energy balance , the ionization and the statistical equilibria , the transfer equations , in a plane - parallel geometry , for the lines and continuum . then , given the thermal and ionization stratification , the computation of the emitted spectrum from 1 kev to a few hundre - ds kev is performed with which uses a monte - carlo method taking into account direct and inverse compton scattering ( it allows also to study various geometries ) . adresses the case of more diluted and thin media , and is similar to with however some differences , and is specially devoted to the computation of the line fluxes , including very weak lines , using the most recent available atomic data and a full treatment of the statistical equilibrium equations for a great number of levels . these codes can be used to model a wide variety of astrophysical media , particularly those in which the energy transport is purely radiative , but also plasmas heated by other mechanisms ( viscosity , shocks , energetic particules ... ) . they have already been used in several published papers ( collin - souffrin et al . 1996 , czerny & dumont 1998 , porquet et al . 1998 , abrassart 1999 ) . the three codes , and , are described in other papers ( abrassart 2000 , dumont & porquet 2000 ) . in this paper we present and we discuss a few simple cases , schematized by a slab of gas irradiated on one side or on both sides . as far as possible we will perf - orm comparisons with in the range of parameters where both codes can be used , to assess the validity of . however detailed comparisons are not possible , as they use quite different transfer methods in particular . we will also show some examples of the capabilities of in the parameter range which is not accessible to . is mainly designed to determine the structure ( temperature and ionization state ) and the continuum em - ission spectrum of a thick hot photoionized slab of gas . owing to the representation of the ions made in the code it does not give an accurate determination of the weak lines . for a detailed determination of the line spectrum of some ions , it should be complemented by . we briefly summarize below the physical processes ( sect . 2 ) , the transfer method and the iteration procedure ( sect . 3 ) , the thermal equilibrium , ( sect . 4 ) , focussing only on the aspects which are not treated in a standard way . the coupling of and is briefly described in sect . 5 , and some applications are presented in sect .

we describe a code designed for hot media ( t a few 10 k ) , optically thick to compton scattering . the transfer code is coupled with a monte carlo code which allows to take into account compton and inverse compton diffusions , and to compute the spectrum emitted up to mev energies , in any geometry . several applications are mentioned .

we describe a code designed for hot media ( t a few 10 k ) , optically thick to compton scattering . it computes the structure of a plane - parallel slab of gas in thermal and ionization equilibrium , illuminated on one or on both sides by a given spectrum . contrary to the other photoionization codes , it solves the transfer of the continuum and of the lines in a two stream approximation , without using the local escape probability formalism to approximate the line transfer . we stress the importance of taking into account the returning flux even for small column densities ( 10 ) , and we show that the escape probability approximation can lead to strong errors in the thermal and ionization structure , as well as in the emitted spectrum , for a thomson thickness larger than a few tenths . the transfer code is coupled with a monte carlo code which allows to take into account compton and inverse compton diffusions , and to compute the spectrum emitted up to mev energies , in any geometry . comparisons with show that it gives similar results for small column densities . several applications are mentioned .

astro-ph0003220

m

it is not always clear which approximations are used in the different codes . basically the computation of the diffuse radiation field seems to be similar in all codes , except in ross & fabian ( 1993 ) and in subsequent works using this code , where it is computed using the kompaneets equation . ( ferland 1996 ) , ( kallman & krolik , 1995 for the last version ) , ( netzer 1990 , 1993 ) , use a modified version of the on the spot " approximation , which amounts to assuming a kind of escape probability for the diffuse continuum , and one stream approximation in the transfer equation . these approximations are correct only for a continuum optical thickness smaller than unity ( effective or total opacity ) , and when the properties of the cloud do not vary considerably between the point where a photon is emitted and the point where it is reabsorbed . in particular one very important requirement for studying hot and thick media is to take into account the radiation returning from the backside of the slab , even when it is not illuminated . as the medium is optically thick in a large frequency range , this radiation is intense and modifies the physical state of the whole slab , including the illuminated side(see fig . [ fig - gtitancloudyt - col ] ) . all previous photoionization codes , except that of collin - souffrin and dumont ( s. ) ( 1986 ) , treat line transfer by the so - called local escape probability formalism , which uses the probability that a line photon emitted at a given point can escape * in a single flight * from the cloud , assuming that the rest of the cloud is homogeneous and has the same properties as the emitting layer . it amounts to identifying the divergence flux of the statistical equilibrium equations with the escape probability intervening in the line emerging flux . this approximation is valid only in the case of complete frequency redistribution , absence of line interlocking , and * if the medium is homogeneous*. its use can have severe consequences on the emission line spectrum and on the energy balance when these conditions are not fulfilled as it was often discussed , see for example by collin & s.dumont ( 1986 ) or elitzur ( 1984 ) . we introduce here the divergence flux in the aim to show that our results are completely different from those obtained by the escape probability formalism . where @xmath91 and @xmath153 are the absorption and emission line profiles , @xmath154 , @xmath155 and @xmath156 , @xmath157 and @xmath158 are the usual radiative ( einstein ) and collisional excitation and deexcitation coefficients , and @xmath32 is the angle averaged intensity . let us now define the _ divergence flux _ of the transition , @xmath159 : according to this equation the divergence flux seems to be equal to the probability that , once emitted at a distance @xmath27 from the surface , a photon can escape from the medium , which is called the escape probability " @xmath167 . several estimates of the escape probability are used in the literature ( see for example kwan & krolik , 1981 , rees , netzer & ferland , 1989 , kallman & mccray , 1982 , ko & kallman , 1994 ) , to account for partial redistribution , for line or continuum interlocking , and for continuum absorption . for instance several ways to take into account the continuum opacity ( or the overlapping of two lines ) have been proposed ( elitzur & netzer , 1984 , netzer , elitzur & ferland , 1985 ) . in the case of the broad line region of agn , which is optically thin for the continuum underlying the main lines , collin - souffrin et al . ( 1981 ) , avrett & loeser ( 1988 ) , have discussed the influence of different approximations for partial or complete redistribution , and how they compare to an exact transfer treatment , and collin - souffrin & dumont s. ( 1986 ) have shown that the escape probability approximation is roughly valid ( it can however lead to a decrease by a factor as large as two of the ratio of a lower to a higher transition , such as h@xmath6/h@xmath88 or l@xmath6/h@xmath6 ) . however these approximations are not valid if @xmath174 is of the order of unity at the line frequency and if the line photons are created in one place and absorbed in another place where the physical conditions are different . this happens for instance for euv and soft x - ray lines created in the hot region and absorbed in ionizing he@xmath175 ions in a cooler region . if the local escape probability approximation breaks down , it has a severe consequence : _ the emitted line spectrum and the thermal and the ionization balance are not correctly computed_. for instance the divergence flux takes frequently negative values in our computations , even for intense lines , and even in the reflected spectrum . this is not allowed with escape probabilities . we illustrate this discussion with some examples in sect .

we stress the importance of taking into account the returning flux even for small column densities ( 10 ) , and we show that the escape probability approximation can lead to strong errors in the thermal and ionization structure , as well as in the emitted spectrum , for a thomson thickness larger than a few tenths .

we describe a code designed for hot media ( t a few 10 k ) , optically thick to compton scattering . it computes the structure of a plane - parallel slab of gas in thermal and ionization equilibrium , illuminated on one or on both sides by a given spectrum . contrary to the other photoionization codes , it solves the transfer of the continuum and of the lines in a two stream approximation , without using the local escape probability formalism to approximate the line transfer . we stress the importance of taking into account the returning flux even for small column densities ( 10 ) , and we show that the escape probability approximation can lead to strong errors in the thermal and ionization structure , as well as in the emitted spectrum , for a thomson thickness larger than a few tenths . the transfer code is coupled with a monte carlo code which allows to take into account compton and inverse compton diffusions , and to compute the spectrum emitted up to mev energies , in any geometry . comparisons with show that it gives similar results for small column densities . several applications are mentioned .

1211.4250

i

partitioning a phase space into orbits is a central step in the study of any physical or formal dynamics . immediately after the introduction of graph ( /stabilizer ) states in quantum coding theory @xcite and in the context of measurement - based quantum computation @xcite , it was evident that the related task , when considering the dynamics at the subsystems level , requires approaches of combinatorial flavour . while substantial attention has been given to orbits obtained by the application of local unitaries ( with a clear motivation coming from the classification of multipartite entanglement @xcite ) , the question to decide whether two graph states are equivalent under the action of the local clifford group has been settled , by showing @xcite that the equivalence classes are in one - to - one correspondence with local complementation orbits ( also called _ kotzig orbits _ @xcite ) . in other words , the existence of a sequence of local complementations relating the associated graphs guarantees equivalence under local clifford operations and _ viz_. even though this link does not embrace full local unitary equivalence , having now counterexamples to the lu - lc conjecture ji10 , sarvepalli10 , it unveils a rich interface between the structure of useful multi - qubit systems and a number of mathematical ideas . indeed , local complementation ( or , equivalently , @xmath2-transformation ) is a fundamental operation for studying circle graphs @xcite . this notion has been instrumental for unifying certain properties of eulerian tours and matroids via isotropic systems @xcite , constructs associated to vector spaces over @xmath3 ; and it appears in string reconstruction problems ( related to dna sequencing ) and graph polynomials @xcite . given an equivalence class induced by local complementation , in the present work we shall describe a method for constructing a larger graph associated to the equivalence class . the method makes use of the stabilizer group of an arbitrary graph state from the class . each of these graphs is identified with an exclusivity structure and a related _ non - contextuality inequality _ ( for short , nc inequality ) . such an inequality is an upper bound on the sum of probabilities of a set of events , with some exclusivity constraints ( a technical discussion about events and exclusivity will be given in section [ con ] ) . nc inequalities are satisfied by any non - contextual hidden variable theory , _ i.e. _ , any physical theory for which the probability of seeing an event is independent of the choice of measurements . quantum mechanics or more general theories can violate such inequalities . for more details , see @xcite . in this reference , the graph ( and more generally an hypergraph ) , whose vertices are events , is employed to characterize the correlations for classical and general probabilistic theories satisfying that the sum of probabilities of pairwise exclusive events can not be larger than 1 . the maximum values for the three physical theories : classical , general , and quantum , were computed through the three well - known combinatorial parameters : the independence number , the fractional packing number , and the lovsz number , respectively . as a consequence , it becomes evident that quantum and general probabilistic correlations satisfying that the sum of probabilities of pairwise exclusive events can not be larger than 1 have semidefinite and linear characterizations , respectively . quantum mechanics is _ sandwiched _ between the other two theories . the framework introduced in @xcite permits to quantitatively discuss classical , quantum , and more general theories through the analysis of a single mathematical object and to have a general technique to single out quantum correlations with _ ad hoc _ degree of contextuality . for example , a generic graph with independence number strictly smaller than the lovsz number is associated to a nc inequality violated by quantum mechanics . if , in addition , the graph has equal lovsz and fractional packing number , then it can be associated to a nc inequality that is maximally violated by quantum mechanics , meaning that no general probabilistic theory satisfying that the sum of probabilities of pairwise exclusive events can not be larger than 1 can achieve a larger value . ( of course , there are graphs for which all theories coincide , as , for example , perfect graphs . ) in the present paper , we propose a construction that translates into the combinatorial language developed in @xcite the connection between every graph state of three or more qubits and a bell inequality maximally violated by quantum mechanics found in @xcite . namely , we describe a construction that maps any graph on three or more vertices @xmath0 into a larger graph , @xmath1 , such that its independence number is strictly smaller than its lovsz number which is equal to its fractional packing number . the vertices of @xmath1 represent all possible events consistent with the stabilizer group of the graph state associated to @xmath0 and exclusive events are adjacent . the construction has also applications in zero - error information theory . it leads to a straightforward protocol achieving the maximum rate of zero - error entanglement - assisted capacity @xcite . we conjecture that this quantity for a graph @xmath1 is always strictly larger than its shannon capacity . a proof of this statement would possibly require a rank bound _ a la haemers_. while it is difficult to compute this bound in general , it may be easier in our case , since @xmath1 has a very particular structure because of the connection with the stabilizer group . the violation of the bell inequality is here expressed by the one - shot version of this capacity being strictly larger than the independence number . the correspondence between graphs and exclusivity structures allows us compute the independence number of the graphs @xmath4 , where @xmath5 is the complete graph , by taking advantage of well - known techniques used in quantum non - locality . since two graphs yield the same ( up to isomorphism ) graph in our construction if and only if they are equivalent under local complementation , the construction can be interpreted as a method to represent local complementation orbits . somehow this is in analogy with the notion of a two - graph , a well - studied mathematical object which represents equivalence classes under the operation of switching ( see ch . 11 of @xcite ) . our work is innovative with respect to @xcite and @xcite in many ways . first , we present a characterization of local complementation orbits , a result of pure combinatorial nature . our representative graphs are obtained via a construction inspired by quantum mechanics . we find tools to analyze the properties of such graphs in @xcite . second , by using the results in @xcite , we discover that local complementation orbits are naturally associated to bell inequalities . we improve the mathematical representation of such bell inequalities by writing down an explicit operational form , namely , a _ pseudo - telepathy game_. the form that we have introduced is often easier to use in both theoretical purposes and the design of laboratory experiments . third , we introduce a novel connection between the results presented in @xcite and @xcite , and zero - error information theory . such a connection is also interesting on its own , since it provides a way to construct families of channels with a separation between classical and quantum capacities starting from _ any _ graph . the remainder of the work is organized as follows . the next section introduces the required terminology and notions : the language of graph theory , non - locality , and channel capacities . the construction is described in section 3 . section 4 discusses the relevant graph - theoretic parameters . section 5 contains examples . we highlight that physical arguments can be useful to consider difficult tasks such as computing the independence number . section 6 is devoted to zero - error capacities . we show that our construction produces infinite families of graphs for which the use of entanglement gives the maximum possible zero - error capacity . section 7 classifies graphs ( or local complementation orbits ) according to the objects obtained via the construction . we point out a link with boolean functions and propose a conjecture about connectedness of the graph representatives .

we describe a construction that maps any connected graph on three or more vertices into a larger graph , , whose independence number is strictly smaller than its lovsz number which is equal to its fractional packing number . the vertices of represent all possible events consistent with the stabilizer group of the graph state associated to , and exclusive events are adjacent . mathematically , the graph corresponds to the orbit of under local complementation . physically , the construction translates into graph - theoretic terms the connection between a graph state and a bell inequality maximally violated by quantum mechanics . in the context of zero - error information theory , the construction suggests a protocol achieving the maximum rate of entanglement - assisted capacity , a quantum mechanical analogue of the shannon capacity , for each . the violation of the bell inequality is expressed by the one - shot version of this capacity being strictly larger than the independence number . finally , given the correspondence between graphs and exclusivity structures , we are able to compute the independence number for certain infinite families of graphs with the use of quantum non - locality , therefore highlighting an application of quantum theory in the proof of a purely combinatorial statement .

we describe a construction that maps any connected graph on three or more vertices into a larger graph , , whose independence number is strictly smaller than its lovsz number which is equal to its fractional packing number . the vertices of represent all possible events consistent with the stabilizer group of the graph state associated to , and exclusive events are adjacent . mathematically , the graph corresponds to the orbit of under local complementation . physically , the construction translates into graph - theoretic terms the connection between a graph state and a bell inequality maximally violated by quantum mechanics . in the context of zero - error information theory , the construction suggests a protocol achieving the maximum rate of entanglement - assisted capacity , a quantum mechanical analogue of the shannon capacity , for each . the violation of the bell inequality is expressed by the one - shot version of this capacity being strictly larger than the independence number . finally , given the correspondence between graphs and exclusivity structures , we are able to compute the independence number for certain infinite families of graphs with the use of quantum non - locality , therefore highlighting an application of quantum theory in the proof of a purely combinatorial statement .

1411.0641

i

the gemini nici planet - finding campaign was a direct - imaging survey of about 250 nearby stars for substellar and planetary - mass companions conducted at gemini south observatory between 2008 and 2012 @xcite . the campaign used the near - infrared coronagraphic imager ( nici , * ? ? ? * ) , which combines adaptive optics , coronagraphy , angular differential imaging @xcite , and dual - channel methane - band infrared imaging to achieve an h - band contrast detection limit of 14.4 magnitudes at 1@xmath2 radius @xcite . the principal scientific results have been published by @xcite , @xcite , @xcite , @xcite , @xcite , and @xcite ; the pipeline processing algorithm is described by @xcite . the multi - epoch imaging data acquired for the campaign require accurate astrometric calibration in order to detect common proper motion and parallax between the host star and any candidate companions and therefore distinguish true companions from background stars . in this paper , we describe the process used to establish the alignment of the nici science detectors relative to the celestial coordinate system and calibrate the world coordinate system ( wcs ) contained in the data headers .

the campaign requires a relative astrometric accuracy of mas across multi - year timescales in order to distinguish true companions from background stars by verifying common proper motion and parallax with their parent stars . most of the campaign data in the gemini science archive are accurate to this level but we identify a number of anomalies and present methods to correct the errors .

we describe the astrometric calibration of the gemini nici planet - finding campaign . the campaign requires a relative astrometric accuracy of mas across multi - year timescales in order to distinguish true companions from background stars by verifying common proper motion and parallax with their parent stars . the calibration consists of a correction for instrumental optical image distortion , plus on - sky imaging of astrometric fields to determine the pixel scale and image orientation . we achieve an accuracy of mas between the center and edge of the 18 nici field , meeting the 20 mas requirement . most of the campaign data in the gemini science archive are accurate to this level but we identify a number of anomalies and present methods to correct the errors .

1010.3101

i

the study of eleven dimensional @xmath7 invariant half - bps supergravity configurations started in @xcite . they depend on a single scalar function satisfying a non - linear toda equation . when there is an extra rotational @xmath8 isometry , there exists an implicit change of variables mapping the latter to a laplace equation , and consequently , to an electrostatic problem . the purpose of this paper is to discuss the geometry of smooth and singular configurations with these symmetries at finite radius of curvature . unlike the case of @xmath9 bps configurations in type iib with @xmath10 symmetry where the precise boundary conditions imposed by regularity were explicitly spelled out in @xcite , a similar treatment of their eleven dimensional counterparts was still missing . there was no understanding of neither the electrostatic configuration responsible for the asymptotics nor the boundary conditions describing the physical solutions to the laplace equation . in this paper we provide a precise answer to both questions , allowing us to state the precise boundary problem describing the most general smooth and singular configurations with these symmetries and to compute their masses . just as smooth translationally invariant configurations have a finite discrete set of conducting disks as their building blocks @xcite , the same will be true for the rotationally invariant ones . first , we study the vacuum configurations . ads@xmath1s@xmath2 is described by a semi - infinite line charge density and a single conducting disk attached to it . the electrostatic problem is that of solving laplace s equation in the presence of a background potential , due to the line charge density , inducing some charge on the conducting disk , with the boundary condition that the potential at the disk is some given constant value . the latter is an integral equation with a unique solution found by copson @xcite . the potential at the disk is fixed by regularity , whereas its size determines the ads radius of curvature . ads@xmath3s@xmath4 has a similar structure but instead of a finite conducting disk , it involves an infinite conducting plane . the electrostatic problem can be solved by the method of images . the distance between the line charge density and this plane determines the ads@xmath11 radius of curvature . a given configuration allows an infinite number of equivalent electrostatic descriptions due to the existence of conformal invariance in the original llm coordinates @xcite . we describe the effect that these conformal transformations have on the electrostatic data describing a single geometry . excited configurations are obtained either by moving the original conducting disk in the ads@xmath1s@xmath2 or by adding extra finite conducting disks . we identify the set of coupled integral equations dealing with the appropriate boundary conditions to this problem , but we only discuss the simplest example for such excited configurations . even though we can not solve for the most general smooth configurations , we compute their masses . we do this by examining the electrostatic potential in a multipole expansion at large distances . matching the asymptotic metric expansion with the one for the singular superstar configurations @xcite , whose mass is well - known , we obtain @xmath12 where @xmath13 stands for the mass in an asymptotic ads@xmath14 with radius of curvature @xmath15 . these expressions are the finite curvature gravity analogues of similar results obtained in field theory , either by analysing the spectrum of half - bps configurations @xcite in abjm @xcite or by considering the @xmath16 limit in some matrix model dual formulations @xcite associated to taking the penrose limit in the gravity description . the singular type iib superstar geometry was described in terms of a continuous distribution of rings and the origin of the singularity was interpreted in terms of coarse - graining of the quantum mechanical information characterising the quantum state in the fermionic phase space formulation of the system @xcite . we prove that the ads@xmath1s@xmath2 and ads@xmath3s@xmath4 superstars @xcite are described in terms of continuous distributions of conducting disks . any such distribution will describe a singular geometry , because the radial electric field component must vanish inside the continuous conductor . geometrically , this forces both the 5-sphere and 2-sphere shrink to zero size at the same time in a non - smooth way , while the time coordinate becomes null . we develop a general boundary condition describing general superstar - like singular configurations in terms of the shape of the continuous boundary distribution of disks . the connection between singular geometries and continuous conductors was already pointed out in @xcite . they used the statistical methods developed in @xcite , to identify singular geometries dual to thermal / typical states in different ensembles of half - bps states . it would be interesting to identify a generic singular configuration in terms of typical states in abjm . to achieve that one needs to understand the precise dictionary between the shape of the conductor and the properties of the quantum states in the field theory .

this allows us to identify the appropriate boundary conditions describing the most general smooth and superstar - like singular configurations . we also compute their masses , matching the expected result from their microscopic interpretation , but now at finite radius of curvature . + _ theoretical physics group , blackett laboratory , + imperial college , london sw7 2az , u.k .

we describe the geometry of the invariant half - bps m - theory configurations considered in llm in terms of their electrostatic variables . we discuss both regular configurations , such as adss and adss vacua or simple excited solutions , and singular ones such as the superstar geometries . this allows us to identify the appropriate boundary conditions describing the most general smooth and superstar - like singular configurations . we also compute their masses , matching the expected result from their microscopic interpretation , but now at finite radius of curvature . + _ theoretical physics group , blackett laboratory , + imperial college , london sw7 2az , u.k . _ + _ school of mathematics and maxwell institute for mathematical sciences , + king s buildings , edinburgh eh9 3jz , united kingdom _ +

cond-mat0207167

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an important property of most quantum phase transitions studied to date in systems with a metallic fermi surface in spatial dimensions @xmath0 is that the critical field theory for the order parameter is a free gaussian theory @xcite . this result has its origin in the fact that the order parameters considered can be expressed as a fermion bilinears , and consequently the order parameter fluctuations are efficiently overdamped and suppressed by fermionic particle and hole excitations near the fermi surface . the temperature dependencies of physical observables near the quantum critical point have been perturbatively computed @xcite , and these can be understood as corrections to scaling@xcite at the gaussian critical point@xcite . the quantum and thermal fluctuations near quantum phase transitions in fermi systems have been used to interpret experiments in a variety of correlated electron materials . in the cuprate superconductors , the anomalous properties in the normal state have been described in terms of the proximity to a quantum phase transition associated with the onset of spin density wave ( sdw ) or charge density wave ( cdw ) order in a fermi liquid @xcite . however , the observed anomalous properties extend to quite high temperatures , and it would be preferable to explain these in theories with stronger non - linearities among the order parameter modes . further , many of the anomalous properties extend to the optimal doping regime where there is no strong evidence of a large correlation length of the sdw and cdw orders . this paper describes an alternative class of quantum critical points whose critical theories are non - gaussian , and which remain strongly coupled even in the presence of a fermi surface because they are below their upper critical dimension . only in such theories can the order parameter relaxation rate , and possibly the quasiparticle energy width , be generically equal to @xmath1 times a universal numerical constant@xcite ( @xmath2 is the absolute temperature ) . examples of such quantum phase transitions abound in insulators and superconductors@xcite , and some of these have been used to explain low temperature properties of the cuprate superconductors @xcite . this paper will discuss transition in metals with a fermi surface , and so the possible regime of applicability is restricted to higher temperatures where superconductivity is absent . our primary focus will be on a transition with a non - local `` topological '' order associated with certain defects in the sdw / cdw order . however , long - range sdw or cdw order will not be present on either side of the critical point . this transition ( shown in fig . [ phase ] below ) is being offered as a candidate@xcite for a possible optimal doping quantum critical point @xcite in the cuprate superconductors . this proposal for the optimal doping quantum critical point must be distinguished from a conventional sdw ordering transition in a _ superconductor _ discussed recently by one of us@xcite ; the latter transition occurs at lower doping concentrations ( near 1/8 ) and was used to predict and explain a number of recent _ low temperature _ neutron scattering and stm experiments . here we are interested in higher dopings and temperatures , where , as we have already noted , the correlation length of conventional sdw / cdw order is surely quite small , but , as we shall discuss below , correlations in a topological order may be far more robust . we also hope for applications of our theory in other correlated materials , like the heavy fermion systems , where many experiments are in disagreement with the conventional weakly coupled theories@xcite . in particular , we will show that the strongly - coupled critical points predict a scaling structure for physical observables which is quite similar to those proposed by schrder _ @xcite related scaling structures are also known to appear near strongly - coupled spin glass quantum critical points , and this is reviewed in appendix [ app : qsg ] . there is one simple route to obtaining a strongly coupled field theory in the presence of a fermi surface that has been discussed earlier @xcite : use restrictions from momentum conservation to prevent the order parameter from coupling linearly to low energy fermionic excitations . for example , a transition with the onset of sdw order at the wavevector @xmath3 , but the geometry of the fermi surface such that no two points on the fermi surface are separated by @xmath3 . in such a situation the order parameter excitations remain undamped , and the fermions appear to be innocuous bystanders to the transition . however , it turns out that the fermi surface can still be relevant for the structure of the critical theory in certain situations ; these effects are related to those that arise in the transitions we do discuss below , and so we defer discussion of this point until section [ sec : sdw ] . turning to transitions characterized by a non - local , ` topological ' order parameter , a situation that has been much discussed in the recent literature@xcite has the electron , @xmath4 , ( @xmath5 is a spin index ) fractionalize into a spinless charge @xmath6 boson , @xmath7 , and a neutral spin 1/2 fermion @xmath8 : @xmath9 this fractionalization transition is described by a @xmath10 gauge theory @xcite , and both @xmath7 and @xmath8 carry a unit gauge charge ; the physical fermion , @xmath4 , is , of course , gauge neutral . if we denote the @xmath10 gauge field by @xmath11 ( @xmath12 are site labels ) , then terms like @xmath13 will generically appear in the effective hamiltonian @xcite . in the fractionalized phase , where the fluctuations of @xmath11 are effectively quenched , this term is a bcs - like pairing of the @xmath8 fermions , and it implies that the fermi surface will generically be gapped out ( except possibly at special points if the pairing is anisotropic ) . consequently , this fractionalization transition does not provide us with a candidate quantum phase transition in the presence of a fermi surface , and we will not consider it further in this paper . the main focus of this paper shall be on a fractionalization transition that does less damage to the integrity of the electron : the electron ( and hence its fermi surface ) remains intact on both sides of the transition , but charge neutral collective modes ( in the particle - hole sector ) do fractionalize ; only at the quantum critical point , and in the associated non - zero temperature quantum critical region , is the electronic quasiparticle ill - defined . _ @xcite have recently given an appealing pictorial description of such a transition . a transition with closely related physical content was introduced in ref . ; we will follow the latter approach here , and will describe the physical content and experimental motivation below in section [ sec : op ] . there have also been earlier discussions of the fractionalization of order parameters in other physical contexts @xcite . after introducing the order parameters in section [ sec : op ] , we write down and classify quantum field theories for the critical points in section [ sec : qft ] . we pause briefly in section [ sec : sdw ] to consider the conventional transitions mentioned above , in which the fermion bilinear order parameter is not damped by fermi surface excitations because of restrictions arising from momentum conservation , and show that it is described by field theories similar to those in section [ sec : qft ] . the latter are subjected to a renormalization group analysis in section [ sec : rg ] , and the physical implications of the results are noted in section [ sec : phys ] .

we describe two dimensional models with a metallic fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension . the primary examples involve transitions with a topological order parameter associated with dislocations in collinear spin density wave ( `` stripe '' ) correlations : the suppression of dislocations leads to a fractionalization of spin and charge collective modes , and this transition has been proposed as a candidate for the cuprates near optimal doping .

we describe two dimensional models with a metallic fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension . the primary examples involve transitions with a topological order parameter associated with dislocations in collinear spin density wave ( `` stripe '' ) correlations : the suppression of dislocations leads to a fractionalization of spin and charge collective modes , and this transition has been proposed as a candidate for the cuprates near optimal doping . the coupling between the order parameter and long - wavelength volume and shape deformations of the fermi surface is analyzed by the renormalization group , and a runaway flow to a non - perturbative regime is found in most cases . a phenomenological scaling analysis of simple observable properties of possible second order quantum critical points is presented , with results quite similar to those near quantum spin glass transitions and to phenomenological forms proposed by schrder _ et al . _ ( nature * 407 * , 351 ( 2000 ) ) .

1207.6042

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we have described a large ( more than 400 nights ) ground - based survey which started in 2007 and is expected to end in 20132014 , aimed at building a grid of spss for the flux calibration of gaia spectra and magnitudes . the technical complexity of gaia requires a large ( @xmath0200 ) set of spss flux tables , calibrated in flux with high precision ( @xmath01% ) and accuracy ( @xmath03% with respect to vega ) , and covering a range of spectral types . spss candidates need to be monitored for constancy ( within @xmath15 mmag ) to ensure the quoted precision in the final calibration . we discussed the adopted calibration strategy , the selection requirements and a list of candidate spss . a brief overview of the adopted data reduction and analysis procedures was also presented , and more details will be discussed in a series of future papers dealing with all technical aspects , data products , photometric catalogues , flux tables , and lightcurves . some preliminary results were presented , showing the data quality , a few problematic cases of candidate spss that were rejected because of identification problems , close companions , and variability . in particular , we detected a new variable star , a calspec standard which is most probably a @xmath2 scuti variable ; follow - up observations for its characterization are ongoing . all data products will be eventually made public together with each gaia data release , within the framework of the dpac ( data processing and analysis consortium ) publication policies . at the moment the accumulated data and literature information are stored locally and can be accessed upon request .

we describe two ground based observing campaigns aimed at building a grid of approximately 200 spectrophotometric standard stars ( spss ) , with an internal% precision and tied to vega within% , for the absolute flux calibration of data gathered by gaia , the esa astrometric mission . in fact , all candidates are also monitored for constancy ( within mmag , approximately ) . in particular , we report on a calspec standard , 1740346 , that we found to be a scuti variable during our short - term monitoring ( 12 h ) campaign .

we describe two ground based observing campaigns aimed at building a grid of approximately 200 spectrophotometric standard stars ( spss ) , with an internal% precision and tied to vega within% , for the absolute flux calibration of data gathered by gaia , the esa astrometric mission . the criteria for the selection and a list of candidates are presented , together with a description of the survey strategy and the adopted data analysis methods . we also discuss a short list of notable rejected spss candidates and difficult cases , based on identification problems , literature discordant data , visual companions , and variability . in fact , all candidates are also monitored for constancy ( within mmag , approximately ) . in particular , we report on a calspec standard , 1740346 , that we found to be a scuti variable during our short - term monitoring ( 12 h ) campaign . [ firstpage ] catalogs techniques : spectroscopic techniques : photometric stars : variables .

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the nature of non - luminous matter that is not part of detected and catalogued galaxies remains unsolved by modern astrophysics . as mentioned in a recent thesis , low surface brightness ( lsb ) objects may prove to be the `` icebergs '' of the extragalactic world ( de blok 1997 ) . some searches for non - luminous matter have been successful , the detection of a giant hi ring around the small group of galaxies in leo centered on m96 ( schneider 1983 ) , extended hi emission in the m81 group ( lo & sargent 1979 ) , hi companions to dwarf galaxies ( for @xmath025% of the cases : taylor 1996 ) , and a large neutral hydrogen cloud in the southern outskirts of the virgo cluster ( hi 1225 + 01 : giovanelli & haynes 1989 ) . along with hi clouds , a few large lsb galaxies have been identified : malin-1 ( bothun 1987 ) , f568 - 6 ( bothun 1990 ) , and 1226 + 0105 ( sprayberry 1993 ) . their typical star formation rates are @xmath00.1 m@xmath1/yr and the metallicities are @xmath01/3 solar . the hi rotation curves , measured by de block ( 1997 ) and by pickering ( 1997 ) , indicate that their gaseous component is dynamically significant at all radii and that the galaxies are fully dark - matter dominated ; their detected baryonic component is less than 4% of the total mass . this last conclusion is valid at least as long as we do not accept any of the more exotic theories of gravitation . the lsb galaxies lack bulges , bars , and nuclear activity , as well as co or ir emission ( have no molecules or dust ) . there have also been a few intriguing reports of presumably intergalactic dust clouds . a cloud with 0.5 - 1.2 mag of extinction was identified in microscopium by hoffmeister ( 1962 ) . three other similar objects were listed by rudnicki ( 1986 ) ; they extinguish background objects by 0.57 to 1.2 mag . in all reports the main point of contention was the actual distance to the cloud , which could put it in extragalactic space but could also locate it in the halo of the milky way ( mw ) . sometimes , the argument for an extragalactic location was based on a comparison of the properties of objects whose distance could be estimated and which were located behind the cloud with those of similar objects clearly not within the cloud limits ( rr lyrae stars ; murawski 1983 ) . the extragalactic nature is only fairly confidently established for the abadi - edmunds cloud at @xmath03 mpc ( abadi & edmunds 1978 ) . hi 21 cm line emission was detected from this object , whereas in other cases it was not . however , in other cases far - infrared ( fir ) emission was detected and could be identified ( on morphological and positional criteria ) with the obscuring clouds . fir and hi emission were clearly detected in the case of the okroy cloud ( wszolek 1988a , 1989 ) . fir emission was only marginally detected from the rudnicki - baranowska cloud ( wszolek 1988b ) . this indicates that the physical conditions in this kind of objects are far from being uniform . more such examples must be identified and their properties examined . it is possible that the phenomenon of intergalactic hydrogen clouds could be related to the high - velocity cloud ( hvc ) complexes . these are hi structures whose radial velocities deviate by several 100 km s@xmath2 from the conventional galactic rotation . a recent review of hvcs is by wakker & van woerden ( 1997 ) . their table 2 lists a few cloud complexes at distances @xmath325 kpc ; some of these may not belong at all to the mw . iras searches for fir emission of hvc were negative ( wakker & boulanger 1986 ) , indicating that either the hvcs are dust - free or that their dust grains are much cooler than could be detected with iras . in this context we also mention the proposition by blitz ( 1999 ) that the hvcs make up the missing mass by being essentially dark halos with low velocity dispersions . we report here results from a study of a diffuse ring - like fir feature at high galactic latitude , which we interpret as `` local '' , not extragalactic , despite first indications to the contrary . the region toward which this feature is located is the center of the virgo cluster of galaxies . this part of the sky has been studied in exquisite detail , yet new studies always detect interesting features . for example , katsiyannis ( 1998 ) produced a very deep image of the central regions of the cluster from a combination of 13 deep kodak techpan films obtained with the uk schmidt telescope . the image shows large variations in the brightness of the intra - cluster medium , with the brightest regions north of the cluster center . m87 is fairly central in the region of enhanced brightness , close to the upper left corner of the `` very high contrast image '' in their fig . previous deep imaging of the central vc region ( weil 1997 ) revealed a diffuse extension of ( presumably stellar ) material extending @xmath0100 kpc to the se of m87 . intergalactic red giant stars were apparently discovered near m87 by ferguson ( 1998 ) . it is therefore relevant to search for , and to try and explain , any extended feature one may detect in the direction of the center of the cluster . in this context , we mention the study of haikala ( 1995 ) who examined the uv emission detected in the direction of a dust globule close to the north galactic pole , slightly north of the virgo cluster ( vc ) . any material that could produce extinction needs to be accounted for . to the best of our knowledge , nobody attempted to study the obscuration and fir emission by ism or igm in the direction of a rich , nearby cluster of galaxies . this is particularly important for the vc , which serves as one of the key stones in the distance ladder leading up to the determination of the hubble constant ( van den bergh 1996 ) . the hst key project on the extragalactic distance scale , where the required accuracy of the determination of h@xmath4 is 10% , could be affected significantly by unaccounted extinction . until now , seven galaxies within 10@xmath5 of the virgo center have been observed for cepheids in this context ( macri 1999 ) . the plan of the paper is as follows : we first describe the fir observations , which revealed the feature , and present confirmatory evidence of its reality . we then attempt to derive additional properties of the feature , which has an approximate ring shape , using data in the optical and radio domains . we show that the dust in the feature does not seem to affect the stars in the milky way but that it apparently reddens galaxies in the vc and beyond . the full data set is discussed in the last section of the paper , in which we also derive some properties of the dust grains in the feature .

we detected a ring - like distribution of far - infrared emission in the direction of the center of the virgo cluster . we studied this feature in the fir , radio , and optical domains , and deduced that the dust within the feature reddens the galaxies in the direction of the virgo cluster but does not affect stars within the milky way . this is likely to be a dusty feature in the foreground of the virgo cluster , presumably in the galactic halo . this is particularly important for studies of the virgo cluster , for example in the determination of the hubble constant from cepheids in cluster galaxies .

we detected a ring - like distribution of far - infrared emission in the direction of the center of the virgo cluster . we studied this feature in the fir , radio , and optical domains , and deduced that the dust within the feature reddens the galaxies in the direction of the virgo cluster but does not affect stars within the milky way . this is likely to be a dusty feature in the foreground of the virgo cluster , presumably in the galactic halo . the hi distribution follows the morphology of the fir emission and shows peculiar kinematic behavior . we propose that a highly supersonic past collision between an hi cloud and the galactic hi formed a shock that heated the interface gas to soft x - ray temperatures . hi remnants from the projectile and from the shocked galactic hi rain down onto the disk as intermediate velocity gas . our finding emphasizes that extragalactic astronomy must consider the possibility of extinction by dust at high galactic latitude and far from the galactic plane , which may show structure on one - degree and smaller scales . this is particularly important for studies of the virgo cluster , for example in the determination of the hubble constant from cepheids in cluster galaxies . # 1#2#3#4#5#6#7 to#2 ' '' ''

astro-ph9905295

c

we identified a ring - like feature of fir emission at high galactic latitude , which is distant from the main body of the galaxy and extinguishes light from galaxies in the central part of the virgo cluster ( vc ) . there is no way to establish a distance to the extinguishing cloud with the data we presented above , except to note that it is probably @xmath241 kpc . a nearby dust feature , observed by haikala ( 1995 ) in the far - uv , has been located at @xmath0120 pc using the distribution of e@xmath42 color excesses . this dust cloudlet produces a visual extinction [email protected] mag and is located at ( l=251.1 , b=+73.3 ) ; this location is very similar to what we found for the virgo ring ( vr ) and may indicate that either our distance evaluation is wrong , or that the location technique of the haikala feature did not use a sufficient number of more distant stars . indications that the dust cloud can not be a nearby feature originate mainly from the lack of influence on the distribution of stars . supporting evidence to the same comes from the reddening study of knude ( 1996 ) . he used uvbyh@xmath44 measurements of a3-g0 stars with [email protected] mag and @xmath46b@xmath47 to determine the distribution of extinction . his results for e@xmath42 , broken by galactic latitude and by longitude quadrants , are of particular interest . the area of interest for our study is located between the 3rd and 4th quadrants at b@xmath48 ; the reddening to this region is small , e@xmath49 , which translates into [email protected] . the stars studied by knude ( 1996 ) are closer than 1.5 kpc ( for main sequence a stars brighter than 11.5 mag ) , thus the color - dependent extinction of the vc galaxies we detected , which is equivalent to [email protected] mag , should be produced by material more distant than 1.5 kpc . if the cloud would be in the vc itself , its physical size would be @xmath01.5 mpc , very large indeed ! the issue of possible diffuse dust in clusters of galaxies has been studied by ferguson ( 1993 ) . he concluded , from the lack of a difference between cluster and field galaxies in the correlation of the mg@xmath51 index and ( b v ) , that dust is not present in the virgo cluster ( upper limit e(b v)@xmath520.06 mag . ) . a similar conclusion for a large number of abell clusters , based on the ( v i ) color indices of radio quasars seen in their background , was reached by maoz ( 1995 ) . not accounting for foreground dust may affect adversely some key observations . our finding confirms the supposition of zonn ( 1957 ) and zonn & stodolkiewicz ( 1958 ) , that because of the patchy structure of the interstellar dust _ it is not enough to correct for extinction assuming that the dust is localized in a narrow slab near the galactic equator , but the detailed distribution of dust must be investigated to account properly for the extinction . _ in particular , many observations of the virgo cluster and of objects within ( the hst cepheid key project : graham 1998 , macri 1999 ) may carry significant errors because of improper extinction corrections . in this section we estimate the dust temperature and dust - to - gas ratio . to evaluate the temperature of the dust in vr we subtracted from the map intensities the minimal value for the central part of the vr , near m87 , in the 100 and 240@xmath6 m cobe / dirbe bands ( 8 and 3.5 mjy sr@xmath2 respectively ) . to determine the color temperature for the dust in the vr cloud we assumed that the dust particles are in thermal equilibrium and that the foreground galactic ir radiation and ir emission from all point sources in the region have been subtracted accurately . these assumptions may not be necessarily fulfilled in our case . the subtraction of the intensity of the inner part of the ring would be accurate only if the distribution of the foreground galactic radiation is fairly smooth ; this is not the case even at high galactic latitudes . some galactic features may add non - negligible fir contributions to the foreground . the radiation from very cold dust grains ( t@xmath303k ) could not be detected by the means used here . we could not rule out the possibility that transient heating of dust grains takes place , and that only occasional excitation by energetic photons or particles causes them to emit brief pulses of the radiation measured by cobe / dirbe and iras . with all these caveats in mind , we calculated the temperature of two regions with maximal fir intensities within regions delimited by : @xmath20 : 185@xmath5186@xmath5 , @xmath22 : 13@xmath514@xmath5 ( approximately the main blob = mb region ) and @xmath20 : 189@xmath5190@xmath5 , @xmath22 : 12@xmath513@xmath5 ( slightly off the secondary fir peak ) . the temperature was calculated with the relation : @xmath53 from schlegel ( 1998 ) , where r=@xmath54 is the ratio of the fir intensities in the cobe / dirbe bands . the results are 22 and 20k for the first and the second region , respectively . these values can be accepted as upper limits for the dust temperature in vr due to both effects mentioned above . the temperatures do not differ significantly from those usually adopted for interstellar dust clouds and are at the high end of the range for the `` warm '' cirrus component ( lagache 1998 ) . the difference between the two regions , with the mb being `` hotter '' than the secondary fir blob , is marginally significant , because the formal error in the derivation of temperatures is 1 - 2k . a study of the optical depth effects of high latitude clouds ( chlewicki & laureijs 1988 ) found that typically @xmath55=0.7 mjy ster@xmath2/10@xmath39 atoms @xmath56 . deul & burton ( 1990 ) studied the hi content and gas kinematics of seven cirrus clouds detected in the iras maps . they established that the fir to hi ratio varies between 0.9 and 3.0 mjy ster@xmath2/10@xmath39 atoms @xmath40 . the color temperature varies much less , between 0.20 and 0.27 for @xmath57 . unfortunately , we did not detect 60@xmath6 m emission from the vr , thus a direct comparison with the color temperature derived by deul & burton ( 1990 ) is not possible . however , the ratio @xmath55 we find for the fir ridges ( @xmath01.5 mjy ster@xmath2/10@xmath39 atoms @xmath40 ) is in the range of that measured for cirrus clouds . we determined n(hi ) from the brightness temperature using data from fig . 9 and applying the conversion @xmath58 assuming that the hi is optically thin . the vr is located close to the northernmost point of the north polar spur ( nps ) and could , in principle , be part of it . the nps is presumably the remnant of a @xmath015 myr old explosive event in the direction of the galactic center , which released 10@xmath59 ergs and could be the outcome of @xmath60 supernovae produced in a small region within one million years . the giant loop is detected in a number of wavebands , from the x - ray to the radio continuum ( sofue 1994 ) . the possibility that the vr is part of a small structure , extending to lower galactic longitudes from near the northernmost apex of the large nps feature in sofue s fig . 2 ( plate l11 ) , can not be excluded . it is also clear that the virgo ring ( vr ) is not a known high velocity cloud , because the compilation of deul & van woerden ( 1990 ) lists as nearest object hvc 2 at 12:09 + 15:32 and v@xmath61=100.7 km s@xmath2 , covering 3.2 square degrees of the sky . wakker & van woerden ( 1997 ) list a possible small hvc near the vr location . this is an hi feature associated with optical absorption lines observed in sn 1994d , located at [email protected] ; [email protected] and @xmath0240 km s@xmath2 lsr . this sn occured in ngc 4526 , and the absorbing gas ( with five absorption systems ) was found by ho & filippenko ( 1996 ) at the same velocity as the hi measured by kumar & thonnard ( 1983 ) . ho & filippenko mention other similar absorption features in the spectrum of sn 1991 t ( at l=292.59 ; b=65.18 , in ngc 4527 ) , which is @xmath62 away from sn1994d . it seems that there is material in the general direction of the vr with lsr velocities a few 100 km s@xmath2 , and that it contains at least ca ii and na i. in the vicinity of the vr , velocities in excess of 100 km s@xmath2 are required in order to qualify an hi feature as a hvc . our analysis of the hi distribution and kinematics , using the lds survey data , indicates that there is a significant disturbance of the hydrogen at the location of the vr . in particular , the three - peak structure of the velocity - column density is peculiar . there are a number of possible explanations for this hi peculiarity , starting from an expanding supernova ( sn ) shell , a collision between galactic hi and a high - velocity cloud , an ejection of a number of shells from a red ( super)giant , etc . each of these possibilities imposes some constrains on the problem . of all these possibilities , we consider the most likely to be that of a past collision between a small hi cloud and galactic hydrogen . the hi remnant of this event could be the feature seen at 30 km s@xmath2 in the high - fir area and the galactic hi would be the prevalent emission at 7 to 9 km s@xmath2 , which shows up in all plots . at a velocity difference of @xmath020 km s@xmath2 the collision would be highly supersonic . we note that the immediate vicinity of the vr has been studied in exactly this context by stark ( 1994 ) . the region most likely to be part of the same complex is the bx field ( see table 1 of stark 1994 ) , where the x feature peaks near 8 km s@xmath2 ( lsr ) but there are parts of the b feature where velocities up to 40 km s@xmath2 are observed . stark ( 1994 ) interpreted the `` intermediate negative velocity '' ( inv ) gas , with v@xmath4520 km s@xmath2 , as material at local velocity displaced by a shock following a collision with a high velocity cloud . the difference in lsr velocity between the bx features and candidate hvcs in this vicinity ( at a few 100 km s@xmath2 positive ) forced stark to propose scenarios for the dissipation of the impinging hvc . they asserted that this cloud has evaporated and is now present as high - temperature gas . collisions of hvcs with the galactic disk have been studied by kerp ( 1996 ) . they show that a collision with a differential velocity of 25 km s@xmath2 may increase the temperature of the post - shock material from 10@xmath63 to 10@xmath64k ; such temperatures are consistent with the euve measurements ( lieu 1996 ) . it is possible to estimate the parameters of the main blob ( mb ) using the hi information from the ldss . with the t@xmath65 value from 30 to 20 km s@xmath2 we find @xmath66 this implies a gas - to - dust ratio for the mb of @xmath675 10@xmath39 @xmath40 mag@xmath2 , different from the canonical value for the galaxy ( @xmath68=5.4 10@xmath69 @xmath40 mag@xmath2 ; bohlin 1975 ) . the mb appears , therefore , to be dust - rich ( or hi - poor ) . its projected angular size is @xmath70 ; this translates to a size of 10(@xmath71 ) pc and a total hydrogen mass of @xmath72 with an average ( volume ) density of @xmath04 @xmath73 cm@xmath13 assuming a spherical configuration . the cloudlet carries significant kinetic energy , considering its velocity relative to the galactic hi ( assumed to be @xmath75 km s@xmath2 ) ; e@xmath763 10@xmath77 ergs . also , the hi profile observed in its direction ( see top panel of fig . 9 ) is significantly wider than that of the second blob ( bottom panel of fig . this could be an indication of higher turbulence within the mb relative to other hi entities in the same vicinty but at less negative lsr velocities . it is significant that the mb , an infalling hi gas cloudlet , contains dust grains as evidenced by the extinction it produces . this indicates that any shocks that the material in mb might have encountered did not heat up its material to temperatures high enough to completely destroy the grains . however , its highly supersonic interaction with the ambient hi distribution caused a wider 21 cm profile . the mb produces significant extinction and is fairly distant from the mw plane while having an intermediate lsr velocity . this is different from the findings of knude & h@xmath78 g ( 1999 ) , who concluded that intermediate - velocity hi clouds show no extinction . the detection of hi condensations on sub - degree scales and high above the galactic plane is relevant for the studies of galaxies in the virgo cluster and beyond . a spectroscopic survey of objects in the background clusters at [email protected] could reveal absorption lines produced by material within the mb cloudlet . this , along with a measure of the ionization presumably taking place at the interface between the mb and the ambient hi , could reveal its composition and location . the essential finding is , however , the small scale on which significant extinction variations are encountered at high @xmath46b@xmath46 . this shows that the derivation of `` average extinction dependences '' , with galactic latitude ( knude 1996 ) , is not very relevant to the determination of cosmologically - important parameters from studies of individual vc galaxies . our study shows that dust can affect the light of background galaxies in the vc and , through this , the determination of h@xmath4 by using cepheid photometry . this hst key project relies on a canned approach to deredden individual stars and is based on the `` standard '' mw extinction law with r=@xmath79=3.3 ( c.f . madore & freedman 1991 ) . it remains to be proven that this relation applies for high galactic latitude dust clouds , such as those studied here .

we propose that a highly supersonic past collision between an hi cloud and the galactic hi formed a shock that heated the interface gas to soft x - ray temperatures . hi remnants from the projectile and from the shocked galactic hi rain down onto the disk as intermediate velocity gas . our finding emphasizes that extragalactic astronomy must consider the possibility of extinction by dust at high galactic latitude and far from the galactic plane , which may show structure on one - degree and smaller scales .

we detected a ring - like distribution of far - infrared emission in the direction of the center of the virgo cluster . we studied this feature in the fir , radio , and optical domains , and deduced that the dust within the feature reddens the galaxies in the direction of the virgo cluster but does not affect stars within the milky way . this is likely to be a dusty feature in the foreground of the virgo cluster , presumably in the galactic halo . the hi distribution follows the morphology of the fir emission and shows peculiar kinematic behavior . we propose that a highly supersonic past collision between an hi cloud and the galactic hi formed a shock that heated the interface gas to soft x - ray temperatures . hi remnants from the projectile and from the shocked galactic hi rain down onto the disk as intermediate velocity gas . our finding emphasizes that extragalactic astronomy must consider the possibility of extinction by dust at high galactic latitude and far from the galactic plane , which may show structure on one - degree and smaller scales . this is particularly important for studies of the virgo cluster , for example in the determination of the hubble constant from cepheids in cluster galaxies . # 1#2#3#4#5#6#7 to#2 ' '' ''

1501.07442

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the identification of high - energy ( regge ) dynamics in qcd processes has been long since theoretically investigated . with the advent of high - energy colliders like hera , tevatron and lhc such studies have become possible at experimental level too . the processes which are expected to be more sensitive to this peculiar dynamical regime , where the center - of - mass energy @xmath1 is much larger than all hard scales involved in the scattering , are the so - called _ mueller - navelet _ ( mn ) _ jets _ at hadron - hadron colliders @xcite and _ forward jets _ at electron - hadron colliders @xcite . both of them are defined by the presence of qcd jets at large rapidity , accompanied by any hadronic activity which is inclusively collected in the central region . such processes can be theoretically described by factorization formulae which involve several ingredients : the partonic distribution functions ( pdfs ) of the incoming hadron(s ) , the gluon green s function ( ggf ) describing the high - energy dynamics of emitted and exchanged partons mostly ( reggeized ) gluons and finally the so - called jet vertices , describing the production of a forward jet from the interaction of one incoming parton and a reggeized gluon . in the case of an incoming electron , an additional quantity , the photon impact factor , has to be considered too . at present , all ingredients are known at next - to - leading level in the respective parameters : the pdfs which resum logarithms of collinear type , the ggf resumming logarithms of the energy , and the jet vertices ( and impact - factors ) which are computed at finite perturbative order . focusing for definiteness on mn jets in hadron - hadron collision , the process - dependent part of the cross section is represented by the jet vertex @xcite , which depends on the jet variables and the actual jet algorithm . by following the work of ivanov and papa @xcite , in this paper we reconsider the computation of the jet vertex in the small - cone approximation ( sca ) , namely for jets whose extension in the rapidity - azimuthal angle @xmath2-plane is small . in particular we apply their method to determine the analytic expressions of the jet vertex for two particular choices of jet algorithms : the _ kt algorithm _ @xcite and the _ cone algorithm _ @xcite . these are the mostly used algorithms in modern jet phenomenology , in particular the kt one . on the contrary , the algorithm used in @xcite can be traced back to the one considered by furman @xcite in early studies of qcd radiation , but not used for practical purposes anymore , being infra - red unsafe . the aim of our work is twofold : on one hand we want to give a precise estimate of the error introduced by the small - cone approximation in the description of qcd observables at high energies , i.e. , at large rapidities , so as to possibly justify its use in phenomenological analyses . on the other hand , we want to estimate the differences occurring by choosing different jet algorithms for the same process . the jet algorithm dependence has already been studied in the past , and a detailed analysis of the cone and kt algorithms in the sca was presented in ref . @xcite in the context of collinear factorization . here we carry out a similar analysis in the framework of high - energy ( kt - dependent ) factorization , the basic tool for the description of the regge regime in perturbative qcd . one should keep in mind that the small - cone expressions are fully analytic ( before their convolution with the pdfs ) and compact , and allow a simple implementation in numerical codes that run much faster than those with the exact jet vertices . for this reason the sca jet vertices have already been used@xcite in quantitative comparison with available data@xcite . however , the experimental results were extracted by clustering jets with the kt algorithm , while the sca jet vertices used for the theoretical calculation were those obtained with the furman algorithm by ivanov and papa ( fip ) . also the small - cone analysis performed in ref . @xcite compared calculations with the exact jet vertices in the kt algorithm versus the small - cone ones in the fip algorithm . starting from these premises , and after reviewing in sec . [ s : ts ] the theoretical setup for the description of mueller - navelet jets in terms of the collinear and high - energy factorization formulae , in sec . [ s : jetalg ] we discuss in detail the differences among the three ( kt , cone and fip ) jet algorithms in the relevant case of two near particles and we determine the kinematical configurations in the limit of small jet `` radius '' @xmath3 . we then derive the small - cone jet vertices for the kt and cone algorithms in sec . [ s : scjv ] , by computing their differences with respect to the fip algorithm induced by the different kinematical conditions . in sec . [ s : nc ] we perform a numerical study in order to asses the quantitative difference between the exact and small - cone jet vertex in the kt algorithm , by comparing the vertices themselves as well as a typical differential cross section for mn jets and some angular coefficients measuring the azimuthal decorrelation between the jets . in addition we also determine the discrepancies of the same quantities induced by a different choice of the jet algorithm . we discuss the results in sec . [ s : conc ] , where we conclude that the wrong choice of algorithm causes sizeable errors on the predictions , while the sca within the same algorithm provides a good approximation to the exact quantities and can therefore be used as a valuable tool for a quantitative description of mn and forward jets .

we determine the jet vertex for mueller - navelet jets and forward jets in the small - cone approximation for two particular choices of jet algoritms : the kt algorithm and the cone algorithm . the differences with the original calculations of the small - cone jet vertex by ivanov and papa , which is found to be equivalent to a formerly algorithm proposed by furman , are shown at both analytic and numerical level , and turn out to be sizeable . a detailed numerical study of the error introduced by the small - cone approximation is also presented , for various observables of phenomenological interest . for values of the jet `` radius ''

we determine the jet vertex for mueller - navelet jets and forward jets in the small - cone approximation for two particular choices of jet algoritms : the kt algorithm and the cone algorithm . these choices are motivated by the extensive use of such algorithms in the phenomenology of jets . the differences with the original calculations of the small - cone jet vertex by ivanov and papa , which is found to be equivalent to a formerly algorithm proposed by furman , are shown at both analytic and numerical level , and turn out to be sizeable . a detailed numerical study of the error introduced by the small - cone approximation is also presented , for various observables of phenomenological interest . for values of the jet `` radius '' , the use of the small - cone approximation amounts to an error of about 5% at the level of cross section , while it reduces to less than 2% for ratios of distributions such as those involved in the measure of the azimuthal decorrelation of dijets .

1302.4593

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the study of effective smooth torus actions on compact , smooth manifolds has a rich and long tradition in the theory of smooth transformation groups ( cf . @xcite ) . in riemannian geometry , starting with hsiang and kleiner s topological classification of compact riemannian @xmath0-manifolds of positive ( sectional ) curvature with an effective isometric circle action @xcite , isometric actions of tori have been successfully used to obtain classification results on compact riemannian manifolds with positive or nonnegative curvature and large isometry groups ( cf . @xcite ) . the present paper s main contribution is the observation that several results on smooth torus actions on compact smooth simply connected manifolds , and on isometric torus actions on compact simply connected riemannian manifolds with positive or nonnegative curvature , hold under less restrictive conditions which do not involve the existence of a group action . indeed , many of these results do not hold because of the presence of a torus action , but rather because the orbit decomposition of the manifold has the structure of a _ singular riemannian foliation _ whose leaves are diffeomorphic to flat tori of possibly different dimensions . to make this statement precise , we introduce a special class of singular riemannian foliations , _ b - foliations _ , which generalize isometric torus actions on complete riemannian manifolds . roughly speaking , a b - foliation @xmath2 is a partition of a complete riemannian manifold @xmath3 into connected closed submanifolds , called the _ leaves _ of @xmath4 , all of which are homeomorphic to some flat manifold and are at a constant distance from each other . more generally , b - foliations are a particular instance of singular riemannian foliations whose leaves are homeomorphic to some closed aspherical manifold . we will call such singular riemannian foliations _ a - foliations_. the fact that a - foliations are more general than isometric torus actions is clear for several reasons . on the one hand , the leaves need not be tori . on the other hand , even when the leaves of an a - foliation @xmath2 on a complete riemannian manifold @xmath3 are diffeomorphic to standard tori , the foliation may not be homogeneous , i.e. there might not be a global torus action on @xmath3 inducing the given singular riemannian foliation @xmath4 . this occurs , for example , when the distribution of the tangent spaces of the torus leaves is not orientable . moreover , we assume the leaves of an a - foliation to be homeomorphic to aspherical manifolds , but not necessarily diffeomorphic . therefore , our main results hold when the leaves carry exotic smooth structures , e.g. in the case of exotic tori . nevertheless , we do not know of any non - trivial examples of singular riemannian foliations whose leaves are exotic tori . it would be interesting to find b - foliations by exotic tori on simply connected manifolds and , in particular , on spheres . in this paper we focus our attention on a- and b - foliations on compact simply connected riemannian manifolds . although every aspherical manifold can appear as the regular leaf of an a - foliation , our first result implies that the simply connected case is considerably more rigid . [ t : fund_gp ] let @xmath2 be a closed singular riemannian foliation on a compact , simply connected riemannian manifold @xmath3 . if @xmath5 is a regular leaf of @xmath4 , then @xmath6 is isomorphic to @xmath7 , where @xmath8 is abelian and @xmath9 is a finite @xmath10 step nilpotent @xmath10-group . in particular , we have the following corollary : [ c : torus_leaves]let @xmath2 be an a - foliation on a compact riemannian manifold @xmath3 . if @xmath3 is simply connected , then the regular leaves are homeomorphic to tori . observe that @xmath10 step nilpotent @xmath10-groups already appear as fundamental groups of regular leaves of codimension one singular riemannian foliations and hence can not be avoided in the statement of theorem a ( cf . * table 1.4 ) ) . this occurs , for example , in the cohomogeneity one @xmath11 action on @xmath12 . with theorem [ t : fund_gp ] and corollary [ c : torus_leaves ] in place , we extend to a- and b - foliations several basic results on smooth effective torus actions on smooth compact manifolds ( cf . we prove : [ t : kobayashi ] let @xmath2 be a b - foliation on a compact riemannian manifold @xmath3 and let @xmath13 denote the stratum of @xmath14-dimensional leaves . then @xmath15 . [ t : codim_1_bfol_sc ] the only codimension @xmath16 a - foliations on compact , simply connected riemannian manifolds are the homogeneous singular riemannian foliations @xmath17 and @xmath18 . [ t : bfol_codim2 ] let @xmath19 be a codimension @xmath10 a - foliation on a compact , simply connected riemannian manifold @xmath20 with @xmath21 . then either @xmath22 and @xmath4 is given by a weighted hopf action , or the following hold : + 1 . the leaf space @xmath23 is homeomorphic to a @xmath10-disk , the interior of @xmath24 is smooth , and the boundary @xmath25 consists of at least @xmath26 totally geodesic segments meeting at an angle of @xmath27 . let @xmath28 be a generic leaf and @xmath29 a singular leaf . then there is a submersion @xmath30 , with fiber @xmath31 if @xmath29 belongs to a geodesic in @xmath25 , or with fiber @xmath32 , if @xmath29 belongs to a vertex of @xmath25 . another generalization of isometric torus actions are the so - called _ f - structures _ , introduced by cheeger and gromov @xcite . these structures are , roughly speaking , generalized local torus actions and play a central role in the cheeger - fukaya - gromov theory of collapsed riemannian manifolds with bounded sectional curvature ( cf . the so - called _ pure _ f - structures ( see @xcite ) give rise to b - foliations with leaves diffeomorphic to flat manifolds . recall that , by work of cheeger , fukaya and gromov , there exists a constant @xmath33 , such that any compact riemannian manifold @xmath34 with curvature @xmath35 , @xmath36 and @xmath37 admits a pure f - structure ( see @xcite and references therein ) . therefore , @xmath34 is b - foliated . although b - foliations resemble f - structures , the two concepts are independent . a b - foliation on a riemannian manifold does not necessarily correspond to an f - structure since , for instance , b - foliations with exotic torus leaves can not be generated by f - structures . on the other hand , certain f - structures among those that are not pure do not generate a b - foliation . + as an application of our results , we extend work in @xcite on positively and nonnegatively curved compact , simply connected riemannian manifolds with large effective isometric torus actions to the case of a - foliations . recall that a riemannian manifold @xmath38 is said to have _ quasi - positive curvature _ if @xmath38 has nonnegative ( sectional ) curvature and a point with strictly positive curvature . [ t : qpc_d4_codim2 ] let @xmath39 be a compact , simply connected riemannian @xmath26-manifold with quasi - positive curvature supporting a codimension @xmath10 a - foliation . if @xmath40 , then @xmath41 is diffeomorphic to @xmath12 or @xmath42 . + 2 . if @xmath43 , then @xmath44 is diffeomorphic to @xmath45 . [ t : nnc_d4_codim2 ] let @xmath39 be a compact , simply connected riemannian @xmath26-manifold with nonnegative curvature and a codimension @xmath10 a - foliation . + 1 . if @xmath40 , then @xmath41 is diffeomorphic to @xmath12 , @xmath42 or homeomorphic to @xmath46 or @xmath47 . + 2 . if @xmath43 , then @xmath44 is diffeomorphic to @xmath45 or to one of the two @xmath48-bundles over @xmath49 . [ t : d4_s1fol ] let @xmath3 be a compact , simply connected riemannian @xmath0-manifold with a singular riemannian foliation by circles . then the foliation is induced by a smooth circle action and the following hold : + 1 . if @xmath3 has positive curvature , then @xmath3 is diffeomorphic to @xmath12 or @xmath42 . + 2 . if @xmath3 has nonnegative curvature , then @xmath3 is diffeomorphic to @xmath12 , @xmath42 , @xmath46 or @xmath47 . + in part ( 1 ) of theorem [ t : nnc_d4_codim2 ] the classification is only up to homeomorphism because we do not know whether the a - foliation is induced by a smooth torus action . we call a b - foliation _ euclidean _ if its regular leaves are flat with the induced riemannian metric and define the _ euclidean rank _ of a riemannian manifold @xmath38 as the maximum dimension of euclidean b - foliations on @xmath3 compatible with the fixed metric @xmath50 . this invariant generalizes the symmetry rank of @xmath38 ( cf . it follows from otsuki s lemma ( * ? ? ? * lemma 3.3 , p. 224 ) ( cf . also an argument due to wilking found in @xcite ) that the euclidean rank of a compact , quasi - positively curved riemannian @xmath26-manifold is less than or equal to @xmath51 . in dimension @xmath52 , it is easy to show , following the comparison arguments in the proof of theorem [ t : nnc_d4_codim2 ] , that the euclidean rank of a compact , simply connected riemannian @xmath26-manifold of nonnegative curvature is bounded above by @xmath53 . these bounds coincide with the corresponding bounds for the symmetry rank ( cf . @xcite ) . our paper is structured as follows . in section [ basic ] we recall some basic facts on singular riemannian foliations . in section [ s : b_fol ] we introduce a- and b - foliations and show that the infinitesimal foliation at any point of a manifold with an a- or a b - foliation is also an a- or a b - foliation , respectively . sections [ s : fundgp_leaves ] through [ s : codim_2 ] contain the proofs of theorems [ t : fund_gp ] through [ t : bfol_codim2 ] . section [ s : curv_1 ] contains the proof of theorems [ t : qpc_d4_codim2 ] and [ t : nnc_d4_codim2 ] . finally , in section [ s : curv_2 ] we prove theorem [ t : d4_s1fol ] . throughout our paper we will assume all manifolds to be connected and without boundary , unless stated otherwise . the second named author thanks xiaoyang chen for some initial conversations . both authors wish to acknowledge the hospitality of the mathematisches forschungsinstitut oberwolfach , where the work presented in this paper was initiated . the authors also thank wolfgang ziller for comments on a first version of this paper , alexander lytchak for suggestions which led to the proofs of theorems [ t : fund_gp ] and [ t : fibration - flat ] , and the referee for suggesting improvements to our original results .

we also study closed singular riemannian foliations whose leaves are homeomorphic to aspherical or to bieberbach manifolds . these foliations , which we call _ a - foliations _ and _ b - foliations _ , respectively , generalize isometric torus actions on riemannian manifolds . we apply our results to the classification problem of compact , simply connected riemannian- and-manifolds with positive or nonnegative sectional curvature . [ multiblock footnote omitted ]

we determine the structure of the fundamental group of the regular leaves of a closed singular riemannian foliation on a compact , simply connected riemannian manifold . we also study closed singular riemannian foliations whose leaves are homeomorphic to aspherical or to bieberbach manifolds . these foliations , which we call _ a - foliations _ and _ b - foliations _ , respectively , generalize isometric torus actions on riemannian manifolds . we apply our results to the classification problem of compact , simply connected riemannian- and-manifolds with positive or nonnegative sectional curvature . the author is part of sfb 878 : _ groups , geometry & actions _ , at the university of mnster . ] [ multiblock footnote omitted ]

1306.1999

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gaussian process ( gp ) models provide a flexible , probabilistic approach to regression and are widely used . however , application of gp models to large data sets is challenging as the memory and computational requirements scale as @xmath0 and @xmath1 respectively , where @xmath2 is the number of training data points . various sparse gp approximations have been proposed to overcome this limitation . a unifying framework of existing sparse methods is given in @xcite . we consider the stationary sparse spectrum gp regression model introduced by @xcite , where the spectrum of the covariance function is sparsified instead of the usual spatial domain . the ssgp algorithm developed by @xcite for fitting this model uses conjugate gradients to optimize the marginal likelihoood with respect to the hyperparameters and spectral points . comparisons with other state - of - the - art sparse gp approximations such as the fully independent training conditional model ( first introduced as sparse pseudo - input gp in * ? ? ? * ) and the sparse multiscale gp @xcite , showed that ssgp yielded significant improvements . however , optimization with respect to spectral frequencies increases the tendency to underestimate predictive uncertainty and poses a risk of overfitting in the ssgp algorithm . in this paper , we develop a fast variational approximation scheme for the sparse spectrum gp regression model , which enables uncertainty in covariance function hyperparameters to be treated . in addition , we propose an adaptive local neighbourhood approach for dealing with nonstationary data . although accounting for hyperparameter uncertainty may be of little importance when fitting globally to a large data set , local fitting within neighbourhoods results in fitting to small data sets even if the full data set is large , and here it is important to account for hyperparameter uncertainty to avoid overfitting . our examples show that our methodology is particularly beneficial when combined with the local fitting approach for this reason . our approach also allows hierarchical models involving covariance function parameters to be constructed . this idea is implemented in the context of functional longitudinal models by mensah _ ( 2014 ) so that smoothness properties of trajectories can be related to individual specific covariates . gps have diverse applications and various methods have been developed to overcome their computational limitations for handling large data sets . a good summary of approximations used in modelling large spatial data sets is given in @xcite . computational costs can also be reduced through local gp regression as a much smaller number of training data is utilized in each partition . this approach has been considered in machine learning ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) and in spatial statistics ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? @xcite propose fitting gp models in local neighbourhoods which are defined online for each test point . however , covariance hyperparameters are estimated only for a subset of all possible local neighbourhoods . different local experts are then combined using a mixture model capable of handling multimodality . our idea of using adaptive nearest neighbours in gp regression is inspired by techniques in classification designed to mitigate the curse of dimensionality @xcite . for each test point , we fit two models . in the first instance , the neighbourhood is determined using the euclidean metric . lengthscales estimated from the first fitting are then used to redefine the distance measure determining the neighbourhood for fitting the second model . experiments suggest that this approach improves prediction significantly in data with nonstationarities , as hyperparameters are allowed to vary across neighbourhoods adapted to each query point . weighting dimensions according to lengthscales downweights variables of little relevance and also leads to automatic variable selection . our approach differs from methods where local neighbourhoods are built sequentially to optimize the choice of the neighbourhood . examples include @xcite and @xcite , where the gaussian likelihood is approximated by the use of an ordering and conditioning on a subset of past observations . in @xcite , an empirical bayes mean - square prediction error criterion is optimized . while greedy searches usually rely on fast updating formulae available only in the gaussian case , our approach works in non - gaussian settings as well . @xcite suggest making neighbourhoods non - local to improve learning of covariance parameters , but local neighbourhoods may work better when the motivation is to handle nonstationarity . @xcite make a connection between discrete spatial markov random fields and continuous gaussian random fields with covariance functions in the matrn class . for fitting the sparse spectrum gp regression model , we derive a variational bayes ( vb , * ? ? ? * ) algorithm that uses nonconjugate variational message passing @xcite to derive fast and efficient updates . vb methods approximate the intractable posterior in bayesian inference by a factorized distribution . this product density assumption is often unrealistic and can lead to underestimation of posterior variance @xcite . however , optimization of a factorized variational posterior can be decomposed into local computations that only involve neighbouring nodes in the factor graph and this often gives rise to fast computational algorithms . vb has also been shown to be able to give reasonably good estimates of the marginal posterior distributions and excellent predictive inferences ( e.g. * ? ? ? * ; * ? ? ? variational message passing @xcite is a general - purpose algorithm that allows vb to be applied to conjugate - exponential models @xcite . nonconjugate variational message passing extends variational message passing to nonconjugate models by assuming that the factors in vb are members of the exponential family . we use nonconjugate variational message passing to derive efficient updates for the variational posteriors of the lengthscales , which are assumed to be gaussian . @xcite use vb for spatial modelling via gp , where they also treat uncertainty in the covariance function hyperparameters . however , they propose using importance sampling within each vb iteration to handle the intractable expectations associated with the covariance function hyperparameters . variational inference has also been considered in machine learning for sparse gps that select the inducing inputs and hyperparameters by maximizing a lower bound to the exact marginal likelihood @xcite , and heteroscedastic gp regression models where the noise is input dependent @xcite . vb is known to suffer from slow convergence when there is strong dependence between variables in the factors . to speed up convergence , @xcite propose parameter expanded vb to reduce coupling in updates , while @xcite considered partially noncentered parametrizations . here , we introduce an adaptive strategy to accelerate convergence in nonconjugate variational message passing , which is inspired by adaptive overrelaxed bound optimization methods @xcite . previously , @xcite showed that nonconjugate variational message passing is a natural gradient ascent algorithm with step size one and step sizes smaller than one correspond to damping . here , we propose using step sizes larger than one which can help to accelerate convergence in fixed point iterations algorithms ( see * ? ? ? * ) . instead of searching for the optimal step size , we use an adaptive strategy which ensures that the lower bound increases after each cycle of updates . empirical results indicate significant speedups . @xcite considered combining parameter - wise updates to form a diagonal direction for a line search . a general iterative algorithm for computing vb estimators ( defined as means of variational posteriors ) has also been proposed by @xcite and its convergence properties investigated for normal mixture models . section [ ssgpmodel ] describes the sparse spectrum gp regression model and section [ variational inference ] develops the nonconjugate variational message passing algorithm for fitting it . section [ adaptive strategy ] presents an adaptive strategy for accelerating convergence in nonconjugate variational message passing . section [ pred distn ] discusses how the predictive distribution can be estimated and the measures used for performance evaluation . section [ neigh ] describes the adaptive neighbourhood approach for local regression . section [ eg ] considers examples including real and simulated data and section [ conclusion ] concludes .

we develop a fast variational approximation scheme for gaussian process ( gp ) regression , where the spectrum of the covariance function is subjected to a sparse approximation . our approach enables uncertainty in covariance function hyperparameters to be treated without using monte carlo methods and is robust to overfitting . our article makes three contributions . first , we present a variational bayes algorithm for fitting sparse spectrum gp regression models that uses nonconjugate variational message passing to derive fast and efficient updates .

we develop a fast variational approximation scheme for gaussian process ( gp ) regression , where the spectrum of the covariance function is subjected to a sparse approximation . our approach enables uncertainty in covariance function hyperparameters to be treated without using monte carlo methods and is robust to overfitting . our article makes three contributions . first , we present a variational bayes algorithm for fitting sparse spectrum gp regression models that uses nonconjugate variational message passing to derive fast and efficient updates . second , we propose a novel adaptive neighbourhood technique for obtaining predictive inference that is effective in dealing with nonstationarity . regression is performed locally at each point to be predicted and the neighbourhood is determined using a measure defined based on lengthscales estimated from an initial fit . weighting dimensions according to lengthscales , this downweights variables of little relevance , leading to automatic variable selection and improved prediction . third , we introduce a technique for accelerating convergence in nonconjugate variational message passing by adapting step sizes in the direction of the natural gradient of the lower bound . our adaptive strategy can be easily implemented and empirical results indicate significant speedups . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

1306.1999

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in this paper , we have presented a nonconjugate variational message passing algorithm for fitting sparse spectrum gp regression models where closed form updates are possible for all variational parameters , except for the evaluation of @xmath116 . we note that @xmath116 can be evaluated very efficiently using quadrature and there is almost no computational overhead when compared to updates based on conditionally conjugate inverse - gamma priors for the variance parameters . however , half - cauchy priors lead to much better predictive inference especially in the adaptive neighbourhood approach where the amount of training data is small . a bayesian approach has been adopted for parameter estimation which allows covariance function hyperparameter uncertainty to be treated and empirical results suggest that this improves prediction ( especially in the mnlp values ) and prevents overfitting . we also propose a novel adaptive neighbourhood technique for obtaining predictive inference which is adept at handling data with nonstationarities and this approach can be extended to large data sets as well . the simulated data sets showed that weighting the dimensions according to the lengthscales estimated from an initial fit is very effective at downweighting variables of little relevance , leading to automatic variable selection and improved prediction . in addition , we introduce a technique for accelerating convergence in nonconjugate variational message passing by taking step sizes larger than one in the direction of the natural gradient of the lower bound . we do not attempt to search for the optimal step size but adopt an adaptive strategy that can be easily implemented , and empirical results indicate significant speed - ups . algorithm [ alg2 ] is thus an attractive alternative for fitting sparse spectrum gp regression models , which is stable , robust to overfitting for small data sets and capable of dealing with highly nonstationary data as well when used in combination with the adaptive neighbourhood approach . we thank lucy marshall for supplying the rainfall - runoff data set . linda tan was partially supported as part of the singapore delft water alliance s tropical reservoir research programme . david nott , ajay jasra and victor ong s research was supported by a singapore ministry of education academic research fund tier 2 grant ( r-155 - 000 - 143 - 112 ) . we also thank the referees and associate editor for their comments which have helped improved the manuscript . references amari , s. : natural gradient works efficiently in learning . neural computation 10 , 251276 ( 1998 ) attias , h. : inferring parameters and structure of latent variable models by variational bayes . in laskey , k. and prade , h. ( eds . ) proceedings of the 15th conference on uncertainty in artificial intelligence , pp . morgan kaufmann , san francisco , ca ( 1999 ) attias , h. : a variational bayesian framework for graphical models . in solla , s. a. , leen , t. k. and mller , k .- advances in neural information processing systems 12 , pp . mit press , cambridge , ma ( 2000 ) blei , d. m. and jordan , m. i. : variational inference for dirichlet process mixtures . bayesian analysis 1 , 121144 ( 2006 ) boughton , w. : the australian water balance model . environmental modelling and software 19 , 943956 ( 2004 ) braun , m. and mcauliffe , j. : variational inference for large - scale models of discrete choice . journal of the american statistical association 105 , 324335 ( 2010 ) gelman , a. : prior distributions for variance parameters in hierarchical models . bayesian analysis 1 , 515533 ( 2006 ) gramacy , r. b. and apley , d. w. ( 2014 ) . local gaussian process approximation for large computer experiments . journal of computational and graphical statistics . to appear . haas , t. c. : local prediction of a spatio - temporal process with an application to wet sulfate deposition . journal of the american statistical association 90 , 11891199 ( 1995 ) hastie , t. and tibshirani , r. : discriminant adaptive nearest neighbor classification . ieee transactions on pattern analysis and machine intelligence 18 , 607616 ( 1996 ) hoffman , m. d. , blei , d. m. , wang , c. and paisley , j. : stochastic variational inference . journal of machine learning research 14 , 13031347 ( 2013 ) honkela , a. , valpola , h. and karhunen , j. : accelerating cyclic update algorithms for parameter estimation by pattern searches . neural processing letters 17 , 191203 ( 2003 ) huang , h. , yang , b. and hsu , c. ( 2005 ) . triple jump acceleration for the em algorithm . in han , j. , wah , b. w. , raghavan , v. , wu , x. and rastogi , r. ( eds . ) proceedings of the 5th ieee international conference on data mining , pp . ieee computer society , washington , dc , usa . , mallicka , b. k. and holmesa , c. c. : analyzing nonstationary spatial data using piecewise gaussian processes . journal of the american statistical association 100 , 653668 ( 2005 ) knowles , d. a. , minka , t. p. : non - conjugate variational message passing for multinomial and binary regression . in shawe - taylor , j. , zemel , r. s. , bartlett , p. , pereira , f. and weinberger , k. q. ( eds . ) advances in neural information processing systems 24 , pp . red hook , ny : curran associates , inc . ( 2011 ) lzaro - gredilla , m. , quionero - candela , j. , rasmussen , c. e. and figueiras - vidal , a. r. : sparse spectrum gaussian process regression . journal of machine learning research 11 , 18651881 ( 2010 ) lzaro - gredilla , m. and titsias , m. k. : variational heteroscedastic gaussian process regression . in getoor , l. and scheffer , t. ( eds . ) proceedings of the 28th international conference on machine learning , pp . omnipress , madison , mi , usa ( 2011 ) lindgren , f. , rue , h. and lindstrm , j. : an explicit link between gaussian fields and gaussian markov random fields : the stochastic partial differential equation approach . journal of the royal statistical society : series b 73 , 423498 ( 2011 ) magnus , j. r. and neudecker , h. : matrix differential calculus with applications in statistics and econometrics . wiley , chichester , uk ( 1988 ) nguyen - tuong , d. , seeger , m. and peters , j. : model learning with local gaussian process regression . advanced robotics 23 , 20152034 ( 2009 ) nott , d. j. , tan , s. l. , villani , m. and kohn , r. : regression density estimation with variational methods and stochastic approximation . journal of computational and graphical statistics 21 , 797820 ( 2012 ) ormerod , j. t. and wand , m. p. : explaining variational approximations . the american statistician 64 , 140153 ( 2010 ) park , s. and choi , s. : hierarchical gaussian process regression . in sugiyama , m. and yang , q. ( eds . ) proceedings of 2nd asian conference on machine learning , pp . 95110 ( 2010 ) qi , y. and jaakkola , t. s. : parameter expanded variational bayesian methods . in schlkopf , b. , platt , j. and hofmann , t. ( eds . ) advances in neural information processing systems 19 , pp . 10971104 . mit press , cambridge ( 2006 ) quinlan , r. : combining instance - based and model - based learning . in proceedings on the tenth international conference of machine learning , 236 - 243 . university of massachusetts , amherst . morgan kaufmann ( 1993 ) quionero - candela , t. and rasmussen , c. e. : a unifying view of sparse approximate gaussian process regression . journal of machine learning research 6 , 19391959 ( 2005 ) rasmussen , c. e. and williams , c. k. i. : gaussian processes for machine learning . mit press , cambridge , ma ( 2006 ) ren , q. , banerjee , s. , finley , a. o. and hodges , j. s. : variational bayesian methods for spatial data analysis . computational statistics and data analysis 55 , 31973217 ( 2011 ) salakhutdinov , r. and roweis , s. : adaptive overrelaxed bound optimization methods . in fawcett , t. and mishra , n. ( eds . ) proceedings of the 20th international conference on machine learning , pp . 664671 . aaai press , menlo park , california ( 2003 ) snelson , e. and ghahramani , z. : sparse gaussian processes using pseudo - inputs . in weiss , y. , schlkopf , b. and platt , j. ( eds . ) advances in neural information processing systems 18 , pp . 12571264 . mit press , cambridge , ma . ( 2006 ) snelson , e. and ghahramani , z. : local and global sparse gaussian process approximations . in meila , m. and shen , x. ( eds ) jmlr workshop and conference proceedings volume 2 : aistats 2007 , pp . 524531 ( 2007 ) stan development team : rstan : the r interface to stan , version 2.5.0 . http://mc-stan.org/rstan.html ( 2014 ) stein , m. l. , chi , z. and welty , l. j. : approximating likelihoods for large spatial data sets . journal of the royal statistical society : series b 66 , 275296 ( 2004 ) tan , l. s. l. and nott , d. j. : variational inference for generalized linear mixed models using partially non - centered parametrizations . statistical science 28 , 168188 ( 2013 tan , l. s. l. and nott , d. j. : a stochastic variational framework for fitting and diagnosing generalized linear mixed models . bayesian analysis ( 2014 ) . doi : 10.1214/14-ba885 titsias , m. k. : . variational learning of inducing variables in sparse gaussian processes . in van dyk , d. and welling , m. ( eds . ) proceedings of the 12th international conference on artificial intelligence and statistics , pp . 567574 ( 2009 ) urtasun , r. and darrell , t. : sparse probabilistic regression for activity - independent human pose inference . in ieee conference on computer vision and pattern recognition 2008 , pp . 18 ( 2008 ) vecchia , a. v. : estimation and model identication for continuous spatial processes . journal of the royal statistical society : series b 50 , 297312 ( 1988 ) walder , c. , kim , k. i. and schlkopf , b. : sparse multiscale gaussian process regression . in mccallum , a. and roweis , s. ( eds . ) proceedings of the 25th international conference on machine learning pp . acm press , new york ( 2008 ) wand , m. p. , ormerod , j. t. , padoan , s. a. and frhrwirth , r. : mean field variational bayes for elaborate distributions . bayesian analysis 6 , 847900 ( 2011 ) wand , m. p. : fully simplified multivariate normal updates in non - conjugate variational message passing . journal of machine learning research 15 , 13511369 ( 2014 ) wang , b. and titterington , d. m. : inadequacy of interval estimates corresponding to variational bayesian approximations . in cowell , r. g. and ghahramani , z. ( eds . ) , _ proceedings of the 10th international workshop on artificial intelligence and statistics _ , pp . 373380 . society for artificial intelligence and statistics ( 2005 ) wang , b. and titterington , d. m. : convergence properties of a general algorithm for calculating variational bayesian estimates for a normal mixture model . bayesian analysis 3 , 625650 ( 2006 ) winn , j. and bishop , c.m . : variational message passing . journal of machine learning research 6 , 661694 ( 2005 )

second , we propose a novel adaptive neighbourhood technique for obtaining predictive inference that is effective in dealing with nonstationarity . weighting dimensions according to lengthscales , this downweights variables of little relevance , leading to automatic variable selection and improved prediction . third , we introduce a technique for accelerating convergence in nonconjugate variational message passing by adapting step sizes in the direction of the natural gradient of the lower bound . our adaptive strategy can be easily implemented and empirical results indicate significant speedups .

we develop a fast variational approximation scheme for gaussian process ( gp ) regression , where the spectrum of the covariance function is subjected to a sparse approximation . our approach enables uncertainty in covariance function hyperparameters to be treated without using monte carlo methods and is robust to overfitting . our article makes three contributions . first , we present a variational bayes algorithm for fitting sparse spectrum gp regression models that uses nonconjugate variational message passing to derive fast and efficient updates . second , we propose a novel adaptive neighbourhood technique for obtaining predictive inference that is effective in dealing with nonstationarity . regression is performed locally at each point to be predicted and the neighbourhood is determined using a measure defined based on lengthscales estimated from an initial fit . weighting dimensions according to lengthscales , this downweights variables of little relevance , leading to automatic variable selection and improved prediction . third , we introduce a technique for accelerating convergence in nonconjugate variational message passing by adapting step sizes in the direction of the natural gradient of the lower bound . our adaptive strategy can be easily implemented and empirical results indicate significant speedups . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

1101.5805

i

as advances in technology allow for the collection and storage of vast databases , there is a growing need for advanced machine learning techniques for speeding up the execution of queries on such large datasets . in this work we focus on the fundamental task of estimating the selectivity , or output size , of a database query , which is a crucial step in a number of query processing tasks such as execution plan optimization and resource allocation in parallel and distributed databases . the task of efficiently obtaining such accurate estimates has been extensively studied in previous work with solutions ranging from storage of pre - computed statistics on the distribution of values in the tables , to online sampling of the databases , and to combinations of the two approaches @xcite . histograms , simple yet powerful statistics of the data in the tables , are the most commonly used solution in practice , thanks to their computational and space efficiency . however , there is an inherent limitation to the accuracy of this approach when estimating the selectivity of queries that involve either multiple tables / columns or correlated data . running the query on freshly sampled data gives more accurate estimates at the cost of delaying the execution of the query while collecting random samples from a disk or other large storage medium and then performing the analysis itself . this approach is therefore usually more expensive than a histogram lookup . our goal in this work is to exploit both the computational efficiency of using pre - collected data and the provable accuracy of estimates obtained by running a query on a properly sized random sample of the database . we apply the statistical concept of vc - dimension @xcite to develop and analyze a novel technique to generate accurate estimates of query selectivity . roughly speaking , the vc - dimension of a collection of indicator functions ( hypotheses ) is a measure of its complexity or expressiveness ( see sect . [ sec : vcdim ] for formal definitions ) . a major theoretical contribution of this work , which is of independent interest , is an explicit bound to the vc - dimension of any class of queries , viewed as indicator functions on the cartesian product of the database tables . in particular , we show that the vc - dimension of a class of queries is a function of the maximum number of boolean , select and join operations in any query in the class , but it is not a function of the number of different queries in the class . by adapting a fundamental result from the vc - dimension theory to the database setting , we develop a method that for any class of queries , defined by its vc - dimension , builds a concise sample of the database , such that with high probability , the execution of _ any _ query in the class on the sample provides an accurate estimate for the selectivity of the query on the original large database . the error probability holds _ simultaneously _ for the selectivity estimate of _ all _ queries in the collection , thus the same sample can be used to evaluate the selectivity of multiple queries , and the sample needs to be refreshed only following major changes in the database . the size of the sample does not depend on the size ( number of tuples ) in the database , just on the complexity of the class of queries we plan to run , measured by its vc - dimension . both the analysis and the experimental results show that accurate selectivity estimates can be obtained using a sample of a surprising small size ( see table [ tab : samplesize ] for concrete values ) , which can then reside in main memory , with the net result of a significant speedup in the execution of queries on the sample . a technical difficulty in applying the vc - dimension results to the database setting is that they assumes the availability of a uniform sample of the cartesian product of all the tables , while in practice it is more efficient to store a sample of each table separately and run the queries on the cartesian product of the samples , which has a different distribution than a sample of the cartesian product of the tables . we develop an efficient procedure for constructing a sample that circumvents this problem ( see sect . [ sec : applications ] ) . we present extensive experimental results that validate our theoretical analysis and demonstrate the advantage of our technique when compared to complex selectivity estimation techniques used in postgresql and the microsoft sql server . the main advantage of our method is that it gives provably accurate predictions for the selectivities of all queries with up to a given complexity ( vc - dimension ) specified by the user before creating the sample , while techniques like multidimensional histograms or join synopses are accurate only for the queries for which they are built . note that we are only concerned with estimating the selectivity of a query , not with approximating the query answer using a sample of the database ( das @xcite presents a survey of the possible solutions to this latter task ) . [ [ outline . ] ] outline . + + + + + + + + the rest of the paper is organized as follows . we review the relevant previous work in sect . [ sec : prevwork ] . in sect . [ sec : prelim ] we formulate the problem and introduce the vapnik - chervonenkis dimension and the related tools we use in developing our results . our main analytical contribution , a bound on the vc dimension of class of queries is presented in sect . [ sec : vcdimqueries ] . the application of these results for selectivity estimation is given in sect . [ sec : applications ] . experiments are presented in sect . [ sec : experiments ] .

we develop a novel method , based on the statistical concept of the _ vapnik - chervonenkis dimension _ , to evaluate the selectivity ( output cardinality ) of sql queries a crucial step in optimizing the execution of large scale database and data - mining operations . the major theoretical contribution of this work , which is of independent interest , is an explicit bound to the vc - dimension of a range space defined by all possible outcomes of a collection ( class ) of queries . we prove that the vc - dimension is a function of the maximum number of boolean operations in the selection predicate and of the maximum number of select and join operations in any individual query in the collection , but it is neither a function of the number of queries in the collection nor of the size ( number of tuples ) of the database . we leverage on this result and develop a method that , given a class of queries , builds a concise random sample of a database , such that with high probability the execution of _ any _ query in the class on the sample provides an accurate estimate for the selectivity of the query on the original large database . the error probability holds _ simultaneously _ for the selectivity estimates of _ all _ queries in the collection , thus the same sample can be used to evaluate the selectivity of multiple queries , and the sample needs to be refreshed only following major changes in the database . the sample representation computed by our method is typically sufficiently small to be stored in main memory . we present extensive experimental results , validating our theoretical analysis and demonstrating the advantage of our technique when compared to complex selectivity estimation techniques used in postgresql and the microsoft sql server .

we develop a novel method , based on the statistical concept of the _ vapnik - chervonenkis dimension _ , to evaluate the selectivity ( output cardinality ) of sql queries a crucial step in optimizing the execution of large scale database and data - mining operations . the major theoretical contribution of this work , which is of independent interest , is an explicit bound to the vc - dimension of a range space defined by all possible outcomes of a collection ( class ) of queries . we prove that the vc - dimension is a function of the maximum number of boolean operations in the selection predicate and of the maximum number of select and join operations in any individual query in the collection , but it is neither a function of the number of queries in the collection nor of the size ( number of tuples ) of the database . we leverage on this result and develop a method that , given a class of queries , builds a concise random sample of a database , such that with high probability the execution of _ any _ query in the class on the sample provides an accurate estimate for the selectivity of the query on the original large database . the error probability holds _ simultaneously _ for the selectivity estimates of _ all _ queries in the collection , thus the same sample can be used to evaluate the selectivity of multiple queries , and the sample needs to be refreshed only following major changes in the database . the sample representation computed by our method is typically sufficiently small to be stored in main memory . we present extensive experimental results , validating our theoretical analysis and demonstrating the advantage of our technique when compared to complex selectivity estimation techniques used in postgresql and the microsoft sql server .

1209.3071

i

cooling and trapping polyatomic molecules is a promising research direction within the rapidly expanding field of cold molecular gases @xcite . because of their rich internal structure and coupled vibrational degrees of freedom , polyatomic molecules offer new research opportunities at the interface between chemistry , physics , combustion @xcite , atmospheric chemistry @xcite , and astrochemistry @xcite . studies of intramolecular energy redistribution in complex organic molecules yield insight into a broad range of phenomena , ranging from biochemical reactions involved in visual transduction @xcite to quantum decoherence in mesoscopic systems @xcite . unlike diatomic molecules , polyatomic molecules composed of four ( or more ) atoms can exist in the form of left and right - handed isomers and high - precision spectroscopy of cold molecular ensembles can provide insight into parity violation @xcite and hund s paradox @xcite . internal cooling increases the population of low - lying rovibrational states and hence the molecular response to external field perturbations , while cooling of external ( translational ) degrees of freedom enhances the molecule - field interaction time . high - precision spectroscopy of cold polyatomic molecules may thus enable ultrasensitive molecular detection and separation of different conformers @xcite as well as the development of novel time and frequency standards @xcite . while indirect cooling techniques such as photo - association and magneto - association are highly efficient at producing ultracold alkali - dimers @xcite , they can not be extended in a straightforward manner to cool polyatomic molecules due to the lack of efficient laser cooling methods for all but a handful of atomic species @xcite . direct cooling techniques such as sympathetic cooling @xcite , velocity filtering @xcite , rotating nozzle slowing @xcite , and stark deceleration @xcite are free from these difficulties , as demonstrated by recent experiments on the production of cold ensembles of fully deuterated ammonia @xcite , benzonitrile @xcite , formaldehyde @xcite , and naphthalene @xcite . slow beams of polyatomic molecules thus produced have already been used , in combination with electromagnetic traps , to explore the dynamics of oh + nd@xmath6 @xcite and li + sf@xmath7 @xcite collisions at low temperatures . however , quantum collision dynamics of polyatomic molecules in the presence of external electromagnetic fields remains poorly understood , necessitating the development of theoretical tools for _ ab initio _ modeling of these pioneering experiments as well as for the realization of efficient strategies for controlled molecular cooling @xcite . theoretical studies of polyatomic molecule collisions in the absence of external fields were pioneered by green @xcite , who developed a formal quantum theory of collisions involving asymmetric tops , and carried out scattering calculations on various problems of astrophysical interest , including he + hcn , he + h@xmath2o , and he + nh@xmath6 @xcite . many authors employed green s formalism to carry out accurate scattering calculations of rotational cooling rates for interstellar molecules colliding with atomic and molecular species based on accurate _ ab initio _ interaction potentials @xcite . several theoretical studies have used a combination of high - level _ ab initio _ and quantum scattering calculations to explore the dynamics of collision - induced rovibrational relaxation of methylene ( ch@xmath8 ) and methyl ( ch@xmath6 ) radicals in room - temperature he buffer gas @xcite , for which accurate rate measurements have recently become available @xcite . a number of related theoretical studies have focused on field - free collisions of h@xmath2o , co@xmath2 , and benzene molecules with he atoms at temperatures below 1 k @xcite . these calculations were motivated by the ongoing experiments on sympathetic cooling of optically decelerated @xcite polyatomic molecules with rare gas atoms @xcite . in particular , evidence was reported for slow rotational energy transfer in cold collisions of highly rotationally excited co@xmath2 molecules with he atoms @xcite . a recent classical trajectory study of he - naphthalene scattering @xcite has shown that the unexpected lack of cluster formation observed in buffer - gas cooling experiments on naphthalene @xcite can be attributed to the short lifetime of the he - naphthalene complex . we have recently presented a rigorous quantum scattering methodology for numerical calculations of collisional properties of polyatomic molecular radicals with @xmath9-state atoms in the presence of an external magnetic field @xcite . the method is based on the fully uncoupled space - fixed representation of the scattering wave function originally introduced by volpi and bohn @xcite and krems and dalgarno @xcite to investigate collisions of diatomic molecules in a magnetic field . in ref . we studied the quantum dynamics of spin relaxation in collisions of spin-1/2 and spin-1 polyatomic molecular radicals induced by collisions with he atoms . we found that many of these polyatomic molecules have favorable collisional properties ( that is , large ratios of elastic to inelastic collisions rates ) with he atoms , making them amenable to cryogenic buffer - gas cooling and possibly sympathetic cooling with @xmath9-state atoms in a magnetic trap @xcite . here , we present a full account of the theory and computational methodology outlined in our previous work @xcite . we begin with the derivation of coupled - channel quantum scattering equations for a polyatomic molecule colliding with an @xmath9-state atom in the presence of an external magnetic field ( sec . iib ) . in sec . iii , we use the newly developed scattering methodology to address the question of collisional stability of methylene radicals in cold @xmath10he gas in the presence of an external magnetic field . after a brief outline of the _ ab initio _ techniques employed to obtain the adiabatic pes for the he - ch@xmath2 complex ( sec . iiia ) , we present and discuss the main results for elastic and inelastic cross sections and thermal rate constants for spin relaxation in he + ch@xmath2 collisions ( sec . we then analyze the scaling properties of the inelastic cross sections and discuss the mechanism of spin relaxation of different nuclear spin isomers ( sec . iiic ) and isotopomers ( sec . iiid ) of ch@xmath2 . section iv summarizes the main results of this work . atomic units are used throughout unless stated otherwise .

we develop a rigorous quantum mechanical theory for collisions of polyatomic molecular radicals with s - state atoms in the presence of an external magnetic field . the theory is based on a fully uncoupled space - fixed basis set representation of the multichannel scattering wavefunction . explicit expressions are presented for the matrix elements of the scattering hamiltonian for spin-1/2 and spin-1 polyatomic molecular radicals interacting with structureless targets . the theory is applied to calculate the cross sections and thermal rate constants for spin relaxation in low - temperature collisions of the prototypical organic molecule methylene [ ch with he atoms . to this end , our calculations show that spin relaxation in collisions of ch , chd , and cd molecules with he atoms occurs at a much slower rate than elastic scattering over a large range of temperatures ( 1k 1 k ) and magnetic fields ( 0.01 1 t ) , suggesting excellent prospects for cryogenic helium buffer - gas cooling of ground - state-ch molecules in a magnetic trap .

we develop a rigorous quantum mechanical theory for collisions of polyatomic molecular radicals with s - state atoms in the presence of an external magnetic field . the theory is based on a fully uncoupled space - fixed basis set representation of the multichannel scattering wavefunction . explicit expressions are presented for the matrix elements of the scattering hamiltonian for spin-1/2 and spin-1 polyatomic molecular radicals interacting with structureless targets . the theory is applied to calculate the cross sections and thermal rate constants for spin relaxation in low - temperature collisions of the prototypical organic molecule methylene [ ch with he atoms . to this end , two highly accurate three - dimensional potential energy surfaces ( pess ) of the he - ch complex are developed using the state - of - the - art ccsd(t ) method and large basis sets . both pess exhibit shallow minima and are weakly anisotropic . our calculations show that spin relaxation in collisions of ch , chd , and cd molecules with he atoms occurs at a much slower rate than elastic scattering over a large range of temperatures ( 1k 1 k ) and magnetic fields ( 0.01 1 t ) , suggesting excellent prospects for cryogenic helium buffer - gas cooling of ground - state-ch molecules in a magnetic trap . furthermore , we find that-ch undergoes collision - induced spin relaxation much more slowly than-ch , which indicates that magnetic trapping can be used to separate nuclear spin isomers of open - shell polyatomic molecules .

0811.4768

i

we use the term _ protodisc _ to refer to the disc region that is initially formed when wind material from a star is channelled by dipole - type magnetic fields towards the equatorial plane . the material in a protodisc region has no radial motion and rotates with the magnetic field . it is bounded above and below by shock boundaries . we develop models for the structure and evolution of protodiscs around magnetic rotator stars . we study protodiscs as separate entities while recognising that they may be precursors of quasi - steady discs , such as those of be stars . we do not construct models of quasi - steady discs in this paper but indicate how protodiscs relate to models of be star discs . for example , a protodisc region could initially be present in the inner part of the quasi - steady disc model with slow outflow studied by @xcite . also , a more detailed study of protodiscs is important to verify how centrifugal outflow in protodiscs of rapidly rotating stars ( e.g. , * ? ? ? * ; * ? ? ? * ) affects the formation of quasi - steady discs around magnetic rotator stars . in this paper we consider protodiscs around stellar models with both uniform and differential rotation . we study how their radial extents change with time and we determine the conditions under which mri will occur to affect the angular velocity distribution and the radial outflow in the disc region . there has been a tremendous increase in observations of emission line b stars , including polarisation , interferometry and magnetic diagnostics , but the question of how discs with near keplerian rotation speeds are formed around them is has not been fully answered . there can be other mechanisms that are responsible for disc formation in different stars depending on their properties . for example , @xcite have proposed a decretion disc model for be stars with near maximal rotation speeds . there is no magnetic force in their model and angular momentum is transported by viscous forces . be stars are known to rotate rapidly ( e.g. , see * ? ? ? * ) and the presence of significant magnetic fields in ob stars has been reported by several authors ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the concept of a wind compressed disc was initially developed by @xcite . subsequently , @xcite proposed a magnetically torqued disk(mtd ) model in which a sufficiently strong magnetic field channels a flow of wind material towards the equatorial plane to form a disc and provides the torque required by the disc to maintain quasi - keplerian rotation speeds . @xcite developed the magnetic rotator wind disk(mrwd ) model in which keplerian discs may be formed with stellar magnetic fields that do not have to be as strong as those required in the mtd model . @xcite presented an amended version of the mtd model to include stellar gravity darkening and @xcite suggested that this should be further modified to include the effect of gravity arising from finite thickness of the disc . @xcite have studied the properties of discs with slow radial outflow and address criticisms of the mtd model . in the mrwd model for rotating stars with winds , when magnetic field lines that emerge from the stellar surface loop back to the star , a transient disc that has no meridional motion and corotates with the star is initially formed . after the local density in the disc has increased to a value where the centrifugal force exceeds the sum of gravity and the magnetic force , material diffuses radially outwards while stretching out the magnetic field lines . @xcite suggested that such material can diffuse into quasi - steady discs and that the presence of viscosity during this stage would enable the formation of keplerian discs of larger radial extent . on the other hand , numerical simulations by @xcite for the flow of wind material along dipole magnetic field lines display centrifugal breakout in the form of transient bursts and they concluded that mtd type models were not appropriate to explain disc formation . however , there are problems with their simulations : ( a ) as pointed out by @xcite they did not follow changes for a sufficiently long duration of time . ( b ) the simulations are essentially two dimensional . ( c ) numerical mhd simulations do not always provide accurate results because discretization of the mhd induction equation leads to the introduction of artificial magnetic diffusivity that is several orders of magnitude larger than the real magnetic diffusivity in discs . this can yield spurious results for magnetic reconnection that may not be realistic . ( d ) their models fail to consider differentially rotating stars and , therefore , do not obtain differentially rotating disc regions that are subject to the onset of mri . the occurrence of mri can significantly affect the rotation speed in a disc region . we carry out an analytical study and obtain time - dependent solutions for uniform and differentially rotating stars . we find that when the stellar angular velocity increases along the surface towards the equator there is a broad range of stellar parameters for which mri occurs in a sufficiently large part of the protodisc region . we consider a stellar model in which the magnetic field is dipole - type over some region of the stellar surface , so that field lines leaving the stellar surface pass through the equatorial plane and return to the star . wind material flowing along such lines is channelled into a dense equatorial protodisc region . since the flow of supersonic wind material into this region from above and below are in opposite directions , this material will cross shock surfaces that form the upper and lower boundaries of the disc region . we refer to the region between the sonic surface of the wind and the shock boundary of the disc as the _ wind zone_. thus , we need not be concerned about gas pressure effects on the wind flow , which is treated in an empirical fashion in that the velocity is chosen to obey a beta law and the density is assumed to follow from a global mass conservation relation . in section [ sec - windzone ] , we set up the relevant properties of axially symmetric wind zones that enable us to determine values of physical quantities at points on the wind side of the shock boundary from known values at the stellar surface . we develop formalism to account for the presence of differential rotation along the region of the stellar surface from which wind material flows into the disc region . the material in a protodisc region has no radial motion and rotates with magnetic field lines because the centrifugal and pressure gradient forces that are directed outwards are balanced by gravity and magnetic force . in section [ sec - proto - region ] we describe the general concept of a protodisc , which is a more generalised version of the pre - keplerian disc developed in the mrwd model . also , we describe the physical processes that are involved in their formation and evolution . in section [ sec - shock - proto - jump - conditions ] , we develop mhd generalisations of the rankine - hugoniot jump conditions that are appropriate for shock boundaries of protodiscs so that we can compute changes in values of quantities across shock surfaces . we take into account the vertical motion of shock surfaces caused by continuous filling up of a protodisc region by wind material . in section [ sec - disc - proto - eqns ] , we develop the equations that govern the structure of the models of protodiscs that we consider . we explicitly include the effect of the component of stellar gravity perpendicular to discs and , because of shock heating of the disc region , we include the vertical and radial components of the thermal pressure gradient in the respective momentum equations for protodiscs . even though the heights of protodiscs may be relatively small , the presence of a vertical component of stellar gravity leads to a vertical gradient of pressure and density . the equatorial density of material in the protodisc increases with time as the disc fills up . this has the effect of increasing the centrifugal force in relation to the magnetic force as well as increasing the thermal pressure in relation to magnetic pressure . the first of these effects tends to cause material at the outer edge of a protodisc to move radially outwards whereas the latter leads to the onset of mri within the protodisc . to determine the relative importance of these competing effects , in section [ sec - onset - mri - protodiscs ] we derive criteria that influence the evolution of protodiscs . also , we discuss the conditions under which the shrinking of a protodisc caused by centrifugal outflow is halted by the onset of mri . this leads to viscous readjustment of the rotation speed of the disc region . in section [ sec - disc - proto - applics - results ] , we apply our equations and jump conditions to protodiscs of different stellar models and present the results of our computations . in section [ sec - evln - protodisc - after - mri ] , we discuss important factors that affect the evolution of protodisc material after the onset of mri and refer to some relevant quasi - steady models . our conclusions regarding the formation and evolution of protodiscs around rotating magnetic stars with winds are summarised in section [ sec - discussion ] . an important objective of this paper is to relate the properties of protodisc regions to values of quantities at the stellar surface . therefore , we include all the equations that are necessary to solve for the different physical quantities in the wind zone , at the shock surface and in the protodisc region .

we develop equations and obtain solutions for the structure and evolution of a protodisc region that is initially formed with no radial motion and super - keplerian rotation speed when wind material from a hot rotating star is channelled towards its equatorial plane by a dipole - type magnetic field .

we develop equations and obtain solutions for the structure and evolution of a protodisc region that is initially formed with no radial motion and super - keplerian rotation speed when wind material from a hot rotating star is channelled towards its equatorial plane by a dipole - type magnetic field . its temperature is aroundk because of shock heating and the inflow of wind material causes its equatorial density to increase with time . the centrifugal force and thermal pressure increase relative to the magnetic force and material escapes at its outer edge . the protodisc region of a uniformly rotating star has almost uniform rotation and will shrink radially unless some instability intervenes . in a star with angular velocity increasing along its surface towards the equator , the angular velocity of the protodisc region decreases radially outwards and magnetorotational instability ( mri ) can occur within a few hours or days . viscosity resulting from mri will readjust the angular velocity distribution of the protodisc material and may assist in the formation of a quasi - steady disc . thus , the centrifugal breakout found in numerical simulations for uniformly rotating stars does not imply that quasi - steady discs with slow outflow can not form around magnetic rotator stars with solar - type differential rotation . [ firstpage ] circumstellar matter stars : early type stars : emission - line , be stars : magnetic fields stars : rotation stars : winds , outflows

0811.4768

c

in this paper , we set up equations and jump conditions to study the formation , structure and evolution of protodiscs around rotating magnetic stars with winds . we obtain solutions for a variety of stellar models with different rotation rates and magnetic field strengths . when the magnetic field of a rotating hot star is strong enough to channel the flow of wind material towards the equatorial plane and field lines from the stellar surface cross the equatorial plane and return to the star , a protodisc with super - keplerian rotation and no radial motion will be formed in an equatorial region . initially , the sum of the magnetic force and gravity in this region is sufficient to prevent any radial outflow that may be caused by the centrifugal force and thermal pressure . as wind material continues to flow into the protodisc , its equatorial density and height increase with time . the resulting increase in centrifugal force relative to the magnetic force causes the material at the outer edge of the protodisc to move outwards so that the radial extent of the protodisc region decreases . shock heating causes protodisc temperatures rise to values of order @xmath338k . because the radiative cooling time is longer than the heating up time , protodiscs retain their high temperatures . there is no meridional flow of material within a protodisc and the continuing increase in density causes the thermal pressure in the protodisc to increase in relation to the magnetic pressure . when the rotation rate of the central star satisfies the condition @xmath214 and the angular velocity of the protodisc region decreases radially outwards , mri will occur before the radial extent of the protodisc can decrease significantly . in the case of most stars with near critical rotation rates such that @xmath216 , the time taken for the onset of mri is longer than the time by the protodisc to shrink to a thin ring . the evolution of protodiscs is strongly influenced by the inflow of wind material , centrifugal outflow and the occurrence of mri . the protodisc phase of a disc region terminates either when it shrinks completely or when some instability such as mri sets in . we derive conditions for centrifugal outflow at the outer edge of a protodisc and for the onset of mri in a protodisc . we perform numerical computations to study the structure and properties of protodiscs of several different stellar models and to determine how the protodisc phase terminates . our results show that there are situations involving different field strength domains that lead to the formation of protodiscs that suffer mri soon after their formation or shrink to a thin ring when no instability intervenes . equation ( [ eqn - proto - relation - omega - omega ] ) gives the angular velocity of a protodisc in terms of that of the central star . when the central star has uniform rotation , the protodisc has approximately uniform rotation and if no instability intervenes , its radial extent continues to decrease . a protodisc region may take a long time to shrink completely and during most of this time it would appear like a ring . however , it is not clear whether steady uniform rotation is possible in the surface regions of rapidly rotating early type stars because large scale meridional circulations must occur in the radiative envelopes of such stars . meridional circulation will transport angular momentum and disrupt the angular velocity distribution to cause differential rotation . studies by @xcite showed that steady rotation may be possible in the interior of the radiative envelope with angular velocity constant along field lines and having about @xmath339 percent variation from uniform rotation . however , because of the sensitivity of meridional circulation near the stellar surface to perturbations in angular velocity , steady uniform rotation may not possible in the surface region . other efforts to develop models of steady uniform or differential rotation in early type stars with magnetic fields have been discussed by @xcite and @xcite . we are not aware of any conclusive theoretical or observational evidence that early type stars with fast rotation and magnetic fields will have steady unform rotation along the surface . when the stellar surface has differential rotation with angular velocity increasing towards the equator , equation ( [ eqn - proto - relation - omega - omega ] ) shows the angular velocity of the protodisc decreases radially outwards . in this case , mri occurs in the protodisc within a few hours or days . we know that such rotation occurs in the sun , where the differential rotation is maintained by meridional circulation and convection ( see e.g. , * ? ? ? recently , @xcite have suggested that convection zones will be present near the surface of rotating massive stars . this situation is the same as in the surface regions of the sun where convective motions and meridional circulation are present . thus , we suggest that it is reasonable to expect that there are massive stars with solar - type differential rotation . our study of protodiscs was motivated in large part by the claim that discs will not form around magnetic rotator stars because of centrifugal breakout found by @xcite in numerical simulations of uniformly rotating stars . @xcite had previously pointed out that centrifugal outflow of protodisc material due to increased density could diffuse into keplerian , especially when viscosity was present . in studying the evolutionary properties of protodiscs , we have focussed on centrifugal outflow and the onset of mri . it is possible that there are other mhd instabilities that may also play a role in the evolution of protodiscs to quasi - steady discs . we have been able to show that under certain highly plausible conditions at the stellar surface , mri can occur in protodiscs before they shrink significantly through centrifugal outflow . protodiscs in which mri occurs in an inner part before the outer edge shrinks to that part are of interest because viscosity arising from the onset of mri may be able to redistribute the angular velocity of the disc so that material may diffuse into a quasi - steady disc region with slow outflow . although , constructing detailed models of quasi - steady discs is beyond the scope our present work , we simply point out that there are such models that are plausible . in the first model , the disc magnetic field remains connected to the stellar field and a quasi - steady disc forms with inflow from the wind zone and slow radially outward flow with field lines stretching out with the flow ( e.g. , * ? ? ? another possible quasi - steady model is one in which a protodisc evolves after the onset of mri into a magnetic rotator decretion disc ( analogous to the model of * ? ? ? * ) with inflow of super - keplerian wind material . therefore , the centrifugal breakouts found in the numerical simulations of @xcite in uniformly rotating models does not mean that quasi - steady discs can not form around differentially rotating magnetic rotator stars . we have not addressed the question of how protodiscs may be detected observationally . because the duration of the protodisc phase in most cases is rather short , being of the order of a few hours to many days , special observational efforts will be required during disc formation phases to infer their presence . in some special cases , protodiscs can survive for a few years in the form of rings .

its temperature is aroundk because of shock heating and the inflow of wind material causes its equatorial density to increase with time . the centrifugal force and thermal pressure increase relative to the magnetic force and material escapes at its outer edge . the angular velocity of the protodisc region decreases radially outwards and magnetorotational instability ( mri ) can occur within a few hours or days . viscosity resulting from mri will readjust the angular velocity distribution of the protodisc material and may assist in the formation of a quasi - steady disc . thus , the centrifugal breakout found in numerical simulations for uniformly rotating stars does not imply that quasi - steady discs with slow outflow can not form around magnetic rotator stars with solar - type differential rotation . [ firstpage ] circumstellar matter stars : early type stars : emission - line , be stars : magnetic fields stars : rotation stars : winds , outflows

we develop equations and obtain solutions for the structure and evolution of a protodisc region that is initially formed with no radial motion and super - keplerian rotation speed when wind material from a hot rotating star is channelled towards its equatorial plane by a dipole - type magnetic field . its temperature is aroundk because of shock heating and the inflow of wind material causes its equatorial density to increase with time . the centrifugal force and thermal pressure increase relative to the magnetic force and material escapes at its outer edge . the protodisc region of a uniformly rotating star has almost uniform rotation and will shrink radially unless some instability intervenes . in a star with angular velocity increasing along its surface towards the equator , the angular velocity of the protodisc region decreases radially outwards and magnetorotational instability ( mri ) can occur within a few hours or days . viscosity resulting from mri will readjust the angular velocity distribution of the protodisc material and may assist in the formation of a quasi - steady disc . thus , the centrifugal breakout found in numerical simulations for uniformly rotating stars does not imply that quasi - steady discs with slow outflow can not form around magnetic rotator stars with solar - type differential rotation . [ firstpage ] circumstellar matter stars : early type stars : emission - line , be stars : magnetic fields stars : rotation stars : winds , outflows

alg-geom9706004

i

suppose we are given linear subspaces @xmath0 of @xmath1 with @xmath2 and @xmath3 . our problem is to find all @xmath4-dimensional linear subspaces of @xmath1 which meet each @xmath5 nontrivially . when the given linear subspaces are in general position , the condition @xmath6 guarantees that there is a finite number @xmath7 of such @xmath4-planes . the classical schubert calculus @xcite gives the following recipe for computing the number @xmath8 . let @xmath9 be indeterminates with @xmath10 . for each integer sequence @xmath11 we define the following polynomial : @xmath12 here @xmath13 and @xmath14 if @xmath15 or @xmath16 . let @xmath17 be the ideal in @xmath18 $ ] generated by those @xmath19 with @xmath20 and @xmath21 . the quotient ring @xmath22/i$ ] is the cohomology ring of the grassmannian of @xmath4-planes in @xmath1 . it is artinian with one - dimensional socle in degree @xmath23 . in the socle we have the relation @xmath24 thus we can compute the number @xmath8 by normal form reduction modulo any grbner basis for @xmath17 . more efficient methods for computing in the ring @xmath25 are implemented in the maple package sf @xcite . in the important special case @xmath26 there is an explicit formula for @xmath8 : @xmath27 the integer on the right hand side is the degree of the grassmannian in its plcker embedding . this formula is due to @xcite ; see also ( * ? ? ? * xiv.7.8 ) and section 2.3 below . the objective of this paper is to present semi - numerical algorithms for computing all @xmath8 solution planes from the input data @xmath0 . this amounts to solving certain systems of polynomial equations . our algorithms are based on the paradigm of _ numerical homotopy methods _ @xcite . homotopy methods have been developed for the following classes of polynomial systems : 1 . complete intersections in affine or projective spaces @xcite , 2 . complete intersections in products of projective spaces @xcite , 3 . complete intersections in toric varieties @xcite . in these cases the number of paths to be traced is optimal and equal to the standard combinatorial bounds : 1 . the bzout number (= the product of the degrees of the equations ) 2 . the generalized bzout number for multihomogeneous systems 3 . the bkk bound @xcite (= mixed volume of the newton polytopes ) none of these known homotopy methods is applicable to our problem , as the following simple example shows : take @xmath28 , @xmath29 , and @xmath30 , that is , we seek the @xmath31-planes in @xmath32 which meet six general @xmath33-planes nontrivially . by formula ( 1.3 ) there are @xmath34 solutions . formulating this in plcker coordinates gives @xmath35 homogeneous equations in ten variables , the five quadrics in display ( [ i23 ] ) below and six linear equations ( [ sixlin ] ) . a formulation in local coordinates ( [ sagbieqs ] ) has 6 quadratic equations in 6 unknowns , giving a bzout bound of 64 . these 6 equations all have the same newton polytope , which has normalized volume 17 , giving a bkk bound of 17 . in section 2 we give two homotopy algorithms which solve our problem in the special case @xmath36 , when the number of solutions equals ( 1.3 ) . the first algorithm is derived from a grbner basis for the plcker ideal of a grassmannian and the second from a sagbi basis for its projective coordinate ring . ( see @xcite or ( * ? ? ? 11 ) for an introduction to sagbi bases ) . both the _ grbner homotopy _ and _ sagbi homotopy _ are techniques for finding linear sections of grassmannians in their plcker embedding . in section 3 we address the general case of our problem , that is , we describe a numerical method for solving the polynomial equations defined by _ special schubert conditions_. this is accomplished by applying a sequence of delicate intrinsic deformations , called _ pieri homotopies _ , which were introduced in @xcite . pieri homotopies first arose in the study of enumerative geometry over the real numbers @xcite . for the experts we remark that it is an open problem to find _ littlewood - richardson homotopies _ , which would be relevant for solving polynomial equations defined by general schubert conditions . a main challenge in designing homotopies for the schubert calculus is that one is not dealing with complete intersections : there are generally more equations than variables . in section 4 we discuss some of the numerical issues arising from this challenge , and how we propose to resolve them . in section 5 we discuss applications of these algorithms to control theory and real enumerative geometry . finally , in section 6 we present computational results . in closing the introduction let us emphasize that all homotopies described in this paper are optimal in the sense the number of paths to be traced equals the number @xmath8 . this means that for generic input data @xmath0 no paths diverge .

we develop numerical homotopy algorithms for solving systems of polynomial equations arising from the classical schubert calculus . these homotopies are optimal in that generically no paths diverge . for problems defined by hypersurface schubert conditions we give two algorithms based on extrinsic deformations of the grassmannian : one is derived from a grbner basis for the plcker ideal of the grassmannian and the other from a sagbi basis for its projective coordinate ring . the more general case of special schubert conditions is solved by delicate intrinsic deformations , called pieri homotopies , which first arose in the study of enumerative geometry over the real numbers . computational results are presented and applications to control theory are discussed .

we develop numerical homotopy algorithms for solving systems of polynomial equations arising from the classical schubert calculus . these homotopies are optimal in that generically no paths diverge . for problems defined by hypersurface schubert conditions we give two algorithms based on extrinsic deformations of the grassmannian : one is derived from a grbner basis for the plcker ideal of the grassmannian and the other from a sagbi basis for its projective coordinate ring . the more general case of special schubert conditions is solved by delicate intrinsic deformations , called pieri homotopies , which first arose in the study of enumerative geometry over the real numbers . computational results are presented and applications to control theory are discussed .

astro-ph0401356

i

growing numbers of large - scale jets in powerful extragalactic radio sources are now being observed at optical and x - ray frequencies ( see , e.g. , * ? ? ? new , and in many ways unexpected , results call for a wide discussion of the physical conditions within these objects , and in particular of the processes responsible for accelerating radiating particles to the required ultrarelativistic energies . until now , few observations had gone beyond the integrated spectral properties of multiwavelength emission from large - scale jets . however , the high angular resolution of hubble space telescope ( hst ) and chandra x - ray observatory ( cxo ) have given us the opportunity to analyze the morphological characteristics of jets at optical and x - ray photon energies , allowing for the comparison of jet morphology at different frequencies . here we discuss the structure of large - scale quasar jets , in order to determine the origin of their x - ray radiation and the nature of the particle acceleration responsible for their multiwavelength emission . cxo has detected about ten quasar jets with observed x - ray luminosities @xmath0 erg s@xmath1 and projected lengths ranging from a few tens up to a few hundred kpc . the x - ray emission is usually much too intense to be explained in terms of synchrotron radiation by the same , single - power - law electron energy distribution that produces the radio - to - optical emission . nor can it be explained in terms of synchrotron - self compton ( ssc ) radiation of a _ homogeneous _ , few - kpc - long knot region , _ unless _ the energy density is far above the equipartition value , which would imply extremely high jet powers ( e.g. , * ? ? ? * ; * ? ? ? * for the case of pks 0637 - 752 ) . this led to the idea that the x - ray emission results from inverse - compton up - scattering of cosmic microwave background ( cmb ) photons ` external inverse - compton ' ( eic ) emission by the low - energy part of the electron energy distribution @xcite . such a model , however , requires highly relativistic jet velocities at distances of a few hundred kpc from the active nuclei ( bulk lorentz factors @xmath2 ) , in apparent disagreement with radio observations ( e.g. , * ? ? ? on the other hand , the eic model was claimed to be additionally supported by energetic considerations @xcite . in this respect , discoveries of large - scale x - ray jets in the gigahertz - peaked ( gps ) objects pks 1127 - 145 and b2 0738 + 313 ( * ? ? ? * ; * ? ? ? * respectively ) , as well as in the high - redshift source gb 1508 + 5714 ( @xmath3 , * ? ? ? * ) are particularly interesting . x - ray emission of large - scale quasar jets , if due to the eic process , has also cosmological implications , as pointed out by @xcite . therefore , it is important to discuss whether comptonization of the cmb within highly relativistic flow is really the most plausible explanation of the cxo quasar jet observations , and to look for possibilities of discriminating between this and other models ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? analysis of the morphology of the emitting regions constitutes an interesting approach to this problem . the most apparent characteristic of quasar jets is their knotty morphology with high knot - to - interknot brightness contrast , but also with distinct ( in some cases ) inter - knot diffuse emission . in addition , knot profiles seem to be frequency - independent , and knot extents are similar when observed at radio , optical and x - ray photon energies . detailed observations of the 3c 273 jet @xcite reveal also that spectral changes along the flow are not correlated with brightness changes this may be a general characteristic of these objects . finally , in some cases spatial offsets between the maxima of the x - ray and radio emission within the knot regions were noted ( e.g. , pks 1127 - 145 , * ? ? ? * ) . it is not clear whether all of these features can be explained in a framework of models involving extended shock waves within continuous jet flow . in fact , we argue that the morphological characteristics can not be explained in this way , and that substantial modifications of the standard picture are required . such modifications are especially needed if the x - ray emission of quasar jets is due to the eic process . we propose that at least some aspects of the hst and cxo observations can be understood in terms of intermittent ( modulated ) jet activity . in this context , we comment on both the external - compton scenario of quasar jet x - ray emission , and on a model of boundary layer acceleration and resulting high - energy radiation @xcite . in particular , in 2 we emphasize the problems with modeling x - ray knots of quasar jets as stationary regions of particle acceleration . in 3 we consider the possibility that the knots are moving sources of non - thermal radiation , propose a possible connection of this scenario to models of intermittent jet activity , and discuss the particle acceleration processes possibly involved in such a scenario . the discussion and final conclusions are presented in 4 and 5 ,

we discuss morphological properties of the large - scale jets in powerful radio sources , which are now observed at radio , optical and x - ray frequencies , in order to determine the origin of their x - ray radiation and the nature of the particle acceleration responsible for their multiwavelength emission . we suggest a possible connection between this scenario and the idea of intermittent / highly modulated jet activity .

we discuss morphological properties of the large - scale jets in powerful radio sources , which are now observed at radio , optical and x - ray frequencies , in order to determine the origin of their x - ray radiation and the nature of the particle acceleration responsible for their multiwavelength emission . we show that modeling knots of the these objects as stationary regions of energy dissipation within the uniform and continuous jet flow leads to several problems . such problems are especially pronounced if the observed x - ray emission is due to inverse - compton scattering of the cmb radiation . we explore another possibility , namely that the knots represent moving and separate portions of the jet matter , with excess kinetic power . we suggest a possible connection between this scenario and the idea of intermittent / highly modulated jet activity . the proposed model can explain some morphological properties of quasar jets like high knot - to - interknot brightness contrasts , frequency - independent knot profiles and almost universal extents of the knot regions independently of the exact emission mechanism responsible for producing the x - rays . in this context , we consider different possibilities for the production of such x - ray radiation , and discuss the related issue of particle acceleration . we conclude that the appropriate process can not be designated for certain yet . we suggest , however , that x - ray observations of the jet in 3c 120 ( in which intermittent jet activity is quite distinct ) already seem to support the synchrotron origin of the x - ray emission , at least in this object .

astro-ph0401356

c

we propose that the knots observed in large - scale quasar jets in radio , optical and x - rays represent portions of the jet with an excess of kinetic power due to intermittent high activity of the jet engine . the appropriate time scales for jet activity and quiescent epochs ( @xmath71 yr and @xmath125 yr , respectively ) are roughly consistent with the ones estimated in different contexts for powerful radio sources @xcite . the proposed scenario can explain some morphological properties of quasar jets , independently of the exact emission process responsible for production of x - rays . indeed , the dominant emission process can not be designated for certain yet . it is possible that the x - ray emission of quasar jets is due to inverse - compton scattering of the cmb by low - energy electrons accelerated in internal shocks . on the other hand , it is also possible that the observed kev photons are synchrotron in origin , being a manifestation of high - energy electrons piled - up at the critical energy @xmath126 tev due to the second - order fermi process and/or multiple shock acceleration . the fact that an exceptionally high doppler factor is required to explain the 3c 120 x - ray data in the framework of the eic scenario , suggests that synchrotron emission is likely to be the dominant process in this object , at least . whatever emission mechanism prevails in most large - scale quasar jets , intermittent jet activity assures , in a natural way , high knot - to - interknot brightness contrasts , frequency - independent knot profiles , and almost universal extents of the knots ( @xmath91 kpc ) . s , ms and mo were supported by the grant pbz - kbn-054/p03/2001 . s acknowledges also financial support from fundacja astronomii polskiej . mcb acknowledges support from national science foundation grant ast-0307502 . a part of this work was done during the stay of s and ms at jila , university of colorado .

such problems are especially pronounced if the observed x - ray emission is due to inverse - compton scattering of the cmb radiation . the proposed model can explain some morphological properties of quasar jets like high knot - to - interknot brightness contrasts , frequency - independent knot profiles and almost universal extents of the knot regions independently of the exact emission mechanism responsible for producing the x - rays . in this context , we consider different possibilities for the production of such x - ray radiation , and discuss the related issue of particle acceleration . we conclude that the appropriate process can not be designated for certain yet .

we discuss morphological properties of the large - scale jets in powerful radio sources , which are now observed at radio , optical and x - ray frequencies , in order to determine the origin of their x - ray radiation and the nature of the particle acceleration responsible for their multiwavelength emission . we show that modeling knots of the these objects as stationary regions of energy dissipation within the uniform and continuous jet flow leads to several problems . such problems are especially pronounced if the observed x - ray emission is due to inverse - compton scattering of the cmb radiation . we explore another possibility , namely that the knots represent moving and separate portions of the jet matter , with excess kinetic power . we suggest a possible connection between this scenario and the idea of intermittent / highly modulated jet activity . the proposed model can explain some morphological properties of quasar jets like high knot - to - interknot brightness contrasts , frequency - independent knot profiles and almost universal extents of the knot regions independently of the exact emission mechanism responsible for producing the x - rays . in this context , we consider different possibilities for the production of such x - ray radiation , and discuss the related issue of particle acceleration . we conclude that the appropriate process can not be designated for certain yet . we suggest , however , that x - ray observations of the jet in 3c 120 ( in which intermittent jet activity is quite distinct ) already seem to support the synchrotron origin of the x - ray emission , at least in this object .

1206.0969

i

the famous no - go theorem @xcite states that lattice fermion actions with chiral symmetry , locality and other common features must produce massless degrees of freedom in multiples of two in a continuum limit . this is contradictory with a phenomenological fact that there exist only three quarks with masses below the qcd scale . by now several fermion constructions to bypass the no - go theorem have been developed , although all of them have their individual shortcomings : the explicit chiral symmetry breaking with the wilson fermion approach @xcite results in an additive mass renormalization , which in turn requires a fine - tuning of the mass parameter for qcd simulations . domain - wall @xcite and overlap fermions @xcite produce a single fermion mode by modifying the definition of chiral symmetry or introducing the momentum - dependent chiral charge , although they lead to rather expensive simulations algorithms .. these approaches attempt to realize single fermionic degrees of freedom by breaking the requisite conditions for the no - go theorem . on the other hand , there is another direction to approach numerical simulations . according to @xcite , hypercubic symmetry and reflection positivity of actions result in @xmath2 species of fermions where @xmath3 stands for the dimension . thus it is potentially possible to reduce the number of species by breaking hypercubic symmetry properly . actually , the staggered fermion approach @xcite , with only 4 species of fermions does this and possesses flavored - hypercubic symmetry instead . however this requires rooting procedures for the physical @xmath4 or @xmath5-flavor qcd simulation . a possible goal in this direction is a lattice fermion with @xmath4 species , the minimal number required by the no - go theorem . such a minimal - doubling action was first proposed by karsten , and later by wilczek @xcite . other than the original type , two more types are known as creutz - borici type @xcite and twisted - ordering type @xcite . these fermions all possess one exact chiral symmetry and ultra locality . as such they could be faster for simulation , at least for two - flavor qcd , than other chirally symmetric lattice fermions . however it has been shown @xcite that we need to fine - tune several parameters for a continuum limit with these actions . this is because they lack sufficient discrete symmetry to prohibit redundant operators from being generated through loop corrections @xcite . thus the minimally doubled fermions have not been extensively used so far . nevertheless , there is the possibility to apply them to simulations if one can efficiently perform the necessary fine - tuning of parameters . in this paper we pursue the chiral phase structure in the parameter plane for minimal - doubling lattice qcd for two purposes : one purpose is to understand properties of these formulations theoretically . the other purpose is to show their applicability to lattice qcd simulations since understanding a nontrivial phase diagram , as with the aoki phase in wilson fermion @xcite , can be useful in showing the applicability to lattice qcd . we first show that minimal - doubling fermions can be seen as a special case of lattice fermions with species - dependent ( imaginary ) chemical potential terms . we focus on the karsten - wilczek formulation with one relevant parameter @xmath0 , which corresponds to a mass parameter in the analogy of wilson fermion . we next investigate the chiral phase structure in the space of the gauge coupling and this relevant parameter . we analyze strong - coupling lattice qcd , and show that chiral symmetry is spontaneously broken in a certain range of the parameter while the chiral condensate is zero outside the range . we find a second - order phase transition between these chiral symmetric and broken phases . we also show that pion becomes massless as a nambu - goldstone boson in the chiral - broken phase while the sigma meson becomes massless on the second - order phase boundary due to the critical behavior of the second - order phase transition . we investigate the lattice gross - neveu model to capture an entire phase structure . from these results we suppose a similar chiral phase structure in 4d qcd with flavored - chemical - potential lattice fermions , and discuss their applicability to lattice qcd simulations . in sec . [ sec : fcp ] , we study lattice fermions with flavored chemical potential , or minimal - doubling fermions . in sec . [ sec : slq ] , we investigate a chiral phase structure in the framework of strong - coupling lattice qcd . in sec . [ sec : gn ] , we study the gross - neveu model to obtain information of the whole phase diagram . in sec . [ sec : qcd ] , we discuss a phase structure in 4d qcd from the results of the last two sections . section [ sec : sd ] is devoted to a summary and discussion .

we study strong - coupling lattice qcd with the karsten - wilczek formulation , which has one relevant parameter as well as gauge coupling and a mass parameter . we find a nontrivial chiral phase structure with a second - order phase transition between chiral symmetric and broken phases . to capture the whole structure of the phase diagram , we study the related lattice gross - neveu model .

we discuss the chiral phase diagram in the parameter space of lattice qcd with minimal - doubling fermions , which can be seen as lattice fermions with flavored chemical potential terms . we study strong - coupling lattice qcd with the karsten - wilczek formulation , which has one relevant parameter as well as gauge coupling and a mass parameter . we find a nontrivial chiral phase structure with a second - order phase transition between chiral symmetric and broken phases . to capture the whole structure of the phase diagram , we study the related lattice gross - neveu model . the result indicates that the chiral phase transition also exists in the weak - coupling region . from these results we speculate on the- chiral phase diagram in lattice qcd with minimal - doubling fermions , and discuss their application to numerical simulations

1003.1744

i

starlight produced by the first galaxies is the leading candidate for ionizing the hydrogen as well as singly ionizing the helium at @xmath10 . it takes a harder source of radiation to doubly ionize the helium , so the reionization of this species is likely deferred until @xmath11 when quasars produce a sufficient hard uv background @xcite . however , the helium could have been doubly ionized at nearly the same cosmic time that hydrogen was reionized if more exotic sources ionized the hydrogen , such as the first generation of metal - free stars @xcite or miniquasars @xcite . in a third potential scenario , early sources doubly ionized the helium and then shut off . afterward , the he ii recombined such that quasars could again reionize it at @xmath11 @xcite . if he ii reionization were completing at @xmath12 , an epoch for which there are numerous observations of the intergalactic medium ( igm ) , it should be an easier task to definitively detect this process compared to detecting @xmath13 reionization processes . furthermore , if he ii reionization were ending at @xmath12 , it should have significantly affected the temperature of the intergalactic gas and the ultraviolet radiation background . these motivations , along with recent additions to the hubble space telescope ( hst ) , have inspired a significant effort of late to understand the signatures and the detection prospects of he ii reionization @xcite . three separate observations of the @xmath11 igm suggest that he ii reionization was ending around this redshift : first , several studies have measured the temperature of the intergalactic gas from the widths of the narrowest lines in the h i ly@xmath1 forest , and the majority of these studies have found evidence for an increase in the igm temperature of @xmath14 k between @xmath15 and @xmath16 , before a decline to lower redshift @xcite . these trends have been attributed to the heating from he ii reionization . second , observations of he ii ly@xmath1 absorption from gas at @xmath17 show tens of comoving mpc ( cmpc ) regions with no detected transmission @xcite , which may indicate that he ii reionization was not complete . thirdly , @xcite and @xcite detected evolution in the column density ratios of certain highly ionized metals at @xmath16 , which they argued was due to a hardening in the ionizing background around @xmath18ev and , thus , the end of he ii reionization . however , the interpretations of all of these indications for he ii reionization are controversial . temperature measurements of the igm are difficult , and not all measurements detected the aforementioned trends . it is often argued that he ii ly@xmath1 absorption saturates at he ii fractions that are too small ( @xmath19 at the mean density ) to study he ii reionization ( although , see @xcite ) . lastly , inferences from metal lines require significant modeling , and studies have reached different conclusions regarding the degree of their evolution at @xmath11 @xcite . this paper discusses intergalactic absorption by the @xmath20 transitions of he i as an unsaturated observable of he ii reionization . we primarily focus on the strongest and longest wavelength of these absorption lines , the he i @xmath21 , @xmath0 line . for a given optical depth in the h i ly@xmath1 forest , the amount of absorption in the he i forest can be directly estimated if both the fraction of helium that is he ii and the ratio of the h i and he i photoionization rates are known . in addition , because the he i ionization edge is relatively close to that of hydrogen , the photoionization rate that he i experiences is similar to this for hydrogen . thus , the most important determinant of the amount of he i @xmath22 absorption is the he ii fraction . other studies have discussed the he i forest , but did not focus on its usefulness as a probe of helium reionization . @xcite was the first to discuss intergalactic absorption by the he i @xmath0 , and this study attempted unsuccessfully to detect this absorption in the spectrum of a @xmath23 quasar . @xcite targeted he i absorption from @xmath24 h i lyman - limit systems , and reported the first ( and at present only ) detection of intergalactic he i @xmath0 absorption . finally , @xcite showed that the he i forest could be a useful probe of the hardness of the ultraviolet background , and they focused on using this absorption to rule out a particular nonstandard model for the dark matter . @xcite followed up on this idea , arguing that the @xmath25 he i forest could be a useful diagnostic of the hardness of the ultraviolet background after hydrogen reionization . as with the he ii ly@xmath1 transition at @xmath26 , the he i @xmath0 transition falls blueward of the hydrogen lyman limit and , therefore , is subject to continuum absorption by hydrogen , in this case from h i systems with @xmath27 . this continuum absorption may even be worse in terms of obscuring the he i @xmath0 forest compared to the he ii ly@xmath1 forest because this spectral region is more affected by higher redshift h i continuum absorbers . it is unlikely that there are more than a handful of quasar sightlines at @xmath28 with sufficient near ultraviolet ( nuv ) flux for detection with the present generation of instruments ( and almost certainly not at @xmath29 , during he i reionization ; @xcite ) . therefore , our focus is on applications of he i absorption at @xmath30 . we have performed a cursory search for candidate he i sightlines among the relatively few published heii lya forest spectra that extend redward to @xmath31 . of note , qso oq 172 ( @xmath32 ) has @xmath33erg s@xmath34 @xmath35 @xmath34 at @xmath36 @xcite , and qso 0055 - 269 ( @xmath37 ) has @xmath38 ( gabor worseck , priv . com . ) . in fact , we were surprised to find that most he ii sightlines in our search had significant flux in the relevant band . many of the existing he ii sightlines had been selected by their far ultraviolet flux . nuv selection would be more optimal for identifying candidate he i forest sightlines . for example , hs 1140 + 3508 ( @xmath39 ) is obscured in the far ultraviolet by a lyman - limit system , but has a nuv flux of @xmath40 ( gabor worseck , priv . com . ) . another difficulty with the he i forest is that line absorption from foreground systems can contaminate the he i forest , the most important of which is h i ly@xmath1 absorption . h i ly@xmath1 absorption from a system with a redshift of @xmath41 falls directly on top of the he i absorption from a redshift of @xmath42 . fortunately , the ly@xmath1 forest is quite thin at relevant @xmath43 ( with a flux decrement of several percent ) , and we find that both this contaminant s mean transmission and variance tend to be comparable to that of the he i forest . also , the he i forest correlates strongly with the coeval h i ly@xmath1 forest , which allows it to be extracted in cross correlation despite this contamination . this study is timely because the hst reservicing mission installed the cosmic origins spectrograph ( cos ) in may 2009 . cos is capable of measurements of hei @xmath0 absorption at redshifts relevant to he ii reionization ( @xmath44 ) , and ground - based spectrographs can cover higher redshifts ( @xmath45 , corresponding to @xmath46 ) . cos is able to achieve higher signal - to - noise ratios than previous instruments in the ultraviolet . a @xmath47hr exposure with cos would achieve a signal - to - noise ratio of @xmath48 at @xmath49 for a flux of @xmath50erg s@xmath34 @xmath35 @xmath34 ( the flux of qso oq 172 and hs 1140 + 3508 ) at @xmath51 ( he i absorption from @xmath52 ) . a @xmath53hr exposure with cos would achieve a signal - to - noise ratio of @xmath48 for this flux at @xmath54 at @xmath55 ( @xmath56 ) . times higher than specifications ( and than what is assumed by this etc ) , and , thus , a significantly longer observation is required unless this issue is resolved . ] this paper is organized as follows . section [ sec : forest ] discusses the physics of the he i forest . section [ sec : calculations ] contrasts simulated spectra for this forest under different assumptions regarding the ionization state of the helium . section [ sec : tests ] quantifies the spectral quality an observation must achieve to verify whether he ii reionization was occurring from the he i forest . appendix [ sec : hardness ] outlines how to measure the hardness of the ionizing background with he i absorption , and appendix [ ap : snrcc ] derives formulae for the significance with which he i absorption can be detected in cross correlation with the coeval ly@xmath1 forest . this paper assumes a flat @xmath57cdm cosmology with @xmath58 , @xmath59 , @xmath60 , @xmath61 , @xmath62 , and @xmath63 , consistent with recent measurements @xcite . however , the simulation used to calculate the ly@xmath1 forest spectra at @xmath64 , the d5 simulation in @xcite , assumes a slightly different cosmology , with the most notable differences being @xmath65 and @xmath66 . the photoionization and recombination rates used in this study are from @xcite .

we find that this objective can be accomplished ( using coeval h i ly absorption to mask dense regions and in cross correlation ) with a spectral resolution of and a signal - to - noise ratio per resolution element of . we also discuss how he i absorption can be used to measure the hardness of the ionizing background above ev .

we discuss the potential of using the he i forest to detect and study he ii reionization . significant absorption is expected from intergalactic he ii regions , whereas there should be no detectable absorption from low density gas in he iii regions . unlike he ii ly absorption ( the subject of much recent study ) , the difficulty with using this transition to study he ii reionization is not saturation but rather that the absorption is weak . the gunn - peterson optical depth for this transition is^{9/2}$ ] , where is the fraction of helium in he ii and is the density in units of the cosmic mean . in addition , he i absorption is contaminated by lower redshift h i ly absorption with a comparable flux decrement . we estimate the requirements for a definitive detection of redshifted he i absorption from low density gas ( ) , which would indicate that he ii reionization was occurring . we find that this objective can be accomplished ( using coeval h i ly absorption to mask dense regions and in cross correlation ) with a spectral resolution of and a signal - to - noise ratio per resolution element of . such specifications may be achievable on a few known quasar sightlines with the cosmic origins spectrograph on the hubble space telescope . we also discuss how he i absorption can be used to measure the hardness of the ionizing background above ev .

1003.1744

c

this paper discussed the usefulness of the he i @xmath0 forest to study he ii reionization at @xmath313 . the optical depth of the he i @xmath0 line is proportional to the optical depth in h i ly@xmath1 by the factor @xmath314 ( ignoring differences in the amount of thermal broadening between h i and he i ) . the factor @xmath3 should have been spatially variable , but the ratio @xmath315 should have been essentially spatially independent and roughly equal to unity at relevant redshifts . therefore , this absorption can be used to study he ii reionization through its dependence on @xmath3 . our best method at present to probe he ii reionization , he ii ly@xmath1 absorption , saturates at neutral fractions of a part in a thousand at the cosmic mean density . in contrast , he i @xmath0 absorption is unsaturated in all except the densest regions , even for @xmath78 . this absorption provides a complementary window into the ionization state of intergalactic helium at @xmath11 that can definitively test whether an opaque region in the he ii ly@xmath1 forest was due to a large - scale he ii region . even for realistic amounts of instrumental noise and foreground h i ly@xmath1 absorption , we showed that the coeval h i ly@xmath1 forest absorption can be used to construct a matched filter that can detect the he i absorption at high significance from a single quasar sightline . a detection of he i absorption from @xmath213 gas at @xmath12 would definitively indicate that he ii reionization was occurring . if a significant fraction of the intergalactic helium was in he ii , we found that he i @xmath0 forest absorption from low density gas could be identified in a quasar spectrum with snr @xmath316 and @xmath317 in an interval of @xmath318 . these specifications may be achievable with the cos instrument on the hst for a few known @xmath319 targets . + we thank claude - andr faucher - gigure , wayne hu , gabor worseck , and especially j. xavier prochaska for useful discussions . we also thank claude - andr faucher - gigure , lars hernquist , adam lidz , and volker springel for providing the simulations used in this work . e. s. acknowledges support by nsf physics frontier center grant phy-0114422 to the kavli institute of cosmological physics . + , i. i. , levshakov , s. a. , reimers , d. , fechner , c. , tytler , d. , simcoe , r. a. , & songaila , a. 2007 , , 461 , 893 , a. , sargent , w. l. w. , & rauch , m. 2003 , submitted to astrophysical journal supplement . astro - ph/0307557 , j. s. , oh , s. p. , & furlanetto , s. r. 2009 , , 396 , 2405 bromm , v. , kudritzki , r. p. , & loeb , a. 2001 , , 552 , 464 , k. l. , & furlanetto , s. r. 2009 , , 706 , 970 , c. , lidz , a. , zaldarriaga , m. , & hernquist , l. 2009 , , 703 , 1416 , c .- a . , lidz , a. , hernquist , l. , & zaldarriaga , m. 2008a , , 688 , 85 , c .- a . , prochaska , j. x. , lidz , a. , hernquist , l. , & zaldarriaga , m. 2008b , , 681 , 831 , c. , & reimers , d. 2007 , , 461 , 847 , s. , & dixon , k. 2009 , arxiv:0910.5246 , s. r. , & oh , s. p. 2008 , , 681 , 1 , j. e. , & peterson , b. a. 1965 , , 142 , 1633 , f. , & madau , p. 1996 , , 461 , 20 , s. r. , williger , g. m. , smette , a. , hubeny , i. , sahu , m. s. , jenkins , e. b. , tripp , t. m. , & winkler , j. n. 2000 , , 534 , 69 , l. , & gnedin , n. y. 1997 , , 292 , 27 , l. j. , dopita , m. a. , sutherland , r. s. , heisler , c. a. , & trevena , j. 2001 , , 556 , 121 , d. , tytler , d. , lubin , d. , & charlton , j. 2007 , , 376 , 1227 , e. , et al . 2009 , , 180 , 330 , a. , faucher - giguere , c. , dallaglio , a. , mcquinn , m. , fechner , c. , zaldarriaga , m. , hernquist , l. , & dutta , s. 2009 , arxiv e - prints , r. w. , cohen , r. d. , junkkarinen , v. t. , burbidge , e. m. , & beaver , e. a. 1995 , , 110 , 1544 , p. , haardt , f. , & rees , m. j. 1999 , , 514 , 648 , m. 2009 , , 704 , l89 , m. , lidz , a. , zaldarriaga , m. , hernquist , l. , hopkins , p. f. , dutta , s. , & faucher - gigure , c .- a . 2009 , , 694 , 842 , m. , & switzer , e. r. 2009 , , 80 , 063010 , j. , & ostriker , j. p. 1992 , , 392 , 15 , w. h. , & rybicki , g. b. 1993 , , 418 , 585 , j. x. , worseck , g. , & omeara , j. m. 2009 , , 705 , l113 prochaska , j. x. , omeara , j. m. , & worseck , g. 2009 , arxiv:0912.0292 , d. , kohler , s. , wisotzki , l. , groote , d. , rodriguez - pascual , p. , & wamsteker , w. 1997 , , 327 , 890 , d. , & vogel , s. 1993 , , 276 , l13 , m. , gnedin , n. y. , & shull , j. m. 2000 , , 534 , 41 , m. r. , & loeb , a. 2003 , astro - ph/0304130 , j. , theuns , t. , rauch , m. , efstathiou , g. , & sargent , w. l. w. 2000 , , 318 , 817 , a. 1998 , , 115 , 2184 , v. , & hernquist , l. 2003 , , 339 , 312 , d. , et al . 2009a , , 690 , 1181 , d. , anderson , s. f. , zheng , w. , haggard , d. , meiksin , a. , schneider , d. p. , & york , d. g. 2009b , arxiv:0909.3962 , r. c. , zheng , w. , kriss , g. a. , & davidsen , a. f. 2002 , , 565 , 773 , t. m. , green , r. f. , & bechtold , j. 1990 , , 364 , l29 tumlinson , j. , venkatesan , a. , & shull , j. m. 2004 , , 612 , 602 wyithe , s. , & loeb , a. 2003 , , 588 , l69 venkatesan , a. , tumlinson , j. , & shull , j. m. 2003 , , 584 , 621 , m. , & gnedin , n. y. 2009 , , 703 , 2113 zheng , w. , et al . 2004 , , 605 , 631

we discuss the potential of using the he i forest to detect and study he ii reionization . we estimate the requirements for a definitive detection of redshifted he i absorption from low density gas ( ) , which would indicate that he ii reionization was occurring . such specifications may be achievable on a few known quasar sightlines with the cosmic origins spectrograph on the hubble space telescope .

we discuss the potential of using the he i forest to detect and study he ii reionization . significant absorption is expected from intergalactic he ii regions , whereas there should be no detectable absorption from low density gas in he iii regions . unlike he ii ly absorption ( the subject of much recent study ) , the difficulty with using this transition to study he ii reionization is not saturation but rather that the absorption is weak . the gunn - peterson optical depth for this transition is^{9/2}$ ] , where is the fraction of helium in he ii and is the density in units of the cosmic mean . in addition , he i absorption is contaminated by lower redshift h i ly absorption with a comparable flux decrement . we estimate the requirements for a definitive detection of redshifted he i absorption from low density gas ( ) , which would indicate that he ii reionization was occurring . we find that this objective can be accomplished ( using coeval h i ly absorption to mask dense regions and in cross correlation ) with a spectral resolution of and a signal - to - noise ratio per resolution element of . such specifications may be achievable on a few known quasar sightlines with the cosmic origins spectrograph on the hubble space telescope . we also discuss how he i absorption can be used to measure the hardness of the ionizing background above ev .

hep-ph9812230

i

the search for supersymmetry ( susy ) @xcite plays an important rle in the experimental program at the colliders lep2 and tevatron . it will be even more important at future colliders , e.g. an upgraded tevatron , lhc , an @xmath6 linear collider or a @xmath7 collider . therefore many phenomenological studies have been carried out in recent years ( see e.g. @xcite and references therein ) . within the supersymmetric extensions of the standard model ( sm ) the minimal supersymmetric standard model ( mssm ) @xcite is the most investigated one . the mssm implies that every sm fermion has two spin 0 partners called sfermions @xmath8 and @xmath9 . in general sfermions decay according to @xmath10 where @xmath11 and @xmath12 denote neutralinos and charginos , respectively . here we assume that the lightest neutralino is the lightest supersymmetric particle ( lsp ) . owing to large yukawa couplings the sfermions of the third generation have a quite different phenomenology compared to those of the first two generations ( see e.g. @xcite and references therein ) . the large yukawa couplings imply a large mixing between @xmath8 and @xmath9 and large couplings to the higgsino components of neutralinos and charginos . this is in particular the case for the lighter top squark @xmath5 because of the large top quark mass @xcite . the large top quark mass also implies the existence of scenarios where all two - body decay modes of @xmath5 ( e.g. @xmath13 ) are kinematically forbidden at tree - level . in these scenarios higher order decays of @xmath5 become relevant : @xcite : @xmath14 where @xmath15 denotes @xmath16 . in @xcite it has been shown that decays into sleptons are dominating over the decays into @xmath17 if they are kinematically allowed . however , they have used the approximation : @xmath18 , @xmath19 ( @xmath20 ) , @xmath21 . in @xcite it has been shown that for small @xmath22 the decay @xmath0 in general dominates over @xmath23 whereas for large @xmath22 their branching ratios can be of comparable size . in this paper we present the complete formulas for the three - body decays which are so far missing in the literature . we also perform a numerical analysis for the mass range of an upgraded tevatron , the lhc , and a future lepton collider including the possibility that all of the above decay channels are simultaneously open . in particular it turns out that the inclusion of the bottom and tau yukawa couplings @xmath24 and @xmath25 is important . this paper is organized as follows : in sect . ii we fix our notation and give the analytical expressions for the decay amplitudes together with the relevant parts of the mssm lagrangian . in sect . iii we present our numerical results for the branching ratios of the three - body decays in scenarios accessible either at the tevatron run ii , lhc , or a future lepton collider . our conclusions are drawn in sect . the analytical formulas for the squared amplitudes are listed in appendix [ appa ] , and appendix [ appb ] gives the various couplings .

we discuss the three - body decays , , , and ( ) of the lighter top squark within the minimal supersymmetric standard model . we give the complete analytical formulas for the decay widths and present a numerical study in view of an upgraded tevatron , the cern lhc , and a future lepton collider demonstrating the importance of these decay modes .

we discuss the three - body decays , , , and ( ) of the lighter top squark within the minimal supersymmetric standard model . we give the complete analytical formulas for the decay widths and present a numerical study in view of an upgraded tevatron , the cern lhc , and a future lepton collider demonstrating the importance of these decay modes .

astro-ph0307056

i

afterglow emission , spanning from radio to x - ray , and observable from minutes to weeks after the event , appears to be a ubiquitous feature of long - duration gamma - ray burst explosions . afterglows result from radiation emitted by electrons accelerated in a relativistic shock produced by the explosion of a progenitor ( e.g. , * ? ? ? * ; * ? ? ? as the shock propagates outward into the surrounding medium , the resulting broadband synchrotron radiation evolves in a manner dependent on a number of fundamental characteristics of the explosion , as well as on the details of the shock evolution and the density profile of the medium it expands into ( for a review of the theory , see * ? ? ? the physics of relativistic shocks , the mechanism of collisionless shock acceleration , and the means by which magnetic fields can be amplified to levels needed to produce the observed synchrotron emission are poorly understood . basic understanding of these elements will eventually result from improved magnetohydrodynamic simulations , which may ultimately prescribe such factors as the appropriate electron energy distribution , what fraction of shock energy goes into magnetic field , and how this evolves with the shock expansion . additional uncertainties arise from the fact that the outflow geometry , and the structure of the circumburst medium are unobservable , and could potentially be complex . in spite of the lack of detailed understanding , the basic features of the grb afterglow can be described by relatively simple theoretical models for the outflow and shock ( e.g. with relativistic flow as in * ? ? ? simple assumptions about the shock microphysics and geometry appear to fit the basic features of the afterglow in a number of cases ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? in addition , many events appear consistent with the expansion of the shock into a medium with either a constant or a simple @xmath5 powerlaw in density . ideally , high - quality broadband afterglow observations , interpreted in the context of basic theoretical models , could be used to constrain the explosion parameters , geometry , and the structure of the surrounding medium . in addition , if the data are of sufficiently high quality , it should be possible to test the validity of the basic model assumptions ; or at least the range over which they may be varied and still describe the data . given a relatively large number of model parameters , however , only a few data sets are of sufficient quality to provide interesting constraints . in this paper , we examine four high - quality broadband afterglow data sets , fitting them to a basic afterglow model . we investigate the similarity of the derived explosion , shock , and environmental parameters . in addition , we investigate selected model assumptions and the range over which they can be varied . in particular , we consider whether the fraction of energy in the post - shock magnetic field can evolve as some power of the bulk lorentz factor , and the range of possible matter density gradients . finally , we consider which future observations provide the most promise for better constraining both the model and its physical parameters .

we employ a fireball model of the gamma - ray burst explosion to constrain intrinsic and environmental parameters of four events with good broadband afterglow data ; grb 970508 , grb 980329 , grb 980703 , and grb 000926 . using the standard assumptions of constant circumburst density and no evolution of the fraction of the explosion energy in the post - shock magnetic field , we investigate the uniformity of the derived explosion and shock physics parameters among these events . we also investigate the level to which the data constrain the standard model assumptions , such as the magnetic field evolution , and the allowed density profiles of the medium .

we employ a fireball model of the gamma - ray burst explosion to constrain intrinsic and environmental parameters of four events with good broadband afterglow data ; grb 970508 , grb 980329 , grb 980703 , and grb 000926 . using the standard assumptions of constant circumburst density and no evolution of the fraction of the explosion energy in the post - shock magnetic field , we investigate the uniformity of the derived explosion and shock physics parameters among these events . we find a variety of parameters : densities that range from those of the ism to diffuse clouds , energies comparable to the total grb-ray energy , collimations from near - isotropy to 0.04 radians , substantial electron energy fractions of 10 - 30% with energy distribution indices of 2.1 - 2.9 and magnetic energy fractions from 0.2 - 25% . we also investigate the level to which the data constrain the standard model assumptions , such as the magnetic field evolution , and the allowed density profiles of the medium . fits generally improve slightly with an increasing magnetic energy fraction . good fits can be produced with magnetic energy accumulating or decaying with the shock strength over the afterglow as ; . the data are not very sensitive to increasing density profiles , allowing good fits even with density . some parameter values change by up to an order of magnitude under such altered assumptions ; the parameters of even good fits can not be taken at face value . the data are sensitive to decreasing densities ; profiles may produce reasonable fits , but steeper profiles , even , will not fit the data .

astro-ph0307056

c

we fit four well - studied bursts with extensive radio through x - ray afterglow datasets to a fireball model with simple assumptions concerning the microphysics and environment . we find a range of reasonable environmental and geometrical parameters . we find all four fit best with a constant density medium , one with a value similar to the milky way s ism density , @xmath157@xmath31 , the other three typical of diffuse clouds @xmath158@xmath31 . their kinetic energies are comparable to the total grb @xmath0-ray energy . the collimation varies from near - isotropy to a half - angle of 0.04 radians . we also find a striking diversity in the fitted microphysical parameter values , far beyond the statistical uncertainties . the electron energy distribution index varies from @xmath159 and the magnetic energy fraction varies from 0.2% to 25% . as shock physics should depend merely on shock strength , we investigated whether the spread could be due to model uncertainty , but did not find a set of assumptions which fit the data via universal microphysics parameters . we allowed for changes to be made to the model assumptions : @xmath160 and independently @xmath136 . we find considerable flexibility in the values of @xmath93 and @xmath124 that can still produce reasonable fits : @xmath2 ; @xmath3 and @xmath123 , with @xmath161 through @xmath162 . moreover , some parameter values change by up to an order of magnitude when the assumptions underlying the model are altered . clearly , even the results of very good fits are not unique and the parameters can not be taken at face value . the model assumptions are not strongly constrained by the datasets available to date . with this model uncertainty , the evidence for massive stellar progenitors from other sources ( positions within hosts , possible sn associations , see * ? ? ? * ) is not hard to reconcile with the lack of clear @xmath163 wind signatures in the best fits . massive stars may not produce a true @xmath5 profile , or its effect upon the spectrum could be masked by an inaccuracy in other model assumptions . finally , we compared the spectral evolution of the range of acceptable fits with differing assumptions to identify observational strategies that would produce better constraints . two areas are most promising . first , as for now a good fit need only line up with a small time range of x - ray observations , the _ swift _ satellite s expected early , well - sampled x - ray lightcurves will better constrain the spectral evolution ( as well as the ic upscatters of photons to the x - ray band and their consistency with the synchrotron model ) . as well , the peak has only been definitively observed at radio frequencies , passing through the mid - ir and submm during most of the afterglow . new submm instruments such as _ alma _ should increase the reach of direct peak detections . this will constrain the peak flux evolution , which is sensitive to the model assumptions . in the future it would be useful to investigate further constraints upon the assumptions . these might include variable energy @xmath60 ( under investigation in the context of events such as 021004 , e.g. , * ? ? ? * ) , and the possibility that the electron energy ( parameterized by @xmath10 ) , or their acceleration ( parameterized by the powerlaw index @xmath14 ) , could vary with shock strength . we thank roger blandford for helpful discussions . this work was supported in part by a nasa atp grant awarded to rs . fah acknowledges support from a presidential early career award . the national radio astronomy observatory is a facility of the national science foundation operated under cooperative agreement by associated universities , inc . we made extensive use of the gcn archive , maintained by scott barthelmy and the laboratory for high - energy astrophysics . ccccccccccccc 596 & 257 & 0.082 & 183 & 203 & 3.7@xmath164 & 1.6 & 0.84@xmath165 & 0.20@xmath166 & 0.14@xmath167 & 2.1223@xmath168 & 0.342@xmath169 & 25.0@xmath170 + 115 & 90 & 6.1 & 0.12 & 70 & 126@xmath171 & 170 & 0.036@xmath172 & 20@xmath173 & 1.9@xmath174 & 2.88@xmath175 & 0.12@xmath167 & 17@xmath176 + 170 & 147 & 1.4 & 3.4 & 50 & 11.8@xmath177 & 13 & 0.234@xmath178 & 28@xmath179 & 1.15@xmath180 & 2.54@xmath181 & 0.27@xmath165 & 0.18@xmath182 + 138 & 93 & 3.4 & 2.6 & 79 & 12@xmath183 & 15 & 0.162@xmath184 & 16@xmath176 & 0.022@xmath185 & 2.79@xmath186 & 0.15@xmath187 & 2.2@xmath188 + cccc @xmath189 & @xmath190 & @xmath191 @xmath192 & @xmath193 @xmath192 + @xmath194 & @xmath195 & @xmath191 @xmath196 & @xmath197 @xmath198 + @xmath199 & @xmath200 & @xmath201 @xmath202 & @xmath203 @xmath204 + @xmath205 & @xmath206 & @xmath207 @xmath208 & @xmath203 @xmath209 + @xmath189 & @xmath210 & @xmath211 @xmath212 & @xmath211 @xmath213 + @xmath214 & @xmath215 & @xmath216 @xmath217 & @xmath218 @xmath219 + @xmath220 & @xmath221 & @xmath222 @xmath223 & @xmath218 @xmath224 + @xmath225 & @xmath206 & @xmath207 @xmath208 & @xmath203 @xmath209 + cccccccccccccc @xmath226 & 945 & 257 & 1.7 & 223 & 223 & 1.6 & 1.8 & 0.87 & 2.23 & max & 2.2 & 0.19 & iso + @xmath227 & 695 & 257 & 0.57 & 322 & 322 & 1.8 & 1.5 & 0.21 & 2.20 & 80 & 8.2 & 0.24 & iso + @xmath228 & 596 & 257 & 0.082 & 183 & 203 & 3.7 & 1.6 & 0.20 & 2.12 & 25 & 25 & 0.34 & 0.84 + @xmath229 & 600 & 257 & 0.028 & 246 & 246 & 7.1 & 1.6 & 0.15 & 2.09 & 22 & 220 & 0.45 & iso + -2 & 569 & 257 & 0.0015 & 289 & 289 & 27 & 1.5 & 0.10 & 2.07 & 21 & 2400 & 0.59 & iso + -2 & 703 & 257 & 0.0011 & 498 & 498 & 13 & 2.0 & 0.032 & 2.14 & max & 5.9e4 & 0.24 & iso + + 4 & 112 & 90 & 6.5 & 76 & 76 & 2.9 & 4.7 & 220 & 2.31 & 21 & 0.021 & 0.23 & iso + + 1 & 117 & 90 & 0.30 & 1.1 & 151 & 4100&3900 & 150 & 2.0007 & 64 & 4.7 & 0.027 & 0.075 + 0 & 115 & 90 & 6.1 & 0.12 & 70 & 130 & 170 & 20 & 2.88 & 17 & 17 & 0.12 & 0.036 + -1 & 107 & 90 & 0.66 & 0.16 & 79 & 174 & 170 & 15 & 2.56 & 3.0 & 29 & 0.061 & 0.040 + -4 & 114 & 90 & - & 0.38 & 73 & 50 & 27 & 6.4 & 2.35 & max & 2.7e13 & 0.090 & 0.064 + -4 & 124 & 90 & - & 0.45 & 83 & 2000 & 35 & 6.9 & 2.43 & max & 1.2e13 & 0.074 & 0.066 + + 3 & 230 & 147 & 3.4 & 121 & 121 & 0.74 & 1.2 & 2.1 & 2.13 & max & 1.3 & 0.39 & iso + + 1 & 194 & 147 & 1.3 & 75 & 85 & 1.4 & 1.6 & 1.2 & 2.05 & max & 13 & 0.68 & 0.83 + 0 & 170 & 147 & 1.4 & 3.4 & 50 & 12 & 13 & 28 & 2.54 & 0.18 & 0.18 & 0.27 & 0.23 + -1 & 165 & 147 & 1.2 & 3.5 & 52 & 14 & 16 & 22 & 2.21 & 0.083 & 0.62 & 0.51 & 0.23 + -3 & 180 & 147 & 0.026 & 1.7 & 76 & 120 & 12 & 2.3 & 2.06 & 0.42 & 370 & 1 & 0.13 + -3 & 174 & 147 & 0.044 & 1.9 & 76 & 170 & 20 & 3.8 & 2.06 & 0.16 & 140 & 1 & 0.14 + -(4@xmath230 ) & 180 & 147 & 0.36 & 73 & 93 & 3.8 & 1.9 & 0.51 & 2.03 & max & 1.5e6 & 0.92 & 0.78 + + 1 & 209 & 93 & 6.0 & 8.2 & 80 & 3.8 & 5.3 & 14 & 2.88 & 20 & 2.5 & 0.15 & 0.28 + 0 & 138 & 93 & 3.4 & 2.6 & 79 & 12 & 15 & 16 & 2.79 & 2.2 & 2.2 & 0.15 & 0.16 + -1 & 127 & 93 & 3.4 & 1.7 & 80 & 23 & 32 & 23 & 2.61 & 0.26 & 2.5 & 0.23 & 0.13 + -3 & 198 & 93 & 0.043 & 0.79 & 100 & 28 & 15 & 2.4 & 2.18 & 11 & 1.5e4 & 0.20 & 0.079 + -3 & 217 & 93 & 0.25 & 0.25 & 111 & 85 & 66 & 2.7 & 2.21 & 6.6 & 1.0e4 & 0.15 & 0.042 + ccccccccccccccc 600 & 257 & 0.028 & 246 & 246 & 7.1@xmath231 & 1.6 & iso & 0.146@xmath232 & 0.09@xmath233 & 2.088@xmath234 & 0.45@xmath235 & 4.8@xmath236 & 22 & 100 + 107 & 90 & 0.66 & 0.16 & 79 & 174@xmath237 & 170 & 0.040@xmath238 & 15@xmath239 & 1.46@xmath240 & 2.56@xmath241 & 0.061@xmath169 & 2.4@xmath242 & 3.0 & 29 + 165 & 147 & 1.2 & 3.5 & 52 & 14@xmath243 & 16 & 0.23@xmath244 & 22@xmath179 & 1.25@xmath245 & 2.21@xmath182 & 0.51@xmath246 & 0.091@xmath247 & 0.083 & 0.62 + 127 & 93 & 3.4 & 1.7 & 80 & 23@xmath248 & 32 & 0.131@xmath249 & 23@xmath250 & 0.036@xmath251 & 2.61@xmath252 & 0.23@xmath253 & 0.47@xmath254 & 0.26 & 2.5 + ccccccccccccccccc 12.5 & 617 & 257 & 0.0044 & 52 & 52 & 8.3 & 0.75 & 0.087 & 0.14 & 1.0 & 1.9 & 1.3 & 2.08 & 3.2 & 0.56 & iso + 0 & 596 & 257 & 0.082 & 183 & 203 & 3.7 & 1.6 & 0.20 & 0.20 & 0.57 & 0.20 & 2.7 & 2.12 & 25 & 0.34 & 0.84 + -2.5 & 832 & 257 & 4.5 & @xmath255 & @xmath255 & 0.44 & 0.50 & 0.021 & 3.3 & 0.13 & 0.0023 & 2.4 & 2.32 & max & 0.052 & iso + -2.5 & 1012 & 257 & 3.8 & @xmath256 & @xmath256 & 1.8 & 2.6 & 0.25 & 170 & 0.0074 & 0.30 & 0.93 & 2.28 & 0.095 & 0.20 & iso + 12 & 160 & 93 & 1.8 & 1.6 & 23 & 4.3 & 5.4 & @xmath257 & 70 & 0.31 & 320 & 0.35 & 2.14 & 0.34 & 0.35 & 0.27 + 12 & 141 & 93 & 2.2 & 2.2 & 26 & 7.5 & 9.7 & @xmath258 & 73 & 0.35 & 530 & 0.42 & 2.64 & 0.026 & 0.31 & 0.29 + 10 & 135 & 93 & 2.1 & 1.9 & 26 & 6.7 & 8.2 & @xmath259 & 92 & 0.30 & 560 & 0.36 & 2.45 & 0.046 & 0.26 & 0.27 + 0 & 138 & 93 & 3.4 & 2.6 & 79 & 12 & 15 & 16 & 16 & 0.29 & 16 & 0.37 & 2.79 & 2.2 & 0.15 & 0.16 + -2.5 & 196 & 93 & 0.35 & @xmath260 & @xmath260 & 48 & 47 & 0.17 & 1.2 & 0.46 & 0.00056 & 9.9 & 2.88 & 0.046 & 0.033 & iso + cccc @xmath189 & @xmath261 & @xmath262 & @xmath263 + @xmath194 & @xmath264 & @xmath265 & @xmath266 + @xmath199 & @xmath267 & @xmath268 & @xmath269 + @xmath205 & @xmath270 & @xmath271 & @xmath272 + @xmath189 & @xmath273 & @xmath274 & @xmath275 + @xmath214 & @xmath276 & @xmath277 & @xmath278 + @xmath220 & @xmath279 & @xmath280 & @xmath281 + @xmath225 & @xmath270 & @xmath271 & @xmath272 +

we find a variety of parameters : densities that range from those of the ism to diffuse clouds , energies comparable to the total grb-ray energy , collimations from near - isotropy to 0.04 radians , substantial electron energy fractions of 10 - 30% with energy distribution indices of 2.1 - 2.9 and magnetic energy fractions from 0.2 - 25% . some parameter values change by up to an order of magnitude under such altered assumptions ; the parameters of even good fits can not be taken at face value .

we employ a fireball model of the gamma - ray burst explosion to constrain intrinsic and environmental parameters of four events with good broadband afterglow data ; grb 970508 , grb 980329 , grb 980703 , and grb 000926 . using the standard assumptions of constant circumburst density and no evolution of the fraction of the explosion energy in the post - shock magnetic field , we investigate the uniformity of the derived explosion and shock physics parameters among these events . we find a variety of parameters : densities that range from those of the ism to diffuse clouds , energies comparable to the total grb-ray energy , collimations from near - isotropy to 0.04 radians , substantial electron energy fractions of 10 - 30% with energy distribution indices of 2.1 - 2.9 and magnetic energy fractions from 0.2 - 25% . we also investigate the level to which the data constrain the standard model assumptions , such as the magnetic field evolution , and the allowed density profiles of the medium . fits generally improve slightly with an increasing magnetic energy fraction . good fits can be produced with magnetic energy accumulating or decaying with the shock strength over the afterglow as ; . the data are not very sensitive to increasing density profiles , allowing good fits even with density . some parameter values change by up to an order of magnitude under such altered assumptions ; the parameters of even good fits can not be taken at face value . the data are sensitive to decreasing densities ; profiles may produce reasonable fits , but steeper profiles , even , will not fit the data .

1406.3741

i

dislocations are line defects in crystalline materials which play an important role in governing the deformation and failure mechanisms in solids . the energetics of dislocations and their interactions with other defects solute atoms , precipitates , grain boundaries , surfaces and interfaces significantly influence the mechanical properties of crystalline materials ( cf . e.g. @xcite ) . for instance , the kinetic barriers for dislocation motion dislocation glide and climb and their dependence on crystallographic planes and directions govern ductility and creep in metals @xcite . interaction of dislocations with vacancies , solute atoms and precipitates results in solid - solution strengthening / softening , precipitate hardening and aging in metals @xcite . further , dislocation interactions with grain boundaries and surfaces are responsible for the observed strengthening mechanisms like the hall - petch effect @xcite , and enhanced yield strength in surface dominated nanostructures @xcite . the behavior of dislocations ( nucleation , kinetics , evolution ) in crystalline materials is governed by physics on multiple length - scales . in particular , a dislocation produces elastic fields that are long - ranged , and through these elastic fields interacts with other defects and external loads at macroscopic scales . on the other hand , the quantum - mechanical and atomistic scale interactions play an important role in governing the nucleation and kinetics of these defects . while atomistic scale interactions can significantly influence the behavior of dislocations , these are localized to a region around the dislocation line referred to as the dislocation - core . thus , the energy of a dislocation comprises of the stored elastic energy ( @xmath2 ) , associated with the elastic fields outside the dislocation - core , and a core - energy ( @xmath3 ) associated with quantum - mechanical and atomistic scale interactions inside the dislocation - core . continuum theories based on elastic formulations have been widely used to study deformation and failure mechanisms mediated through dislocations ( cf . e. g. @xcite ) , where the energetics of dislocations are solely determined by the elastic energy and the core - energy is often assumed to be an inconsequential constant . in order to overcome the inability of continuum theories to describe the dislocation - core , explicit atomistic calculations based on empirical interatomic potentials have also been employed to study deformation mechanisms mediated by dislocations ( cf . e. g. @xcite ) , and have provided many useful insights . however , interatomic potentials , whose parameters are often fit to bulk properties , may not accurately describe the defect - core which is governed by the electronic - structure ( cf . e. g. @xcite ) . electronic - structure calculations using plane - wave implementations of density functional theory ( dft ) have been employed to study the dislocation core - structure in a wide range of crystalline materials ( cf . e. g. @xcite ) and the energetics of dislocation - solute interactions in metals with different crystallographic symmetries @xcite . as the displacement fields produced by isolated dislocations are not compatible with periodic boundary conditions , these calculations have either been restricted to artificial dipole and quadrapole configurations of dislocations or free - surfaces have been introduced to contain isolated dislocations . recent efforts have also focused on the development of flexible boundary conditions by extending the lattice green s function method to electronic - structure calculations @xcite . flexible boundary conditions accurately account for the long - ranged elastic fields of an isolated dislocation @xcite , however , the electronic - structure in these studies is computed by introducing free surfaces to accommodate the restrictive periodic boundary conditions associated with plane - wave based dft implementations . while these aforementioned studies have provided useful insights into the dislocation core - structure , a direct quantification of the dislocation core - energy solely from electronic - structure calculations and its role in governing dislocation behavior has remained elusive thus far . we note that some prior _ ab initio _ studies using a dipole or quadrapole configuration of dislocations ( cf . e.g. @xcite ) , have attempted to indirectly compute the core - energy of an isolated dislocation by subtracting from the total energy the elastic interaction energy between dislocations in the simulation cell and their periodic images . this approach assumes the spacing between dislocations is large enough that the dislocation - cores do not overlap . however , these prior studies have been conducted on computational cells containing a few hundred atoms , which , as demonstrated in this work , are much smaller than the core - size of an isolated perfect edge dislocation in aluminum . in this work , we conduct large - scale electronic - structure calculations using orbital - free density functional theory to study an edge dislocation in aluminum . in our study , we use the wgc kinetic energy functional @xcite which has been shown to be in good agreement with kohn - sham dft for a wide range of material properties in aluminum @xcite . we employ a local real - space formulation of orbital - free density functional theory @xcite , where the extended interactions are reformulated as local variational problems . this real - space formulation of orbital - free density functional theory is used in conjunction with the finite - element basis that enables the consideration of complex geometries and general boundary conditions , which is crucial in resolving the aforementioned limitations of plane - wave basis in the study of energetics of isolated dislocations . we begin our study by computing the size of the dislocation - core for a perfect edge dislocation in aluminum . to this end , we consider a perfect edge dislocation with the atomic positions given by isotropic elasticity theory . for these fixed atomic positions , we identify the region where the perturbations in the electronic - structure arising from the defect - core are significant and have a non - trivial contribution to the dislocation energy . this allows us to unambiguously identify the dislocation - core from the viewpoint of energetics . our study suggests that the dislocation core - size of a perfect edge dislocation is about @xmath4 , where @xmath5 denotes the burgers vector . this estimate is much larger than conventional estimates based on displacement fields , which suggest a dislocation core - size of @xmath6 @xcite , and underscores the long - ranged nature of the perturbations in the electronic fields arising from defects . we note that a similar long - ranged nature of the electronic fields was observed in recent studies on point defects @xcite . as a next step in our study , we allow for atomic relaxations , and the perfect edge dislocation dissociates into shockley partials with a partial separation distance of @xmath1 . the dislocation energy per unit length of the relaxed shockley partials in the simulation domain corresponding to the identified core - size , which denotes the dislocation core - energy , is computed to be @xmath7 @xmath8 . we next study the role of macroscopic deformations on the dislocation core - energy and core - structure . in particular , we considered a wide range of macroscopic deformations including : ( i ) equi - triaxial strains representing volumetric deformations ; ( ii ) uniaxial strains along the the burgers vector , normal to the slip plane , and along the dislocation line ; ( ii ) equi - biaxial strains along these crystallographic directions ; ( iii ) shear strains along these crystallographic directions , excepting the one which results in dislocation glide . interestingly , we find that the dislocation core - energy is significantly influenced by applied macroscopic deformations . in particular , we find that this core - energy dependence on macroscopic strains is non - linear and non - monotonic . further , this core - energy dependence on macroscopic deformations suggests that the dislocation experiences an additional configurational force beyond the peach - koehler force . this additional force arising from core - effects , and referred to as the core - force , is proportional to the strain gradients and can be significant in regions of inhomogeneous deformations . in particular , we estimate that , in the case of a dislocation dipole with the two dislocations aligned at @xmath9 to the slip direction , the core - force has a glide component which is greater than the peierls nabarro force even at a distance of @xmath10 . while we observe a significant influence of macroscopic deformations on the core - energy , the core - structure , studied using differential displacement plots , did not change significantly in response to the applied macroscopic uniaxial , biaxial and triaxial strains . however , the shear strain which exerts a glide force on the screw components of the shockley partials showed a significant influence , as expected , on the core - structure . the remainder of this paper is organized as follows . section [ sec : ofdft ] presents an overview of the local real - space formulation of orbital - free dft employed in this work . section [ sec : results ] presents our electronic - structure study of the edge dislocation in aluminum , along with a discussion of the new findings and its implications . we finally conclude with an outlook in section [ sec : conclusions ] .

we employed a real - space formulation of orbital - free density functional theory using finite - element basis to study the defect - core and energetics of an edge dislocation in aluminum . our study shows that the core - size of a perfect edge dislocation is around ten times the magnitude of the burgers vector . consistent with prior electronic - structure studies , we find that the perfect edge dislocation dissociates into two shockley partials with a partial separation distance of .

we employed a real - space formulation of orbital - free density functional theory using finite - element basis to study the defect - core and energetics of an edge dislocation in aluminum . our study shows that the core - size of a perfect edge dislocation is around ten times the magnitude of the burgers vector . this finding is contrary to the widely accepted notion that continuum descriptions of dislocation energetics are accurate beyond burgers vector from the dislocation line . consistent with prior electronic - structure studies , we find that the perfect edge dislocation dissociates into two shockley partials with a partial separation distance of . interestingly , our study revealed a significant influence of macroscopic deformations on the core - energy of shockley partials . we show that this dependence of the core - energy on macroscopic deformations results in an additional force on dislocations , beyond the peach - koehler force , that is proportional to strain gradients . further , we demonstrate that this force from core - effects can be significant and can play an important role in governing the dislocation behavior in regions of inhomogeneous deformations . density functional theory , real space , dislocation , core size , core energy

1406.3741

r

we now present our study of an edge dislocation in aluminum using large - scale electronic - structure calculations . in particular , we unambiguously identify the size of the dislocation core , directly compute the dislocation core - energy , study the effect of macroscopic deformations on dislocation core - energy and core - structure , and investigate its implications on dislocation behavior . in this study , we employ orbital - free density functional theory calculations using the wang - govind - carter ( wgc ) kinetic energy functional @xcite ( second order taylor expansion of the density dependent kernel , cf . @xcite ) , a local density approximation ( lda ) for the exchange - correlation energy @xcite , and goodwin - needs - heine pseudopotential @xcite . while orbital - free dft uses an approximation for the kinetic energy functional , it has been demonstrated that the wgc kinetic energy functional is in good agreement with kohn - sham dft for a wide range of material properties in aluminum , which include bulk and defect properties @xcite . further , orbital - free dft is inherently linear - scaling in the number of electrons and enables the consideration of large system sizes , which is necessary , as will be demonstrated in this work , for an accurate study of the energetics of dislocations . in the present work , we employ recently developed local real - space formulation of orbital - free dft ( cf . section [ sec : ofdft ] and @xcite ) and a finite - element discretization of the formulation @xcite to compute the energetics of an edge dislocation in aluminum . in this real - space formulation , all the extended interactions , which include the electrostatic interactions and the kernels energies in the wgc kinetic energy functional , are reformulated into local variational problems in auxiliary potential fields that include the electrostatic potential and kernel potentials . the finite - element basis employed in the present work enables consideration of complex geometries and general boundary conditions ( dirichlet , periodic and semi - periodic ) , which is another crucial aspect that enables an accurate quantification of the energetics of isolated dislocations . the accuracy of the local real - space formulation of orbital - free dft and the convergence of the finite - element discretization of the formulation have been demonstrated for both bulk and defect properties in aluminum @xcite . in the present study , we use quadratic hexahedral finite - elements in all our calculations , where the basis functions correspond to a tensor product of quadratic polynomials in each dimension . the finite - element discretization and other numerical parameters quadrature rules and stopping tolerances on iterative solvers are chosen such that the errors in the computed dislocation energies are less than @xmath50 @xmath51 . in all our calculations , the atomic relaxations are performed till the maximum force on any atom is less than @xmath52 @xmath8 . in order to compute the dislocation core - energy , we begin by first estimating the dislocation core - size . continuum theories estimate the dislocation core - sizes based on displacement fields , and prior studies suggest the dislocation core - size to be @xmath53 @xmath54 @xmath55 @xcite , where @xmath5 denotes the burgers vector . while the displacement and strain fields may be well described by elastic formulations outside of a @xmath54 @xmath55 core region , the perturbations in electronic - structure due to the dislocation may be present on a larger region . the energetic contributions from these electronic - structure effects can not be captured in continuum elasticity theories or atomistic calculations using empirical potentials . thus , in the present work , we consider the dislocation - core to be the region where electronic - structure effects and their contribution to the defect energy are significant . we consider a perfect edge dislocation in face - centered - cubic aluminum to determine the dislocation core - size . we align our coordinate system , @xmath56 axes ( or equivalently @xmath57 ) , along @xmath58-[1\,\overline{1}\,1]-[1\,\overline{1}\,\overline{2}]$ ] crystallographic directions , respectively . we begin by considering a perfect crystal of size @xmath59 where @xmath60 denotes the lattice parameter and @xmath61 is an integer - valued scaling factor used to consider a sequence of increasing simulation domain sizes . a perfect edge dislocation with burgers vector @xmath62 $ ] is introduced at the center of the simulation domain by removing two consecutive half - planes normal to @xmath63 $ ] and applying the continuum displacement fields of an edge dislocation to the positions of atoms . we note that this approach of creating the edge dislocation is devoid of the asymmetry that can otherwise arise by applying the volterra solution in the most obvious manner by creating slip ( cf . @xcite ) . in this work , the displacement fields from isotropic elasticity @xcite are employed as anisotropic effects are not strong in aluminum . upon the application of displacement fields , the geometry of the computational domain is no longer cuboidal , and , thus , the use of a finite - element basis which can accommodate complex geometries is crucial to the present study . in order to simulate a perfect edge dislocation , we hold the positions of the atoms fixed and compute the electronic - structure using orbital - free dft . we employ dirichlet boundary conditions on the electronic fields comprising of electron density , electrostatic potential and kernel potentials in the @xmath64 and @xmath65 directions and use periodic boundary conditions along the @xmath66 direction . the dirichlet boundary conditions are determined under the cauchy - born approximation , where the values of electronic fields on the dirichlet boundary are computed from periodic unit - cells undergoing the deformations produced by the edge dislocation . the electronic - structure , thus computed , represents an isolated edge dislocation in bulk with the electronic - structure perturbations from the edge dislocation vanishing on the dirichlet boundary . the local real - space formulation of orbital - free dft and the finite - element basis are key to employing these boundary conditions , which are not possible to realize in fourier - space based formulations . we computed the electronic - structure and ground - state energy of the perfect edge dislocation for varying simulation domains with @xmath67 . figure [ fig : contours ] shows the contours of the electron density for @xmath68 . we note that a scaling factor @xmath61 corresponds to a domain - size where the distance from dislocation line to the boundary along @xmath63 $ ] is @xmath69 . the dislocation energy ( @xmath70 ) for these various simulation domains is computed as @xmath71 where @xmath72 denotes the energy of the @xmath11 atom system comprising of the dislocation and occupying a volume @xmath73 , and @xmath74 denotes energy of a perfect crystal containing the same number of atoms and occupying the same volume . we first computed the dislocation energy at equilibrium volume ( i.e. @xmath75 ) for the various domain - sizes considered in this study , and the results are presented in table [ tab : elasticelec ] . the computed dislocation energy increases with increasing domain - size , and has an asymptotic logarithmic divergence as expected from continuum theories . in order to understand the extent of electronic relaxations , we consider the change in dislocation energy by increasing the domain - size for instance , from a domain - size of @xmath76 to @xmath77and denote this change by @xmath78 . this change in the energy has two contributions : ( i ) the increase in the elastic energy due to the increase in the domain - size , which we denote by @xmath79 ; ( ii ) electronic contribution from perturbations in the electronic - structure , which we denote by @xmath80 . as the elastic energy contribution to the dislocation energy is due to the elastic deformation fields produced by the dislocation , we estimate @xmath79 by integrating the elastic energy density in the region of interest . the elastic energy density at any point , in turn , is computed from an orbital - free dft calculation on a unit - cell undergoing the macroscopic deformation produced by the edge dislocation at that point . we verified that the discretization errors in the computation of @xmath79 are of the order of @xmath81 . upon computing @xmath79 , we infer @xmath80 from @xmath78 ( @xmath82 ) . the computed @xmath79 and @xmath80 are reported in table [ tab : elasticelec ] . it is interesting to note from the results that @xmath80 is comparable to @xmath79 up to a domain - size of @xmath4 , suggesting that the electronic - structure perturbations are significant up to distances as far as @xmath4 from the dislocation line . this result is in strong contrast to conventional estimates of core - sizes to be @xmath83 . further , we note that a core - size of @xmath4 contains over @xmath84 atoms , which is much larger than the computational cells employed in most prior electronic - structure studies of dislocations , and underscores the need to consider sufficiently large simulation domains to accurately compute the energetics of dislocations . in the remainder of this work , we consider @xmath4 to be the core - size of edge dislocation , and the dislocation energy corresponding to this core - size as the dislocation core - energy . for a perfect edge dislocation , the computed core - energy is @xmath85 , or , equivalently , the core - energy per unit length of dislocation line is @xmath86 . a plot of the dislocation energies ( @xmath70 ) reported in table [ tab : elasticelec ] as a function of domain - size is provided in figure [ fig : cellsize ] , which shows the expected asymptotic logarithmic divergence of the dislocation energy . ( corresponding to a domain of @xmath87 along @xmath63-[1\overline{1}1]-[1\overline{1}\overline{2}]$]).,scaledwidth=65.0% ] as a next step in our study , we allowed for internal atomic relaxations in the simulation domain corresponding to @xmath4 by holding the positions of atoms fixed on the boundary . upon atomic relaxations , the perfect edge dislocation split into shockley partials . figure [ fig : dd ] shows the edge and screw components of the differential displacements @xcite and indicates the location of the shockley partials . the partial separation distance computed from the edge - component differential displacement plot is @xmath88 ( @xmath89 ) , and that computed from the screw - component differential displacement plot is @xmath90 ( @xmath91 ) . this is in good agreement with other dft studies on an edge dislocation in aluminum which have reported partial separation distances between @xmath92 @xcite . the core - energy of shockley partials is computed to be @xmath93 , or , equivalently , the core - energy per unit length of dislocation line is @xmath94 . the core - energy of the relaxed shockley partials , as expected , is significantly lower than that of the perfect edge dislocation . in the remainder of this paper , all the reported core - energies correspond to the relaxed shockley partials . we note that holding the positions of atoms fixed on the boundary , prescribed by the displacement fields of a perfect edge dislocation , can result in finite cell - size effects that influence the core - structure of the shockley partials and the core - energy . in order to investigate the influence of this possible finite cell - size effect , we considered simulation domains corresponding to @xmath95 and @xmath96 and computed the core - structure in these simulation domains , and compared it with the core - structure obtained from the @xmath4 simulation domain . the partial separation distance of both the edge- and screw - components did not change by increasing the simulation domain . further , we computed the difference in the positions of atoms ( in the region corresponding to @xmath4 simulation domain ) obtained from the @xmath96 and @xmath4 simulation domains . the maximum difference in the positions of atoms is @xmath97 , which is close to the tolerance associated with force relaxations . these results suggest that the finite cell - size effects arising from the fixed spatial boundary conditions on atomic positions are not important in simulation domains of size @xmath4 and beyond . while the computed partial separation distance is in good agreement with prior electronic - structure studies , the partial separation distances are over - predicted in dft compared to experimental investigations . the partial separation distance of the edge dislocation in aluminum is estimated to be @xmath98 using weak - field tem @xcite . one plausible cause of this deficiency in dft calculations can be the use of pseudopotentials , especially since the stacking fault energy is sensitive to the choice of the pseudopotential @xcite . while pseudopotential dft calculations have been shown to be accurate for the prediction of bulk properties in solids , their transferability to accurately predict defect properties is yet to been ascertained to this end , there is a growing need for the development of efficient large - scale real - space methods for all - electron kohn - sham dft calculations , and we refer to @xcite for recent efforts in this direction . most continuum and mesoscale models describing deformation and failure mechanisms in crystalline solids account for the role of defects through the elastic interactions between various defects , as well as , elastic interactions between defects and macroscopically applied loads . however , recent electronic - structure studies on point defects @xcite suggest that the defect - core can play a significant role in governing the overall energetics of these defects , and that there is a strong influence of macroscopic deformations on the electronic - structure of the defect - core and its energetics . further , a recent electronic - structure study also reported a sizeable effect of pressure on the dislocation - core properties in semiconductor materials @xcite . thus , as a next step in our study , we investigate the effect of macroscopic deformations on the core - energy and core - structure of an edge dislocation in aluminum . we begin with a perfect edge dislocation in @xmath4 simulation domain , which corresponds to the core - size of the edge dislocation . we subsequently apply an affine deformation on the simulation domain corresponding to a macroscopic strain @xmath99 , and , by holding the positions on the boundary fixed , compute the electronic - structure as well as the atomic structure of the relaxed shockley partials . in these simulations , as discussed earlier , dirichlet boundary conditions are applied on the electronic fields in the @xmath64 and @xmath65 directions , where the boundary values are computed using the cauchy - born hypothesis . we note that the applied macroscopic strain manifests into the boundary conditions on the positions of atoms , as well as , the values of the electronic fields on the dirichlet boundary . following equation , the dislocation energy of this @xmath4 simulation domain ( dislocation core - energy ) as function of macroscopic strain is computed as @xmath100 in the above expression , @xmath101 denotes the ground - state energy ( after internal atomic relaxations ) of the @xmath4 simulation domain , which contains the dislocation , under an affine deformation corresponding to macroscopic strain @xmath102 , and @xmath103 denotes the energy of a perfect crystal under the same affine deformation , containing the same number of atoms and occupying the same volume . we begin our investigation by studying the effect of macroscopic volumetric strain ( @xmath104 ) , corresponding to equi - triaxial strain , on the core - energy of shockley partials and the core - structure . in this study , we consider volumetric strains of @xmath105 , @xmath106 , @xmath107 , @xmath108 , @xmath109 and @xmath110 . the computed core - energy demonstrated a strong dependence on volumetric strain , and is shown in figure [ fig : volumetric_strain ] . the core - energy ( per unit length of dislocation line ) changed from @xmath111 at @xmath105 volumetric strain to @xmath112 at @xmath110 volumetric strain , and this change corresponds to a significant fraction ( @xmath113 ) of the core - energy at equilibrium . this finding is in sharp contrast to the assumptions in continuum formulations that ignore the core - energy in determining the energetics of dislocations and their interactions . the core - structure , analyzed using the differential displacement ( dd ) plots , is also found to be marginally influenced by the applied macroscopic volumetric strain . in particular , for the range of volumetric strains considered , the partial separation in the edge - component dd plots is in the range of @xmath114 , and the partial separation in the screw - component dd plot is in the range of @xmath115 . we next study the effect of uniaxial strains along the coordinate directions , @xmath58-[1\,\overline{1}\,1]-[1\,\overline{1}\,\overline{2}]$ ] , on the dislocation core - energy and core - structure . we consider uniaxial strains of @xmath116 , @xmath117 , @xmath118 , @xmath119 , @xmath120 and @xmath121 along each of the coordinate directions . figures [ fig : uniaxial1 ] , [ fig : uniaxial2 ] , and [ fig : uniaxial3 ] show the core - energy dependence on @xmath122 ( uniaxial strain along @xmath58 $ ] ) , @xmath123 ( uniaxial strain along @xmath124 $ ] ) and @xmath125 ( uniaxial strain along @xmath126 $ ] ) , respectively . as in the case of volumetric strains , the core - energy monotonically decreases from compressive strains to tensile strains ( for the range of strains considered ) for uniaxial strains @xmath122 ( along the burgers vector ) and @xmath125 ( along the dislocation line ) . however , the core - energy dependence is non - monotonic and non - linear for @xmath123 uniaxial strain ( along the normal to the slip plane ) . these results show that the core - energy of an edge dislocation can have a complex and non - linear dependence on macroscopic strains . as in the case of volumetric strains , the core - structure is found to be marginally sensitive to uniaxial strains . for the range of uniaxial strains considered in this study , the partial separation in the edge - component dd plots is in the range of @xmath114 and the partial separation in the screw - component dd plots is in the range of @xmath127 . the fact that the core - energy shows a strong dependence on the volumetric and uniaxial strains , while the core - structure is only marginally influenced by these strains , suggests that the electronic - structure at the core can play a dominant role in governing the energetics of dislocations and that the core - structure alone may not completely characterize the defect - core . we next investigate the effect of biaxial strains on the edge dislocation . to this end , we consider equi - biaxial states of strain along the coordinate directions , and computed the core - energies and core - structures under these applied macroscopic strains . figures [ fig : biaxial12 ] , [ fig : biaxial13 ] , [ fig : biaxial23 ] show the dependence of core - energy on equi - biaxial strains @xmath128 , @xmath129 and @xmath130 , respectively . as in the case of uniaxial strains , the core - energy dependence on biaxial strains is found to be non - monotonic when there is macroscopic strain along @xmath124 $ ] , the direction normal to the slip plane ( cf . figures [ fig : biaxial12 ] , [ fig : biaxial23 ] ) . these results again underscore the highly non - linear nature of core - energy dependence on macroscopic strains . the biaxial strains also influenced the core - structure , and to a greater extent than uniaxial strains . for the range of uniaxial strains considered in this study , the partial separation in the edge - component dd plots is in the range of @xmath131 and the partial separation in the screw - component dd plots is in the range of @xmath132 . we next consider shear strains @xmath133 and @xmath134 and their influence on the core - energy and core - structure . in the present work , we do not study the influence of @xmath135 strain , as , even at small values of shear stress resulting from this shear strain ( @xmath136 , cf . @xcite ) , the edge dislocation glides by overcoming the peierls barrier . the computed core - energy dependence on @xmath133 and @xmath134 shear strains is shown in figure [ fig : shear_strain ] . it is interesting to note that the core - energy dependence is symmetric in @xmath133 , to within the discretization errors of @xmath137 . on the other hand , the core - energy dependence on @xmath134 strain is asymmetric . this qualitative change in core - energy dependence can be rationalized from the forces created by these macroscopic shear strains on the shockley partials . the shear stress associated with @xmath133 results in climb forces , in opposite directions , on the screw components of shockley partials . upon changing the sign of the shear stress , the direction of the climb forces on each of the shockley partials is reversed , but these configurations are symmetry related and thus the core - energy variation is symmetric with respect to @xmath133 . in contrast , the shear stress associated with @xmath134 results in glide forces , in opposite directions , on the screw component of shockley partials . thus , the sign of this shear stress has an effect of either increasing or decreasing the partial separation distance between the shockley partials , which is the source of the asymmetry in core - energy dependence on @xmath134 . this is also further corroborated from the core - structure , which shows a significant change in the partial separation distance in the screw - component dd plot in response to @xmath134 strain . in particular , the partial separation in the screw - component of the dd plot changes from @xmath138 at @xmath139 to @xmath140 at @xmath141 ( cf . figure [ fig : dd_screw_e23 ] ) . further , the partial separation in the edge - component of the dd plot also changes from @xmath89 at @xmath139 to @xmath142 at @xmath141 . on the other hand , the core - structures are found to be similar for both negative and positive @xmath133 strains of a given magnitude , as expected from symmetry . for the range of @xmath133 shear strains considered in the present work , the partial separation in the edge - component dd plots is in the range of @xmath114 and the partial separation in the screw - component dd plots is in the range of @xmath127 . the study on the effect of macroscopic strains revealed a strong dislocation core - energy dependence on macroscopic deformations . interestingly , the slope of the core - energy dependence on macroscopic strains is non - zero at zero strain . this suggests that the energetics of dislocation - cores play a non - trivial role in governing the behavior of dislocations even at small strains and at macroscopic scales . in order to elucidate the role of dislocation core - energy in influencing dislocation behavior , we consider the force on a unit length of dislocation line segment resulting from external loads or other defects . the classical force on the dislocation arising from elastic interactions is given by the peach - koehler force @xcite : @xmath143 where @xmath144 denotes the stress tensor , @xmath5 denotes the burgers vector and @xmath145 denotes the unit vector along the dislocation line . however , since the core - energy is dependent on macroscopic strains at the dislocation core , there is an additional configurational force associated with this dependence , referred to as the core - force , and is given by @xmath146 given the non - linear nature of the core - energy dependence on macroscopic strains , @xmath147 , in general , is a function of the macroscopic strain at the dislocation core . however , for typical strains of @xmath148 occurring in most deformations in solids , @xmath147 can be computed , to leading order , from the slopes of the core - energy dependence on various uniaxial and shear strains at zero strain ( cf . figures [ fig : uniaxial1]-[fig : uniaxial3 ] , [ fig : shear13]-[fig : shear23 ] ) , i.e. , @xmath149 . it is interesting to note that , while the peach - koehler force depends on the stress - tensor ( which is related to the strain - tensor ) , the core - force depends on the gradient of strain - tensor and can be significant in regions of inhomogeneous deformations . we note that past studies ( cf . e.g. @xcite ) , employing elastic formulations to model the defect - core using dislocation dipoles and line forces , have investigated the interaction of dislocation cores with applied pressure and have suggested corrections to the peach - koehler force based on these interactions . however , a direct quantification of this core - force solely from electronic - structure calculations has been beyond reach heretofore . in order to understand the implications of the core - energy dependence on macroscopic strains on the behavior of dislocations , we consider the interaction between two dislocations . in particular , we consider a dislocation dipole , with one dislocation ( dislocation @xmath150 ) along the @xmath151axis located at @xmath152 with a burgers vector ( @xmath5 ) of @xmath153 $ ] and another dislocation ( dislocation @xmath154 ) , also along @xmath151axis , located at @xmath155 with a burgers vector of @xmath156 $ ] ( @xmath157 ) . the peach - koehler force @xcite on a unit length of dislocation @xmath154 due to the elastic fields from dislocation @xmath150 is given by @xmath158 where @xmath159 denotes the stress tensor associated with the elastic fields produced by dislocation @xmath150 at the location of dislocation @xmath154 , and @xmath160 denotes the unit vector along the dislocation line of @xmath154 ( unit vector along @xmath151axis ) . we note that the peach - koehler force ( @xmath161 ) decays as @xmath162 , where @xmath163 denotes the distance between the two dislocations , which follows from the asymptotic behavior of the elastic field of a dislocation . on the other hand , the core - force force resulting from the macroscopic strain dependence of the core - energy is given by @xmath164 where @xmath165 denotes the core - energy of dislocation a in the elastic field of b ( @xmath166 ) , and @xmath167 denotes the core - energy of dislocation b in the elastic field of a ( @xmath168 ) . for the dipole configuration , we note that @xmath169 @xcite , and , from symmetry , @xmath170 . thus , @xmath171 noting that @xmath172 is @xmath173 , the core - force for dipole interactions decays as @xmath173 . thus , this is a shorter - ranged force in dislocation - dislocation interactions compared to the peach - koehler force . to the glide - plane.,scaledwidth=100.0% ] in order to further investigate the quantitative aspects of this core - force and its implications on dislocation - dislocations interactions , we consider two specific cases as shown in figure [ fig : casestudy ] . in the first case , the dislocations are aligned along the glide - plane , whereas in the second case they are at an angle of @xmath9 . for these two cases , we computed the peach - koehler force and the core - force on dislocation b. _ case ( i ) : _ for the first case , using the stress tensor associated with the elastic fields of a stationary edge dislocation @xcite , the peach - koehler force is given by @xmath174 where @xmath175 , @xmath176 , @xmath177 denote unit vectors along @xmath56 axis , and @xmath178 . the corresponding core - force , using the strain field of a stationary edge dislocation , is given by @xmath179 the second equality in the above expression for core - force uses the fact @xmath180 ( from the strain field of a stationary edge dislocation ) , and @xmath181 , from symmetry , for an edge dislocation . it is interesting to note that , for this case , while the peach - koehler force is a glide force on the dislocation , the core - force is a climb force . _ case ( ii ) : _ for the second case , the peach - koehler force and the core - force are given by @xmath182 @xmath183 the above expression for core - force uses the fact @xmath180 ( from the strain field of a stationary edge dislocation ) , and @xmath181 from symmetry . it is interesting to note that , for this case , while the peach - koehler force is a climb force on the dislocation , the core - force has both glide and climb components . we next investigate the relative importance of the core - force in governing the dislocation behavior . to this end , we estimated the glide component of the core - force for _ case ( ii ) _ from equation , and compared it to the peierls - nabarro force the critical force that will cause dislocation glide . for these calculations , we used the computed elastic constants @xmath184 . using @xmath185 for the peierls stress @xcite , we computed the peierls - nabarro force ( from equation [ eqn : pk ] ) on a @xmath186 length of dislocation line to be @xmath187 @xmath8 . using @xmath188 and @xmath189 , estimated from the data in figures [ fig : uniaxial1 ] and [ fig : uniaxial2 ] , the glide component of the core - force from case ( ii ) on a @xmath186 length of dislocation line is computed to be @xmath190 @xmath8 where @xmath163 is the distance between the dislocations @xmath150 and @xmath154 measured in angstroms . it is interesting to note that even at a distance of @xmath10 , the magnitude of core - force is larger than the magnitude of peierls - nabarro force . these results suggest that the short - ranged core - force , resulting from the dependence of core - energy on macroscopic deformations , is significant up to tens of nanometers and can play an important role in governing the behavior of dislocations , especially in regions of inhomogeneous deformations .

this finding is contrary to the widely accepted notion that continuum descriptions of dislocation energetics are accurate beyond burgers vector from the dislocation line . interestingly , our study revealed a significant influence of macroscopic deformations on the core - energy of shockley partials . further , we demonstrate that this force from core - effects can be significant and can play an important role in governing the dislocation behavior in regions of inhomogeneous deformations . density functional theory , real space , dislocation , core size , core energy

we employed a real - space formulation of orbital - free density functional theory using finite - element basis to study the defect - core and energetics of an edge dislocation in aluminum . our study shows that the core - size of a perfect edge dislocation is around ten times the magnitude of the burgers vector . this finding is contrary to the widely accepted notion that continuum descriptions of dislocation energetics are accurate beyond burgers vector from the dislocation line . consistent with prior electronic - structure studies , we find that the perfect edge dislocation dissociates into two shockley partials with a partial separation distance of . interestingly , our study revealed a significant influence of macroscopic deformations on the core - energy of shockley partials . we show that this dependence of the core - energy on macroscopic deformations results in an additional force on dislocations , beyond the peach - koehler force , that is proportional to strain gradients . further , we demonstrate that this force from core - effects can be significant and can play an important role in governing the dislocation behavior in regions of inhomogeneous deformations . density functional theory , real space , dislocation , core size , core energy

0906.0286

c

for the first time in the literature we have estimated the cross section for exclusive @xmath0 meson ( glueball candidate ) production not far from the threshold . we have included both gluon induced diffractive and triangle - double - diffractive mechanisms as well as the pion - pion exchange contributions . the qcd diffractive component was obtained by extrapolating down the cross section in the khoze - martin - ryskin approach with unintegrated gluon distributions from the literature as well as using two - gluon impact factor approach . a rather large uncertainties are associated with the qcd diffractive component . at present only upper limit can be obtained for the diffractive component as the @xmath302 decay coupling constant remains unknown . the coupling constant could be extracted only in high - energy exclusive production of @xmath0 where other mechanisms are negligible . we have found rather large contribution of pionic - triangle - double - diffractive component at higher energies ( @xmath303 10 gev ) . however , at the gsi hesr energies this contribution is strongly damped because of the phase space limitations on the @xmath127 subchannel energies . the calculation of the mec contribution requires introducing extra vertex form factors . at largest panda energies they are relatively well known and the pion - pion fusion can be reliably calculated . the situation becomes more complicated very close to the threshold where rather large @xmath304 and @xmath305 are involved . the cross section for energies close to the threshold is very sensitive to the functional form and parameters of vertex form factor . therefore a measurement of @xmath0 close to its production threshold could limit the so - called @xmath216 form factors in the region of exchanged four - momenta never tested before . we predict the dominance of the pion - pion contribution close to the threshold . our calculation shows that the diffractive components ( in fact its upper limit for the qcd mechanism ) are by more than order of magnitude smaller than the pion - pion fusion component in the energy region of future panda experiment . the diffractive components may dominate over the pion - pion component only for center - of - mass energies @xmath257 15 gev . taking into account rather large uncertainties the predictions of this component should be taken with some grain of salt . clearly an experimental program is required to disentangle the reaction mechanism at energies @xmath257 15 gev . disentangling the mechanism of the exclusive @xmath0 production not far from the meson production threshold would require study of the @xmath203 , @xmath204 processes with the panda detector at fair and @xmath118 reaction at j - parc . in the case the pion exchange mechanism is a dominant process one expects : @xmath306 . at high energies , when the gluonic , or double - diffractive with intermediate triangle , components dominate over mec components @xmath307 . at intermediate energies one can not exclude a priori subleading reggeon exchanges like @xmath218 for instance . however , we do not know how to reliably calculate them from first principles . we believe that the distortions from the pion - pion at low energies and/or distortions from the qcd gluonic mechanism at high energy may tell us more and allow for a phenomenological analysis taking into account the @xmath218 component explicitly . we leave this problem for a future analysis when experimental data will be available . only a careful studies of different final channels in the broad range of energies could help to shed light on coupling of ( nonperturbative ) gluons to @xmath0 and therefore would give a new hint on its nature . the experimental studies of exclusive production of @xmath0 are not easy at all as in the @xmath224 decay channel one expects a large continuum . we have performed an involved calculation of the four - body @xmath308 background . our calculation shows that imposing extra cuts should allow to extract the signal of the glueball @xmath0 candidate at the highest panda energy . a partial wave @xmath224 analysis should be helpful in this context . the two - pion continuum will be studied in more detail in our future work . a smaller continuum may be expected in the @xmath309 or four - pion @xmath0 decay channel . this requires , however , a good geometrical ( full solid angle ) coverage and high registration efficiencies . panda detector seems to fulfill these requirements , but planning real experiment requires a dedicated monte carlo simulation of the apparatus . it is a central problem of our field if @xmath0 is a @xmath5 or glueball type . unfortunately , our analysis does not allow to give a definite answer to this important question . some information on baryon - baryon correlation may be helpful but certainly not decisive . if the cross section at high energies ( where the contribution of subleading reggeon exchanges may be neglected ) is much smaller than predicted based on the kmr method it means that gluons only weakly couple to @xmath0 . this could provide some indirect information on the @xmath0 structure . a direct comparison of the shape of differential distributions at high energies may provide a valuable test of the kmr method originally proposed for exclusive higgs production ( the latter experiment is very difficult as very small statistics is predicted ) . a possible disagreement with the prediction for exclusive @xmath0 production at high energies could put into question the kmr approach , at present state of art in the field . experiments at rhic could be useful in this context and could shed light on the nonperturbative coupling of gluons to @xmath0 . s. narison , g. veneziano , int . j. mod * a4 * ( 1989 ) 2751 ; + s. narison , nucl . b509 * ( 1998 ) 312 ; + s. narison , phys . * d73 * ( 2006 ) 114024 . tao huang , hong ying jin and ai - lin zhang , phys . * d59 * ( 1998 ) 034026 . kisslinger , j. gardner and c. vanderstraeten , phys . lett . * b410 * ( 1997 ) 1 . d. harnett , t.g . steele , nucl . * a695 * ( 2001 ) 205 . g. orlandini , t.g . steele , d. harnett , nucl.phys . * a686 * ( 2001 ) 261 . steele , d. harnett , g. orlandini , aip conf . * 688 * ( 2004 ) 128 , [ arxiv : hep - ph/0308074 ] . c. amsler et al . ( crystal barrel collaboration ) , phys . b327 * ( 1994 ) 425 ; + c. amsler et al . ( crystal barrel collaboration ) , phys . b333 * ( 1994 ) 277 ; + c. amsler et al . ( crystal barrel collaboration ) , phys . * b340 * ( 1994 ) 259 . khoze , a.d . martin and m.g . ryskin , phys . lett . * b401 * ( 1997 ) 330 ; + v.a . khoze , a.d . martin and m.g . ryskin , eur . j. * c23 * ( 2002 ) 311 ; + a.b . kaidalov , v.a . khoze , a.d . martin and m.g . ryskin , eur . j. * c31 * ( 2003 ) 387 , [ arxiv : hep - ph/0307064 ] ; + a.b . kaidalov , v.a . khoze , a.d . martin and m.g . ryskin , eur . j. * c33 * ( 2004 ) 261 ; + v.a . khoze , a.d . martin , m.g . ryskin and w.j . stirling , eur . j. * c35 * ( 2004 ) 211 .

, pion - pion meson exchange current ( mec ) components as well as double - diffractive mechanism with intermediate pionic loop are calculated for the first time in the literature . the pion - pion component , which can be reliably calculated , dominates close to the threshold while the diffractive component may take over only for larger energies . at the moment only upper limit for the qcd - diffractive component can be obtained . the diffractive component is calculated based on two - gluon impact factors as well as in the framework of khoze - martin - ryskin approach proposed for diffractive higgs boson production . different unintegrated gluon distribution functions ( ugdfs ) from the literature are used . the production of close to threshold could limit the so - called form factor in the region of larger pion virtualities .

we evaluate differential distributions for exclusive scalar meson ( glueball candidate ) production for ( fair@gsi ) and ( j - parc@tokai ) . both qcd diffractive , pion - pion meson exchange current ( mec ) components as well as double - diffractive mechanism with intermediate pionic loop are calculated for the first time in the literature . the pion - pion component , which can be reliably calculated , dominates close to the threshold while the diffractive component may take over only for larger energies . at the moment only upper limit for the qcd - diffractive component can be obtained . the diffractive component is calculated based on two - gluon impact factors as well as in the framework of khoze - martin - ryskin approach proposed for diffractive higgs boson production . different unintegrated gluon distribution functions ( ugdfs ) from the literature are used . rather large cross sections due to pion - pion fusion are predicted for panda energies , where the gluonic mechanism is shown to be negligible . the production of close to threshold could limit the so - called form factor in the region of larger pion virtualities . we discuss in detail the two - pion background to the production of the meson .

1603.00495

i

we have identified on _ galex _ images the furthest out distinct @xmath0 knot in the little things sample of dirr and bcd galaxies that we are confident belong to the galaxy . these knots are found at distances from the center of the galaxies of 1 to 8 disk scale lengths and have ages of @xmath1 myrs and masses of 20 m_@xmath2 to @xmath3 m_@xmath2 . the presence of young clusters in the outer disks of dwarf galaxies shows that dirrs do have _ in situ _ star formation taking place in their outer disks . most regions are found around an h@xmath4i surface density of 1 m_@xmath2 pc@xmath6 , making this look like a threshold for the formation of prominent ob associations . the environments of these remote star - forming regions are extreme compared to the solar neighborhood and inner milky way ( [ environ ] ) , or even compared to the inner parts of dirr galaxies . the average pressures and midplane densities are lower by a factor of @xmath78 , the disks are relatively thick compared to the radial extents @xcite , and the metallicities are @xmath79 times lower . consequently , self - gravity is weak in the interstellar medium , cloud contraction times are long , @xmath80 myr or more , and molecules are sparse . moreover , the threshold column density for strong gravity inside clouds should be @xmath81 times lower than it is locally , placing this collapse threshold firmly in the optically thin regime where atomic gas should still dominate . presumably molecules form after the collapse begins @xcite . the star formation rates in the most remote @xmath0 knots fall short by a factor of @xmath79 of the average rates obtained from the kennicutt - schmidt relation for these types of regions . only for the most massive @xmath0 knots are the rates comparable . either we are missing other discrete star - forming regions owing to faintness or rapid dispersal , or the star formation rate drops below the ks relation for outer disks starting at around @xmath11 pc@xmath6 . in the latter case , stellar scattering from the inner disk would have to fill the outer disks with stars , which go out much further than the last @xmath0 knot seen here . we are grateful to the lowell observatory research fund for funding , including a summer internship for eg . we are also grateful to john and meg menke for a donation to lowell observatory that covered part of the page charges and to ibm for covering the remainder . dah also appreciates the considerable help on installing and running python to produce figure 1 from joe llama ( university of st . andrews ) , michael mommert ( nau ) , and david trilling ( nau ) . we appreciate helpful comments by the referee . ashley , t. , simpson , c. e. , & elmegreen , b. g. 2013 , , 146 , 42 ashley , t. , elmegreen , b.g . , johnson , m. , nidever , d.l . , simpson , c.e . , pokhrel , n.r . 2014 , , 148 , 130 bellazzini , m. , beccari , g. , fraternali , f. , et al . 2014 , a&a , 566 , 44 bigiel , f. , leroy , a. , walter , f. , brinks , e. , de blok , w. j. g. , madore , b. , & thornley , m. d. 2008 , aj , 136 , 2846 bigiel , f. , leroy , a. , walter , f. , blitz , l. , brinks , e. , de blok , w.j.g . , madore , b. 2010 , aj , 140 , 1194 billett , o. h. , hunter , d. a. , & elmegreen , b. g. 2002 , , 123 , 1454 burstein , d. , & heiles , c. 1984 , , 54 , 33 cannon , j. m. , oleary , e. m. , weisz , d. r. , et al . 2012 , , 747 , 122 cardelli , j. a. , clayton , g. c. , & mathis , j. s. 1989 , , 345 , 245 carraro , g. , villanova , s. , demarque , p. , mcswain , m. v. , piotto , g. , & bedin , l. r. 2006 , , 643 , 1151 de blok , w. j. g. , & walter , f. 2000 , , 537 , l95 de blok , w. j. g. , walter , f. , brinks , e. , trachternach , c. , oh , s .- h . , & kennicutt , r. c. , jr . 2008 , , 136 , 2648 elmegreen , b.g . 2015 , , 814 , l30 elmegreen , b.g . , & struck , c. , 2013 , , 775 , l35 elmegreen , b. g. , & hunter , d. a. 2015 , , 805 , 145 elmegreen , d.m . , elmegreen , b.g . , snchez almeida , j. , muoz - tun , c. , mendez - abreu , j. , gallagher , j.s . rafelski , m. , filho , m. , & ceverino , d. 2016 , apj , submitted glover , s.c.o . & clark , p.c . 2012 , mnras , 421 , 9 herrmann , k. a. , hunter , d. a. , & elmegreen , b. g. 2013 , , 146 , 104 hodge , p. w. , & hitchcock , j. l. 1966 , pasp , 78 , 7 hunter , d. a. , & elmegreen , b. g. 2004 , , 128 , 2170 hunter , d. a. , & elmegreen , b. g. 2006 , , 162 , 49 hunter , d. a. , elmegreen , b. g. , dupuy , t. j. , & mortonson , m. 2003 , , 126 , 1836 hunter , d. a. , elmegreen , b. g. , & ludka , b. c. 2010 , , 139 , 447 hunter , d. a. , elmegreen , b. g. , oh , s .- h . , et al . 2011 , 142 , 121 hunter , d. a. , ficut - vicas , d. , ashley , t. , et al . 2012 , , 144 , 134 kennicutt , r. c. , jr . 1989 , , 344 , 685 kennicutt r. c. , & evans n. j. , 2012 , ara&a , 50 , 531 komiyama , y. , okamura , s. , yagi , m. , et al . 2003 , , 590 , l17 krumholz , m.r . 2012 , , 759 , 9 lada , c.j . , lombardi , m. , & alves , j.f . 2010 , , 724 , 687 landolt , a. u. 1992 , , 104 , 340 leitherer , c. , schaerer , d. , goldader , j. d. , et al . 1999 , , 123 , 3 martin , d.c . , fansom , j. , schiminovich , d. , et al . 2005 , , 619 , l1 martn - navarro , i. , trujillo , i. , knapen , j.h . , bakos , j. , fliri , j. 52 2014 , mnras , 441 , 2809 melena , n. w. , elmegreen , b. g. , hunter , d. a. , & zernow , l. 2009 , , 138 , 1203 minchev , i. , famaey , b. , quillen , a. c. , di matteo , p. , combes , f. , vlajic , m. , erwin , p. , bland - hawthorn , j. 2012 , a&a , 548 , a126 nidever , d. , ashley , t. , slater , c. t. , et al . 2013 , apjl , 779 , l15 oh , s .- h . , hunter , d. a. , brinks , e. , et al . 2015 , , 149 , 180 padoan , p. , haugblle , t. , nordlund , . , 2012 , , 759 , l27 ] pellerin , a. , meyer , m. , harris , j. , & calzetti , d. 2008 , aspc , 388 , 379 radburn - smith , d. j. , roskar , r. , debattista , v. p. , et al . 2012 , , 753 , 138 roskar , r. , debattista , v. p. , quinn , t. r. , stinson , g. s. , & wadsley , j. 2008 , , 684 , l79a rubio , m. , elmegreen , b.g . , hunter , d.a . , brinks , e. , corts , j.r . , & cigan , p. 2015 , nature , 525 , 218 saha , a. , olszewski , e. w. , brondel , b. snchez almeida , j. , muoz - tun , c. elmegreen , d. , elmegreen , b. , & mendez - abreu , j. 2013 , apj , 767 , 74 snchez almeida , j. morales - luis , a.b . , muoz - tun , c. , elmegreen , d.m . , elmegreen b.g . , & mendez - abreu , j. 2014a , apj , 783 , 45 snchez almeida , j. elmegreen , b.g . , munoz - tunon , c. , elmegreen d.m . , perez - montero , e. , amorin , r. , filho , m.e . , ascasibar , y. , papaderos , p. , & vilchez , j.m . 2015 , apjl , 810l , 15 salpeter , e. e. 1955 , , 121 , 161 toomre , a. 1964 , , 139 , 1217 van den bergh , s. 1988 , pasp , 100 , 344 walter , f. , brinks , e. , de blok , w. j. g. , et al . 2008 , , 136 , 2563 wang , j. , fu , j. , aumer , m. , kauffmann , g. , jzsa , g.i.g . , serra , p. , huang , m .- l . , brinchmann , j. , van der hulst , t. , bigiel , f. 2014 mnras , 441 , 2159 wyder , t. k. , et al . 2007 , , 173 , 293 zhang , h .- x . , hunter , d. a. , elmegreen , b. g. , gao , y. , & schruba , a. 2012 , , 143 , 47

we examine images of the little things sample of nearby dwarf irregular ( dirr ) and blue compact dwarf ( bcd ) galaxies to identify distinct young regions in their far outer disks . the knots are found at distances from the center of the galaxies of 1 to 8 disk scale lengths and have ages of myrs and masses of 20 m_ to m_ . the presence of young clusters and ob associations in the outer disks of dwarf galaxies shows that dirrs do have star formation taking place there in spite of the extreme nature of the environment . most regions are found where the hi surface density is m_pc , although both the hi and dispersed old stars go out much further . either star formation in dirrs at surface densities pc occurs without forming distinct associations , or the kennicutt - schmidt relation over - predicts the rate beyond this point . in the latter case , the stellar disks in the far - outer parts of dirrs result from scattering of stars from the inner disk .

we examine images of the little things sample of nearby dwarf irregular ( dirr ) and blue compact dwarf ( bcd ) galaxies to identify distinct young regions in their far outer disks . we use these data , obtained with the _ galaxy evolution explorer _ satellite , to determine the furthest radius at which _ in situ _ star formation can currently be identified . the knots are found at distances from the center of the galaxies of 1 to 8 disk scale lengths and have ages of myrs and masses of 20 m_ to m_ . the presence of young clusters and ob associations in the outer disks of dwarf galaxies shows that dirrs do have star formation taking place there in spite of the extreme nature of the environment . most regions are found where the hi surface density is m_pc , although both the hi and dispersed old stars go out much further . this limiting density suggests a cutoff in the ability to form distinct ob associations and perhaps even stars . we compare the star formation rates in the regions to the average rates expected at their radii and beyond from the observed gas , using the conventional correlation for gas - rich regions . the localized rates are typically 10% of the expected average rates for the outer disks . either star formation in dirrs at surface densities pc occurs without forming distinct associations , or the kennicutt - schmidt relation over - predicts the rate beyond this point . in the latter case , the stellar disks in the far - outer parts of dirrs result from scattering of stars from the inner disk .

cond-mat0206176

i

to the best of our knowledge , the concept of the non - hermitian effective hamiltonian appeared first in feshbach s papers @xcite in connection with the general theory of resonance nuclear reactions @xcite and , independently , in livic s study of open systems @xcite . a typical atomic nucleus forms near an excitation energy @xmath6 above the threshold of nucleon emission a rich set of long - lived compound states with a very dense energy spectrum . for relatively small excitation energies , these states manifest themselves as narrow isolated resonances in collisions of nucleons and target nuclei . the sharp energy dependence of the corresponding cross sections near a given resonance is described by the universal breit - wigner formula . any smoother variations can be ignored in the domain of an isolated resonance . at higher @xmath6 , the resonance states begin to overlap and strongly interfere . nevertheless , one can still neglect the smooth energy dependence within a group of close interfering resonances . in this approximation , the propagation of the unstable system created on the intermediate stage of the collision is characterized by the resolvent of an energy - independent non - hermitian matrix @xcite . the latter describes in the time picture the irreversible evolution of the excited intermediate state and can therefore be interpreted as the effective hamiltonian @xmath1 whose anti - hermitian part , originating from on - shell self - energy contributions , is responsible for decays into open channels . the complex eigenvalues of the effective hamiltonian determine the energies and widths of the resonances . the method of the effective hamiltonian proved to be a success for describing many important resonance phenomena , especially in the context of chaotic scattering @xcite . it must be stressed that , similar to the breit - wigner formula , the notion of the effective hamiltonian is _ local _ in energy although the general approaches @xcite work in much wider energy intervals where smooth variations become important and should already be taken into account . for the very concept of the effective hamiltonian to be consistent , the scales of resonant and smooth variations must be appreciably different . otherwise the resonance behavior of scattering amplitudes will be distorted or even completely destroyed . the smooth dependence influences the background phases as well as the parameters of the resonances situated in different energy domains . such effects can not be described by simply enlarging the dimension of the matrix of the effective hamiltonian . instead , a large energy - dependent matrix @xmath7 emerges whose simple interpretation as a time - shift operator is no longer valid . there is , generally , no one - to - one correspondence between the complex energies of resonance states on the one hand and the @xmath6-dependent eigenvalues of this large matrix on the other . the current intensive studies , theoretical as well as experimental , of chaotic scattering of a particle by an open two - dimensional cavity ( see , e.g. , @xcite and references therein ) renewed interest in the hamiltonian approach to the resonance scattering theory and , in particular , to the concept and properties of the effective non - hermitian hamiltonian @xcite . although the scattering processes considered are purely potential , the theory is formulated in close analogy with the formalism developed in @xcite for nuclear collisions . the configuration space is divided into two parts , internal and external . the feshbach projection technique is employed to express the scattering matrix in the specific form that explicitly reveals the sharp resonant energy dependence while all smoother variations show up only indirectly via changes of the matrix elements . related is the problem of electromagnetic field quantization in open optical cavities @xcite . while the probability amplitudes of the physical processes are fixed unambiguously , the projection procedure exploited is not unique . there exists a rather wide freedom in choosing the surface of separation as well as the boundary conditions ( bcs ) on this surface . therefore , the amplitudes of interest are expressed in terms of quantities that depend on the details of the formalism . the independence of the final results of the calculations is not , as a rule , directly seen . therefore , a certain caution is necessary to avoid incorrect assertions . an unexpected dependence on the ( auxiliary ) boundary condition at the cavity - lead interface was found , for example , in @xcite . moreover , poor agreement with numerically calculated exact poles of the @xmath8 matrix was revealed for poles distant from the real axis . these points , partly attributed by the authors to numerical limitations , require further clarification . additional physical arguments should sometimes be involved to reasonably restrict the freedom . it is important to recognize that the density of levels in billiard - like cavities is much lower than that of the many - body nuclear systems . actually , strong overlap and interference of different resonance states are not , as a rule , possible in the single two - dimensional cavities ordinarily considered @xcite . the simple breit - wigner approximation is usually sufficient in this case for any individual resonance ( see , e.g. , @xcite ) . noticeable interference can occur only in the rare event of accidental near degeneracy of resonances . experimental observation of such an interference of few resonances in an open microwave cavity has recently been reported in @xcite . stronger overlap and a non trivial effective hamiltonian matrix can , however , appear when open chains of a number of similar potential wells connected to each other are considered . the energy spectrum has a band structure in this case with much denser spectrum within a given band . a schematic model of such a kind was considered in @xcite . a similar example was also investigated in @xcite in the framework of graph theory @xcite . some general aspects of scattering in periodic structures have also been considered in @xcite . in this paper we examine the notion of the effective hamiltonian in potential scattering . the questions we are concerned with do not depend on the regular or irregular character of the motion . thus , we restrict ourselves to the simplest case of the single - channel @xmath9-wave scattering . the extension to higher partial waves is straightforward . a consistent self - adjoint formulation of the problem of scattering on a finite - size potential in terms of the internal and external subproblems is presented in sec . ii . the ( one - dimensional ) @xmath8 matrix is expressed in terms of a non - hermitian energy - dependent operator @xmath10 whose form , together with the form of the associated @xmath11 function ( sec . iii ) , _ depends _ on the bc and the radius @xmath12 of separation in the configuration space . different bcs define different representations of the internal and external parts of the ( unique ) scattering wave function . the role of the fictitious direct reflection at the separation point @xmath12 is also discussed . in sec . iv the exactly solvable open kronig - penney model is considered as an example of potential scattering with interfering resonances . closed expressions are found for both scattering @xmath13 and staying - wave @xmath14 functions as well as wigner s function @xmath15 . their analytical properties in the complex @xmath16 and energy planes are analyzed in detail . hereafter we compare these exact results with those obtained in the framework of the projection formalism of the previous sections . we analyze two typical choices of the bcs for the internal motion : the cases of neumann and dirichlet bcs . in the second case , the internal problem corresponds to a closed counterpart of the system under consideration that allows one to follow the changes of the motion due to the interference of resonances when the openness grows . the latter is in line with numerous applications considered in the literature . non - hermitian effective hamiltonians for a fixed band of resonance states are built up in both cases . we summarize our main findings in the concluding sec .

the scattering amplitude is expressed in terms of the resolvent of a non - hermitian operator . we note that the simple breit - wigner approximation is as a rule valid for any individual resonance in the case of few - channel scattering on a flat billiard - like cavity , leaving no room for non - trivial to appear . we construct for the two commonly considered types of the boundary conditions ( neumann and dirichlet ) for the internal motion . although the final results are in perfect coincidence , somewhat different physical patterns arise of the trend of the system with growing openness .

we examine the notion and properties of the non - hermitian effective hamiltonian of an unstable system using as an example potential resonance scattering with a fixed angular momentum . we present a consistent self - adjoint formulation of the problem of scattering on a finite - range potential , which is based on separation of the configuration space into two segments , internal and external . the scattering amplitude is expressed in terms of the resolvent of a non - hermitian operator . the explicit form of this operator depends on both the radius of separation and the boundary conditions at this place , which can be chosen in many different ways . we discuss this freedom and show explicitly that the physical scattering amplitude is , nevertheless , unique although not all choices are equally adequate from the physical point of view . the _ energy - dependent _ operator should not be confused with the non - hermitian effective hamiltonian which is usually exploited to describe interference of overlapping resonances . we note that the simple breit - wigner approximation is as a rule valid for any individual resonance in the case of few - channel scattering on a flat billiard - like cavity , leaving no room for non - trivial to appear . the physics is appreciably richer in the case of an open chain of connected similar cavities whose spectrum has a band structure . for a fixed band of overlapping resonances , the smooth energy dependence of can be ignored so that the constant submatrix approximately describes the time evolution of the chain in the energy domain of the band and the complex eigenvalues of define the energies and widths of the resonances . we apply the developed formalism to the problem of a chain of barriers whose solution is also found independently in a closed form . we construct for the two commonly considered types of the boundary conditions ( neumann and dirichlet ) for the internal motion . although the final results are in perfect coincidence , somewhat different physical patterns arise of the trend of the system with growing openness . formation in the outer well of a short - lived doorway state shifted in the energy is explicitly demonstrated together with the appearance of long - lived states trapped in the inner part of the chain .

cond-mat0206176

c

in this paper we analyzed the relevance of the concept of the non - hermitian effective hamiltonian in finite - range potential scattering . single - channel @xmath9-wave resonance scattering is considered as an example . the scattering function @xmath13 is meromorphic in this case , i.e. , has only isolated poles in the complex plane of the wave numbers . the number of poles is , generally , infinite but only a finite part of them can be interpreted as resonances . we first presented ( secs . ii and iii ) a consistent self - adjoint formulation of the scattering problem , which is based on separation of the configuration space into internal and external segments . in this way , the @xmath13 function is represented in terms of a non - hermitian energy - dependent operator @xmath443 . there exists a wide freedom in choosing the radius @xmath12 of separation as well as the boundary conditions at this point . different choices yield different explicit forms of this operator together with the @xmath13 and @xmath15 functions . this can , in particular , come out strongly if one truncates the matrix @xmath0 to calculate numerically the positions of the poles of @xmath8 function in the complex @xmath16 plane . nevertheless , the true complex poles of the @xmath8 function and this function itself depend , as we explicitly demonstrate , neither on the bc nor on the radius @xmath12 . although all choices are formally allowed , this does not mean that they are equally adequate from the physical point of view . for instance , a fictitious immediate reflection takes place at the ( arbitrarily chosen ) point of separation @xmath12 . the artificial separation of the phase of this reflection results , in turn , in the appearance of an infinite number of remote poles of the function @xmath15 , which describe the smooth contribution from the interior region @xmath444 . the phase of the immediate reflection must be compensated by the contributions of such poles for the radius @xmath12 to disappear finally from the scattering amplitude . this can cause unjustified complications in intermediate stages of calculations . we argue that the harm is minimized if the separation radius matches an outer potential barrier when it is strong enough to make immediate reflection at this point quite probable . the notion of the non - hermitian effective hamiltonian first introduced in the theory of resonance nuclear reactions emerges when a group of very close resonance states strongly overlap and interfere . we stress that , in contrast to the nuclear reactions , in the cases of the potential resonance scattering usually discussed in the literature the density of the energy spectrum is too low and the ordinary breit - wigner approximation of isolated resonances usually suffices . the complex energy of the @xmath334th resonance which dominates in the scattering amplitudes near the scattering energy @xmath445 . there is no room for an effective hamiltonian in this case or , more strictly , it is embodied by the @xmath446 `` matrix '' @xmath447 . we emphasize that the energy dependent operator @xmath443 should not be confused with the effective hamiltonian . energy dependent eigenvalues of this operator are not , generally , in one - to - one correspondence with the complex energies of the actual resonance states . overlap and interference of the resonances can become possible in the cases when the energy spectrum has a band structure . as an example of this kind we investigate a periodically disposed chain of a finite number @xmath2 of radial @xmath4 barriers . all @xmath8 , @xmath234 and @xmath11 functions are found in closed forms in terms of an @xmath3 @xmath16-dependent matrix propagator . this allows us to study in detail all analytical properties in the complex @xmath16 plane and to verify the correspondence with the projection formalism used . there exist a finite number of separated bands of close resonances . within the @xmath334th band which lie near the scattering energy @xmath448 one can neglect all smooth variations with @xmath16 . in this approximation , the mentioned propagator proved to coincide with the resolvent of the @xmath3 block @xmath449 of the matrix @xmath450 _ taken at the fixed value _ just this matrix plays the role of the effective hamiltonian of the system in the energy interval within the band . different choices of bcs yield different patterns of the resonance interference . in particular , the spectrum of the poles of the @xmath11 function is exactly reproduced in the framework of the projection technique with the bc ( [ cnint ] ) of neumann type fixed at the position @xmath196 of the outer barrier . the corresponding energy levels depend on the penetrability constant @xmath387 of the outer barrier . shifts of the levels due to the coupling to the continuum are included in this case from the very beginning . utilization of the dirichlet bc for the intrinsic motion gives another but yet equivalent formulation of the scattering problem considered . the internal problem in this case fixes a closed counterpart of the open system under consideration . this enables us to investigate the change of the regime of the internal motion of the system as its openness grows . the interaction via the continuum shifts the original @xmath387-independent levels of the internal motion along both real and imaginary axes . a transition is explicitly demonstrated from the bunch of @xmath2 similar narrow resonances to the formation of a relatively broad resonance strongly shifted with respect to the band , which exists in the outer well . the other resonances turn out to be trapped in the inner part of the system . this is quite similar to the results of earlier investigations which rely upon the notion of the non - hermitian effective hamiltonian of an open system .

we examine the notion and properties of the non - hermitian effective hamiltonian of an unstable system using as an example potential resonance scattering with a fixed angular momentum . we present a consistent self - adjoint formulation of the problem of scattering on a finite - range potential , which is based on separation of the configuration space into two segments , internal and external . the _ energy - dependent _ operator should not be confused with the non - hermitian effective hamiltonian which is usually exploited to describe interference of overlapping resonances . the physics is appreciably richer in the case of an open chain of connected similar cavities whose spectrum has a band structure . for a fixed band of overlapping resonances , the smooth energy dependence of

we examine the notion and properties of the non - hermitian effective hamiltonian of an unstable system using as an example potential resonance scattering with a fixed angular momentum . we present a consistent self - adjoint formulation of the problem of scattering on a finite - range potential , which is based on separation of the configuration space into two segments , internal and external . the scattering amplitude is expressed in terms of the resolvent of a non - hermitian operator . the explicit form of this operator depends on both the radius of separation and the boundary conditions at this place , which can be chosen in many different ways . we discuss this freedom and show explicitly that the physical scattering amplitude is , nevertheless , unique although not all choices are equally adequate from the physical point of view . the _ energy - dependent _ operator should not be confused with the non - hermitian effective hamiltonian which is usually exploited to describe interference of overlapping resonances . we note that the simple breit - wigner approximation is as a rule valid for any individual resonance in the case of few - channel scattering on a flat billiard - like cavity , leaving no room for non - trivial to appear . the physics is appreciably richer in the case of an open chain of connected similar cavities whose spectrum has a band structure . for a fixed band of overlapping resonances , the smooth energy dependence of can be ignored so that the constant submatrix approximately describes the time evolution of the chain in the energy domain of the band and the complex eigenvalues of define the energies and widths of the resonances . we apply the developed formalism to the problem of a chain of barriers whose solution is also found independently in a closed form . we construct for the two commonly considered types of the boundary conditions ( neumann and dirichlet ) for the internal motion . although the final results are in perfect coincidence , somewhat different physical patterns arise of the trend of the system with growing openness . formation in the outer well of a short - lived doorway state shifted in the energy is explicitly demonstrated together with the appearance of long - lived states trapped in the inner part of the chain .

astro-ph9609051

c

using the power ratios ( @xmath164 ) of buote & tsai ( 1995 bta ; 1996 btb ; tsai & buote 1996 tb ) we have examined the sensitivity of galaxy cluster morphologies to @xmath0 and @xmath1 using large , high - resolution n - body simulations . x - ray images are generated from the dark matter by letting the gas density trace the dark matter . we argue that the @xmath71 should not be seriously biased by this approximation because a real gas in hydrostatic equilibrium with potentials of cdm clusters is rounder , but also has a larger core radius , the effects of which partially cancel . we also argue that the approximation should be reasonable during mergers because of the agreement shown between the evolution of the dark matter and gas found by tb who analyzed the hydrodynamical simulation of navarro et al . ( 1995a ) . finally , the @xmath71 generated from the n - body simulations in this paper agree with results from the navarro et al . hydrodynamical simulation ( tb ) . similar agreement is seen between the results of the n - body simulations of jing et al . ( 1995 ) and the hydrodynamical simulations of mohr et al . ( 1995 ) . from analysis of several variants of the standard cold dark matter model , we have shown that the @xmath71 can distinguish between models with different @xmath0 and @xmath1 . generally , @xmath0 influences the means of the @xmath71 distributions such that larger values of @xmath0 primarily imply larger average pr values . the slope of the power spectrum and @xmath5 primarily influence the variances of the @xmath71 ; smaller @xmath6 and @xmath5 generally imply smaller @xmath71 variances . for examining @xmath0 , our analysis indicates that @xmath73 is the best @xmath71 since its mean is quite sensitive to @xmath0 but very insensitive to @xmath1 . it is advantageous also to consider @xmath72 when a cosmological constant is introduced since its means differ for the scdm and lcdm models by @xmath133 whereas @xmath73 only distinguishes the models at the @xmath134 level . the dependence of the mean of @xmath72 on @xmath1 is not overly serious for studying differences in @xmath0 because the differences in means due to @xmath1 are always accompanied by larger differences in the variances ; i.e. different means but consistent variances mostly reflect differences in @xmath0 for @xmath72 . typically , the best apertures for segregating models are @xmath97 mpc . we did not find it advantageous to compare the distributions along and perpendicular to the `` evolutionary tracks '' in the @xmath165 and @xmath166 planes ( see btb and tb ) . the distributions along the tracks performed essentially as a weighted sum of the constituent @xmath71 . the distributions perpendicular to the tracks were in almost all cases consistent for the models . hence , although the evolutionary tracks are useful for categorizing the dynamical states of clusters , they do not allow more interesting constraints on @xmath0 and @xmath1 to be obtained over the individual @xmath71 . the consistency of the distributions perpendicular to the evolutionary tracks seems to be a generic feature of the cdm models . we compared the @xmath71 of the cdm models to the @xmath11 cluster sample of buote & tsai ( 1996 ) . we find that the means of the @xmath167 ocdm and @xmath11 clusters are consistent , but the means of @xmath73 for the lcdm and @xmath11 clusters are formally inconsistent at the @xmath168 level . we assert that this discrepancy should be considered marginal due to various issues associated with the simulation observation comparison . however , the means of @xmath73 for the scdm and bcdm models ( with @xmath14 ) exceed the @xmath11 means by almost a full decade with a high level of significance @xmath12 . though the formal significance level of this @xmath13 / x - ray comparison should be considered only an approximation , we argue that taking into account the hydrodynamics and cooling will not reconcile a discrepancy this large . _ we conclude that the @xmath14 cdm models can not produce the observed @xmath71 of the @xmath11 clusters , and that the discrepancy in @xmath71 means is due to @xmath0 being too large . _ this agrees with our conclusions obtained in tb for the small sample of clusters drawn from the hydrodynamic simulation of navarro et al . ( 1995a ) . these conclusions are also consistent with other indicators of a low value of @xmath0 such as the dynamical analyses of clusters ( e.g. , carlberg et al . 1995 ) , the large baryon fractions in clusters ( e.g. , white et al . 1993 ) , and the heating of galactic disks ( toth & ostriker 1992 ) . our conclusions are inconsistent with those of mohr et al . ( 1995 ) who instead concluded that their _ cluster sample favored @xmath14 , cdm over equivalents of our low - density models , ocdm and lcdm . we argue that this type of discrepancy is unlikely due to numerical differences between our simulations . we discuss possible differences due to how btb and mohr et . al . computed their statistics on the real cluster data . large hydrodynamical simulations are necessary to render the comparison to the @xmath11 data more robust . in addition , the effects of combining data at different redshifts needs to be explored since cluster formation rates should behave differently as a function of @xmath169 in different models ( e.g. , richstone et . al . 1992 ) . it may also prove useful to apply @xmath71 to mass maps of clusters obtained from weak lensing ( kaiser & squires 1993 ) ) can distinguish between low - density and critical density models . ] , though for cosmological purposes it is not clear whether @xmath170 will be as responsive as @xmath171 to different @xmath0 and @xmath1 . we gratefully acknowledge j. tsai for his role in facilitating this collaboration . we thank e. bertschinger for suggesting to us the scheme to normalize the scale - free models using @xmath28 , t. beers for providing his rostat programs to compute ai and ti , and a. edge for providing the expression for @xmath172 . we appreciated the anonymous referee s prompt reviewing and comments that helped improve the presentation of the paper . dab was supported by grants nasgw-2681 ( through subcontract svsv2 - 62002 from the smithsonian astrophysical observatory ) and nag5 - 2921 , and acknowledges the hospitality of the institute of astronomy where the final stages of this work were carried out . dab also expresses gratitude to several senior scientists who offered encouragement during the early stages of this project . gx acknowledges support from nfs hpcc grant asc93 - 18185 and thanks the pittsburgh supercomputer center for use of the cray - t3d machine . lccccccc + name & @xmath0 & @xmath27 & @xmath6 & @xmath5 & @xmath22 & @xmath173 + scdm & 1 & 0 & 1 & 1.00 & 0.5 & 20 + ocdm & 0.35 & 0 & 1 & 0.79 & 0.7 & 25 + lcdm & 0.35 & 0.65 & 1 & 0.83 & 0.7 & 39 + bcdm & 1 & 0 & 1 & 0.51 & 0.5 & 20 + sf00 & 1 & 0 & 0 & @xmath174 & @xmath174 & @xmath174 + sf10 & 1 & 0 & -1.0 & @xmath174 & @xmath174 & @xmath174 + sf15 & 1 & 0 & -1.5 & @xmath174 & @xmath174 & @xmath174 + sf20 & 1 & 0 & -2.0 & @xmath174 & @xmath174 & @xmath174 + lrc|rc|rc|rc|rc|rc + & & + + & & & & & & + & avg & @xmath175 & avg & @xmath175 & avg & @xmath175 & avg & @xmath175 & avg & @xmath175 & avg & @xmath175 + + + scdm & -5.14 & 0.86 & -5.16 & 0.83 & -5.38 & 0.76 & -6.72 & 0.73 & -6.82 & 1.01 & -7.06 & 0.98 + ocdm & -5.55 & 0.61 & -5.82 & 0.78 & -5.93 & 1.03 & -7.40 & 0.81 & -7.56 & 1.13 & -7.59 & 1.28 + lcdm & -5.45 & 0.83 & -5.69 & 0.85 & -5.87 & 0.83 & -7.08 & 0.83 & -7.32 & 1.00 & -7.38 & 1.02 + bcdm & -5.01 & 0.57 & -5.24 & 0.60 & -5.41 & 0.63 & -6.83 & 0.65 & -6.98 & 0.67 & -7.07 & 0.68 + sf00 & -5.34 & 0.82 & -5.64 & 1.00 & -5.75 & 0.97 & -7.12 & 1.02 & -7.28 & 1.14 & -7.35 & 1.10 + sf10 & -5.02 & 0.57 & -5.22 & 0.71 & -5.47 & 0.85 & -6.89 & 0.87 & -7.09 & 1.02 & -7.36 & 1.18 + sf15 & -5.20 & 0.85 & -5.22 & 0.94 & -5.40 & 0.91 & -6.92 & 0.99 & -6.93 & 1.02 & -7.05 & 0.96 + sf20 & -5.07 & 0.60 & -5.24 & 0.62 & -5.45 & 0.57 & -7.01 & 0.71 & -7.13 & 0.75 & -7.20 & 0.79 + ccc|rrr|rrr|rrr + & & & & & + & & & & & & & & & & & + & ( % ) & ( % ) & ( % ) & ( % ) & ( % ) & ( % ) & ( % ) & ( % ) & ( % ) + + + + + scdm & vs. & ocdm & 1.63 & 4.09 & 0.94 & 0.06 & 71.71 & 0.07 & 0.89 & 7.18 & 0.94 + scdm & vs. & lcdm & 10.47 & 87.90 & 21.79 & 0.74 & 89.05 & 1.97 & 0.83 & 58.78 & 3.90 + ocdm & vs. & lcdm & 54.64 & 5.79 & 51.42 & 47.52 & 61.72 & 21.79 & 78.26 & 20.53 & 34.56 + scdm & vs. & bcdm & 43.06 & 1.51 & 98.09 & 65.19 & 4.65 & 21.79 & 83.52 & 24.87 & 34.56 + sf00 & vs. & sf20 & 10.76 & 6.35 & 7.31 & 4.19 & 0.38 & 0.94 & 10.44 & 0.13 & 3.90 + + + + + scdm & vs. & ocdm & 0.02 & 52.99 & 0.18 & 0.31 & 46.71 & 0.94 & 4.43 & 10.64 & 7.31 + scdm & vs. & lcdm & 4.44 & 43.91 & 21.79 & 3.26 & 97.10 & 7.31 & 15.88 & 81.58 & 51.42 + ocdm & vs. & lcdm & 9.10 & 88.39 & 21.79 & 30.99 & 44.52 & 51.42 & 43.51 & 16.61 & 51.42 + scdm & vs. & bcdm & 49.58 & 47.26 & 70.85 & 40.62 & 1.39 & 34.56 & 97.46 & 2.48 & 70.85 + sf00 & vs. & sf20 & 57.65 & 2.89 & 21.79 & 49.89 & 1.28 & 21.79 & 50.92 & 4.31 & 12.97 + llll|lll + & & + models & @xmath176 & @xmath177 & @xmath178 & @xmath176 & @xmath177 & @xmath178 + + + + + scdm & 0.60e-01 & 0.12e-01 & 0.68e-03 & 0.14e-01 & 0.24e+01 & 0.33e-01 + bcdm & 0.10e-04 & 0.12e+02 & 0.56e-04 & 0.12e-01 & 0.20e+02 & 0.12e-01 + ocdm & 0.23e+02 & 0.52e+01 & 0.16e+02 & 0.68e+02 & 0.23e-01 & 0.43e+02 + lcdm & 0.11e+02 & 0.21e-01 & 0.13e+01 & 0.41e+02 & 0.69e+00 & 0.23e+02 + + + + + scdm & 0.15e-03 & 0.71e+02 & 0.69e-01 & 0.17e+01 & 0.20e+02 & 0.10e+02 + bcdm & 0.64e-03 & 0.28e+02 & 0.32e-02 & 0.35e+00 & 0.46e+02 & 0.12e+02 + ocdm & 0.22e+02 & 0.80e+02 & 0.42e+02 & 0.93e+02 & 0.83e+00 & 0.29e+02 + lcdm & 0.44e+00 & 0.69e+02 & 0.97e+00 & 0.33e+02 & 0.14e+02 & 0.32e+02 + contour plots of the `` x - ray images '' for 16 of the 39 clusters analyzed in the scdm model obtained from projecting @xmath180 . each image is @xmath46 @xmath47 mpc@xmath48 and the axes units are @xmath49 mpc pixels . the standard deviation as a function of the average value of the prs in the @xmath98 mpc aperture for the models in [ omega ] . the error bars represent @xmath181 errors estimated from 1000 bootstrap resamplings . the standard deviation as a function of the average value of the prs in the @xmath98 mpc aperture for the models in [ spectrum ] . the error bars represent @xmath181 errors estimated from 1000 bootstrap resamplings . the standard deviation as a function of the average value of the prs in the @xmath89 mpc aperture for the rosat clusters and the models discussed in [ rosat ] . the error bars represent @xmath181 errors estimated from 1000 bootstrap resamplings .

we examine the sensitivity of the spatial morphologies of galaxy clusters to and using high - resolution n - body simulations with large dynamic range . finally , we compared these models to a sample of clusters and find that the pr means of the scdm clusters exceed the means with a high formal level of significance . though the formal significance level of this / x - ray comparison should be considered only approximate , we argue that taking into account the hydrodynamics and cooling will not reconcile a discrepancy this large . the pr means of the ocdm clusters are consistent , and the means of the lcdm clusters are marginally consistent , with those of the clusters .

we examine the sensitivity of the spatial morphologies of galaxy clusters to and using high - resolution n - body simulations with large dynamic range . variants of the standard cdm model are considered having different spatial curvatures , scdm , ocdm , lcdm , and different normalizations , . we also explore critical density models with different spectral indices , , of the scale - free power spectrum , . cluster x - ray morphologies are quantified with power ratios ( prs ) , where we take for the x - ray emissivity , which we argue is a suitable approximation for analysis of prs . we find that primarily influences the means of the pr distributions whereas the power spectrum ( and ) primarily affects their variances : is the cleanest probe of since its mean is very sensitive to but very insensitive to . the pr means easily distinguish the scdm and ocdm models , while the scdm and lcdm means show a more modest , but significant , difference . the ocdm and lcdm models are largely indistinguishable in terms of the prs . finally , we compared these models to a sample of clusters and find that the pr means of the scdm clusters exceed the means with a high formal level of significance . though the formal significance level of this / x - ray comparison should be considered only approximate , we argue that taking into account the hydrodynamics and cooling will not reconcile a discrepancy this large . the pr means of the ocdm clusters are consistent , and the means of the lcdm clusters are marginally consistent , with those of the clusters . thus , we conclude that cluster morphologies strongly disfavor , cdm while favoring low density , cdm models with or without a cosmological constant .

0810.1104

i

neutrino oscillation experiments involving neutrinos and antineutrinos coming from astrophysical and terrestrial sources @xcite have found compelling evidence that neutrinos have mass . to accommodate this observation , the minimal standard model ( sm ) must be extended . some sensible ways to do this include : ( a ) type i seesaw with three heavy right - handed ( rh ) majorana neutrinos @xcite , ( b ) the use of an electroweak higgs triplet to directly provide the left - handed ( lh ) neutrinos with small majorana masses ( type ii seesaw @xcite ) , ( c ) introducing a fermion triplet ( type iii seesaw @xcite ) , ( d ) the generation of three dirac neutrinos through an exact parallel of the sm method of giving mass to charged fermions , and ( e ) the radiative generation of neutrino masses as per the zee or babu models @xcite . but in the absence of more experimental data , it is impossible to tell which , if any , of these is actually correct . the focus of this paper is on method ( a ) , the seesaw framework with three heavy rh majorana neutrinos ( denoted @xmath1 throughout ) . it is an attractive possibility because it simply posits the existence of these @xmath1 s to parallel the multiplet structure of the other fermions while providing a simple explanation for why the light neutrinos are so much less massive than the charged leptons . since the setup uses the most general renormalisable lagrangian consistent with the sm gauge symmetry , both the yukawa couplings of the lh leptons to the rh neutrinos and bare majorana masses are permitted for the rh neutrinos . consequently , the additional assumption that the rh majorana mass scale is much higher than that of the charged fermions leads to a tiny mass for ordinary neutrinos through the famous seesaw relation : @xmath2 , where @xmath3 is the majorana mass for a light neutrino and @xmath4 is a large rh majorana mass ( @xmath5 ) with @xmath6 being most naturally of the order of a charged fermion mass . the three light neutrino mass eigenstates are accompanied by three heavy neutral lepton mass eigenstates . depending on the parameter space for the rh neutrino bare masses and yukawa couplings , additional benefits may flow : thermal leptogenesis @xcite if there are appropriate @xmath0-violating decays and if the lightest of the heavy @xmath1 s has mass greater than about @xmath7 gev @xcite ; leptogenesis through @xmath0-violating oscillations of the @xmath1 s as in the akhmedov - rubakov - smirnov mechanism @xcite ; or @xmath1 s as a warm dark matter candidate @xcite . since the mass eigenstate heavy neutral leptons are to a good approximation sterile with respect to gauge interactions , they are difficult to detect experimentally . this is especially true if they are also extremely massive , as in the thermal leptogenesis alternative . on the other hand , if they are not as massive and are in the tev scale , then they can be looked for in colliders through their yukawa interactions , and through their suppressed but nonzero weak interactions ( induced through the mass mixing with regular active neutrinos ) . to experimentally test the seesaw scenario , it would be helpful if one knew the parameters governing the @xmath1-sector including their interactions with other sm particles . in the minimal seesaw model , these parameters are arbitrary , so one has to go beyond the minimal model to achieve this goal . the purpose of this paper is to illustrate how symmetries may be used to determine the rh majorana mass matrix as a function of low - energy mass , mixing angle and @xmath0-violating phase observables by constructing several representative models . we then examine these models to see if thermal leptogenesis can succeed or if experimentally accessible heavy @xmath1 s are predicted . in the next section we discuss the general model building symmetry requirements for relating the @xmath1-sector parameters to low - energy observables . section [ sec : symmetry - basics ] then revises the basic properties of the identified symmetries , followed by sec . [ sec : models ] which details specific models . section [ sec : phenomenology ] presents a phenomenological study of those models , and we conclude in sec . [ sec : conclusion ]

we explore how the seesaw sector in neutrino mass models may be constrained through symmetries to be completely determined in terms of low - energy mass , mixing angle and-violating phase observables . implications for leptogenesis and collider detection of heavy neutral leptons are discussed . the model where the neutrino dirac mass matrix equals the charged - lepton mass matrix can yield a heavy neutral lepton as light as about 1 tev , but detecting such a particle will be difficult .

we explore how the seesaw sector in neutrino mass models may be constrained through symmetries to be completely determined in terms of low - energy mass , mixing angle and-violating phase observables . the key ingredients are intra - family symmetries to determine the neutrino dirac mass matrix in terms of the charged - lepton or quark mass matrices , together with inter - family or flavor symmetries to determine diagonalization matrices . implications for leptogenesis and collider detection of heavy neutral leptons are discussed . we show that leptogenesis can succeed in small regions of parameter space for the case where the neutrino dirac mass matrix equals the up - quark mass matrix . the model where the neutrino dirac mass matrix equals the charged - lepton mass matrix can yield a heavy neutral lepton as light as about 1 tev , but detecting such a particle will be difficult .

nucl-th0512002

i

the three - body problem has a long history from macroscopic celestial classical mechanics , e.g. sun - earth - moon @xcite to microscopic quantum mechanics , e.g. the helium atom @xcite , three nucleons @xcite or three quarks @xcite . the modern treatment was boosted by the formulation of the faddeev equations @xcite originally aimed at scattering problems , but also successfully applied for bound states @xcite . the more recent interest in bound state halo structures and borromean systems are by now fairly well understood in terms of the basic two - body interactions @xcite . the success is at least indisputable for three - body systems with only one or a few bound states . on the other hand , the corresponding three - body properties for positive energies ( energies above breakup ) are much less established although studied thoroughly for both short and long range interactions @xcite . contributions from both short and long - range interactions make computations numerically difficult . the three - body coulomb problem itself is still considered unsolved @xcite and three - body resonances for strongly interacting particles are still debated @xcite . this is unfortunate , since the continuum structure often form the basis in descriptions of the dynamic behavior of a given system . crucial properties of the continuum are revealed by information about the resonances and virtual states defined as poles of the @xmath0-matrix . together with the discrete set of bound negative - energy states we also have a discrete set of unbound complex - energy states with their corresponding wave functions . for completeness also the continuous non - singular background states are needed , but the singularities of the scattering matrix are very often decisive . important examples using different methods within few - body physics are astrophysical reaction rates @xcite , adiabatic reaction processes arising at low energies or for large impact parameters @xcite , three - body decays @xcite , three - body resonances for faddeev operators @xcite , for nucleons @xcite , for electrons and positrons @xcite and four - body nuclear continuum states @xcite . this list could be extended . continuum structure is in general more difficult than bound state problems although various methods have been designed to overcome the technical problems at least for resonances , see for example @xcite . an understanding of the generic origin of @xmath0-matrix poles would be tremendously helpful especially if recognizable traces of a well - structured origin are left in the realistic spectra . no doubt this would allow easier interpretation of complicated numerical results , allowed design of better methods , and indicate which effects to look for in different contexts . the purpose of this work is to investigate how the two - body interactions determine the three - body continuum structure . we focus on three - body continuum states where none of the two - body subsystems is bound ( borromean systems ) . when two - body bound states are possible , different three - body structures can appear , as for instance , unbound three - body states with negative energy . however , these systems can very often be understood as two - body systems made by a two - body bound state and the remaining third particle in the continuum . with the help of the hyperspheric adiabatic expansion method we determine which three - body bound or virtual states and resonances result from given sets of corresponding two - body properties . taking a simple system as starting point , it is then possible to observe how the three - body states evolve in the complex energy plane when more and more realistic features are incorporated into the calculation . in section ii we give details about the complex scaled adiabatic expansion methods . in section iii the schematic system of an infinitely heavy core and two mutually non - interacting light particles is described analytically , while in section iv the general properties of the system are described after numerical studies of specific systems . in section v we relate the spectra from the schematic model with those obtained in realistic calculations for systems with zero ( @xmath1he , @xmath1li , @xmath1be ) and non - zero core - spin ( @xmath2ne ) . we finish in section vi with some qualitative estimates for other systems and in section vii we give a short summary and the conclusions .

we expose the relation between the properties of the three - body continuum states and their two - body subsystems . these properties refer to their bound and virtual states and resonances , all defined as poles of the-matrix . for one infinitely heavy core and two non - interacting light particles , these generic relations are modified by center - of - mass effects which alone can produce a borromean system . we show how the three - body states evolve inhe ,li , andbe when the nucleon - nucleon interaction is continuously switched on . the schematic model is able to reproduce the main properties in their spectra .

we expose the relation between the properties of the three - body continuum states and their two - body subsystems . these properties refer to their bound and virtual states and resonances , all defined as poles of the-matrix . for one infinitely heavy core and two non - interacting light particles , the complex energies of the three - body poles are the sum of the two two - body complex pole - energies . these generic relations are modified by center - of - mass effects which alone can produce a borromean system . we show how the three - body states evolve inhe ,li , andbe when the nucleon - nucleon interaction is continuously switched on . the schematic model is able to reproduce the main properties in their spectra . realistic calculations for these nuclei are shown in detail for comparison . the implications of a core with non - zero spin are investigated and illustrated forne (o++ ) . dimensionless units allow predictions for systems of different scales .

1101.0365

i

cosmology tells us that about 25% of the total mass density in the universe is dark matter that can not be accounted for by conventional baryons @xcite . alongside observation , intense theoretical efforts are made in order to elucidate the nature and properties of this unknown form of matter . in this context , electrically neutral and colorless weakly interacting massive particles ( wimps ) form an attractive scenario . their broad properties are : masses in the range of one to a few hundred gev , coupling constants in the milli - weak scale and lifetimes longer than the age of the universe . recent data from the direct - detection experiments dama / libra @xcite and cogent cogent , and the recent analysis of the data from the fermi gamma ray space telescope @xcite , if interpreted as signal for dark matter , require light wimps in the range of 5 to 10 gev @xcite . also , galactic substructure requires still lighter dark matter masses @xcite . in this regard , it is useful to note in passing that the xenon100 collaboration has provided serious constraints on the region of interest to dama / libra and cogent @xcite , assuming a constant extrapolation of the liquid xenon scintillation response for nuclear recoils below 5 kev , a claim disputed in @xcite . most recently , the cdms collaboration has released the analysis of their low - energy threshold data @xcite which seems to exclude the parameter space for dark matter interpretation of dama / libra and cogent results , assuming a standard halo dark matter model with an escape velocity @xmath1 km / s and neglecting the effect of ion channeling @xcite . however , with a highly anisotropic velocity distribution , it may be possible to reconcile the cogent and dama / libra results with the current exclusion limits from cdms and xenon @xcite ( see also comments on p.6 in @xcite about the possibility of shifting the exclusion contour in @xcite above the cogent signal region ) . in addition , cresst , another direct detection experiment at gran sasso , which uses cawo@xmath2 as target material , reported in talks at the idm 2010 and wonder 2010 workshops an excess of events in their oxygen band instead of tungsten band . if this signal is not due to neutron background a possible interpretation could be the elastic scattering of a light wimp depositing a detectable recoil energy on the the lightest nuclei ( oxygen ) in the detector @xcite . while this result has to await confirmation from the cresst collaboration , it is clear that it is important as well as interesting to study light dark matter . the most popular candidate for dark matter is the neutralino , a neutral @xmath3-odd supersymmetric particle . indeed , they are only produced or destroyed in pairs , thus rendering the lightest susy particle ( lsp ) stable @xcite . in the minimal version of the supersymmetric extension of the standard model , the neutralino is a linear combination of the fermionic partners of the neutral electroweak gauge bosons ( gauginos ) and the neutral higgs bosons ( higgsinos ) . they can annihilate through a t - channel sfermion exchange into standard model fermions , or via a t - channel chargino - mediated process into @xmath4 , or through an s - channel pseudoscalar higgs exchange into fermion pairs and they can undergo elastic scattering with nuclei mainly through scalar higgs exchange @xcite . if these neutralinos were light , they would then be overproduced in the early universe and , in the minimal model , would not have an elastic - scattering cross section large enough to account for the dama / libra and cogent results due to constraints from other experiments such as the lep , tevatron , and rare decays @xcite . therefore , with no clear clue yet as to what the internal structure of these wimps is , if any , a pedestrian approach can be attractive . in this logic , the simplest of models is to extend the standard model by adding a real scalar field , the dark matter , a standard - model gauge singlet that interacts with visible particles via the higgs field only . to ensure stability , it is endowed with a discrete @xmath0 symmetry that does not spontaneously break . such a model can be seen as a low - energy remnant of some higher - energy physics waiting to be understood . in this cosmological setting , such an extension has first been proposed in @xcite and further studied in @xcite where the unbroken @xmath0 symmetry is extended to a global u(1 ) symmetry . a more extensive exploration of the model and its implications was done in burgess - pospelov - veldhuis , specific implications on higgs detection and lhc physics discussed in @xcite and one - loop vacuum stability looked into and perturbativity bounds obtained in @xcite . the work of @xcite considers also this minimal extension and uses constraints from the experiments xenon10 @xcite and cdmsii @xcite to exclude dark matter masses smaller than 50 , 70 and 75gev for higgs masses equal to 120 , 200 and 350 gev respectively . in order to allow for light dark matter , it is therefore necessary to go beyond the minimal one - real - scalar extension of the standard model . the natural next step is to add another real scalar field , endowed with a @xmath0 symmetry too , but one which is spontaneously broken so that new channels for dark matter annihilation are opened , increasing this way the annihilation cross - section , hence allowing smaller masses . this auxiliary field must also be a standard model gauge singlet . after this brief introductory motivation , we present the model in the next section . we perform the spontaneous breaking of the electroweak and the additional @xmath0 symmetries in the usual way . we clarify the physical modes as well as the physical parameters . there is mixing between the physical new scalar field and the higgs , and this is one of the quantities parametrizing the subsequent physics . in section three , we impose the constraint from the known dark matter relic density on the dark - matter annihilation cross section and study its effects . of course , as we will see , the parameter space is quite large , and so , it is not realistic to hope to cover all of it in one single work of acceptable size . representative values have to be selected and the behavior of the model as well as its capabilities are described . our main focus in this study is the mass range 0.1gev 100gev and we find that the model is rich enough to bear dark matter in most of it , including the very light sector . in section four , we determine the total cross section @xmath5 for non relativistic elastic scattering of dark matter off a nucleon target and compare it to the current direct - detection experimental bounds and projected sensitivity . for this , we choose the results of cdmsii and xenon100 , and the projections of supercdms @xcite and xenon1 t @xcite . here too we can not cover all of the parameter space nor are we going to give a detailed account of the behavior of @xmath5 as a function of the dark matter mass , but general patterns are mentioned . the last section is devoted to some concluding remarks . note that as a rule , we have avoided in this first study narrowing the choice of parameters using particle phenomenology . of course , such phenomenological constraints have to be addressed ultimately and this is left to a forthcoming investigation , contenting ourselves in the present work with a limited set of remarks mentioned in this last section . finally , we have gathered in an appendix the partial results regarding the calculation of the dark matter annihilation cross section .

we extend the standard model by adding two gauge - singlet-symmetric scalar fields that interact with visible matter only through the higgs particle . one is a stable dark matter wimp , and the other one undergoes a spontaneous breaking of the symmetry that opens new channels for the dark matter annihilation , hence lowering the mass of the wimp . we study the effects of the observed dark matter relic abundance on the annihilation cross section and find that in most regions of the parameters space , light dark matter is viable . we also compare the elastic scattering cross - section of our dark matter candidate off nucleus with existing ( cdmsii and xenon100 ) and projected ( supercdms and xenon1 t ) experimental exclusion bounds .

we extend the standard model by adding two gauge - singlet-symmetric scalar fields that interact with visible matter only through the higgs particle . one is a stable dark matter wimp , and the other one undergoes a spontaneous breaking of the symmetry that opens new channels for the dark matter annihilation , hence lowering the mass of the wimp . we study the effects of the observed dark matter relic abundance on the annihilation cross section and find that in most regions of the parameters space , light dark matter is viable . we also compare the elastic scattering cross - section of our dark matter candidate off nucleus with existing ( cdmsii and xenon100 ) and projected ( supercdms and xenon1 t ) experimental exclusion bounds . we find that most of the allowed mass range for light dark matter will be probed by the projected sensitivity of xenon1 t experiment .

0910.3132

i

in the absence of flavor symmetries , the yukawa couplings between the standard model ( sm ) fermions and the higgs field are in general complex arbitrary matrices which , after electroweak symmetry breaking ( ewsb ) , become the mass matrices of the quarks and charged leptons . in the case of neutrinos , the mass matrix will be in general complex symmetric . all these matrices contain more parameters than physical observables and an explicit computation of these observables ( fermion masses and mixings ) in terms of the original matrix elements can be quite cumbersome in general . indeed this would require us to solve a @xmath2 eigenvalue problem for each fermion matrix , and then compose the unitary transformations ( formed with the calculated eigenvectors ) of the up and down quark sectors and then also of the charged lepton and neutrino sectors . we observe however that it may be useful to address the question not as an eigenvalue problem , but as an eigenvector problem , treating the eigenvalues as input parameters and not as output . the first reason for this is that except for the neutrino sector , all the mass eigenvalues are quite well known . but the main point we make is that by keeping explicitly the mass eigenvalues as input parameters , the eigenvector solutions of each mass matrix become surprisingly simple and can be written as compact functions of both the mass matrix elements and the eigenvalues ( the fermion masses ) . such a parametrization of the mixing matrices , directly in terms of the original mass parameters and the fermion masses might prove to be useful in the studies aiming to explain the observed flavor structure of the sm by way of symmetries or textures or patterns @xcite at the level of the fermion mass matrices . it is true , though , that to proceed we need to work with hermitian matrices , but it is always possible to render the quark mass matrices hermitian in the standard model without loss of generality @xcite . the procedure to obtain hermitian matrices is quite standard , and it involves either working with the hermitian matrix @xmath3 , where @xmath4 is the original fermion mass matrix , or using its polar decomposition , i.e. solving @xmath5 , where @xmath6 is a unitary matrix converting the general complex matrix @xmath4 into a positive semi - definite hermitian matrix @xmath7 ( if @xmath4 is invertible , with distinct non - vanishing eigenvalues , then @xmath7 is positive definite and therefore @xmath6 is unique ) . we will first present our parametrization ( in fact 9 different types ) for the unitary matrix @xmath8 which diagonalizes a general hermitian matrix @xmath1 in the most compact way possible . then , to start taking advantage of it , we then propose a simple and mildly constraining ansatz for the flavor structure of the sm fermion sector . it assumes that the unitary transformations diagonalizing @xmath9 and @xmath10 can each be decomposed as only two rotations , instead of three . the idea is to assume that the third rotation angle is zero ( or much smaller than the other two ) and therefore one of the entries of each transformation matrix @xmath11 and @xmath12 will be zero or close to zero . we call this setup the two - angle ansatz and we will concentrate in only one of the many possible cases . our parametrization allows us to quickly obtain very simple dependences of the fermion mixing matrices @xmath13 and @xmath14 @xcite in terms of the masses and the original mass matrix elements . we can thus study easily the interesting properties of this type of ansatz as well as the consequences it has in the original mass matrices , in both the quark and the lepton sectors . a particularly interesting observation is that the specific value of some elements of @xmath9 and @xmath10 has no effect ( or very mild effect ) on the observed values of masses and mixings .

we then study a special class of fermion mass matrices , defined by the requirement that all of the diagonalizing unitary matrices ( in the up , down , charged lepton and neutrino sectors ) contain at least one mixing angle much smaller than the other two . our new parametrization allows us to quickly extract information on the patterns and predictions emerging from this scheme .

we first obtain the most general and compact parametrization of the unitary transformation diagonalizing any hermitian matrix , as a function of its elements and eigenvalues . we then study a special class of fermion mass matrices , defined by the requirement that all of the diagonalizing unitary matrices ( in the up , down , charged lepton and neutrino sectors ) contain at least one mixing angle much smaller than the other two . our new parametrization allows us to quickly extract information on the patterns and predictions emerging from this scheme . in particular we find that the phase difference between two elements of the two mass matrices ( of the sector in question ) controls the generic size of one of the observable fermion mixing angles : i.e. just fixing that particular phase difference will `` predict '' the generic value of one of the mixing angles , irrespective of the value of anything else .

0910.3132

c

in this work , we started by obtaining the simplest parametrization for the diagonalization of a @xmath222 hermitian matrix , as a function of both its matrix elements and its eigenvalues . since the masses of fermions in the sm are well known , the problem to attack is not an eigenvalue problem , but an eigenvector problem . in other words , we are able to obtain the eigenvectors of a hermitian matrix in an algebraically compact form because we treated the eigenvalues as known parameters , instead of unknown . with this parametrization in hand , we wanted then to show how it could simplify and make quite transparent the analysis and study of some flavor schemes . to this end we defined a new flavor scheme which imposes some ( arguably obscure ) constraints on the flavor structure in the fermion sector . the constraint imposed is the requirement of the vanishing of one of the mixing angles of the diagonalization matrix of each hermitian fermion mass matrix of the sm . we called this the `` two - angle '' ansatz ( i.e. out of three angles to diagonalize a hermitian matrix , we consider the family of hermitian matrices diagonalized by only two angles ) , and it is bottom - up motivated , i.e. it is inspired on the observed structure of both @xmath13 and @xmath14 matrices . nevertheless we also observe that in flavor models where one requires a full symmetry between two of the three families , like the @xmath223 symmetry models , one of the consequences is precisely the vanishing of one of the mixing angles . but we mainly decided to keep the bottom - up approach motivation and study the patterns emerging from our `` two - angle '' ansatz and focused on just one possible implementation , the @xmath88 case , in which the @xmath224 entries of all the diagonalizing matrices happen to vanish . using our parametrization , one can actually write both @xmath13 and @xmath14 in terms of the original matrix elements and eigenvalues . in particular we found a peculiar dependence of one of the mixing angles with the model parameters . we observed that by fixing the phase difference @xmath94 between two parameters of the up and down mass matrices ( or the neutrino and charged lepton mass matrices ) , the mixing angle @xmath104 ( or @xmath175 ) can be `` predicted '' in a statistical sense , i.e. if one makes a random scan allowing the remaining free parameters to take any possible value , including the eigenvalues , one obtains a narrow distribution for the value of @xmath89 ( or @xmath194 ) , and the central value is a monotonic function of the phase difference @xmath94 . this can be seen by rewriting the general formula for @xmath104 in the @xmath88 ansatz ( see eq . ( [ ceq ] ) ) as @xmath225 , @xmath226 and @xmath227 , and @xmath228 and @xmath229 are diagonal elements of the up and down mass matrices respectively . if the mass eigenvalues @xmath230 are unconstrained , the only constraints on the parameters required for a random scan are ^u_1/^u_3 < , < 1 & and & ^d_1/^d_3 < , < 1 since the diagonal elements of a hermitian matrix must be bounded by its largest and lowest eigenvalues . the result of a scan over all these parameters ( including the eigenvalues ) but for fixed @xmath231 is a highly peaked distribution centered at some value . this means that the generic value of @xmath89 is controlled almost exclusively by @xmath94 . of course one may think that after fixing the masses to the experimental values , as well as the other mixing angles , maybe we might loose this statistical prediction . this is not the case as was shown in figure [ vtbdelta ] , where the scan is performed now with only two free parameters , the rest having been fixed by other experimental observables . there is still a clear correlation between the value of the phase difference and the value of the angle @xmath104 . the imposition of this specific two - angle ansatz ( the ( @xmath232 ) case ) on the fermion mass matrices amounts to 2 constraints per mass matrix , and therefore 4 constraints in the quark sector . what we have noted is that with only one more constraint , i.e. the fixing of the phase difference @xmath94 , we are able to give a statistical prediction for the value of the angle @xmath89 ( or @xmath194 ) , and this , irrespective of any other parameter . in particular if @xmath98 we would expect @xmath233 and in the lepton sector , if we fix @xmath191 , then we would expect @xmath234 , both cases being close to the experimental fits . two hermitian matrices contain 18 free parameters altogether and so it is nontrivial that after imposing only 5 constraints on the whole set we obtain one prediction , irrespective of anything else . once noted this nontrivial property , we continued analyzing the rest of consequences of our scheme and showed for example how the cp violating phases in both quark and lepton sectors depend on the phases of the original mass matrix elements . another interesting outcome was the realization of how to treat in a similar way the quarks and charged lepton mass matrices , and use the special case of the neutrino matrix to explain in a transparent way the observed differences between the lepton and quark sectors . in particular we also analyzed the consequences of further imposing a @xmath146 symmetry in the neutrino sector . it is true that out of many possible implementations of the two - angle ansatz we chose to study only one case . we felt that this one case would show the main features of the scheme in a transparent way , and so we leave the systematic case by case study of the scenario for the future , although part of this work is already underway .

we first obtain the most general and compact parametrization of the unitary transformation diagonalizing any hermitian matrix , as a function of its elements and eigenvalues . in particular we find that the phase difference between two elements of the two mass matrices ( of the sector in question ) controls the generic size of one of the observable fermion mixing angles : i.e. just fixing that particular phase difference will `` predict '' the generic value of one of the mixing angles , irrespective of the value of anything else .

we first obtain the most general and compact parametrization of the unitary transformation diagonalizing any hermitian matrix , as a function of its elements and eigenvalues . we then study a special class of fermion mass matrices , defined by the requirement that all of the diagonalizing unitary matrices ( in the up , down , charged lepton and neutrino sectors ) contain at least one mixing angle much smaller than the other two . our new parametrization allows us to quickly extract information on the patterns and predictions emerging from this scheme . in particular we find that the phase difference between two elements of the two mass matrices ( of the sector in question ) controls the generic size of one of the observable fermion mixing angles : i.e. just fixing that particular phase difference will `` predict '' the generic value of one of the mixing angles , irrespective of the value of anything else .

cond-mat0211001

i

issues of quantum measurement in mesoscopic systems have recently garnered considerable interest , both because of their relevance to attempts at quantum computation @xcite and quantum - limited amplifiers @xcite . a general consequence of any quantum measurement is that it must induce decoherence in the system variable conjugate to that being measured . this basic fact naturally leads to the issue of measurement efficiency : what conditions must a particular detector satisfy so that it induces the _ absolute minimum _ amount of dephasing required by quantum mechanics ? this minimum dephasing rate is identical to the measurement rate @xmath0 , the rate at which information is extracted during the measurement process ; thus , the measurement efficiency ratio @xmath1 is defined by @xmath2 , where @xmath3 is the measurement - induced dephasing rate . besides being of great conceptual interest , near - ideal measurement schemes are necessary to detect signatures of coherent qubit oscillations in the output noise of a detector @xcite , and are essential if one wishes to construct a quantum limited amplifier ( i.e. an amplifier whose noise energy is the minimum allowed by quantum mechanics ) @xcite . while the question of measurement efficiency has received attention in the context of general measurement theory @xcite , it is only recently that it has been considered in the context of solid state detectors . averin @xcite has considered the status of the quantum limit in a number of solid state detectors , while recently pilgram and bttiker @xcite considered the quantum limit for a system in which a mesoscopic conductor acts as a detector . in this paper , we formulate general conditions which are needed for an arbitrary detector in the linear - response regime to reach the quantum limit of detection , where @xmath4 . these general conditions are valid for both interacting and non - interacting systems , and can be given a direct physical interpretation . we also discuss the quantum limit in terms of a simple concept from quantum information theory , the accessible information . to make these considerations more concrete , we apply them to a mesoscopic scattering detector similar to that considered in ref . , identifying precise conditions and symmetries needed to reach the quantum limit . we find that the required symmetries are most easily understood if one considers the scattering detector in terms of information ; these symmetries are not the same as those usually considered in mesoscopic systems . for example , we find that time reversal symmetry is not necessary for reaching the quantum limit . we also find that , surprisingly , an adiabatic point contact @xcite system remains a quantum limited detector even for voltages large enough that several channels contribute to transport and that the energy dependence of scattering is important ; previous studies @xcite have only shown that the quantum limit is achieved in the small voltage regime . our results for the mesoscopic scattering detector are complementary to those obtained in ref . .

we formulate general conditions necessary for a linear - response detector to reach the quantum limit of measurement efficiency , where the measurement - induced dephasing rate takes on its minimum possible value . these conditions are applicable to both non - interacting and interacting systems . we assess the status of these requirements in an arbitrary non - interacting scattering based detector , identifying the symmetries of the scattering matrix needed to reach the quantum limit .

we formulate general conditions necessary for a linear - response detector to reach the quantum limit of measurement efficiency , where the measurement - induced dephasing rate takes on its minimum possible value . these conditions are applicable to both non - interacting and interacting systems . we assess the status of these requirements in an arbitrary non - interacting scattering based detector , identifying the symmetries of the scattering matrix needed to reach the quantum limit . we show that these conditions are necessary to prevent the existence of information in the detector which is not extracted in the measurement process .

1012.0591

i

a _ crossing - free straight - edge graph _ @xmath9 is an embedding of a planar graph in the plane such that the vertices are mapped to a set @xmath0 of points in the plane and the edges are pairwise non - crossing line segments between pairs of points in @xmath0 . ( segments are allowed to share endpoints . ) by fry s classical result @xcite , such an embedding is always possible . in this paper , we fix a labeled set @xmath0 of points in the plane , and we only consider planar graphs that admit a straight - edge embedding with vertex set @xmath0 . by _ labeled _ we mean that each vertex of the graph has to be mapped to a unique designated point of @xmath0 . analysis of the number of plane embeddings of planar graphs in which the set of vertices is not restricted to a specific embedding , or when the vertices are not labeled , can be found , for example , in @xcite . a _ triangulation _ of a set @xmath0 of @xmath1 points in the plane is a maximal crossing - free straight - edge graph on @xmath0 ( that is , no additional straight edges can be inserted without crossing some of the existing edges ) . triangulations are an important geometric construct which is used in many algorithmic applications , and are also an interesting object of study in discrete and combinatorial geometry ( recent comprehensive surveys can be found in @xcite ) . improving the bound on the maximum number of triangulations that any set of @xmath1 points in the plane can have has been a major research theme during the past 30 years . the initial upper bound @xmath10 of @xcite has been steadily improved in several paper ( e.g. , see @xcite ) , culminating with the current record of @xmath11 due to sharir and sheffer @xcite . other papers have studied lower bounds on the maximal number of triangulations ( e.g. , @xcite ) , and upper or lower bounds on the number of other kinds of planar graphs ( e.g. , @xcite ) . every triangulation of @xmath0 contains the edges of the convex hull of @xmath0 , and the remaining edges of the triangulation decompose the interior of the convex hull into triangular faces . assume that @xmath0 contains @xmath1 points , @xmath12 of which are on the convex hull boundary and the remaining @xmath13 points are interior to the hull ( we use this notation throughout ) . by euler s formula , every triangulation of @xmath0 has @xmath14 edges ( @xmath12 _ hull _ edges , common to all triangulations , and @xmath15 _ interior _ edges , each adjacent to two triangles ) , and @xmath16 bounded triangular faces . can be flipped to the edge @xmath17 . ( b ) the two bold edges are simultaneously flippable . ( c ) interior - disjoint convex quadrilateral and convex pentagon in a triangulation.,title="fig:",scaledwidth=80.0% ] [ [ edge - flips . ] ] edge flips . + + + + + + + + + + + edge flips are simple operations that replace one or several edges of a triangulation with new edges and produce a new triangulation . as we will see in section [ se : apps ] , edge flips are instrumental for counting various classes of subgraphs in triangulations . in the next few paragraphs , we review previous results on edge flips , and propose a new type of edge flip . we say that an interior edge in a triangulation of @xmath0 is _ flippable _ , if its two adjacent triangles form a convex quadrilateral . a flippable edge can be _ flipped _ , that is , removed from the graph of the triangulation and replaced by the other diagonal of the corresponding quadrilateral , thereby obtaining a new triangulation of @xmath0 . an edge flip operation is depicted in figure 1(a ) , where the edge @xmath18 is flipped to the edge @xmath17 . already in 1936 , wagner @xcite has shown that any _ unlabeled abstract _ triangulation @xmath19 ( in this case , two triangulations are considered identical if we can relabel and change the planar embedding of the vertices of the first triangulation , to obtain the second triangulation ) can be transformed into any other triangulation @xmath20 ( with the same number of vertices ) through a series of edge - flips ( here one uses a more abstract notion of an edge flip ) . when we deal with a pair of triangulations over a specific common ( labeled ) set @xmath0 of points in the plane , there always exists such a sequence of @xmath21 flips , and this bound is tight in the worst case ( e.g. , see @xcite ) . moreover , there are algorithms that perform such sequences of flips to obtain some optimal " triangulation ( typically , the delaunay triangulation ; see @xcite for example ) , which , as a by - product , provide an edge - flip sequence between any specified pair of triangulations of @xmath0 . how many flippable edges can a single triangulation have ? given a triangulation @xmath19 , we denote by @xmath22 the number of flippable edges in @xmath19 . hurtado , noy , and urrutia @xcite proved the following lower bound . [ le : fliporiginal ] _ * @xcite * _ for any triangulation @xmath19 over a set of @xmath1 points in the plane , @xmath23 moreover , there are triangulations ( of specific point sets of arbitrarily large size ) for which this bound is tight . flippable edges.,title="fig:",scaledwidth=45.0% ] to obtain a triangulation with exactly @xmath24 flippable edges ( for an even @xmath1 ) , start with a convex polygon with @xmath25 vertices , triangulate it in some arbitrary manner , insert a new point into each of the @xmath26 resulting bounded triangles , and connect each new point @xmath27 to the three hull vertices that form the triangle containing @xmath27 . such a construction is depicted in figure [ fi : lowflip ] . the resulting graph is a triangulation with @xmath1 vertices and exactly @xmath24 flippable edges , namely the chords of the initial triangulation . next , we say that two flippable edges @xmath28 and @xmath29 of a triangulation @xmath19 are _ simultaneously flippable _ if no triangle of @xmath19 is incident to both edges ; equivalently , the quadrilaterals corresponding to @xmath28 and @xmath29 are interior - disjoint . see figure [ fi : intro](b ) for an illustration . notice that flipping an edge @xmath28 can not affect the flippability of any edge simultaneously flippable with @xmath28 . given a triangulation @xmath19 , let @xmath30 denote the size of the largest subset of edges of @xmath19 , such that every pair of edges in the subset is simultaneously flippable . the following lemma , improving upon an earlier weaker bound in @xcite , is taken from souvaine , tth , and winslow @xcite . [ le : sfliporiginal ] _ * @xcite * _ for any triangulation @xmath19 over a set of @xmath1 points in the plane , @xmath31 . galtier et al . @xcite show that this bound is tight in the worst case , by presenting a specific triangulation in which at most @xmath32 edges are simultaneously flippable . [ [ pseudo - simultaneously - flippable - edge - sets . ] ] pseudo - simultaneously flippable edge sets . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + a set of simultaneously flippable edges in a triangulation @xmath19 can be considered as the set of diagonals of a collection of interior - disjoint convex quadrilaterals . we consider a more liberal definition of simultaneously flippable edges , by taking , within a fixed triangulation @xmath19 , the diagonals of a set of interior - disjoint convex polygons , each with at least four edges ( so that the boundary edges of these polygons belong to @xmath19 ) . consider such a collection of convex polygons @xmath33 , where @xmath34 has @xmath35 edges , for @xmath36 . we can then retriangulate each @xmath34 independently , to obtain many different triangulations . specifically , each @xmath34 can be triangulated in @xmath37 ways , where @xmath38 is the @xmath39-th _ catalan number _ ( see , e.g. , ( * ? ? ? * section 5.3 ) ) . hence , we can get @xmath40 different triangulations in this way . in particular , if a graph @xmath41 ( namely , all the edges of @xmath9 are edges of @xmath19 ) does not contain any diagonal of any @xmath34 ( it may contain boundary edges though ) then @xmath9 is a subgraph of ( at least ) @xmath42 distinct triangulations . an example is depicted in figure [ fi : intro](c ) , where by flipping " ( or rather , redrawing ) the diagonals of the highlighted quadrilateral and pentagon , we can get @xmath43 different triangulations ( including the one shown ) , and any subgraph of the triangulation that does not contain any of these diagonals is a subgraph of these ten triangulations . we say that a set of interior edges in a triangulation is _ pseudo - simultaneously flippable _ ( _ ps - flippable _ for short ) if after the deletion of these edges every bounded face of the remaining graph is convex , and there are no vertices of degree 0 . notice that all three notions of flippability are defined within a fixed triangulation @xmath19 of @xmath0 ( although each of them gives a recipe for producing many other triangulations ) . .bounds for minimum numbers of the various types of flippable edges in a triangulation of @xmath1 points . all of these bounds are tight in the worst case . [ cols="<,^",options="header " , ] [ [ our - results . ] ] our results . + + + + + + + + + + + + in section [ sec : psflip ] , we derive a lower bound on the size of the largest set of ps - flippable edges in a triangulation , and show that this bound is tight in the worst case . specifically , we have the following result . [ le : psflip ] let @xmath0 be a set of @xmath1 points in the plane , and let @xmath19 be a triangulation of @xmath0 . then @xmath19 contains a set of at least @xmath44 ps - flippable edges . this bound is tight in the worst case . table [ ta : flippable ] summarizes the bounds for the minimum numbers of the various types of flippable edges in a triangulation . . when completing it into a triangulation , the added ( dashed ) diagonals form a set of ps - flippable edges . this is one of the @xmath45 possible completions.,title="fig:",scaledwidth=20.0% ] we also relate ps - flippable edges to _ convex decompositions _ of @xmath0 . these are crossing - free straight - edge graphs on @xmath0 such that ( i ) they include all the hull edges , ( ii ) each of their bounded faces is a convex polygon , and ( iii ) no point of @xmath0 is isolated . see figure [ fi : decomposition ] for an illustration . l | c | c | c | c graph type & lower bound & previous & new upper & in the form + & & upper bound & bound & @xmath46 + & & & & + [ -2ex ] plane graphs & @xmath47 @xcite & @xmath48 @xcite & @xmath49 & @xmath50 + [ 0.5ex ] spanning trees & @xmath51 @xcite & @xmath52 @xcite & @xmath53 & @xmath54 + [ 0.5ex ] forests & @xmath55 @xcite & @xmath56 ) @xcite & @xmath57 & @xmath58 + [ 1ex ] [ [ counting - plane - graphs - new - upper - bounds . ] ] counting plane graphs : new upper bounds . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + in section [ se : apps ] , we use lemma [ le : psflip ] to derive several upper bounds on the numbers of planar graphs of various kinds embedded as crossing - free straight - edge graphs on a fixed labeled set @xmath0 . for a set @xmath0 of points in the plane , we denote by @xmath59 the set of all triangulations of @xmath0 , and put @xmath60 . similarly , we denote by @xmath61 the set of all crossing - free straight - edge graphs on @xmath0 , and put @xmath62 . we also let @xmath2 and @xmath63 denote , respectively , the maximum values of @xmath64 and of @xmath65 , over all sets @xmath0 of @xmath1 points in the plane . since a triangulation of @xmath0 has fewer than @xmath66 edges , the trivial upper bound @xmath67 holds for any point set @xmath0 . recently , razen , snoeyink , and welzl @xcite slightly improved the upper bound on the ratio @xmath68 from @xmath69 down to @xmath70 . we give a more significant improvement on the ratio with an upper bound of @xmath71 . combining this bound with the recent bound @xmath72 @xcite , we get @xmath73 . we provide similar improved ratios and absolute bounds for the numbers of crossing - free straight - edge spanning trees and forests ( i.e. , cycle - free graphs ) . table [ ta : upperbounds ] summarizes these results . we also derive similar ratios for the number of crossing - free straight - edge graphs with exactly @xmath74 edges , with at least @xmath74 edges , and with at most @xmath74 edges , for @xmath75 . for the case of crossing - free straight - edge graphs with exactly @xmath74 we obtain the bound , @xmath76 , and @xmath77 , we neglect polynomial factors . ] @xmath78 where @xmath79 . figure [ fi : plot1 ] contains a plot of the base @xmath80 of the exponential factor multiplying @xmath2 in this bound , as a function of @xmath8 . of the exponential factor in the bound on the number of crossing - free straight - edge graphs with @xmath74 edges , as a function of @xmath8 . the maximum is attained at @xmath81 ( see below ) . , title="fig:",scaledwidth=47.0% ] [ [ notation . ] ] notation . + + + + + + + + + here are some additional notations that we use . = 0em for a triangulation @xmath19 and an integer @xmath82 , let @xmath83 denote the number of interior vertices of degree @xmath84 in @xmath19 . given two crossing - free straight - edge graphs @xmath9 and @xmath85 over the same point set @xmath0 , we write @xmath86 to indicate that every edge in @xmath9 is also an edge in @xmath85 . similarly to the case of edges , the _ hull vertices _ , _ interior vertices _ ) of a set @xmath0 of points in the plane are those that are part of the boundary of the convex hull of @xmath0 ( resp . , not part of the convex hull boundary ) . we only consider point sets @xmath0 in general position , that is , no three points in @xmath0 are collinear . for upper bounds on the number of graphs , this involves no loss of generality , because the number of graphs can only increase if collinear points are slightly perturbed into general position . * separable edges . * let @xmath27 be an interior vertex in a convex decomposition @xmath9 of @xmath0 . following the notation in @xcite , we call an edge @xmath28 incident to @xmath27 in @xmath9 _ separable at @xmath27 _ if it can be separated from the other edges incident to @xmath27 by a line through @xmath27 ( see figure [ fi : separable ] , where the separating lines are not drawn ) . equivalently , edge @xmath28 is separable at @xmath27 if the two angles between @xmath28 and its clockwise and counterclockwise neighboring edges ( around @xmath27 ) sum up to more than @xmath87 . following @xcite , we observe the following easy properties , both of which materialize in figure [ fi : separable ] . a. if @xmath27 is an interior vertex of degree @xmath88 in @xmath9 , its three incident edges are separable at @xmath27 , for otherwise @xmath27 would have been a reflex vertex of some face . b. an interior vertex @xmath27 of degree @xmath89 or higher can have at most two incident edges which are separable at @xmath27 ( and if it has two such edges they must be consecutive in the circular order around @xmath27 ) .

we prove a worst - case tight lower bound for the number of pseudo - simultaneously flippable edges in a triangulation in terms of the number of vertices . we use this bound for deriving new upper bounds for the maximal number of crossing - free straight - edge graphs that can be embedded on any fixed set of points in the plane . we obtain new upper bounds for the number of spanning trees and forests as well . specifically , let denote the maximum number of triangulations on a set of points in the plane . then we show ( using the known bound ) that any-element point set admits at most crossing - free straight - edge graphs , spanning trees , and forests . we also obtain upper bounds for the number of crossing - free straight - edge graphs that have , fewer than , or more than edges , for any constant parameter , in terms of and .

we generalize the notions of flippable and simultaneously flippable edges in a triangulation of a set of points in the plane to so - called _ pseudo - simultaneously flippable edges_. such edges are related to the notion of convex decompositions spanned by . we prove a worst - case tight lower bound for the number of pseudo - simultaneously flippable edges in a triangulation in terms of the number of vertices . we use this bound for deriving new upper bounds for the maximal number of crossing - free straight - edge graphs that can be embedded on any fixed set of points in the plane . we obtain new upper bounds for the number of spanning trees and forests as well . specifically , let denote the maximum number of triangulations on a set of points in the plane . then we show ( using the known bound ) that any-element point set admits at most crossing - free straight - edge graphs , spanning trees , and forests . we also obtain upper bounds for the number of crossing - free straight - edge graphs that have , fewer than , or more than edges , for any constant parameter , in terms of and .

1012.3729

i

a quandle , which was introduced by joyce @xcite , is an algebraic object whose axioms are motivated by knot theory and conjugation in a group . in @xcite , carter , jelsovsky , kamada , langford and saito introduced a quandle homology theory , and they defined the quandle cocycle invariants for classical knots and surface knots . the quandle homology is defined as the homology of a chain complex generated by cubes whose edges are labeled by elements of a quandle . on the other hand the group homology is defined as the homology of a chain complex generated by tetrahedra whose edges are labeled by elements of a group . so it is natural to ask a relation between quandle homology and group homology . this question also arises from the fact that the quandle cocycle invariants were defined as an analogue of the dijkgraaf - witten invariants , which are defined using group cocycles . in @xcite , the authors defined a simplicial version of quandle homology and constructed a homomorphism from the usual quandle homology to the simplicial quandle homology . the important point is that this homomorphism gives a triangulation of a knot complement in algebraic fashion . this enables us to relate the quandle homology to the topology of knot complements . in this paper , we apply the results of @xcite to construct quandle cocycles from group cocycles . first , we demonstrate how to give a quandle cocycle of the dihedral quandle @xmath1 from a group cocycle of the cyclic group @xmath2 for any integer @xmath0 in section [ sec : dihedral ] . we will show that a generator of @xmath6 gives rise to a non - trivial quandle 3-cocycle of @xmath7 . when @xmath3 is an odd prime , since @xmath4 , our quandle 3-cocycle is equal to a constant multiple of the mochizuki 3-cocycle @xcite up to coboundary . then we generalize the construction to wider classes of quandles . let @xmath8 be a group and @xmath9 be an element of @xmath8 , then the set @xmath10 forms a quandle by conjugation . ( it is known by joyce @xcite that any faithful homogeneous quandle has such a presentation . ) when some obstruction in second cohomology vanishes , we will construct a quandle cocycle of @xmath11 from a group cocycle of @xmath8 . dually , we relate the quandle cycle associated with an arc and region coloring ( shadow coloring ) of a knot @xmath5 to a group cycle represented by a cyclic branched covering branched along @xmath5 . let @xmath12 be a diagram of @xmath5 . we can define the notion of arc and region colorings of @xmath12 by a quandle @xmath11 . a pair of an arc and a region coloring is called a _ shadow coloring_. we can associate a cycle of a quandle homology group to a shadow coloring of @xmath12 . using the homomorphism constructed in @xcite , we will construct a group cycle of @xmath8 represented by a cyclic branched covering branched along @xmath5 . this reveals a close relationship between the shadow cocycle invariant of a knot and the dijkgraaf - witten invariant of the cyclic branched cover . we remark that hatakenaka and nosaka defined an invariant of 3-manifolds called the _ 4-fold symmetric quandle homotopy invariant _ @xcite , based on the fact that any 3-manifold can be represented as a 4-fold simple branched covering of @xmath13 along a link . as an application , they showed that the shadow cocycle invariant of a link for the mochizuki @xmath14-cocycle is equal to a scalar multiple of the dijkgraaf - witten invariant of the double branched cover along the link . this paper is organized as follows . in section [ sec : group_homology ] , we recall the definition of group homology and show how to represent a group cycle by a triangulation with a labeling of its @xmath15-simplices . we give a presentation of the fundamental group of a cyclic branched covering branched along a knot in section [ sec : pres_of_cyc_bra_cov ] , which is independent from the other sections . in section [ sec : cyc_rep_by_cyc_bra_cov ] , we construct a group cycle represented by a cyclic branched cover . we recall the definition of quandles and their homology theory in section [ sec : quandle_and_homology ] . we review some results from @xcite in section [ sec : main_map ] and apply them to construct quandle cocycles of the dihedral quandle @xmath1 in section [ sec : dihedral ] . the reader who is interested in the form of the @xmath14-cocycle , consult ( [ eq : the_cocycle ] ) ( and ( [ eq : formula_of_d ] ) ) . we will generalize the construction to wider classes of quandles in section [ sec : gen_const ] . in section [ sec : quandle_cyc_as_cyc_bra_cov ] , we construct a group cycle represented by a cyclic branched covering from the quandle cycle associated with a shadow coloring . the reader who is only interested in the construction of quandle cocycles from group cocycles may skip sections [ sec : group_homology ] [ sec : cyc_rep_by_cyc_bra_cov ] except [ subsec : group_homology ] . * acknowledgement * the author thanks takefumi nosaka for useful discussions . he also thanks the referees for helpful comments to improve the exposition . the author is supported by jsps research fellowships for young scientists .

we give a construction of quandle cocycles from group cocycles , especially , for any integer , quandle cocycles of the dihedral quandle from group cocycles of the cyclic group . we will show that a group 3-cocycle of gives rise to a non - trivial quandle 3-cocycle of . when is an odd prime , since , our 3-cocycle is a constant multiple of the mochizuki 3-cocycle up to coboundary . dually , we construct a group cycle represented by a cyclic branched covering branched along a knot from the quandle cycle associated with a colored diagram of .

we give a construction of quandle cocycles from group cocycles , especially , for any integer , quandle cocycles of the dihedral quandle from group cocycles of the cyclic group . we will show that a group 3-cocycle of gives rise to a non - trivial quandle 3-cocycle of . when is an odd prime , since , our 3-cocycle is a constant multiple of the mochizuki 3-cocycle up to coboundary . dually , we construct a group cycle represented by a cyclic branched covering branched along a knot from the quandle cycle associated with a colored diagram of .

0704.2133

i

adiabatic pair creation ( apc ) has been called unfortunately misleading spontaneous pair creation ( @xcite,@xcite - @xcite,@xcite ) . the creation of electron positron pairs in very strong external classical electromagnetic fields arises straight forwardly from the dirac sea interpretation of negative energy states . after dirac@xcite it has been discussed as an academic problem by klein @xcite , sauter @xcite , heisenberg and euler @xcite , schwinger @xcite and brezin and itzykson @xcite . a more realistic setting was hinted at by beck , steinwedel and smann , @xcite and worked out by gershtein and zeldovich @xcite as apc . in the common physics language it may be described as follows : an adiabatically increasing electric potential lifts a particle from the sea to the positive energy subspace where it scatters and when the potential is gently switched off one has one free electron and one unoccupied state a hole in the sea . the experimental verification needs very strong classical fields @xcite and is discussed elsewhere @xcite . in this respect we would like to remark that a coherent analysis of the existence of apc has been lacking until recently @xcite . earlier quantitative results based on an ad hoc and incoherent analysis ( see for example @xcite , @xcite ) are false concerning the rate and the outgoing momenta of the spontaneously created pairs ( see @xcite ) . there have been also results in the mathematical physics literature related to apc , notably @xcite but those results do not come to grasp at all with the heart of the problem of apc , which is the control of the wavefunction evolution within the neighborhood of the spectral edge @xmath0 . in apc one considers the so called external field problem , where interactions between the charges are neglected . vacuum polarization will in general perturb the external field and - using mean field approximation -(see @xcite ) one may think of the external field as an effective field . the existence of apc in second quantized external field dirac theory ( if the latter exists is equivalent to the existence of certain types of solutions of the dirac equation ( see e.g. @xcite and @xcite ) which we describe below . the existence of apc in terms of the second quantised s - matrix theory of the dirac equation with external field is `` by definition '' equivalent to the existence of these types of solutions of the dirac equation . we shall in fact formulate our result in terms of the solutions of the dirac equation and use the dirac sea picture for the interpretation of the particular solution we prove in this paper to exist . consider the dirac equation with external electric field . then the potential @xmath1 can be chosen as a real valued multiple of the @xmath2 unit matrix . ( we wish to note that the results can be extended to general four potentials . concerning strong magnetic fields we wish to call attention to the recent work of dolbeault et.al . @xcite as well as @xcite ) . @xmath3 gives the potential in the units @xmath4 . we assume that the potential @xmath1 varies slowly with time , expressed by @xmath5 , where @xmath6 is a dimensionless small parameter ( given by the physics , see @xcite for some examples ) which in this work will eventually be sent to zero to obtain limit results . here @xmath7 and @xmath8 are the dimensionless microscopic time- and space - scales and the dirac equation in the standard representation reads with the notation @xmath9 and @xmath10 @xmath11 we introduce in ( [ diracmicalt ] ) the macroscopic time scale @xmath12 . we wish to restrict ourselves to potentials @xmath13 which can be factorized into a space- and a time dependent factor @xmath14 , a restriction of technical nature which eases notations and computations and which furthermore helps to picture a spatial potential well which changes its depth with time . it is helpful to have this picture in mind , because the potential does act as an elevator , as we shall explain below . we thus have @xmath15 furthermore we wish to restrict ourselves to potentials @xmath16 which are smooth , bounded , compactly supported in @xmath17 and @xmath18 and positive . the spectrum of the free dirac operator @xmath19 is absolutely continuous and given by @xmath20\cap[1,\infty)$ ] , defining `` negative and positive energy '' subspaces . in the dirac sea interpretation wavefunctions which lie in the positive energy subspace of the free dirac operator are interpreted as wavefunctions of electrons . the so called vacuum of second quantized dirac equation corresponds in the dirac sea picture to all `` states of the negative energy subspace being occupied by particles''the dirac sea . `` holes '' in the dirac sea are unoccupied negative energy states which are interpreted as anti - electrons , i.e. positrons . [ bild ] as function of @xmath18 . depending on the strength of the potential there may exist bound state energy curves @xmath21 , one or more of which may bridge the spectral gap ( overcritical case ) . also schematically drawn are bound states @xmath22 at various undercritical times . no bound states exist in the lower and upper spectral continua @xmath23 and @xmath24 . pair creation is achieved ( with probability one ) if a particle from the sea which occupied at small times @xmath18 the bound states @xmath22 corresponding to the gap bridging bound state energy curve scatters after the bound state curve has reached the upper spectral set @xmath25 at time @xmath26 , and when that bound state becomes a scattering state . the `` returning bound state '' is then unoccupied producing a hole in the sea . ] the goal of our paper is to assert that there exist solutions of ( [ diracmic ] ) which describe pair creation . we explain what that means . the main idea of apc , as illustrated in figure [ bild ] is as follows . consider first the spectrum of the time dependent dirac operator @xmath27 . at large negative and large positive times when @xmath28 , @xmath29 and we have the spectrum of @xmath19 . at times at which @xmath30 there may be eigenvalues in the gap @xmath31 $ ] , while the continuous spectrum remains unchanged . the eigenvalues change with the strength of the potential , i.e. with time @xmath18 ( bound state energy curve @xmath21 in figure [ bild ] ) . suppose first that no eigenvalue reaches @xmath32 , .i.e . no bound state energy curve bridges the gap ( undercritical case ) . the adiabatic theorem ( see e.g. @xcite ) ensures that there is no tunnelling across spectral gaps meaning that the bound states stay more or less intact when the potentials changes adiabatically . in terms of solutions of the dirac equation ( [ diracmic ] ) that means the following : there exists no solution when @xmath6 goes to zero which for large negative times lies completely within the negative continuous energy subspace and for large positive times has parts in the positive continuous energy subspace . in the dirac sea interpretation that means : the probability of creating a pair is zero . no apc . however , when the external field becomes overcritical ( at time @xmath26 in figure [ bild ] ) , the highest lying eigenvalue curve reaches the positive continuum and the bound state ceases to exist and becomes a continuum state ( a `` resonance '' ) in the positive continuum subspace . then there exists a solution of the dirac equation which follows adiabatically the path of this bound state , which for large negative times must develop into a wavefunction which lies entirely in the negative continuum energy subspace and for positive times may have a part in the positive continuum energy subspace . as indicated in the figure [ bild ] when the potential decreases with increasing time there is again a bound state energy curve bridging the gap . in principle the solution of the dirac equation can have a part which `` follows '' the bound state back into the negative continuous energy subspace and remains there when the potential is switched off . in the dirac sea interpretation such a solution of the dirac equation would correspond to pair creation with a probability determined by the absolute squares of the parts of the wave functions . we show however , that no such `` back sliding '' is adiabatically possible , i.e. no such solution of the dirac equation exists . the former bound state scatters in the positive continuum energy subspace , i.e. it stays there for all later times . in the dirac sea picture the `` returning '' bound state remains for sure empty and upon becoming a state within the negative continuum energy subspace there is now an unoccupied state in the sea : apc is accomplished with probability one . one pictorial way to describe apc is to imagine the potential acting as an elevator , lifting a particle from the sea to the `` upper''(positive ) continuum . the scenario is symmetric under change of sign of the potential : it then transports an unoccupied state ( a hole ) from the positive continuum to the sea and catches a particle from the sea when it is switched off . the hole ( positron ) then scatters . we understand now the type of solution of ( [ diracmic ] ) we wish to study , namely one which at some time at which an overcritical bound state exists equals that bound state . the scenario we described translates mathematically into the task to establish scattering of such solutions of the time - inhomogenous dirac equation ( [ diracmic ] ) . to show to what extend the scenario of apc holds one must control first that the bound states stay on the adiabatic time scale intact until the eigenvalues reach the positive continuum . that is content of an adiabatic lemma without a gap and `` relatively easy '' to establish . the solution of ( [ diracmic ] ) is thus adiabatically essentially represented by the `` time dependent bound states '' until that time . then we must control the propagation of the wavefunction ( the resonance ) emerging from the bound state during over - criticality . we wish to show that it scatters . this task is on the one hand far from being easy , since the dirac operator changes with time . the time evolution will be controlled by generalized eigenfunctions , i.e. by the stationary phase argument , which is of course not standard because the generalized eigenfunctions themselves are depending now on time . but more than that on the other hand we must take into account the bad ( resonant ) behavior of the generalized eigenfunctions near criticality . ( we wish to note that also @xcite is concerned with the wavefunction propagation for time dependent hamiltonians but under generic smallness assumptions on the potential , assumptions which are not fulfilled in our problem ) . they become unbounded for critical @xmath33-values ( which are small ) and hence the situation is very much different from the usual scattering situation governed by `` plane waves '' ( see @xcite for a heuristic argument giving some intuition ) . as we shall find out , the decay time of a wave , say from a bounded spatial region ( i.e. the time in which roughly half of the mass left the region ) , is now ( on the microscopic time ) @xmath34 as compared to @xmath35 in the common plane wave scattering situation . this means that the resonance lingers around the range of the potential for a much longer time than in the usual scattering of wavefunctions . such a metastable state decay has already been suggested by @xcite . we shall give in the next section the result : theorem [ onecrit ] and corollary [ psipropneu ] . the rest of the paper is devoted to the proof of the theorem . the proof is technically very involved . instead of describing here what is in the sections to follow we first give the result and then give in section [ skeleton ] a skeleton of the proof with a description of the contents of the sections .

we give here the proof that pair creation arises from the dirac equation with an external time dependent potential . pair creation happens with probability one if the potential changes adiabatically in time and becomes overcritical , that is when an eigenvalue curve ( as function of time ) bridges the gap between the negative and positive spectral continuum . the potential may be assumed to be zero at large negative and large positive times . the rigorous treatment of this effect has been lacking since the pioneering work of beck , steinwedel and smann in 1963 and gershtein and zeldovich in 1970 . [ section ] [ thm]corollary [ thm]lemma [ thm]proof [ thm]proposition [ thm]definition [ thm]remark [ thm]condition [ thm]notation

we give here the proof that pair creation arises from the dirac equation with an external time dependent potential . pair creation happens with probability one if the potential changes adiabatically in time and becomes overcritical , that is when an eigenvalue curve ( as function of time ) bridges the gap between the negative and positive spectral continuum . the potential may be assumed to be zero at large negative and large positive times . the rigorous treatment of this effect has been lacking since the pioneering work of beck , steinwedel and smann in 1963 and gershtein and zeldovich in 1970 . [ section ] [ thm]corollary [ thm]lemma [ thm]proof [ thm]proposition [ thm]definition [ thm]remark [ thm]condition [ thm]notation

cond-mat0306532

i

half - doped perovskite manganites re@xmath3a@xmath3mno@xmath4 ( re - rare earth , a - alkaline earth ) exhibit very specific properties quite different from manganites with other @xmath5 electron concentrations.@xcite generally , for large size re and a cations or when external pressure is applied@xcite these compounds are in the a - type antiferromagnetic ( af ) , metallic state at low temperatures showing no or only weak sign of charge ordering , and the occupied @xmath5 electron states are predominantly @xmath6 like . recently it has been reported that the a - phase may develop an intrinsic charge - stripe modulation , which controls the transport properties.@xcite with decreasing size of the cations , which implies a decrease of the bandwidth , charge ordering is observed which at lower temperatures is accompanied by the formation of peculiar ferromagnetic ( fm ) zigzag chains@xcite that are staggered antiferromagnetically . this ce spin order , a notation introduced in the pioneering work of wollan and koehler@xcite and goodenough@xcite , is accompanied by a checkerboard charge order ( co ) and directed occupied orbitals on the mn@xmath7 sites amplifying double exchange ( de ) along one lattice diagonal . the ce - structure is a particularly fascinating manifestation of the control of magnetic order due to the orbital degree of freedom@xcite in combination with charge ordering . although a number of approaches have been followed to explain this structure , the mechanism for its stability is still not clear and hotly debated with emphasis put on the role of the de,@xcite the coulomb interaction,@xcite or the coupling to the lattice degrees of freedom.@xcite the ce phase has been observed experimentally both in cubic ( nd , pr)@xmath3(sr , ca)@xmath3mno@xmath4@xcite and in layered lasr@xmath8mn@xmath8o@xmath9@xcite and la@xmath3sr@xmath10mno@xmath11@xcite manganites . in some cases it can coexist with the a - type af spin ordering.@xcite regarding co in the ce phase , some experiments are interpreted in terms of almost perfect co @xcite while others@xcite are considered to be consistent with a smooth charge density wave ( cdw ) of the @xmath5 electron density . although , it is plausible that the complex spin and orbital arrangement in the charge - ordered manganites can result from the competition between de@xcite and af superexchange interactions ( @xmath12 ) , the role played by the co and jahn - teller ( jt ) interactions@xcite in the system is still unclear . finally in systems like e.g. pr@xmath3ca@xmath3mno@xmath4 co and ce - type orbital correlations are found to develop well above the neel temperature@xcite or even coexist with fm spin state,@xcite which indicates that these orbital correlations are not primarily driven by magnetic interactions . this work focuses on a microscopic understanding of the stability of the ce - phase which appears to be the ground state of narrow band manganites at and near quarter - filling . we argue here that the key interaction , apart from the nearest - neighbor coulomb repulsion @xmath13 which supports the charge ordering,@xcite is the next - nearest neighbor jt interaction . this interaction between orbitals at next - nearest neighbor mn@xmath7 ions emerges from the jt - distortions of the mn@xmath7 octahedra which is amplified by the breathing distortion of the intermediate mn@xmath14 octahedra . we show that this interaction generates a narrow regime in the @xmath13-@xmath15 phase diagram where the ce - phase ( and sometimes the c - phase ) is stable . otherwise one encounters a homogeneous fm phase at small @xmath15 fully controlled by de and a conventional nearest - neighbor af phase at larger @xmath15 . an important feature of further neighbor jt interactions are the displacements of the mn@xmath14 ions . we are only aware of work by radaelli _ _ et al.__@xcite where detailed lattice coordinates for the ce - phase in la@xmath3ca@xmath3mno@xmath4 are reported . in particular they observed that the 4 planar o(2 ) move towards the mn@xmath14 ion and the mn@xmath14 ions are found to be displaced from their regular perovskite positions , while the mn@xmath7 ions are not shifted . this observation confirms the importance of the breathing distortion and also shows the mechanism of the further neighbor jt - distortion in the ce - phase . as a consequence the appearance of new bragg reflections in the ce - phase would be associated not primarily with quadrupolar electronic orbital order but rather with the displacements of ions associated with the ce orbital order.@xcite an alternative long - ranged jt based interaction was recently proposed by khomskii and kugel@xcite and by calderon , millis and ahn.@xcite they employ elasticity theory to derive the orbital interaction between jt - distorted mn@xmath7o@xmath16 octahedra for the perfectly charge ordered case . we have also investigated the consequences of this interaction . our numerical simulations confirm the estimate presented in ref . that for perfect charge ordering the af ce phase is stable . yet in this model this requires large nearest neighbor coulomb repulsion @xmath13 , while for moderate values of @xmath13 the ce phase gets unstable . the finite temperature diagonalization@xcite used in our study allows to include the full interplay of spin and orbital states , and to monitor the onset of different orders as function of temperature . this gives us the ability for an unbiased investigation of the formation of different spin - orbital orderings emerging from all multi - electron configurations in the cluster . in this paper we concentrate on the stability and temperature dependence of spin , orbital , and charge ordered states in the two - dimensional ( 2d ) realistic model for half - doped manganites . in our microscopic spin - orbital model co develops as a result of nearest - neighbor coulomb repulsion @xmath13 and as a consequence of further neighbor jt interactions , while the spin - orbital order results from the competition between de ( i.e. kinetic energy ) , af superexchange and further neighbor jt interactions . as shown in sec . [ sec : nnnjt ] the latter interaction can lead to a co state at low temperatures even in the absence of inter - site coulomb repulsion . furthermore we argue that a topological sign in the hopping amplitudes of @xmath5 orbitals@xcite invoked in one - dimensional ( 1d ) models for the ce phase is not sufficient to explain the formation of ce spin - orbital structure in the 2d model studied by us . further motivations to put effort in a better understanding of the interplay of spin , charge , orbitals and lattice in the formation of the ce - phase are the following : it has been argued that the intrinsic mechanism that leads to colossal magnetoresistance are tendencies towards ce - type charge and orbital ordering in the vicinity of @xmath17.@xcite furthermore a ce - insulator to fm - metal transition has been observed in relatively small magnetic field , which is accompanied by a major change of the optical conductivity on a surprisingly large energy scale ( @xmath18 ev).@xcite such dramatic changes in relatively weak magnetic fields are a clear manifestation of the subtle interplay between spin , orbital and co. the present study provides a basis for further investigations of the temperature dependence of e.g. the optical conductivity and the study of spin and orbital excitations in the ce - phase , as well as the effect of doping into the quarter filled state . the paper is organized as follows . in sec . [ sec : model ] we present the model hamiltonian , and describe in sec . [ sec : lanczos ] the finite - temperature lanczos method . [ sec : numerics ] contains numerical results for different two - site correlation functions characterizing the charge , orbital and spin structure . these correlation functions are evaluated as functions of temperature and collected in a form of semi - quantitative phase diagrams in three different regimes : ( i ) including nearest - neighbor effective orbital - orbital ( oo ) interactions ( sec . [ sec : nnjt ] ) ; ( ii ) assuming the elastic form of oo coupling at different distances ( sec . [ sec : elastic ] ) ; ( iii ) considering the local form of next- and nearest - neighbor oo coupling ( sec . [ sec : nnnjt ] ) , while in sec . [ sec : stacking ] the effect of charge stacking is discussed . the paper is summarized in sec . [ sec : summary ] . in the appendix the stability of the ce versus the c phase is analysed for a 1d band model with lifted orbital degeneracy .

we have analyzed different correlation functions in a realistic spin - orbital model for half - doped manganites . using a finite - temperature diagonalization technique the ce phase was found in the charge - ordered phase in the case of small antiferromagnetic interactions between electrons . it is shown that a key ingredient responsible for stabilization of the ce - type spin and orbital - ordered state is the cooperative jahn - teller ( jt ) interaction between next - nearest mn neighbors mediated by the breathing mode distortion of mn octahedra and displacements of mn ions . the topological phase factor in the mn - mn hopping leading to gap formation in one - dimensional models for the ce phase as well as the nearest neighbor jt coupling

we have analyzed different correlation functions in a realistic spin - orbital model for half - doped manganites . using a finite - temperature diagonalization technique the ce phase was found in the charge - ordered phase in the case of small antiferromagnetic interactions between electrons . it is shown that a key ingredient responsible for stabilization of the ce - type spin and orbital - ordered state is the cooperative jahn - teller ( jt ) interaction between next - nearest mn neighbors mediated by the breathing mode distortion of mn octahedra and displacements of mn ions . the topological phase factor in the mn - mn hopping leading to gap formation in one - dimensional models for the ce phase as well as the nearest neighbor jt coupling are not able to produce the zigzag chains typical for the ce phase in our model .

astro-ph0311281

c

we have analysed all the available rxte data of between 1997 february and 2002 may and investigated its spectral and timing properties in correlation . this work has been motivated by recent reports that show that if large data sets are used , the atoll sources displaying the largest ampitude variations in intensity show three - branch patterns in the color - color diagram ( cd ) , reminiscent of z sources ( muno , remillard & chakrabarty 2002 ; gierliski & done 2002 ) . consequently , they conclude that the distinction between atoll and z sources might be no longer justified . the extended island state , island state and banana state of atoll sources would then correspond to the horizontal branch ( hb ) , normal branch ( nb ) and flaring branch ( fb ) , respectively . the results of these studies were based on the spectral properties ( i.e. color - color diagram ) only . in order to be able to distinguish between the different types of low - mass x - ray binaries the rapid aperiodic variability associated with the various spectral states needs to be addressed as well ( hasinger & van der klis 1989 ) , and that is what we have attempted in this paper . we first make a comparison of the timing properties of with those of other atoll sources and then discuss whether ot not it can be considered as a z source . 4u 160852 and are the atoll sources that display the largest dynamic range in x - ray intensity ( @xmath57 ) . thus a comparison between these two sources is of particular interest . 4u 160852 has been extensively studied by van straaten et al . ( 2003 ) . by comparing the shape of the power spectra ( see fig . 7 in van straaten et al . 2003 and our fig . [ pds ] ) and the results of the power spectral fits ( their table 2 and 3 and our table [ fitres ] ) one can find distinct similarities between the two sources : the power spectra of intervals a , b and c in 4u 160852 resemble those of the extreme island state of , while interval d of 4u 160852 is reminiscent of the island state in . likewise , the shape and number of lorentzians appearing in the power spectra of the extreme island state of are similar to those of the three low - luminosity x - ray bursters studied by belloni et al . ( 2002 ) . it is worth noting the relevant role of the hard color in connection with the timing properties of the extreme island state . in the characteristic frequencies of the timing features in the extreme island state increase from left to right this is opposite to what it is seen in 4u 1608 - 52 , where frequencies increase from right to left . however , in both sources the increase in frequencies occurs in correlation with an overall decrease in hard color . we therefore suggest that in the extreme island state it is the hard color , rather than the intensity , which is the main determining factor of the timing properties . we note , that black hole candidates are likewise characterized by power spectral states whose occurrence seems to primarily depend on spectral hardness and which are relatively insensitive to intensity , and which are associated with two - dimensional motion through the color - intensity plane rather than motion along a one - dimensional track ( homan et al . it may be that in the island and extreme island states , the states in which atoll sources are most similar to black holes ( e.g. , van der klis 1994a ; belloni , psaltis & van der klis 2002 ) , possibly because in these states the inner disk radius is furthest from the neutron star surface , this 2-d picture better describes neutron star behavior than the 1-d description appropriate to the banana state and to z sources . leaving aside the khz qpos , the overall shape of the banana - state power spectra of present similarities with those of other atoll sources , namely , a strong red - noise component , the very - low frequency noise ( vlfn ) below @xmath2 1 hz and a broad and a narrow components describing the band - limited noise ( bln ) in the frequency range 1100 hz . compared to 4u 0614 + 09 , 4u 1608 - 52 and 4u 172834 , exbibits the strongest vlfn but the weakest bln . while the vlfn is normally described by either a power law with index between 1.5 - 2.0 or a zero centered lorentzian in the other atoll sources , it requires the use of two model components in , similar to the case of gx 13 + 1 ( schnerr et al . 2003 ) . the broad band - limited noise component @xmath40 in and 4u 1608 - 52 , or equivalently the zero centred lorentzian in 4u 172834 and 4u 0614 + 09 have similar rms values . in contrast , @xmath25 , which is clearly detected in these other atoll sources , is not significant in in the banana state . gierliski & done ( 2002 ) suggested that the name atoll source is no longer appropiate as these type of low - mass x - ray binaries also display a three - branch pattern in the color - color diagram when large data sets of observations are used , reminiscent of the z pattern for which z sources are named . this effect is more pronounced in systems exhibiting large flux variations ( muno et al . 2002 ) , like . the cd of ( fig . [ ccd ] ) does indeed show a branch ( the island state ) that can be interpreted to connect the two main branches like in a z shape . in addition , the correlation between the characteristic frequency of the 120 hz broad lorentzian @xmath29 and the band - limited noise component ( fig . [ corr ] ) at low count rates , suggesting a common origin with the horizontal branch oscillations and lfn in z sources and the discovery of 714 hz qpo at the highest x - ray flux ( fig . [ qpo ] ) , reminiscent of the z - source normal / flaring branch oscillations , strengthen the similarities between and z sources . however , there are a number of systematic differences that clearly puts outside the group of z sources . first , there is the motion in the cd . in the extreme island state as the count rate increases the soft color increases and the hard color decreases . then the source makes a rapid transition to the banana state and proceeds to harder colors ( right ) as the count rate increases further . however , after the peak of the outburst , when the intensity decreases the source does not follow exactly the reverse path . as shown in fig . [ cdmotion ] , enters the banana state ( extreme island state ) at a higher ( lower ) value of the soft color than when it leaves it . the source moves clokcwise following a rectangle track . it should be pointed out that the entrance into the banana state at such high soft color is not caused by the time resolution used ( @xmath2 1 day ) in fig . [ cdmotion ] . a 256-s bin shows the same effect . however , we can not rule out an observational origin since the time gap between the transition from the extreme island state to the banana state is @xmath12 5 days for outburst 5 and @xmath12 2.6 for outburst 4 ( table [ timetran ] ) . if this is the case and the source entered the banana state from the left then the pattern that it would trace out in the cd would be that of an inverted triangle , much like 4u 170544 ( barret & olive 2002 ) . in contrast , the re - entrance into the extreme island state at a low soft color is probably not cause by the lack of data given the relatively short gap between the island state and the extreme island state ( just 1.6 days in outburst 5 ) . in either case this behavior is not that of z sources . in z sources , the nb is not a fast transition between the other two branches , and the source follows the same path whether it is going up or down along the nb . in this respect , is like the other two atoll sources that display high - amplitude flux variations . more detailed looks into the motion of 4u 160852 and 4u 170544 have revealed different topologies from the classical z - shaped track . the motion of 4u 160852 resembles the greek letter @xmath58 ( van straaten et al . 2003 ) and 4u 170544 describes an inverted triangle ( barret & olive 2002 ) . as noted above , these various topologies may simply be different aspects of 2-d motion through the color - intensity plane in which it is hard color that determines the timing properties . second , the amplitude of the x - ray luminosity change over the z track is also different . in the x - ray luminosity throughout the cd , i.e. , from the left of the banana state to the right of the extreme island state is about three orders of magnitude . in z sources , luminosity changes are typically less than a factor of 2 ( di salvo et al . 2000 , 2001 , 2002 ) . third , another difference is the velocity and time spent by the source in each spectral state . jonker et al . ( 2002 ) calculated that the z source gx 51 spent most of the time in the normal branch . in contrast , spends the smallest percentage of the the total observing time in the transition state ( the analogue to the normal branch would be a z source ) . wijnands et al . ( 1997 ) found that cyg x2 moves through the z most slowly on the hb , faster on the nb and fastest on the fb . during a typical x - ray outburst , i.e. , when is x - ray active , it spends most of its time in the banana branch ( the analogue to the flaring branch ) . finally , the properties of the aperiodic variability of also differ from those in z sources , especially at very low count rates . we can establish the following differences : * the very existence of the extreme island state . although the characteristic frequencies in increase along the extreme island state as the count rate increases as z sources do in the hb , the latter never reach the low frequencies that are seen in atoll sources in the extreme island state , even when at the left end of the hb . likewise , the rms amplitude of the noise components in the extreme island state is significantly higher than in a z source hb . the total rms amplitude of those components in amounts to @xmath59% , while typically in z sources , it does not go above @xmath60% . the extreme island - state power spectra are typical of atoll sources . * the peaked noise components , such as @xmath29 and the upper khz qpo are narrow qpos on the hb in z sources , with typical values of the q parameter above 3 for the upper khz qpo , whereas they are considerably broader peaked noise components in the extreme island state in ( q @xmath8 0.5 ) . * in , the normal / flaring branch - like oscillation does not occur during the `` normal / flaring branch '' , i.e. the island or the lower banana branches but in the upper banana branch , just like in other atoll sources . * the strength of the khz qpos decreases as the z source moves along the z track from hb to nb . typically , the khz qpos become undetectable by the time the source reaches the middle of the nb . in contrast , presents khz qpos in the island and banana states . * the time scales of the aperiodic variability tend to decrease ( frequencies increase ) as the z source moves along the fb , which is the opposite behavior to what is is observed in in the banana branch .

these states are respectively identified with the extreme island , island and banana states that characterize the atoll sources . the very - low frequency noise that characterizes the banana - state power spectra below 1 hz can not be described in terms of a single power law but a two - component model is required . in two outbursts a new 6 - 10 hz qpo has been discovered and tentatively identified with the normal / flaring branch - like oscillation observed only at the highest inferred mass accretion rates . we have compared the spectral and timing properties of with those of other atoll and z sources . our results argue against a unification scheme for these two types of neutron - star x - ray binaries .

we have analyzed five x - ray outbursts of the neutron - star soft x - ray transient and investigated the timing properties of the source in correlation with its spectral states as defined by different positions in the color - color and hardness - intensity diagrams . the hard color and the source count rate serve as the distinguishing parameters giving rise to three spectral states : a low - intensity hard state , an intermediate state and a high - intensity soft state . these states are respectively identified with the extreme island , island and banana states that characterize the atoll sources . the large amount of data analyzed allowed us to perform for the first time a detailed timing analysis of the extreme island state . differences in the aperiodic variability between the rise and the decay of the x - ray outbursts are found in this state : at the same place in the color - color diagram , during the rise the source exhibits more power at low frequencies ( 1 hz ) , whereas during the decay the source is more variable at high frequencies ( 100 hz ) . the very - low frequency noise that characterizes the banana - state power spectra below 1 hz can not be described in terms of a single power law but a two - component model is required . in two outbursts a new 6 - 10 hz qpo has been discovered and tentatively identified with the normal / flaring branch - like oscillation observed only at the highest inferred mass accretion rates . we have compared the spectral and timing properties of with those of other atoll and z sources . our results argue against a unification scheme for these two types of neutron - star x - ray binaries . # 1*#1 *

astro-ph0509182

i

a great deal of progress has been made in the last decade in the studies of distant galaxies . the average star formation history of the universe has also been estimated from emission properties of galaxies detected in deep imaging and redshift surveys such as the canada - france redshift survey and the hubble deep field ( e.g. , lilly et al . 1996 ; madau et al . 1996 , 1998 ) . a large population of bright galaxies with high star formation rates ( sfrs ) has been uncovered by means of the lyman - break technique ( e.g. , steidel et al . . however , such flux - limited studies may not be adequate for investigating the evolution of normal galaxies , since such studies are biased toward the brighter or the more actively star forming galaxies . in principle , a less biased sampling of distant galaxies may be obtained by means of the absorption lines they superpose in the radiation from background quasars . the presence of heavy - element absorption lines in quasar spectra preselects regions that have undergone some degree of star formation . there is nothing special about the lines of sight to the absorbers except for the convenient placement of background quasars , assuming that most of the absorbers are intergalactic material and not ejected material near the qso at high , special relativistic velocities . thus , it is very likely that these absorbers are surrounded by other galactic or protogalactic objects at the same redshifts . thus in principle , deep images of quasar absorber fields may reveal star - forming regions at high redshift . since a well - known signature of star forming galaxies is strong ly-@xmath0 or h-@xmath0 emission , a natural strategy to look for the absorber galaxies or their companions is to search for the redshifted emission lines . several previous studies have attempted to detect continuum and line emission from galaxies underlying quasar absorbers . at low redshifts , [ o ii ] or [ o iii ] emission has been detected in mg ii systems with narrow - band imaging ( e.g. , yanny 1990 ; yanny , york , & williams 1990 ; bergeron & boisse 1991 ; yanny & york 1992 ) . searches for low-@xmath9 damped lyman - alpha absorbers ( dlas ) have often imaged , and sometimes spectroscopically confirmed , galaxies with various morphologies ( spirals , irregulars , low surface brightness galaxies etc.e.g . , steidel et al . 1994 , 1995 ; lebrun et al . 1997 ; bowen et al . 2001 ; cohen 2001 ; turnshek et al . 2001 ) . at high redshifts , however , it has been much more difficult to identify and study in detail the galaxies responsible for quasar absorption systems . there have been a few detections of ly-@xmath0 emission in quasar absorber fields ( e.g. lowenthal et al . 1991 ; francis et al . 1996 ; roche , lowenthal , & woodgate 2000 ) . however , most other attempts to detect ly-@xmath0 emission from high-@xmath9 intervening ( @xmath10 ) dlas have produced either non - detections or weak detections ( e.g. smith et al . 1989 ; hunstead et al . 1990 ; lowenthal et al . 1995 ; djorgovski et al . most of the few confirmed ly-@xmath0 detections for high - redshift dlas have been for absorbers with @xmath11 , which may differ from the cosmologically more interesting general population of dlas with @xmath10 ( e.g. warren & moller 1996 ; moller & warren 1998 ; fynbo et al . 1999 ) . most attempts to detect dlas in h-@xmath0 have either yielded non - detections or detected objects separated by large angular distances from the quasars , rather than objects close to quasar sightlines ( see , e.g. , teplitz , malkan , & mclean 1998 ; bechtold et al . 1998 ; mannucci et al . 1998 , bunker et al . these objects , while unlikely to be the absorbing galaxies themselves , are still interesting because they are likely to be companion galaxies in the same cluster as the absorber . a summary of previous attempts to detect high-@xmath9 dlas in emission is given by kulkarni et al . ( 2000 ) . with the goal of obtaining a large sample of sfr estimates in the fields of high - redshift absorbers , we have started a lyman-@xmath0 imaging survey for absorbers at @xmath12 using a fabry - perot imager as a tunable narrow - band filter . here we report our results for six fields with known heavy - element absorption systems . sample selection , observations , and data reduction are described in section 2 . the reduced images and photometry are presented in section 3 . section 4 presents a comparison of our results with previous studies of the same fields and with results of other ly-@xmath0 emitter studies . section 4 also compares the sfr constraints from our study with the estimates from other emission - line searches for quasar absorber galaxies . a comparison with predictions based on global sfr models is also presented .

we compare our results with those from other emission - line studies of absorber fields and with predictions for global average sfr based on the models of cosmic chemical evolution . , these studies suggest that sfrs in a large fraction of objects in the absorber fields may lie below the global mean sfr . however , it is possible that dust attenuation is responsible for the low emission line fluxes in some objects .

we have carried out a deep narrow - band imaging survey of six fields with heavy - element quasar absorption lines , using the goddard fabry - perot ( fp ) system at the apache point observatory ( apo ) 3.5-meter telescope . the aim of these observations was to search for redshifted ly- emission from the galaxies underlying the absorbers at and their companion galaxies . the 3 sensitivity levels ranged between and erg s in observed - frame ly- flux . no significant ly- emitters were detected at level . the absence of significant ly- emission implies limits on the star formation rate ( sfr ) of 0.9 - 2.7 yr per 2-pixel x 2-pixel region , if no dust attenuation is assumed . we compare our results with those from other emission - line studies of absorber fields and with predictions for global average sfr based on the models of cosmic chemical evolution . our limits are among the tightest existing constraints on ly- emission from galaxies in absorber fields , but are consistent with many other studies . in the absence of dust attenuation , these studies suggest that sfrs in a large fraction of objects in the absorber fields may lie below the global mean sfr . however , it is possible that dust attenuation is responsible for the low emission line fluxes in some objects . it is also possible that the star - forming regions are compact and at smaller angular separations from the quasar than the width of our point spread function and , get lost in the quasar emission . we outline future observations that could help to distinguish between the various possibilities .

astro-ph0509182

r

figures 1(a)-6(a ) show @xmath38 sections of the reduced broad - band ( b ) images of the quasar absorber fields of q0216 + 080 , q0636 + 680 , q0956 + 123 , q1209 + 093 , q1442 + 101 , and q2233 + 131 , respectively . the corresponding panels ( b ) show the narrow - band images of the same fields obtained with the blue etalon . the stripes at the borders of some images are an artifact of the coadding of the dithered images . the quasar is absent or considerably dim in the narrow - band images for q0216 + 080 , q1209 + 093 , and q2233 + 131 since the absorbers being studied in these systems are dlas or sub - dlas . figure 7 shows the calibration field 53w002 . the expected b - band continuum must be subtracted from the observed narrow - band fluxes in order to determine if a statistically significant redshifted ly-@xmath0 excess exists for any object seen in both bands . we estimated the continuum in the narrow - band images by scaling the b images using the relative photometric calibrations of the two images . to do this , we subtracted a scaled b band image from the narrow - band image , aligning the images spatially , and adjusting the scaling factor so as to minimize variance in the central portion of the subtracted image . furthermore , to minimize the effect of different seeing in the broad - band and narrrow - band images , the broad and narrow - band images were convolved with a gaussian of the same fwhm before subtraction in idp3 . the subtraction was carried out interactively , using the interactive data language ( idl , version 6.1 ) program image display paradigm-3 ( idp-3 ) version 2.7 , written by d. lytle and e. stobie ( see , e.g. , lytle et al . 1999 ) figs . 1(c)-7(c ) show the resultant continuum - subtracted images for the six quasar absorber fields and the calibration field of 53w002 . finally , figs . 1(d)-7(d ) show @xmath39 close - up views of the continuum - subtracted images . all of the objects in the narrow - band images disappeared almost completely after subtraction of the continuum . the slight residuals left at the positions of some objects arise because of the difficulty in matching the point spread functions ( psfs ) perfectly in the broad and narrow - band images . no significant ly-@xmath0 emission at @xmath7 level was detected from any object in any of the quasar absorber fields . the few vis - b images obtained for three of the fields ( q0216 + 080 , q0636 + 680 , q2233 + 131 ) were also analyzed in a similar manner , and showed no ly-@xmath0 detections either . no significant objects were found even if the images were smoothed using gaussian filters of about 2.5 or 5 pixels fwhm . finally , we also compared our images with broad - band images from the sloan digital sky survey ( sdss ) where available . a few very faint features are seen in our images for q0216 + 080 , but these features are indistinguishable from the noise . in q0636 + 680 and q0956 + 123 , some residual flux is seen close to the quasar after continuum subtraction . however , these regions close to the quasars are not well sampled at our modest angular resolution . thus , it is not clear whether the residuals seen near q0636 + 680 and q0956 + 123 are significant features or artifacts , without obtaining higher resolution images of these fields . in the case of q0956 + 123 , the feature apparent near the left upper corner of fig . 3(d ) is an artifact arising from a residual multipixel cosmic ray event in a single narrow - band image . in the field of q2233 + 131 , three bright galaxies are seen : 17.4@xmath28 east and 1.7@xmath28 south of the quasar ; 28.2@xmath28 east and 51.7@xmath28 south of the quasar ; and 35.2@xmath28 east , 30.2@xmath28 north of the quasar ( fig . all of these galaxies are seen in the sdss . however , all of these galaxies are far too bright to be at @xmath40 ( @xmath41 respectively from sdss ) . it is more likely that the excess emission seen in these objects is [ o ii ] @xmath42 emission from interloper galaxies at @xmath43 . we plan to obtain spectra of these galaxies in the near future to determine their redshifts . to estimate the limits on the ly-@xmath0 fluxes for the absorbers in our fields , we used our calibration observations of the field of the radio galaxy 53w002 . this field is known to have ly-@xmath0 emitters at @xmath44 ( pascarelle et al . 1996a , 1996b ; keel et al . 1999 ) . for calibration purposes , we used the brightest objects seen in our continuum - subtracted narrow - band images of this field , i.e. , objects 3 and 1 of keel et al . ( 1999 ; table 2 ) , labeled o1 and o2 in the bottom panel of figure 7 . aperture photometry of these two objects was carried out using the iraf task phot with aperture sizes @xmath45 times the seeing fwhm . using the ly-@xmath0 fluxes for these from table 2 of keel et al . ( 1999 ) and the counts measured for those objects in our images , we estimated the photometric calibration of our images . to correct for sensitivity differences at the different wavelengths used for our quasar absorbers and the calibration field 53w002 , we used our observations of standard star hz44 . using the photometry of this star in images obtained at the different wavelength settings , and adopting the absolute spectral distribution of this star from oke ( 1990 ) , we estimated the relative sensitivity differences of the fp at the different wavelengths . we next estimated the noise level in the continuum - subtracted blue - etalon images for each field . to do this , we considered a @xmath46 region centered on the quasar and determined the noise profile over this region using idp-3 . while doing this , we disregarded a circular region centered on the quasar with a radius of roughly twice the seeing fwhm to avoid effects of imperfect seeing matches between the broad and narrow band images . we then measured the mean noise level per pixel in concentric annuli of radii ranging from 2 times the seeing to 5 @xmath28 , and finally corrected for the sensitivity differences at the various wavelengths . the noise level per pixel was found to be nearly constant everywhere ( within a few @xmath47 ) in this region . the mean value of the noise per pixel was used to estimate the noise level per 2 pixel x 2 pixel region , assuming poisson statistics . based on this , we estimated the 3 @xmath2 observed - frame ly-@xmath0 point source flux sensitivity reached in our images . if dust attenuation is assumed to be small , these ly-@xmath0 flux limits can be converted to limits on the star formation rates ( sfrs ) . these point - source sfr limits implied by the non - detections of ly-@xmath0 emission in our quasar absorber fields are listed in table 3 and are in the range of 0.9 - 2.7 m@xmath48 yr@xmath5 . here , we have used the prescription of kennicutt ( 1998 ) for converting h-@xmath0 luminosity @xmath49 to the sfr , i.e. , @xmath50 and assumed a ratio @xmath51 for case - b recombination . we also used our continuum - subtracted images to estimate the flux limits for a diffuse foreground absorbing galaxy . to do this , we used the mean value of the noise per pixel to estimate the flux limit over the entire 10 @xmath52 region . this flux limit was used to calculate the limiting ly-@xmath0 luminosity and hence the limiting sfr in the @xmath53 region . at @xmath54 , this region corresponds to a size of @xmath55 kpc@xmath56 centered on the quasar , for the comsology adopted here . the diffuse - source flux limits are in the range of 2.6 - 7.4 @xmath57 erg s@xmath5 @xmath6 summed over the @xmath53 region . the corresponding summed sfr limits are in the range of 12.3 - 36.4 m@xmath48 yr@xmath5 over the entire @xmath53 region .

the 3 sensitivity levels ranged between and erg s in observed - frame ly- flux . no significant ly- emitters were detected at level . the absence of significant ly- emission implies limits on the star formation rate ( sfr ) of 0.9 - 2.7 yr per 2-pixel x 2-pixel region , if no dust attenuation is assumed . our limits are among the tightest existing constraints on ly- emission from galaxies in absorber fields , but are consistent with many other studies . in the absence of dust attenuation we outline future observations that could help to distinguish between the various possibilities .

we have carried out a deep narrow - band imaging survey of six fields with heavy - element quasar absorption lines , using the goddard fabry - perot ( fp ) system at the apache point observatory ( apo ) 3.5-meter telescope . the aim of these observations was to search for redshifted ly- emission from the galaxies underlying the absorbers at and their companion galaxies . the 3 sensitivity levels ranged between and erg s in observed - frame ly- flux . no significant ly- emitters were detected at level . the absence of significant ly- emission implies limits on the star formation rate ( sfr ) of 0.9 - 2.7 yr per 2-pixel x 2-pixel region , if no dust attenuation is assumed . we compare our results with those from other emission - line studies of absorber fields and with predictions for global average sfr based on the models of cosmic chemical evolution . our limits are among the tightest existing constraints on ly- emission from galaxies in absorber fields , but are consistent with many other studies . in the absence of dust attenuation , these studies suggest that sfrs in a large fraction of objects in the absorber fields may lie below the global mean sfr . however , it is possible that dust attenuation is responsible for the low emission line fluxes in some objects . it is also possible that the star - forming regions are compact and at smaller angular separations from the quasar than the width of our point spread function and , get lost in the quasar emission . we outline future observations that could help to distinguish between the various possibilities .

astro-ph0509182

c

for most of our targets , no other imaging information exists in any waveband on a scale comparable to our fields of view . for q0216 + 080 and q2233 + 131 , hst nicmos h - band images are available ( warren et al . the nicmos images of q0216 + 080 show two objects with @xmath58 and 24.34 , located 1.4@xmath28 and 3.8@xmath28 away from the quasar , at position angles of -104.8 and 97.8 degrees east of north , respectively . however , the closer object is likely to be an artifact since it occurs on a diffraction spike . for q2233 + 131 , the nicmos h - band image revealed two objects with @xmath59 and 25.12 , located 2.8@xmath28 and 3.3@xmath28 away from the quasar , at position angles of 158.6 and 68.3 degrees east of north , respectively . of these , the former object has been identified with a lyman limit system at @xmath60 ( djorgovski et al . none of these objects are seen in our b - band or nb images . this could be because of the difference in angular resolutions of our study and the nicmos study . in either case , no information on star - forming emission - line objects is available from these broad - band images . the only additional emission - line constraints available are for q0216 + 080 and q2233 + 131 . the narrow - band imaging study of deharveng et al . ( 1990 ) found no ly-@xmath0 emitters in the q0216 + 080 field , placing a 3 @xmath2 upper limit of @xmath61 erg s@xmath5 @xmath6 on the ly-@xmath0 emission flux . our observations of this field have provided a ly-@xmath0 flux limit @xmath62 times tighter than that of deharveng et al . ( 1990 ) . for q2233 + 131 , our limit agrees closely ( within @xmath63 ) with that of lowenthal et al . ( 1995 ) . [ [ the - space - density - of - ly - alpha - emitters - comparison - with - other - studies ] ] the space density of ly-@xmath0 emitters : comparison with other studies ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ to understand whether the non - detections of ly-@xmath0 emitters ( laes ) in our fields are consistent with other surveys for ly-@xmath0 emitters , we now examine results from some recent lae searches . stiavelli et al . ( 2001 ) detected 58 lae candidates over a field of 1200 arcmin@xmath56 at @xmath64 . based on this , they deduced a completeness - corrected space density of 0.07 laes per arcmin@xmath56 with ly-@xmath0 fluxes above @xmath65 erg @xmath6 s@xmath5 . palunas et al . ( 2004 ) detected 37 absorbers in a 46 @xmath66 46 field of view . based on this , they derived the space density of laes to be 0.019 arcmin@xmath67 in a redshift interval @xmath68 at @xmath69 . these ( stiavelli et al . 2001 , palunas et al . 2004 ) studies imply 0.49 and 0.42 laes per arcmin@xmath56 per unit redshift , respectively . at @xmath70 , lae searches by rhoads et al . ( 2000 ) and malhotra & rhoads ( 2002 ) have found space densities of 4000 deg@xmath67 per unit redshift , i.e. 1.1 lae per arcmin@xmath56 per unit redshift . these other lae searches cover much wider fields of view , and larger redshift ranges @xmath71 ( wider filter bandwidths ) than our study . adopting a mean space density of 0.45 laes per arcmin@xmath56 per unit redshift at @xmath72 from stiavelli et al . ( 2001 ) and palunas et al . ( 2004 ) , and using @xmath73 as a typical redshift range covered by our study , one would expect @xmath74 absorber in our fields with effective monochromatic coverage of @xmath75 , if our fields were similar to the other lae fields . on the other hand , the lae searches of rhoads et al . ( 2000 ) , stiavelli et al . ( 2001 ) , and malhotra & rhoads ( 2002 ) are not selected by the presence of a quasar absorption system . the presence of a well - established heavy - element quasar absorber with mixed ionization implies the existence of a region that has had some star formation . at @xmath69 , our complete fields of view of about 3.4 diameter cover about 2.2 mpc@xmath56 around the absorbing sightline ( assuming @xmath76 , @xmath77 , and @xmath78 km s@xmath5 mpc@xmath5 ) . given the gradient in the central wavelength , the roughly monochromatic ( within @xmath32 km s@xmath5 of the absorber ) fields of view of about 2.1 diameter cover about 0.8 mpc@xmath56 around the quasar sightline . since the absorbing galaxy certainly must lie within this region , one might expect a higher lae density in our fields than that in a blind field . francis et al . ( 1996 , 2004 ) and palunas et al . ( 2004 ) did indeed find a number of laes in wide - field surveys surrounding a field with 3 sub - dlas . however , this region appears to be a filament with higher density than a typical field region . furthermore , the laes in this filament are separated from 2 of the 3 absorber sightlines by more than 2 in radius ( see fig . 4 of palunas et al . such objects would thus not be detectable in a field of view such as ours . thus , overall , the lack of laes in our observations are not inconsistent with the space density of laes found by other studies . we note , however , that detailed comparisons would require a full consideration of the luminosity function of laes since our observations reach fainter flux limits than many of the other lae searches . [ [ the - star - formation - rates - of - quasar - absorbers - and - their - companions ] ] the star formation rates of quasar absorbers and their companions ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ fig . 8 plots our sfr limits in the fields of quasar absorbers together with the results of other searches for ly-@xmath0 , h-@xmath0 , h-@xmath79 , [ o ii ] , and [ o iii ] emission in quasar absorber fields . the filled red triangles show our apo ly-@xmath0 limits , while the unfilled black triangles at @xmath80 show our limits from previous h-@xmath0 imaging with hst / nicmos ( kulkarni et al . 2000 , 2001 ) . other data are from yanny et al . ( 1987 ) ; yanny , york , & williams ( 1990 ) ; yanny ( 1990 ) ; hunstead et al . ( 1990 ) ; deharveng et al . ( 1990 , 1995 ) ; giavalisco et al . ( 1994 ) ; lowenthal et al . ( 1995 ) ; francis et al . ( 1996 ) ; warren & mller ( 1996 ) ; bergvall et al . ( 1997 ) ; mannucci et al . ( 1998 ) ; teplitz et al . ( 1998 ) ; bunker et al . ( 1999 ) ; fynbo et al . ( 1999 , 2000 ) ; bouche et al . ( 2001 ) ; van der werf et al . ( 2000 ) ; mller et al . ( 2002 ) ; meyer , thompson , & mannucci ( 2003 ) ; mller , fynbo , & fall ( 2004 ) ; christensen et al . ( 2004 , 2005 ) ; schulte - ladbeck et al . ( 2004 ) ; chen , kennicutt , & rauch ( 2005 ) ; and weatherley et al . ( 2005 ) . in total , we have plotted 71 detections and 30 upper limits in fig . we note , however , that many of the emission line detections are for candidates that have not yet been confirmed with spectroscopy or multiple narrow - band imaging . for the few objects where multiple emission lines have been detected , we have plotted the values from h-@xmath0 , h-@xmath79 , or [ o ii ] , in that order of preference . all the shown candidate detections and 3 @xmath2 upper limits have been normalized to @xmath76 , @xmath77 , and @xmath78 km s@xmath5 mpc@xmath5 . once again , the prescription of kennicutt ( 1998 ) has been used for the conversion from the h-@xmath0 luminosity @xmath49 to the sfr , and a ratio @xmath51 for case - b recombination has been assumed . no correction has been made for dust attenuation , but we examine this issue in more detail below . our apo fp constraints are among the lowest , but are clearly consistent with many other measurements . the open inverted triangles at @xmath81 are based on spectroscopic ( slit ) observations of h-@xmath0 . the unfilled circles are candidate objects with h-@xmath0 emission detected at the absorber redshift , but are often more than @xmath82 away from the quasar , and have a lower precision in redshift . the curves in fig . 8 are useful for comparing the data with global predictions based on the luminosity density of galaxies from the deep galaxy imaging surveys . since most of the data in fig . 8 are for objects in dla fields , we show the calculations of bunker et al . ( 1999 ) for the predicted cross - section - weighted sfr in dlas . these models use two alternative sets of assumptions about the number of absorbers per unit redshift and the distribution of global sfr among individual absorbers at a given redshift . the thick and thin solid curves show the ld5 and ld0 `` large disk '' calculations ( for @xmath83 and @xmath84 respectively ) , of bunker et al . based on the closed - box pei & fall ( 1995 ) models . the ld models assume that dlas are the progenitors of spiral galaxies , with space density equal to that of local spirals , but with size and sfr of each dla larger in the past compared to that of a local spiral . the dashed curve shows the h5 and h0 predictions of bunker et al . ( 1999 ) ( for @xmath83 and @xmath84 respectively ) for the `` hierarchical '' hypothesis , which assumes that there were multiple dlas at high redshift corresponding to every present - day spiral ( i.e. that dlas were sub - galactic fragments that later merged to form present - day spirals ) . thus in the h5 and h0 models , dlas have the same distribution of gas cross - section sizes as in local spirals , but with a higher space density in the past , and have smaller sfrs than in the corresponding `` large - disk '' models . the ld curve , if computed for @xmath76 , @xmath77 , and @xmath78 km s@xmath5 mpc@xmath5 , would lie between the ld5 and ld0 curves , since the distance and time scales for the former cosmology are intermediate between those for @xmath85 and @xmath86 . this can also be seen by comparing the comoving global sfr predicted by the pei & fall ( 1995 ) closed - box models for @xmath83 and @xmath84 , with that predicted by the @xmath87-cold dark matter ( @xmath87-cdm ) hydrodynamical simulations of nagamine , cen , & ostriker ( 2000 ) . thus , a large fraction of the observed sfrs would appear to fall significantly below the prediction of the large - disk scenario . the h curve for this @xmath87-cdm cosmology would be identical to the h5 and h0 curves ( since the latter curves coincide with each other ) . a large fraction of the data points in fig . 8 thus appear to be more consistent with the hierarchical scenario , suggesting perhaps that many absorbers or their companion galaxies may be arising in star - forming dwarf galaxies or sub - galactic fragments that merged later to form present - day galaxies . however , several detections and upper limits , including our fp limits , appear to be considerably below even the hierarchical prediction . indeed , about 63@xmath88 of the detections and about 73@xmath88 of the limits plotted in fig . 8 are less than 5 @xmath8 yr@xmath5 . such large local deviations for the absorber fields from the global mean would be surprising . taken at face value , fig . 8 suggests that the absorption - based view of the cosmic star formation history could be quite different from the emission - based view , i.e. , from the star formation history inferred on the basis of the direct galaxy imaging surveys such as the hubble deep field . low sfrs for galaxies in absorber fields would also be consistent with the low global metallicities found in dlas ( e.g. , kulkarni et al . 2005 and references therein ) . similar suggestions have also been made by wolfe et al . ( 2003 ) , who inferred relatively high sfr values for some dlas based on c ii * absorption , but found the high sfrs to be inconsistent with the low metallicities observed in the dlas . we note , however , that while the c ii * method may potentially offer an interesting way to estimate sfrs in dlas , it seems less direct and more model - dependent than the emission - line based constraints . there are also other possible interpretations of fig 8 . it is possible that the true sfrs in galaxies in the absorber fields are higher , but their emission lines , especially ly-@xmath0 , are attenuated by dust . it is well known that resonance scattering of ly-@xmath0 , in the presence of dust , can lead to quenching of the lyman-@xmath0 emission in high-@xmath89 systems ( e.g. , charlot & fall 1991 ) . presence of dust in some ly-@xmath0 emitting regions is also suggested from the recent detection of 24 @xmath18 m emission in spitzer space telescope images of laes at @xmath72 in an absorber field ( colbert et al . on the other hand , there are several reasons to expect that ly-@xmath0 emission may still be seen from absorbers and their companion galaxies , in at least some cases . first , the very knowledge of a dla means that the quasar in which it appears is not greatly affected by dust attenuation . ly-@xmath0 is easily seen from regions of such low extinction . second , the dust - to - gas ratios in dlas inferred from relative abundances such as [ cr / zn ] or [ fe / zn ] are much smaller than in the milky way ( e.g. , pettini et al . 1997 ; khare et al . 2004 ; and references therein ) . in a recent study of a large number of sdss quasar spectra , we have recently found evidence for a statistically significant but small amount of dust in quasar absorbers ( york et al . finally , there are several examples of high-@xmath9 ly-@xmath0 emitters with very little dust attenuation ( e.g. , giavalisco et al . 1994 ; francis et al . 1996 ; hu , cowie , & mcmahon 1998 ; kudritzki et al . 2000 ) . the effect of dust attenuation is expected to be much less severe in the h-@xmath0 line . indeed , the sfr constraints based on h-@xmath0 detections in most high-@xmath9 dla candidates or companions shown in fig 8 are considerably higher than the constraints from the ly-@xmath0 emission searches . considering detections alone , the median sfrs from h-@xmath0 , ly-@xmath0 , and [ oii ] are 35.9 , 3.2 , and 0.3 @xmath8 yr@xmath5 , respectively . if both detections and limits are considered , the median sfrs from h-@xmath0 , ly-@xmath0 , and [ oii ] are 28.2 , 2.4 , and 0.3 @xmath8 yr@xmath5 treating the limits as detections , and 18.8 , 0.1 , and 0.3 @xmath8 yr@xmath5 treating the limits as zeros . it is tempting to think that the difference between the median h-@xmath0 and ly-@xmath0 values could be partly caused by dust extinction . however , it is not clear whether this is a significant effect , since ly-@xmath0 measurements ( candidates or limits ) are not available for most of the h-@xmath0 candidates . in the few objects that show detections of multiple emission lines , the sfr estimates from the available lines are usually consistent within a factor of @xmath90 . also , some of the h-@xmath0 candidates are at large angular separations from the quasars and have less accurate redshifts . thus , there is no clear indication that ly-@xmath0 in the h-@xmath0 candidates is attenuated by dust . in any case , dust alone may not explain low ly-@xmath0 emission in every individual case , because the extent of ly-@xmath0 attenuation also depends on several other factors , such as the orientation , the topology of the h ii region , and the distribution of stars , gas and dust within the absorber . finally , dust attenuation can not explain why nearly all of the sfrs inferred from [ o ii ] and @xmath91 of the sfrs inferred from h-@xmath0 are low . another possibility is that the star - forming regions in the absorber galaxies are compact , lie directly in front of the quasars , and hence get lost in the quasar point spread function ( psf ) in our study and other ground - based studies so far . for example , if the absorbing galaxies had star - forming cores comparable in size to those in the lyman - break galaxies [ typically @xmath92 kpc ] aligned perfectly in front of the quasars , it would not be possible to resolve them with studies such as our own ( and most other ground - based studies used in fig . in other words , the sfr constraints derived from such studies may be more appropriate for the companion galaxies of the absorbers , rather than the absorbers themselves . it is difficult to rule out this possibility without high - resolution imaging data . however , the chance of having the star forming region exactly in front of the quasar in _ each _ case is small . indeed , the absence of emission within the ly-@xmath0 absorption profiles in the published spectra for most dlas ( including those from our study ) suggests that they do not have star - forming regions perfectly aligned with the background quasars . even if the absorber galaxies themselves were small , they are unlikely to be isolated objects , since such small galaxies are expected to occur as companions to larger galaxies within a few hundred kpc . in any case , it would still be surprising why the few existing high - resolution imaging studies of absorber galaxies have often failed to detect h-@xmath0 emission or found relatively weak ly-@xmath0 emission ( e.g. , bouche et al . 2001 ; kulkarni et al . 2000 , 2001 ; mller et al . 2002 ) . future narrow - band imaging studies of more high - redshift quasar absorber fields would help to understand whether the low ly-@xmath0 fluxes we find are representative of the absorber galaxies . furthermore , more narrow - band imaging or spectroscopic studies in the near - infrared will give access to the h-@xmath0 emission line from the @xmath93 absorbers . a systematic comparison of the h-@xmath0 and ly-@xmath0 data for the same absorbers can help to understand whether the emission lines in the galaxies in absorber fields are simply attenuated by dust , or whether these galaxies truly have low sfrs . it will thus be interesting to look at ly-@xmath0 emission from the objects reported to show strong h-@xmath0 emission , and to look at h-@xmath0 near the quasars for which we have limits on ly-@xmath0 . finally , more high - resolution narrow - band imaging and/or spectroscopic studies would be especially important to understand whether the star formation in the absorber galaxies is restricted to compact regions . this paper is based on observations obtained with the apache point observatory 3.5-meter telescope , which is owned and operated by the astrophysical research consortium . we thank jonathan brinkmann for assistance with the fabry - perot setup and calibration at the apo . we also thank andrew bunker for helpful discussion and betty stobie for providing and assisting with the idp-3 package . finally , we are grateful to an anonymous referee whose comments helped to improve this paper . vpk , dgt , and jm acknowledge support from the national science foundation grant ast-0206197 and from the university of south carolina research foundation . bechtold , j. , elston , r. , yee , h. k. c. , ellingson , e. , & cutri , r. m. 1998 , in ` the young universe : galaxy formation and evolution at intermediate and high redshift ' , ed . s. dodorico , a. fontana , and e. giallongo , asp conf . series , ( pasp ) , 146 , 241 _ * fig . 1 * apo images of the field of q0216 + 080 . ( a ) @xmath95 b - band image ( top left ) ; ( b ) @xmath95 narrow - band image before continuum subtraction ( top right ) ; ( c ) @xmath95 narrow - band image after continuum subtraction ( bottom left ) ; and ( d ) @xmath39 narrow - band image after continuum subtraction ( bottom right ) . see attached gif images . _ _ measurements of star formation rates ( in @xmath8 yr@xmath5 ) for candidate objects in quasar absorber fields , from narrow - band imaging and spectroscopic searches for ly-@xmath0 , h-@xmath0 , h-@xmath79 , [ o ii ] and [ o iii ] emission lines . data points are from our apo ly-@xmath0 survey ( this work ) , our previous nicmos h-@xmath0 imaging ( kulkarni et al . 2000 , 2001 ) , and other literature ( see text ) . most of the higher values are based on candidate h-@xmath0 emitters , often located far from the quasar lines of sight . the thick solid ( upper ) and thin solid ( middle ) curves show , respectively , the calculations of bunker et al . ( 1999 ) for the predicted cross - section - weighted sfr in the large - disk scenario for @xmath83 and @xmath84 . the dashed curve shows the calculations of bunker et al . ( 1999 ) for the hierarchical scenario for @xmath83 and @xmath84 . all of these curves are based on the closed - box global sfr models of pei & fall ( 1995 ) . _ llllllr qso & r.a.(j2000 ) & dec.(j2000 ) & @xmath96 & @xmath97 & known ions & @xmath98 + & & & & & & ( ) + q0216 + 080&02:18:57.3 & + 08:17:28.0&2.9957&2.2931&civ , aliii , alii,& ... @xmath99 + & & & & & siii , feii ; dla + q0636 + 680&06:42:04.3 & + 67:58:35.6 & 3.1775&2.3112&civ , cii , alii & ... + q0956 + 123&09:58:52.3 & + 12:02:43.2 & 3.306&2.3104&civ , siiv , alii&1.42 + q1209 + 093&12:11:34.9 & + 09:02:22.8 & 3.297&2.5822&civ , alii , feii;&21.2 + & & & & & dla + q1442 + 101&14:45:16.5 & + 09:58:36.2 & 3.535&2.5632&ovi , civ , siiv , & 1.40 + & & & & & ciii , siiii , siii , oi + q2233 + 131&22:36:19.2&+13:26:20.0&3.2978&2.5537&civ , cii , siiv , siiii,&5.35 + & & & & & siii , oi ; sub - dla + 53w002&17:14:14.7&+50:15:29.7 & ... & ... & ... & ... + ( calibration & ... & ... & ... & ... & ... & ... + field ) & ... & ... & ... & ... & ... & ... + q0216 + 080 & 2001/11/10&05:55:28.87&1.111&blue&4050/160&4002.2&2400&14.69 + ... & 2001/11/10&06:36:18.15&1.111&blue&4050/160&4002.2&1200 & + ... & 2001/11/11&05:42:48.66&1.102&blue&4050/160&4002.2&2400 & + ... & 2001/11/11&06:52:30.75&1.125&blue&4050/160&4002.2&1660 & + ... & 2001/11/12&05:20:37.43&1.111&blue&4050/160&4001.3&2400 & + ... & 2001/11/12&06:05:54.94&1.100&blue&4050/160&4001.3&2400 & + ... & 2001/12/15&03:17:36.77&1.107&blue&4050/160&4002.2&2400 & + ... & 2001/12/15&04:00:38.97&1.101&blue&4050/160&4002.2&2400 & + ... & 2001/12/15&04:50:23.34&1.139&blue&4050/160&4002.2&2400 & + ... & 2001/12/15&05:32:31.49&1.216&blue&4050/160&4002.2&2400 & + ... & 2002/11/03&06:59:28.92 & 1.106 & vis - b & 4050/160&4008.0 & 2400 & + ... & 2002/11/03&07:52:40.87&1.163&vis - b&4050/160&4008.0 & 2400 & + ... & 2002/11/08&07:42:27.53&1.180&vis - b&4050/160&4008.0 & 1800 & + & & & & & & & + ... & 2000/10/26&05:23:00.92&1.201& ... &b&4400&480 & + ... & 2000/10/26&05:32:58.88&1.180& ... &b&4400&480 & + ... & 2000/10/26&05:42:02.58&1.164& ... &b&4400&480 & + ... & 2000/10/26&05:51:06.28&1.150& ... &b&4400&480 & + ... & 2000/10/26&06:00:28.58&1.137& ... &b&4400&480 & + ... & 2001/12/15&01:21:29.11&1.338& ... &b&4400&300 & + ... & 2001/12/15&01:27:45.25&1.314& ... &b&4400&300 & + ... & 2001/12/15&01:34:03.80&1.292& ... &b&4400&300 & + ... & 2001/12/15&01:40:22.75&1.272& ... &b&4400&300 & + ... & 2001/12/15&01:46:35.10&1.254& ... &b&4400&300 & + & & & & & & & + & & & & & & & + q0636 + 680 & 2000/10/26&10:51:55.81&1.229&blue&4050/160&4024&2400&14.66 + ... & 2000/10/26&11:33:12.48&1.224&blue&4050/160&4024&2400 & + ... & 2001/02/22&03:20:22.82&1.225&blue&4050/160&4024.3&2400 & + ... & 2001/02/22&04:18:32.24&1.232&blue&4050/160&4024.3&2400 & + ... & 2001/02/22&05:06:11.28&1.260&blue&4050/160&4024.3&2400 & + ... & 2001/12/15&07:15:20.01&1.236&blue&4050/160&4024.2&2400 & + ... & 2001/12/15&07:56:38.23&1.224&blue&4050/160&4024.2&2400 & + ... & 2001/12/15&08:39:13.21&1.228&blue&4050/160&4024.2&2400 & + ... & 2001/12/15&09:27:39.32&1.252&blue&4050/160&4024.2&2400 & + ... & 2002/03/12&02:56:26.66&1.228&blue&4050/160&4024.2&2400 & + ... & 2002/03/12&03:38:47.01&1.247&blue&4050/160&4024.2&2400 & + ... & 2002/11/03&10:45:35.05&1.224&vis - b&4050/160&4030.0&2400 & + ... & 2002/11/03&11:29:28.69&1.229&vis - b&4050/160&4030.0&2400 & + ... & 2002/11/05&09:44:12.32&1.242&vis - b&4050/160&4030.0&2400 & + & & & & & & & + ... & 2000/10/26&10:07:53.96&1.251& ... &b&4400&480 & + ... & 2000/10/26&10:17:24.49&1.244& ... &b&4400&480 & + ... & 2000/10/26&10:26:39.20&1.239& ... &b&4400&480 & + ... & 2000/10/26&10:35:43.11&1.235& ... &b&4400&480 & + ... & 2001/02/25&05:16:15.67&1.281& ... &b&4400&300 & + ... & 2001/02/25&05:22:41.63&1.288& ... &b&4400&300 & + ... & 2001/02/25&05:29:27.60&1.296& ... &b&4400&300 & + & & & & & & & + & & & & & & & + q0956 + 123&2001/02/22&06:23:39.98&1.077 & blue&4050/160 & 4023.3&2400&14.79 + ... & 2001/02/22&07:24:08.73&1.078&blue&4050/160 & 4023.3&2400 & + ... & 2001/02/22&08:16:52.25&1.135&blue&4050/160 & 4023.3&2400 & + ... & 2001/02/22&09:24:17.19&1.312&blue&4050/160 & 4023.3&2400 & + ... & 2001/02/25&08:38:17.40&1.204&blue&4050/160&4023.4&2400 & + ... & 2001/05/22&03:18:47.08&1.258&blue&4050/160&4023.3&2400 & + ... & 2002/03/12&05:13:05.87&1.078&blue&4050/160&4023.2&2400 & + ... & 2002/03/12&05:55:28.03&1.071&blue&4050/160&4023.2&2400 & + ... & 2002/03/12&06:44:56.70&1.104&blue&4050/160&4023.2&2400 & + & & & & & & & + ... & 2001/02/25&06:10:45.09&1.078& ... &b&4400&300 & + ... & 2001/02/25&06:17:40.16&1.074& ... &b&4400&300 & + ... & 2001/02/25&06:24:01.83&1.072& ... &b&4400&300 & + ... & 2001/02/25&06:30:58.02&1.070& ... &b&4400&300 & + ... & 2001/02/25&06:37:32.38&1.069& ... &b&4400&300 & + ... & 2001/02/25&06:49:41.66&1.069& ... &b&4400&300 & + ... & 2001/02/25&07:06:17.69&1.074& ... &b&4400&300 & + ... & 2001/02/25&07:12:54.06&1.078& ... &b&4400&300 & + & & & & & & & + & & & & & & & + q1209 + 093 & 2001/05/20&04:42:28.87&1.154&blue&4300/135&4353.6&2400&7.01 + ... & 2001/05/20&05:28:37.23&1.260&blue & 4300/135 & 4353.6&2400 & + ... & 2001/05/22&05:11:26.45&1.233&blue & 4300/135&4353.5&2400 & + ... & 2001/05/23&03:41:53.18&1.101&blue & 4300/135&4353.7&2400 & + ... & 2001/05/23&04:24:29.14&1.145&blue & 4300/135&4353.6&2400 & + ... & 2002/03/11&08:52:16.27&1.119&blue & 4300/135&4353.5&2400 & + ... & 2002/03/12&08:25:38.11&1.101&blue&4300/135&4353.5&2400 & + ... & 2002/03/12&09:17:40.82&1.159&blue&4300/135&4353.5&2400 & + & & & & & & & + ... & 2001/05/23&05:22:34.56&1.277& ... &b&4400&300 & + ... & 2001/05/23&05:37:57.81&1.332& ... &b&4400&300 & + ... & 2001/05/23&05:44:12.36&1.357& ... &b&4400&300 & + ... & 2001/05/23&05:50:36.43&1.384& ... &b&4400&300 & + ... & 2001/05/23&05:56:55.87&1.413& ... &b&4400&300 & + ... & 2001/05/23&06:03:07.01&1.444& ... &b&4400&300 & + ... & 2001/05/23&06:09:17.35&1.477& ... &b&4400&300 & + ... & 2001/05/23&06:15:38.11&1.514& ... &b&4400&300 & + & & & & & & & + q1442 + 101&2001/05/20&07:29:32.74&1.170&blue&4300/135&4330.5&2400&6.10 + ... & 2001/05/20&08:17:28.39&1.299&blue&4300/135&4330.4&2400 & + ... & 2001/05/21&06:37:53.56&1.104&blue&4300/135&4330.6&2400 & + ... & 2001/05/21&07:27:17.70&1.174&blue&4300/135&4330.5&2400 & + ... & 2001/05/21&08:09:09.42&1.284&blue&4300/135&4330.4&2400 & + ... & 2001/05/22&06:15:29.60&1.091&blue&4300/135&4330.5&2400 & + ... & 2001/05/22&06:57:37.14&1.130&blue&4300/135&4330.5&2400 & + ... & 2001/05/23&06:51:26.89&1.127&blue&4300/135&4330.5&2400 & + ... & 2001/05/23&07:33:07.00&1.204&blue&4300/135&4330.5&2400 & + & & & & & & & + ... & 2001/02/25&10:03:28.53&1.153& ... &b&4400&300 & + ... & 2001/02/25&10:10:44.33&1.141& ... &b&4400 & 300 & + ... & 2001/02/25&10:18:19.75&1.130& ... &b&4400&300 & + ... & 2001/02/25&10:26:38.82&1.120& ... &b&4400&300 & + ... & 2001/02/25&11:21:21.65&1.085& ... &b&4400&300 & + ... & 2001/02/25&11:32:29.47&1.085& ... &b&4400&300 & + ... & 2001/02/25&11:41:09.15&1.087& ... &b&4400&300 & + ... & 2001/02/25&11:48:41.57&1.089& ... &b&4400&300 & + ... & 2001/02/25&11:55:50.50&1.0938& ... &b&4400&300 & + ... & 2001/05/23&08:21:14.63&1.359& ... &b&4400&300 & + ... & 2001/05/23&08:27:35.43&1.387& ... &b&4400&300 & + ... & 2001/05/23&08:33:59.98&1.418& ... &b&4400&300 & + & & & & & & & + & & & & & & & + q2233 + 131&2000/10/26&03:45:44.77&1.066&blue&4300/135&4319&2400&5.59 + ... & 2000/10/27&01:38:14.59&1.150&blue&4300/135&4314.3&2400 & + ... & 2000/10/27&02:41:43.61&1.070&blue&4300/135&4317.0&2400 & + ... & 2000/10/27&03:32:30.68&1.062&blue&4300/135&4318&2400 & + ... & 2000/10/27&04:20:34.25&1.097&blue&4300/135&4318&2400 & + ... & 2000/10/27&05:12:21.30&1.190&blue&4300/135&4318.5&2400 & + ... & 2000/10/27&06:11:24.96&1.398&blue&4300/135&4319&2400 & + ... & 2001/11/10&02:29:02.38&1.060&blue&4313/116&4318.9&2400 & + ... & 2001/11/10&03:10:40.90&1.081&blue&4313/116&4318.9&2400 & + ... & 2001/11/10&03:52:49.45&1.136&blue&4313/116&4318.9&2400 & + ... & 2001/11/10&04:34:24.56&1.233&blue&4313/116&4318.9&2400 & + ... & 2001/11/11&02:01:10.21&1.062&blue&4313/116&4318.9&2400 & + ... & 2001/11/11&02:45:46.09&1.066&blue&4313/116&4318.9&2400 & + ... & 2001/11/12&02:18:11.07&1.060&blue&4313/116&4318.9&2400 & + ... & 2001/11/12&03:01:43.69&1.080&blue&4313/116&4318.9&2400 & + ... & 2002/11/04&03:08:18.76 & 1.064&vis - b&4300/135&4325.0&1740 & + ... & 2002/11/06&01:29:15.00&1.104&vis - b&4300/135&4325.0&2400 & + ... & 2002/11/06&02:31:17.24&1.060&vis - b&4300/135&4325.0&800 & + ... & 2002/11/06&05:02:00.19&1.268&vis - b&4300/135&4325.0&2400 & + & & & & & & & + ... & 2000/10/26&02:42:34.68&1.072& ... &b&4400&480 & + ... & 2000/10/26&02:53:33.87&1.066& ... &b&4400&480 & + ... & 2000/10/26&03:06:41.39&1.061& ... &b&4400&480 & + ... & 2000/10/26&03:17:01.37&1.060& ... &b&4400&480 & + ... & 2000/10/26&03:28:07.59&1.060& ... &b&4400&480 & + ... & 2001/11/11&03:54:43.13&1.147& ... &b&4400&2400 & + ... & 2000/10/25&05:26:24.96&1.205& ... &b&4400&1200 & + & & & & & & & + & & & & & & & + 53w002&2001/05/20&09:45:49.27&1.086&blue&4155/160&4128.4&2400&8.31 + ... & 2001/05/21&09:34:32.16&1.079&blue&4155/160&4128.5&2400 & + ... & 2001/05/21&10:15:54.17&1.126&blue&4155/160&4128.6&2400 & + ... & 2001/05/22&09:08:42.61&1.063&blue&4155/160&4128.3&2400 & + ... & 2001/05/23&09:31:39.77&1.084&blue&4155/160&4128.3&2400 & + & & & & & & & + ... & 2001/05/22&09:57:53.15&1.108 & ... & b&4400&300 & + ... & 2001/05/22&10:04:47.73&1.117 & ... & b&4400&300 & + ... & 2001/05/22&10:10:54.66&1.125 & ... & b&4400&300 & + ... & 2001/05/22&10:17:17.82&1.134 & ... & b&4400&300 & + ... & 2001/05/22&10:23:55.19&1.145 & ... & b&4400&300 & + ... & 2001/05/22&10:34:30.57&1.163 & ... & b&4400&300 & + ... & 2001/05/22&10:41:24.96&1.176 & ... & b&4400&300 & + ... & 2001/05/22&10:52:14.56&1.197 & ... & b&4400&300 & + ... & 2001/05/23&08:44:33.56&1.054 & ... & b&4400&300 & + ... & 2001/05/23&08:51:20.34&1.057 & ... & b&4400&300 & + ... & 2001/05/23&08:57:47.50&1.060 & ... & b&4400&300 & + ... & 2001/05/23&09:05:17.92&1.064 & ... & b&4400&300 & + & & & & & & & + llcc qso & @xmath97 & @xmath102(erg s@xmath5 @xmath6 ) ) & sfr ( @xmath8 yr@xmath5)@xmath103 + q0216 + 080&2.2931&@xmath104&@xmath105 + q0636 + 680&2.3112&@xmath106&@xmath107 + q0956 + 123&2.3104&@xmath108&@xmath105 + q1209 + 093&2.5822&@xmath109&@xmath110 + q1442 + 101&2.5632&@xmath111&@xmath112 + q2233 + 131&2.5537&@xmath113&@xmath114 + @xmath100 : 3 @xmath2 upper limits on lyman-@xmath0 flux for a 2 pixel x 2 pixel region , corresponding to a physical size of @xmath115 kpc x 6.0 kpc at @xmath116 ; @xmath117 : 3 @xmath2 upper limits on sfr .

we have carried out a deep narrow - band imaging survey of six fields with heavy - element quasar absorption lines , using the goddard fabry - perot ( fp ) system at the apache point observatory ( apo ) 3.5-meter telescope . the aim of these observations was to search for redshifted ly- emission from the galaxies underlying the absorbers at and their companion galaxies . it is also possible that the star - forming regions are compact and at smaller angular separations from the quasar than the width of our point spread function and , get lost in the quasar emission .

we have carried out a deep narrow - band imaging survey of six fields with heavy - element quasar absorption lines , using the goddard fabry - perot ( fp ) system at the apache point observatory ( apo ) 3.5-meter telescope . the aim of these observations was to search for redshifted ly- emission from the galaxies underlying the absorbers at and their companion galaxies . the 3 sensitivity levels ranged between and erg s in observed - frame ly- flux . no significant ly- emitters were detected at level . the absence of significant ly- emission implies limits on the star formation rate ( sfr ) of 0.9 - 2.7 yr per 2-pixel x 2-pixel region , if no dust attenuation is assumed . we compare our results with those from other emission - line studies of absorber fields and with predictions for global average sfr based on the models of cosmic chemical evolution . our limits are among the tightest existing constraints on ly- emission from galaxies in absorber fields , but are consistent with many other studies . in the absence of dust attenuation , these studies suggest that sfrs in a large fraction of objects in the absorber fields may lie below the global mean sfr . however , it is possible that dust attenuation is responsible for the low emission line fluxes in some objects . it is also possible that the star - forming regions are compact and at smaller angular separations from the quasar than the width of our point spread function and , get lost in the quasar emission . we outline future observations that could help to distinguish between the various possibilities .

astro-ph0012341

r

figure 1 shows the distribution of the integrated intensity of co j=21 emission . the velocity range is between @xmath17 and @xmath18 , which covers most of the emission . the overlaied contour map shows the 1420 mhz brightness distribution of hb 21 ( t90 ) . the overall distribution of co gas in figure 1 is not very different from the low - resolution map of t90 . but figure 1 shows much detailed structure because of its high resolution , high sensitivity , and complete sampling . figure 1 immediately shows that molecular gas is distributed mainly along the boundary of the snr . ( we observed the central area in figure 1 , which had not been covered in our co j=21 observations , in co j=10 line emission , and have detected only several small [ @xmath19 clumps other than some faint extension associated with the clouds in southern and eastern parts of the remnant . ) but the overall distribution has little correlation either with the distortion of snr boundaries or with the distribution of radio brightness ( cf . 3.2 ) . for the purpose of discussion , we divide the remnant into three areas ( fig . 2 ) : ( 1 ) eastern area ( ra@xmath20 20@xmath21 47@xmath22 ) where three relatively large ( @xmath23 ) clouds and several filamentary clouds are present , ( 2 ) northern area centered at ( 20@xmath21 46@xmath22 , 51@xmath24 00@xmath25 ) , where a small ( @xmath2 ) , very bright u - shaped cloud is noticeable , and ( 3 ) southern area centered at ( 20@xmath21 44@xmath22 , 49@xmath24 50@xmath25 ) , where clumpy and filamentary clouds with complicated structures are present . we detected broad ( 2040 ) emission lines from the clouds in the northern and southern areas , which will be discussed in detail in the next sections . in the following , we summarize the results on the eastern area . in the eastern area , there are three clouds centered at declinations @xmath26 49@xmath25 , @xmath27 15@xmath25 , and @xmath28 @xmath29 . we call these three clouds by clouds a , b , and c following t90 ( see fig . 2 for the location of these clouds ) . figure 3 shows the channel maps of the eastern area . the velocity ranges of the channel maps were chosen to show the essential features clearly . cloud a appears at @xmath30 to @xmath31 and is composed of two velocity components centered at + 6 and @xmath32 , respectively . the former component ( 6 ) , which is seen in figure 3a , is extended and the emission peaks at the southern part ( @xmath33 45@xmath25 ) of the cloud , while the latter component ( @xmath32 ) , which is seen in figures 3b and 3c , is spatially confined and comprises the northern part of the cloud . their maximum brightnesses are @xmath34 and 7 k , respectively . cloud b appears at @xmath35 to @xmath36 and is seen in figures 3c and 3d . the south central part of the cloud , e.g. , the region between @xmath3717@xmath25 , is bright and appears to be connected to cloud c. cloud c has two components at very different velocities , e.g. , one at + 2 to @xmath38 , which is seen in figures 3c and 3d , and the other at + 17 to + 10 , which is not shown in figure 3 but has a distribution similar to the other velocity component . according to the result of t90 , cloud c extends to @xmath39 . an interesting feature in figure 3 is the semi - circular loop that appears above cloud b in figure 3b . the ratio of the minor , which is along the ns direction , to the major axis is 0.8 . if it is at 0.8 kpc , the linear size of the semimajor axis would be @xmath40 pc . the velocity increases systematically from both ends to the northern top of the loop , which is consistent with an expanding loop . the top portion is redshifted with respect to the both ends by @xmath41 . if we assume that the ellipticity is due to projection , then the expansion velocity would be @xmath42 , so that the dynamical age of the ring is probably shorter than @xmath43 yrs . this is much greater than the age ( @xmath44 yrs , koo & heiles 1991 , scaled to 0.8 kpc adopted in this paper ) of hb 21 and , therefore , the loop might not be associated with hb 21 . we suspect that the loop is originated from some energetic phenomena in cloud b. a faint v - shaped structure that connects cloud b and the ends of the loop in figure 3b seems to indicate the association of the two . the cloud in the northern area is composed of a small ( @xmath2 ) , very bright , u - shaped cloud and several clumps scattered around it ( fig . 1 ; see also fig . 9 for enlarged view ) . figure 4 shows its velocity structure . there are several points to be made from figure 4 : first the u - shaped cloud is composed of several clumps , whose central velocities shift systematically from + 3 to @xmath31 as we move from ne to nw along the structure . the integrated intensity attains a maximum at ( 20@xmath21 46@xmath22 [email protected] , 51@xmath24 00@xmath25 00@xmath13 ) , which we call hb21:bml - n1 ( broad molecular line northern position 1 ) , or simply n1 . second , there are several other clumps in the field . these clumps , except the one near the southeastern corner at @xmath46 , appear over a wide ( @xmath47 ) velocity range . among them , the one at ( 20@xmath21 45@xmath22 55.@xmath450 , 51@xmath24 03@xmath25 30@xmath13 ) , which we call hb21:bml - n2 ( or n2 ) , appears over the widest ( @xmath48 ) velocity interval . third , there is a diffuse emission at @xmath49 to the ne of the cloud . its line is narrow ( 23 ) and it is part of a large ( @xmath50 ) cloud that appears to be connected to cloud a. we consider that the clumps aligned along the ne - sw direction in figure 4 are associated and call them cloud n , i.e. , cloud n does not include the diffuse emission in the northeastern area and the clump in the southeastern corner . t90 detected in this area only the diffuse molecular gas at @xmath51 to 6 and called it cloud d. ) as can be expected from figure 4 , most clumps in cloud n have broad emission lines . as an example , we show the spectra of n1 and n2 in the top frames in figure 5 , where we see that the spectrum of n1 is box - shaped and its full width ( at zero intensity ) is 30 km / s , while that of n2 is asymmetric and extends from @xmath52 to + 11 km / s . for comparison , the spectrum of the diffuse , extended structure in the northeastern part of this area has narrow ( 23 ) emission lines centered at @xmath49 , a sample of which is shown in the right bottom frame in figure 5 . we have obtained sensitive j=10 and j=21 spectra of @xmath0co and @xmath6co molecules at the two peak positions , n1 and n2 , and figure 5 shows the spectra . the molecule and transition are marked in each spectrum . the second spectrum from the top is @xmath0co j=21 emission convolved to the j=10 beam size ( @xmath53 ) to be compared with the j=10 spectra . the difference between the top and convolved spectra indicates that some velocity components , e.g. , the narrow component centered at + 4 of n1 and the broad component at @xmath54 of n2 , are confined to small areas . by comparing the j=10 and the convolved j=21 spectra , we notice that the ratio of j=21 to j=10 intensities is high and that it varies over the profile : for n1 , the ratio is between 1.2 and 2.0 in the central parts of the spectrum , while it increases at the wings , e.g. , @xmath55 at + 5 and @xmath5613 . for n2 , the ratio varies between 0.8 and 2.8 , and it is higher between @xmath38 and 0 . the ratios of the @xmath0co j=21 and j=10 integrated intensities @xmath57 are 1.6 and 1.7 for n1 and n2 , respectively . the @xmath6co j=21 line is clearly detected toward n1 , while it is marginally detected toward n2 . for n1 , the line has double peaks centered at + 1 and @xmath36 , while the @xmath0co j=21 line profile toward n1 is composed of several narrow peaks . the narrow peaks might indicate that the emission is from several , unresolved subclumps . presumably , the @xmath6co emission might be from these subclumps too , which is not apparent in the profile in figure 5 because of low signal - to - noise ratio and low velocity resolution . ( note that the velocity resolutions of the @xmath0co j=2 - 1 and @xmath6co j=2 - 1 lines are 0.25 and 0.68 , respectively . ) the ratios of @xmath0co j=21 to @xmath6co j=21 integrated line intensities @xmath58 are @xmath59 and @xmath60 for n1 and n2 , respectively . ( the errors are statistical errors . ) table 1 summarizes the line parameters of the peak positions , i.e. , their coordinate , velocity range ( @xmath61 , @xmath62 ) , co j=21 peak brightness temperature @xmath63 , @xmath57 , @xmath58 , and the ratio of @xmath0co j=10 to @xmath6co j=10 integrated line intensities @xmath64 . the detailed line diagnostics based on the observed line parameters in table 1 is discussed in 3.4 . in the southern part of the snr , the emission is detected at @xmath65 to @xmath66 . the velocity structure is shown in figure 6 . at positive velocities , we see several clouds with narrow lines come and go , e.g. , a diffuse cloud that extends @xmath67 along the ns direction centered at ( 20@xmath21 [email protected] , 50@xmath24 00@xmath25 ) between @xmath68 and + 5 . the co distribution at negative velocities is fairly complicated : the distribution is filamentary , and small ( @xmath5 or 0.3 pc ) , bright clumps are seen along the filamentary structure . the filamentary structure , which we call cloud s , appears to form a loop of @xmath69 in extent , elongated along the ns direction . the eastern part of the loop is particularly clumpy and has a semicircular shape ( see the channel map centered at @xmath70 ) . the clumps generally have broad ( @xmath71 ) lines . among them , three clumps marked by crosses in figure 6 have broadest ( 3040 ) lines and we show the @xmath0co j=21 and j=10 spectra at their peak positions , which we call s1 , s2 , and s3 from east to west ( see fig . 2 ) , in figure 7 . again we show the convolved j=21 spectra together , although the line shapes do not change significantly by convolution toward these peak positions . we have obtained some sensitive j=10 and j=21 spectra of @xmath0co and @xmath6co molecules at these peak positions , and the line parameters are listed in table 1 . note that @xmath57(=1.72.3 ) and @xmath72 toward s1 ) are similar to those of northern positions , while @xmath64 s , although they have large uncertainties , appear to be much greater than that of n1 . the broad co lines are presumably emitted from the shocked gas , where physical parameters vary greatly over a short distance scale . but still it would be worthwhile to estimate their excitation parameters based on elementary considerations . first , the observed @xmath7340 are significantly less than either the average ratio ( @xmath74 ; langer 1997 ) of @xmath0c/@xmath6c in the solar neighborhood or the terrestrial value ( 89 ) , implying that the @xmath0co j=21 lines are _ not _ optically thin . if we adopt @xmath0c/@xmath6c=67 and assume that the emission is thermalized , then the optical depth for the @xmath0co j=21 line @xmath753.4 . on the other hand , the @xmath64(@xmath76 ) close to or greater than the terrestrial value imply that @xmath0co j=10 lines are optically thin , except at n1 where j=10 and j=21 lines appear to have comparable optical depths . this , however , is not conclusive because of large uncertainties associated with @xmath64 . second , the large values of @xmath772.3 imply that the broad - line emitting region is warm and dense . for typical molecular clouds , where the j=2 level is subthermally excited , the ratio is usually less than unity . for example , molecular clouds in the local arm exhibit ratios ranging from 0.53 ( taurus ) to 0.75 ( orion a ) ( sakamoto et al . 1994 , 1997 ) . our spectra of ambient gas also show this , e.g. , see the spectra toward s2 in fig . 7 where the narrow component at + 2 has @xmath78 . but the large ratio is common for the shocked molecular gas in snrs ( see 4.1 ) . third , the low ( @xmath79 k ) brightness temperature of j=21 lines , regardless of their moderate optical depths , imply that the emitting region must be clumpy , i.e. , composed of subclumps , and the emission is beam - diluted . from the above considerations , we may conclude that the broad emission lines are from warm , dense clumps with significant column densities so that the 21 lines are optically thick . we have applied the large - velocity - gradient ( lvg ) model ( scoville & solomon 1974 ; goldreich & kwan 1974 ) to our broad co lines in order to derive their excitation parameters . the model assumes an uniform , spherical cloud with a constant velocity gradient ( @xmath80 ) . if the lines are emitted from the shocked region where temperature and density vary greatly , the resulting parameters may be considered as ` average ' values . since we have found that the emission is beam - diluted , we have used the line ratios , @xmath57 and @xmath58 , instead of brightness temperatures to determine the excitation parameters . according to our lvg analysis , the observed ratios are possible for @xmath81 k. figure 8a shows the result of our model computations when @xmath82 k , where curves of constant @xmath57 and constant @xmath58 are drawn in ( @xmath83 , @xmath84 ) plane . @xmath83 is the fractional abundance of @xmath0co relative to h@xmath85 ( @xmath86 ) per unit velocity gradient interval . the asterisks ( * ) mark the observed ratios toward the peak positions where both ratios are obtained , i.e. , n1 , n2 , and s1 . according to figure 8a , @xmath87@xmath88 @xmath89 and @xmath90@xmath91 pc ( ) @xmath92 at the three peak positions . there are multiple choices for n1 , e.g. , the same ratios are obtainable when @xmath93 @xmath89 and @xmath94 pc ( ) @xmath92 . we adopt the lower density because it is comparable to the densities in the other peak positions and because the density of @xmath95 @xmath89 appears to be too high for the co emission to explore . if the temperature becomes higher , both @xmath84 and @xmath83 need to be greater . in figure 8b , we plot the _ expected _ co j=21 radiation temperature @xmath96 $ ] which is just the brightness temperature when @xmath97 and the expected @xmath64 from the same lvg model . note that the expected radiation temperatures are much greater than the observed main - beam brightness temperature . we have estimated beam filling factors of ( 7.78.8)@xmath98 from the ratio of these two brightnesses . we have estimated the co column densities @xmath99@xmath100 @xmath101 at these peak positions by @xmath102 \delta v$ ] , where @xmath10318 is the velocity width . the excitation parameters derived from the lvg analysis are listed in table 2 . note that the @xmath64 expected from the lvg model differ from the observed ones : at n1 , the observed value is small by a factor of 2 , while , at s1 , it is large by a factor of @xmath104 . considering the weakness of @xmath6co j=10 lines and various uncertainties associated with different telescopes , however , it is not obvious if this difference is critical . we have made a crude estimate of the mass of the broad - line clouds as follows . if the co j=10 line emission is optically thin , then @xmath105 can be obtained from the co j=10 luminosity @xmath106 by @xmath107 $ ] where @xmath108 is the fraction of co molecules at @xmath109 level and the other coefficients have their usual meanings . in our case , co j=10 emission has less optical depth than the j=21 emission , but is not very optically thin , so that the above formula might yield an underestimate . what we have is the luminosity of co j=21 emission @xmath110 , which has moderate optical depth . but , since @xmath772.3 at the peak positions , we may obtain @xmath106 by assuming that @xmath111 where @xmath112 and @xmath113 are co @xmath11410 and @xmath11421 line frequencies respectively . finally we assume @xmath115 , which is a mean value of those ( 0.150.26 ) at the three peak positions obtained from the lvg analysis . we have found that the h@xmath85 masses of clouds n and s are @xmath116 and @xmath117 , respectively . the mass of the central u - shaped part of cloud n is @xmath118 while the masses of the small clumps in cloud s are @xmath1191 .

molecular gas appears to be distributed mainly along the boundary of the snr , but the overall distribution has little correlation either with the distortion of the snr boundary or with the distribution of radio brightness . along the eastern boundary , where the snr was considered to be interacting with molecular clouds in previous studies , the intensity ofco j=21 emission is low ( k ) and the ratio ofco j=21 to j=10 integrated intensities is high ( 1.62.3 ) , which suggests that the emission is from warm , dense , and clumpy gas . we have applied an lvg analysis to derive their physical parameters .

we have carried outco j=21 line observations of the supernova remnant ( snr ) hb 21 in order to search for evidence of interaction with molecular clouds . we mapped the eastern half ( ) of the snr almost completely . molecular gas appears to be distributed mainly along the boundary of the snr , but the overall distribution has little correlation either with the distortion of the snr boundary or with the distribution of radio brightness . along the eastern boundary , where the snr was considered to be interacting with molecular clouds in previous studies , we have not found any strong evidence for the interaction . instead we detected broad ( 2040 ) co emission lines in the northern and southern parts of the snr . in the northern area , the broad - line emitting cloud is composed of a small ( or 0.5 pc ) , very bright , u - shaped part and several clumps scattered around it . there is a significant enhancement of radio emission with flat ( ) spectral index possibly associated with this cloud . in the southern area , the broad - line emitting cloud is filamentary and appears to form an elongated loop of in extent . small ( or 0.3 pc ) , bright clumps are seen along the filamentary structure . we have obtained sensitive j=10 and j=21 spectra ofco andco molecules toward several peak positions . the intensity ofco j=21 emission is low ( k ) and the ratio ofco j=21 to j=10 integrated intensities is high ( 1.62.3 ) , which suggests that the emission is from warm , dense , and clumpy gas . we have applied an lvg analysis to derive their physical parameters . the detected broad co lines are believed to be emitted from the fast - moving molecular gas swept - up by the snr shock . the small ( ) shock velocity suggests that the shock is a non - dissociating c - shock . we discuss the correlation of the shocked molecular gas with the previously detected , shocked atomic gas and the associated infrared emission .

astro-ph0012341

i

we have mapped the eastern half ( @xmath192 ) of the snr hb 21 in @xmath0co j=21 line emission almost completely . our map , which has been completely sampled with @xmath193 resolution , shows the detailed structure of molecular clouds in this area . we have detected broad co lines with large @xmath57 in the northern and southern parts of hb 21 , which is direct evidence for the interaction between molecular clouds and the snr . in the following , we summarize the main results of this paper : \(1 ) we detected shocked molecular clouds , clouds n and s , with broad ( 2040 ) co lines in the northern and southern parts of the snr . cloud n is composed of a small ( @xmath2 or 0.5 pc ) , very bright , u - shaped , clumpy part and several clumps scattered around it . cloud s is filamentary and appears to form an elongated loop of @xmath4 in extent . small ( @xmath5 or 0.3 pc ) , bright clumps are seen along the filamentary structure . the h@xmath85 masses of clouds n and s are @xmath116 and @xmath117 , respectively.(2 ) we have obtained sensitive j=10 and j=21 spectra of @xmath0co and @xmath6co molecules toward several peak positions of clouds n and s. they have @xmath772.3 and @xmath7340 with co j=21 main - beam brightness temperature less than 7 k. according to our lvg analysis , @xmath81 k , and , for @xmath82 k , @xmath194(37)@xmath195 @xmath89 and @xmath196(2.411 ) @xmath197 @xmath101 . the emitting region appears to fill a small ( 0.0770.088 ) fraction of the beam . ( 3 ) there is an enhanced radio emission which attains a maximum exactly inside the central u - shaped part of cloud n. the emission has a spectral index ( @xmath198 ) flatter than that of the whole remnant . the association of this emission with cloud n needs to be explored.(4 ) clouds n and s are visible in the _ iras _ hires images at all four wavelengths ( 12 , 25 , 60 , and 100 @xmath133 m ) . they have the far - infrared color ratio @xmath183 , which is significantly greater than that ( 0.20 ) of the other clouds in this area . this enhanced color , and the morphological correspondence with the broad molecular line emitting regions , suggests that the infrared emission from clouds n and s is due to shocks in propagating into the clouds.(5 ) along the eastern boundary of the snr , three relatively large ( @xmath23 or 3.5 pc ) clouds and several filamentary clouds are present . no broad co emission or enhanced 60/100 @xmath133 m color were detected in any of these clouds , and there is little relationship between the boundaries of the clouds and the snr . therefore , there is no strong evidence for the interaction of the snr with molecular clouds along the eastern boundary . arendt , r. g. 1989 , apjs , 70 , 181 arikawa , y. , tatematsu , k. , sekimoto , y. , & takahashi , t. 1999 , pasj , 51 , l7 aumann , h. h. , fowler , j. w. , & melnyk , m. 1990 , aj , 99 , 1674 beichman , c. a. et al . 1988 , _ infrared astronomical satellite ( iras ) catalogs and atlases : volume 1 . explanatory supplement _ , nasa rp-1190 ( nasa : washington , dc ) blandford , r. d. , & cowie , l. l. 1982 , apj , 260 , 625 boulanger , f. , & prault , m. 1988 , apj , 330 , 964 cesarsky , d. , cox , p. , pineau des forts , g. , van dishoeck , e. f. , boulanger , f. , & wright , c. m. 1999 , a & a , 348 , 945 chevalier , r. a. 1974 , apj , 188 , 501 1999 , apj , 511 , 798 denoyer , l. k. 1979 , apjl , 232 , l165 dsert , f. x. , boulanger , f. , & puget , j .- l . 1990 , a&a , 237 , 215 dickman , r. l. , snell , r. l. , ziurys , l. m. , & huang , y .- l . 1992 , apj , 400 , 203 dobashi , k. , bernard , j .- yonekura , y. , & fukui , y. 1994 , apjs , 95 , 419 draine , b. t. , & anderson , n. 1985 , apj , 292 , 494 draine , b. t. , & mckee , c. f. 1993 , araa , 31 , 373 draine , b. t. , roberge , w. g. , & dalgarno , a. 1983 , apj , 264 , 485 draine , b. t. , & roberge , w. g. 1984 , apj , 282 , 491 erkes , j. w. , & dickel , j. r. 1969 , aj , 74 , 840 frail , d. a. , goss , w. m. , reynoso , e. m. , giacani , e. b. , green , a. j. , & otrupcek , r. 1996 , aj , 111 , 1651 goldreich , p. , & kwan , j. 1974 , apj , 189 , 441 green , d. a. 1986 , mnras , 221 , 473 heiles , c. , reach , w. t. , & koo , b .- c . 1988 , apj , 332 , 313 hill , i. e. 1974 , mnras , 169 , 59 hollenbach , d. , & mckee , c. f. 1980 , apjl , 241 , l47 1989 , apj , 342 , 306 huang , y .- l . , & thaddeus , p. 1986 , apj , 309 , 804 humphreys , r. m. 1978 , apjs , 38 , 309 jones , t. w. , & kang , h. 1993 , apj , 402 , 560 jones , a. p. , tielens , a. g. g. m. , & hollenbach , d. j. 1996 , apj , 469 , 740 keohane , j. w. , petre , r. , gotthelf , e. v. , ozaki , m. , & koyama , k. 1997 , apj , 484 , 350 klein , r. l. , mckee , c. f. , colella , p. 1994 , apj , 420 , 213 koo , b .- c . , & heiles , c. 1991 , apj , 382 , 204 koo , b .- c . & moon , d .- s . 1997 , apj , 485 , 263 langer , w. d. 1997 , in co : twenty - five years of millimeter - wave spectroscopy , iau symp . latter , w. b. et al . ( dordrecht : kluwer ) , 98 leahy , d. a. 1987 , mnras , 228 , 907 leahy , d. a. , & aschenbach , b. 1996 , a&a , 315 , 260 lockett , p. , gautheir , e. , elitzur , m. 1999 , apj , 511 , 235 mac low , m .- mckee , c. f. , klein , r. i. , stone , j. m. , & norman , m. l. 1994 , apj , 433 , 757 mckee , c. f. 1988 , in supernova remnants and the interstellar medium , proceedings of iau colloquium no . roger and t.l . landecker ( cambridge : cambridge ) , 473 oliva , e. , moorwood , a. f. m. , drapatz , s. , lutz , d. , & sturm , e. 1999 , a & a , 343 , 943 reach , w. t. , & rho , j. 1996 , a&a , 315 , l277 . 1999 , apj , 511 , 836 . 2000a , aph0007148 . 2000b , in preparation rengelink , r. b. , tang , y. , de bruyn , a. g. , miley , g. k. , bremer , m. n. , rttgering , h. j. a. , & bremer , m. a. r. 1997 , a&as , 124 , 259 rho , j. , & petre , r. 1998 , apjl , 503 , l167 rho , j. , jarrett , t. , cutri , r. m. , & reach , w. t. 2000 , apj , submitted roh , d .- jung , j. h. 1999 , publications of the korean astronomical society , 14 , 123 sakamoto , s. , hasegawa , t. , handa , t. , hayashi , m. , & oka , t. 1997 , apj , 486 , 276 sakamoto , s. , hayashi , m. , hasegawa , t. , handa , t. , & oka , t. 1994 , apj , 425 , 641 scoville , n. z. , & solomon , p. m. 1974 , apjl , 187 , l67 seta , m. , hasegawa , t. , dame , t. m. , sakamoto , s. , oka , t. , handa , t. , hayashi , m. , morino , j. , sorai , k. , & usuda , k. s. 1998 , apj , 505 , 286 tatematsu , k. , fukui , y. , landecker , t. l. , & roger , r. s. 1990 , a&a , 237 , 189 ( t90 ) tauber , j. a. , snell , r. a. , dickman , r. l. , & ziurys , l. m. 1994 , apj , 421 , 570 van den bergh , s. 1978 , apjs , 38 , 119 van der laan , h. 1962 , mnras , 124 , 179 van dishoeck , e. f. , jansen , d. j. , & phillips , t. g. 1993 , a&a , 279 , 541 wheelock s. l. , gautier , t. n. , chillemi , j. , kester , d. , mccallon , h. , oken , c. , white , j. , gregorich , d. , boulanger , f. , and j. good 1994 , _ iras sky survey atlas : explanatory supplement_. ( jpl / caltech : pasadena ) willis , a. g. , 1973 , a&a , 26 , 237 wilner , d. j. , reynolds , s. p. , & moffett , d. a. 1998 , aj , 115 , 247 hb21:bml - n1 & ( 20 46 03.2 , 51 00 00 ) & @xmath199 & 3.6 & 1.6&@xmath59&@xmath200hb21:bml - n2 & ( 20 45 55.0 , 51 03 30 ) & @xmath201 & 3.1 & 1.7&@xmath202& ... hb21:bml - s1 & ( 20 44 37.2 , 49 47 10 ) & @xmath203 & 2.7 & 1.9&@xmath204&@xmath205hb21:bml - s2 & ( 20 44 31.0 , 49 55 20 ) & @xmath206 & 2.9 & 1.7& ... &@xmath207hb21:bml - s3 & ( 20 42 45.2 , 49 56 50 ) & @xmath208 & 6.9 & 2.3& ... &@xmath209 a & 1.1(0.2 ) & 1.1(0.1 ) & 4.2(0.2 ) & 20.8(2.3 ) & 0.20(0.03)b & 1.7(0.1 ) & 1.8(0.1 ) & 5.9(1.1 ) & 29.5(2.4 ) & 0.20(0.04)c & 1.7(0.1 ) & 1.7(0.1 ) & 8.0(1.1 ) & 38.0(2.4 ) & 0.21(0.03)n & 1.0(0.2 ) & 0.8(0.1 ) & 4.8(0.2 ) & 17.0(2.3 ) & 0.28(0.04)s & 1.2(0.1 ) & 1.2(0.1 ) & 6.8(1.1 ) & 26.3(2.4 ) & 0.26(0.05 )

we have carried outco j=21 line observations of the supernova remnant ( snr ) hb 21 in order to search for evidence of interaction with molecular clouds . instead we detected broad ( 2040 ) co emission lines in the northern and southern parts of the snr . in the northern area , the broad - line emitting cloud is composed of a small ( or 0.5 pc ) , very bright , u - shaped part and several clumps scattered around it . there is a significant enhancement of radio emission with flat ( ) spectral index possibly associated with this cloud . in the southern area , the broad - line emitting cloud is filamentary and appears to form an elongated loop of in extent . small ( or 0.3 pc ) , bright clumps are seen along the filamentary structure . we have obtained sensitive j=10 and j=21 spectra ofco andco molecules toward several peak positions .

we have carried outco j=21 line observations of the supernova remnant ( snr ) hb 21 in order to search for evidence of interaction with molecular clouds . we mapped the eastern half ( ) of the snr almost completely . molecular gas appears to be distributed mainly along the boundary of the snr , but the overall distribution has little correlation either with the distortion of the snr boundary or with the distribution of radio brightness . along the eastern boundary , where the snr was considered to be interacting with molecular clouds in previous studies , we have not found any strong evidence for the interaction . instead we detected broad ( 2040 ) co emission lines in the northern and southern parts of the snr . in the northern area , the broad - line emitting cloud is composed of a small ( or 0.5 pc ) , very bright , u - shaped part and several clumps scattered around it . there is a significant enhancement of radio emission with flat ( ) spectral index possibly associated with this cloud . in the southern area , the broad - line emitting cloud is filamentary and appears to form an elongated loop of in extent . small ( or 0.3 pc ) , bright clumps are seen along the filamentary structure . we have obtained sensitive j=10 and j=21 spectra ofco andco molecules toward several peak positions . the intensity ofco j=21 emission is low ( k ) and the ratio ofco j=21 to j=10 integrated intensities is high ( 1.62.3 ) , which suggests that the emission is from warm , dense , and clumpy gas . we have applied an lvg analysis to derive their physical parameters . the detected broad co lines are believed to be emitted from the fast - moving molecular gas swept - up by the snr shock . the small ( ) shock velocity suggests that the shock is a non - dissociating c - shock . we discuss the correlation of the shocked molecular gas with the previously detected , shocked atomic gas and the associated infrared emission .

1006.5932

c

we have derived an x - ray luminosity function for 12 dwarf novae using archival _ suzaku _ , _ xmm - newton _ , and _ asca _ observations , and obtained new observations for bz uma , sw uma , vy aqr , ss aur , v893 sco and asas j0025 with _ suzaku _ as originally , they were not available in the archive . our results show that the 210 kev luminosities , presented in table [ fluxes ] , span a range between 4 @xmath4 10@xmath6 and 1.5 @xmath4 10@xmath5 erg s@xmath3 , and that most of the source luminosities in the sample are located within 10@xmath1 erg s@xmath3 , see fig . [ histo ] , whereas , the x - ray luminosities of the _ asca _ sample by @xcite were mainly concentrated on higher luminosities between 10@xmath2 and 10@xmath5 erg s@xmath3 . this difference is most likely due to the fact that we did not apply x - ray selection criteria to our sample . also , the objects observed by _ asca _ were known to be x - ray bright , thus the sample of baskill et al . is very likely biased by sources which are x - ray bright . in order to derive the integrated x - ray luminosity function ( xlf ) , n(@xmath17 l ) , for 12 sources within a distance of d = 200 pc , we assumed that the luminosity function is characterized by a power law n(@xmath17 l ) = k(l / l@xmath201)@xmath202 ( see fig . [ lum ] where the best - fit parameters @xmath41 = -0.64 and k = 2.39 @xmath4 10@xmath203 , corresponding to a threshold luminosity of l@xmath201 = 3 @xmath4 10@xmath1 erg s@xmath3 ) . the histogram illustrates the cumulative source distribution per pc@xmath204 in which a break is seen at @xmath0 3 @xmath4 10@xmath1 erg s@xmath3 . this can be due to two possible scenarios : 1 ) a single @xmath41 power law describes the luminosity function of dne , but the sample becomes more incomplete below @xmath0 3 @xmath4 10@xmath1 erg s@xmath3 than it is above this limit , or 2 ) the shape of the true xlf of dne is a broken power law with a break at around 3 @xmath4 10@xmath1 erg s@xmath3 . from these two scenarios , the first one is more likely since the sample contains only a few sources below @xmath0 10@xmath1 erg s@xmath3 . also , as was shown by , e.g. , the study of @xcite , more fainter cvs , such as wz sge types , are expected to exist . based on the obtained power law slope , the sample is dominated by the brighter dne : this is probably caused by the parallax measurement method which favours optically brighter dne which usually have high x - ray luminosities . l ) as a function of x - ray luminosity in log l in the 210 kev energy band . the error bar on the top right represents a typical error on the luminosities.,width=340 ] when calculating the total , integrated luminosity of the sample , we restricted the calculations to the distance of 200 pc , thus excluding bz uma . integrating between the luminosities of 1 @xmath4 10@xmath6 and the maximum luminosity of the sample ( @xmath205 = 1.50 @xmath4 10@xmath5 erg s@xmath3 ) , yields the total integrated luminosity of 1.48 @xmath4 10@xmath5 erg s@xmath3 , whereas the integrated luminosity between the threshold luminosity 3 @xmath4 10@xmath1 and @xmath205 is 1.15 @xmath4 10@xmath5 erg s@xmath3 . these two results show that there are uncertainties in the integrated luminosities , most likely caused by the small number of sources in the sample . in order to obtain more accurate value for the integrated luminosity , the power law slope ( @xmath41 = -0.64 ) should be better established . if the obtained slope is not far from the true power law slope of dne in the solar neighbourhood , estimating the integrated luminosity more accurately and constraining the bright luminosity end ( 10@xmath5 erg s@xmath3 ) requires more dne to be included in the sample . since the source density at @xmath0 10@xmath5 erg s@xmath3 is @xmath0 3 @xmath4 10@xmath206 pc@xmath22 according to fig . [ lum ] , we would need to survey within a volume of 1 @xmath4 10@xmath207 pc@xmath204 to find @xmath0 30 ss cyg -type dne and thus find a statistically significant constraint for the brighter luminosities in the sample . this volume would correspond to a distance of @xmath0 620 pc with a flux limit of @xmath0 3.2 @xmath4 10@xmath131 erg @xmath15 s@xmath3 . following this , we estimated how easy it would be to hide typical dn luminosities in the solar neighbourhood . assuming a typical dwarf nova with a 5 kev bremsstrahlung and a low galactic n@xmath181 = 1 @xmath4 10@xmath61 @xmath15 in webpimms yields a 210 kev flux of 5 @xmath4 10@xmath208 erg @xmath15 s@xmath3 , corresponding to the _ rosat _ pspc count rate of 0.04 ct s@xmath3 which is just below the detection limit ( 0.05 ct s@xmath3 ) of _ rosat _ pspc @xcite . thus , luminosities above 2.4 @xmath4 10@xmath1 erg s@xmath3 within 200 pc or above 6 @xmath4 10@xmath25 erg s@xmath3 within 100 pc should have been found by _ rosat _ and thus should be in the rass . however , given that sources with luminosities of 10@xmath1 erg s@xmath3 and below at a distance of 100 pc were too faint for the rass , and that our xlf peaks at @xmath0 10@xmath1 erg s@xmath3 , we conclude that there is no existing x - ray selected sample that we can use for this line of research . how far is the total luminosity of our sample from accounting for the total cv x - ray emissivity ? in order to estimate this , we calculated the absolute lower limit for the luminosity per cubic parsec volume ( l@xmath11/vol ) . for a distance of r = 200 pc , the volume v = 4/3 @xmath4 @xmath43 @xmath4 ( 200 pc)@xmath204 = 3.3 @xmath4 10@xmath209 pc@xmath204 , and the total summed luminosity l@xmath11 of the sample is 2.39 @xmath4 10@xmath5 erg s@xmath3 ( without bz uma ) . thus , the total absolute lower limit l@xmath11/volume = 7.24 @xmath4 10@xmath210 erg s@xmath3 pc@xmath22 . normalising this value to the local stellar mass density 0.04 m@xmath146 pc@xmath22 @xcite yields 1.81 @xmath4 10@xmath7 erg s@xmath3 m@xmath8 in the 210 kev range . for comparison , @xcite obtained ( 1.1 @xmath211 0.3 ) @xmath4 10@xmath212 erg s@xmath3 m@xmath8 ( 210 kev ) for the total cv x - ray emissivity per unit stellar mass . thus , our sample would account for @xmath0 16 per cent of this value . and finally , how much would our sample account for the grxe ? the galactic ridge x - ray emissivity estimated by @xcite in the 320 kev range was l@xmath11/m @xmath0 ( 3.5 @xmath211 0.5 ) @xmath4 10@xmath212 erg s@xmath3 m@xmath8 , meaning that our sample would account for 5 per cent of the galactic ridge x - ray emissivity . as we estimated the x - ray emissivity of all cvs within 200 pc , we used the exponential vertical density profile @xmath213 of cvs with a scale height for short period systems ( @xmath198 = 260 pc ) as in @xcite , where @xmath214 = @xmath215 sin @xmath216 is the perpendicular distance from the galactic plane and @xmath216 galactic latitude . integrating eq.[density ] over a sphere with a radius of 200 pc gives @xmath0 280 as the total number of dne within 200 pc . if the space density of dne follows the space density of cvs as in @xcite , i.e. , @xmath217 = 1.1@xmath218 @xmath4 10@xmath194 pc@xmath22 , and if a typical dn has an x - ray luminosity corresponding to the mean luminosity ( 2 @xmath4 10@xmath2 erg s@xmath3 ) of our sample of 11 sources ( bz uma excluded ) , then the 210 kev x - ray emissivity of all dne in the solar neighbourhood would be 5.5@xmath219 @xmath4 10@xmath212 erg s@xmath3 m@xmath8 ( these account for the uncertainty on the space density , assuming that this is the dominant source of uncertainty for the x - ray emissivity of dne ) . this would account for more than 100 per cent of the grxe emissivity . if dne were uniformly distributed in the solar neighbourhood , the x - ray emissivity would be overestimated also in this case ( by 2030 per cent ) . however , in both cases , one should remember that the calculated x - ray emissivity of all dne within 200 pc is likely overestimated by the brighter sources in our sample , thus the calculations give excess emission . in order to understand whether the x - ray luminosity and the various parameters ( inclination @xmath220 , orbital period @xmath20 , shock temperature @xmath32 and white dwarf mass @xmath221 ) are correlated , we carried out spearman s rank correlation test . plotting x - ray luminosity versus a few of these parameters ( @xmath220 and @xmath20 ) shows that gw lib seems to appear as an outlier compared to the rest of the sample ( fig . [ orb ] and [ incl ] ) . thus , to explore how the presence / absence of gw lib affects the test results , two test cases were used : 1 ) gw lib was included , and 2 ) gw lib was excluded from the rest of the sample . in addition , we investigated whether a correlation between the white dwarf masses @xmath221 and the shock temperatures @xmath32 ( fig . [ mass_temp ] ) exists , although in this case , gw lib seems to follow the rest of the sample , thus , carrying out test case 2 ) was not necessary . a strong correlation was found at the 99.95 per cent significance level ( 2.8@xmath30 ) between the x - ray luminosities and orbital periods ( fig . [ orb ] ) when gw lib is included in the sample . the correlation still holds when gw lib is excluded ( significance is 99.67 per cent ) . @xcite noted that there was a weak correlation between the x - ray luminosities and the orbital periods in their _ asca _ sample , concluding that the x - ray luminosity probably also correlates with long - term mean accretion rate . the x - ray luminosity and the inclination @xmath220 are not correlated in either case ( fig . [ incl ] ) . the correlation between these parameters was measured when the inclination of bz uma was set to 65@xmath29 , and altering the inclination between 60@xmath29 and 75@xmath29 did not affect the result . since no correlation was found , this result is in contrast with the discovery of anti - correlation between the emission measure and inclination found by @xcite . it is worth noting that the _ rosat _ bandpass was very narrow , covering only 0.12.4 kev where the softer x - ray emission ( and more luminous emission ) is probably intrinsically absorbed by the sources . in addition , an anti - correlation between the x - ray luminosity and inclination was also seen by @xcite in the _ asca _ sample , although , baskill et al . noted that the inclinations might be uncertain , and this can also be the case in our sample . finally , the white dwarf masses @xmath221 and the shock temperatures @xmath32 correlate with a significance of 98.5 per cent when the mass of vy aqr is 0.80 m@xmath146 , but becomes less significant ( 97.4 per cent ) if the mass is 0.55 m@xmath146 . of the rest of the parameters , i.e. the x - ray luminosity @xmath16 versus @xmath32 and @xmath221 , @xmath32 showed evidence of correlation with @xmath16 at a significance of 97.6 per cent when gw lib was included in the sample , but @xmath16 and @xmath221 had a much lower correlation significance ( 69 per cent ) when including gw lib . for the latter correlation test ( @xmath16 versus @xmath221 ) , the result was the same with both @xmath221 values for vy aqr . excluding gw lib decreased the significance to 91 per cent ( @xmath16 versus @xmath32 ) and to 63 per cent ( @xmath16 versus @xmath221 ) .

we have derived an x - ray luminosity function using parallax - based distance measurements of a set of 12 dwarf novae , consisting of _ suzaku _ , _ xmm - newton _ and _ asca _ observations . the total integrated luminosity within a radius of 200 pc is 1.48 10 erg s over the luminosity range of 1 10 erg s and the maximum luminosity of the sample ( 1.50 10 erg s ) . the total absolute lower limit for the normalised luminosity per solar mass is 1.81 10 erg s m which accounts for 16 per cent of the total x - ray emissivity of cvs as estimated by . x - rays : stars x - rays : binaries stars : distances stars : luminosity function

we have derived an x - ray luminosity function using parallax - based distance measurements of a set of 12 dwarf novae , consisting of _ suzaku _ , _ xmm - newton _ and _ asca _ observations . the shape of the x - ray luminosity function obtained is the most accurate to date , and the luminosities of our sample are concentrated between 10 erg s , lower than previous measurements of x - ray luminosity functions of dwarf novae . based on the integrated x - ray luminosity function , the sample becomes more incomplete below 3 10 erg s than it is above this luminosity limit , and the sample is dominated by x - ray bright dwarf novae . the total integrated luminosity within a radius of 200 pc is 1.48 10 erg s over the luminosity range of 1 10 erg s and the maximum luminosity of the sample ( 1.50 10 erg s ) . the total absolute lower limit for the normalised luminosity per solar mass is 1.81 10 erg s m which accounts for 16 per cent of the total x - ray emissivity of cvs as estimated by . [ firstpage ] cataclysmic variables stars : dwarf novae x - rays : stars x - rays : binaries stars : distances stars : luminosity function

1006.5932

c

we have analysed the x - ray spectra of 13 dwarf novae with accurate parallax - based distance estimates , and derived the most accurate shape for the x - ray luminosity function of dne in the 210 kev band to date due to accurate distance measurements and due to the fact that we did not use an x - ray selected sample . the derived x - ray luminosities are located between @xmath0 10@xmath610@xmath5 erg s@xmath3 , showing a peak at @xmath0 10@xmath1 erg s@xmath3 . thus , we have obtained peak luminosities which are lower compared to other previous studies of cv luminosity functions . the shape of the x - ray luminosity function of the source sample suggests that the two following scenarios are possible : 1 ) the sample can be described by a power law with a single @xmath41 slope , but the sample becomes more incomplete below @xmath0 3 @xmath4 10@xmath1 erg s@xmath3 than it is above this limit , or , 2 ) the shape of the real x - ray luminosity function of dwarf novae is a broken power law with a break at around 3 @xmath4 10@xmath1 erg s@xmath3 . the integrated luminosity between 1 @xmath4 10@xmath6 erg s@xmath3 and the maximum luminosity of the sample , 1.50 @xmath4 10@xmath5 erg s@xmath3 , is 1.48 @xmath4 10@xmath5 erg s@xmath3 . in order to better constrain the integrated luminosity and the slope of the x - ray luminosity function , more dwarf novae need to be included in the sample . thus , we suggest more future x - ray imaging observations of dwarf novae in the 210 kev band with accurate distance measurements . the total x - ray emissivity of the sample within a radius of 200 pc is 1.81 @xmath4 10@xmath7 erg s@xmath3 m@xmath222 ( 210 kev ) . this accounts for @xmath0 16 per cent of the total x - ray emissivity of cvs as estimated by @xcite , and @xmath0 5 per cent of the galactic ridge x - ray emissivity . the x - ray luminosities and the inclinations of our sample do not show anti - correlation which has been seen in other previous correlation studies , but a strong correlation is seen between the x - ray luminosities and the orbital periods . also , evidence for a correlation between the white dwarf masses and the shock temperatures exists . in the future , larger dwarf nova samples are needed in order to confirm these results .

the shape of the x - ray luminosity function obtained is the most accurate to date , and the luminosities of our sample are concentrated between 10 erg s , lower than previous measurements of x - ray luminosity functions of dwarf novae . based on the integrated x - ray luminosity function , the sample becomes more incomplete below 3 10 erg s than it is above this luminosity limit , and the sample is dominated by x - ray bright dwarf novae .

we have derived an x - ray luminosity function using parallax - based distance measurements of a set of 12 dwarf novae , consisting of _ suzaku _ , _ xmm - newton _ and _ asca _ observations . the shape of the x - ray luminosity function obtained is the most accurate to date , and the luminosities of our sample are concentrated between 10 erg s , lower than previous measurements of x - ray luminosity functions of dwarf novae . based on the integrated x - ray luminosity function , the sample becomes more incomplete below 3 10 erg s than it is above this luminosity limit , and the sample is dominated by x - ray bright dwarf novae . the total integrated luminosity within a radius of 200 pc is 1.48 10 erg s over the luminosity range of 1 10 erg s and the maximum luminosity of the sample ( 1.50 10 erg s ) . the total absolute lower limit for the normalised luminosity per solar mass is 1.81 10 erg s m which accounts for 16 per cent of the total x - ray emissivity of cvs as estimated by . [ firstpage ] cataclysmic variables stars : dwarf novae x - rays : stars x - rays : binaries stars : distances stars : luminosity function

0811.1616

i

quantum phase transitions originating from quantum fluctuations have been extensively studied as a hot issue in condensed - matter physics . several interesting characteristics of the transitions appear in the low - energy behavior of the systems . two types of approach can capture the phase transitions and critical phenomena precisely when the transition is continuous . one is analyzing the energy - level structure . the other involves considering the ground - state behavior . in the former approach , a standard method is to analyze the structure of the energy levels of finite - size systems based on the finite - size scaling ( fss ) assumption . for example , the scaled energy gap @xcite is often used to estimate the boundary of the gapped phase as the transition point . this is called phenomenological renormalization group ( prg ) analysis . however , it is difficult to estimate the transition point when a logarithmic correction appears in the dependence of the energy difference . a typical example is the berezinskii kosterlitz thouless ( bkt ) transition @xcite . to resolve this difficulty , the level - spectroscopy method has been developed @xcite and precise determinations of phase transitions have been successfully made for various transitions in many models . unfortunately , this analysis is complicated in that appropriate adjustments of the procedure are required according to the type of phase transition , which must also be known in advance . in the latter approach , on the other hand , quantities that characterize the ground state are carefully observed . one of these quantities is the multi - point correlation function . the long - range behavior of correlation functions shows whether the system exhibits long - range order . if a correlation function survives to be nonzero in the long - range limit , it is an appropriate order parameter . however , it is not easy to capture a phase transition using this strategy because reliable and precise data on correlation functions are necessary for large systems . the system sizes that are treated in numerical - diagonalization calculations are insufficient . for this reason , the latter approach has been employed in only a few studies . therefore , no systematic procedure for analyzing ground - state quantities to capture quantum phase transitions has been established to date . in this paper , we develop a procedure to determine the transition point and critical exponents by analyzing correlation functions based only on the scaling assumption . a feature of this approach is that only the common quantities under the same condition are treated irrespective of the type of phase transition . we call the procedure ground - state phenomenological renormalization group ( gsprg ) analysis . to confirm its validity and usefulness in detecting phase transitions , we apply it to a nontrivial ground state in the af @xmath0 @xmath1 chain with uniaxial single - ion anisotropy by the density matrix renormalization group ( dmrg ) method @xcite . in the isotropic case of this system , there exists a nonzero energy gap between the unique ground state and the first excited state , called the haldane gap@xcite . it is known that when anisotropy is introduced , of the single - ion type or of the @xmath1-type exchange interaction , the haldane gap decreases and finally closes . the region where the nonzero haldane gap exists is called the haldane phase . the phase diagram of the af @xmath0 chain with anisotropy of the two types , including the haldane phase , has been extensively studied by analyzing the energy - level structure , assisted by the level - spectroscopy method @xcite . it is well known that in many af spin systems , the standard spin spin correlation function gives so - called n@xmath2el order . in the ground state in the haldane phase , however , the spin spin correlation function decays exponentially with a finite correlation length and the n@xmath2el order no longer exists . in this sense , the haldane phase is a disordered phase . however , the string order parameter is known to characterize the ground state in the haldane phase , in which the longitudinal and transverse string order parameters are nonzero @xcite . from the viewpoint of the string order , it is possible to treat the haldane phase as an ordered phase and capture the phase transition at the boundary . this approach has been applied to numerical - diagonalization data of the haldane phase in @xmath0 systems@xcite . unfortunately , only very small system sizes were available and hence it was quite difficult to capture precisely the critical behavior of the string order near the transition point . in this situation , we can obtain numerical data of the string order of this model for much larger system sizes by using dmrg for gsprg analysis . consequently , it is possible to examine the phase transition at the boundary of the haldane phase from the viewpoint of the string order . we compare our results with those from the analysis of the energy - level structure . this comparison provides a systematic and consistent understanding of the phase transition . this paper is organized as follows . the model hamiltonian and order parameters are defined in section [ sec : level2 ] . the analysis procedure which we have developed is introduced in section [ sec : level3 ] . the numerical results and discussions are given in section [ sec : level4 ] . section [ sec : level5 ] consists of a summary of this work and some remarks .

we have developed a numerical procedure to clarify the critical behavior near a quantum phase transition by analyzing a multi - point correlation function characterizing the ground state . this work presents a successful application of this procedure to the string order parameter of the chain with uniaxial single - ion anisotropy . the finite - size string correlation function is estimated by the density matrix renormalization group method . the quantity is treated in the same manner irrespective of the kind of elements which destroy the order concerned .

we have developed a numerical procedure to clarify the critical behavior near a quantum phase transition by analyzing a multi - point correlation function characterizing the ground state . this work presents a successful application of this procedure to the string order parameter of the chain with uniaxial single - ion anisotropy . the finite - size string correlation function is estimated by the density matrix renormalization group method . we focus on the gradient of the inversed - system - size dependence of the correlation function on a logarithmic plot . this quantity shows that the finite - size scaling sensitively changes at the critical point . the behavior of the gradient with increasing system size is divergent , stable at a finite value , or rapidly decreases to zero when the system is in the disordered phase , at the critical point , or in the ordered phase , respectively . the analysis of the finite - size string correlation functions allows precise determination of the boundary of the haldane phase and estimation of the critical exponent of the correlation length . our estimates of the transition point and the critical exponents , which are determined only by the ground - state quantities , are consistent with results obtained from the analysis of the energy - level structure . our analysis requires only the correlation functions of several finite sizes under the same condition as a candidate for the long - range order . the quantity is treated in the same manner irrespective of the kind of elements which destroy the order concerned . this work will assist in the development of a method to directly observe quantum phase transitions .

0811.1616

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let us first review the behavior of the four order parameters under consideration in a finite - size system and summarize some important relations between them . in a moderately large system , we can see indications of asymptotic behavior in each order parameter , although slow convergence prevents a full description . some are characteristic for a given region of the parameter space , which is specified as one of the haldane , n@xmath2el , large - d , and @xmath96 phases . we illustrate @xmath118 and @xmath119 with @xmath120 or @xmath62 in fig . [ fig.3 ] . the @xmath8-dependences of the order parameters on the line @xmath121 and their @xmath7-dependences on the line @xmath122 are shown in fig . [ fig.3](a ) and [ fig.3](b ) , respectively . dependence of the order parameters for the hamiltonian ( [ eq.1 ] ) on ( a ) the @xmath121 line and ( b ) the @xmath123 line at @xmath124 . @xmath125 : @xmath126 , @xmath127 : @xmath128 , @xmath129 : @xmath130 , @xmath131 : @xmath132 . , width=283 ] we now compare the magnitudes of the four order parameters . ( i ) if @xmath133 , @xmath51 is larger than @xmath134 . this is a known relation found by kennedy and tasaki @xcite . ( ii ) when @xmath123 and @xmath135 , we have @xmath136 due to the isotropy of the system . ( iii ) when @xmath7 is decreased and when @xmath7 crosses a critical point at @xmath137 , @xmath132 is smaller than @xmath130 . this fact will be discussed and utilized in [ sec : level4 - 4 ] . although @xmath138 appears to be nonzero around @xmath139 with @xmath140 and around @xmath141 with @xmath123 , we can confirm that @xmath130 in this region vanishes for the long - ranged limit . on the other hand , @xmath128 around @xmath142 with @xmath123 looks very small but it survives as a nonzero quantity in an infinite system , as shown in [ sec : level4 ] . the phase boundaries of haldane n@xmath2el , haldane large-@xmath8 , and haldane@xmath96 are denoted by dotted lines , though they are given only as indicators as we will determine the boundaries in the following subsections . we can see that some or all of the order parameters vanish at the phase boundaries . also , the order parameters are continuous around the boundaries , which suggests that the phase transitions are continuous . therefore , the fss analysis and the gsprg procedure are feasible for capturing critical phenomena in this case , except for the berezinskii kosterlitz thouless ( bkt ) transition which does not satisfy the conditions of eq . ( [ eq.8a ] ) or ( [ eq.10a ] ) and thus requires extra consideration . for gsprg , however , it is possible for us to capture the transition by looking at the exponent @xmath65 as discussed in [ sec : level4 - 4 ] . we next observe the behavior of the four order parameters in each phase to determine their thermodynamic limits . in fig . [ fig.1 ] , we illustrate the behavior of the order parameters ( [ eq.5 ] ) as a function of the inverse of the system size at the representative points @xmath143 , @xmath144 , @xmath145 , and @xmath146 . these sets of parameters correspond to the n@xmath2el phase , large-@xmath8 phase , haldane phase , and @xmath96 phase , respectively . ) as a function of the inverse of the system size . each panel represents ( a ) the n@xmath2el phase , ( b ) the large-@xmath8 phase , ( c ) the haldane phase , and ( d ) the @xmath96 phase . @xmath125 : @xmath147 , @xmath127 : @xmath128 , @xmath129 : @xmath138 , @xmath131 : @xmath132 . , width=283 ] we observe that in the n@xmath2el phase , only the order parameters in the @xmath62 direction remain nonzero in the limit @xmath24 . all the four parameters vanish in the large-@xmath8 phase in the thermodynamic limit . we note that in the haldane phase , only the string order parameters in the two directions remain nonzero in the thermodynamic limit . it is difficult to judge in fig . [ fig.1](d ) whether both of the transverse order parameters in the @xmath96 phase vanish or remain nonzero in the thermodynamic limit . we plot the same data on a logarithmic scale in fig . [ fig.2 ] . ) in the @xmath96 phase as a function of @xmath77 . a fitting based on @xmath148 is carried out for @xmath149 . @xmath129 : @xmath138 , @xmath131 : @xmath132 . , width=283 ] for large @xmath4 , the data exhibits a linear behavior , which suggests that the transverse order parameters in the @xmath96 phase are critical , consistent with previous reports @xcite . consequently we can confirm that the order parameter @xmath150 vanishes in the @xmath96 phase . in the limit @xmath24 . in this subsection , we examine the transition from the haldane phase to the large-@xmath8 phase . this transition is known to be of gaussian type . as we observe in [ sec : level4 - 1 ] , the string order parameters in the haldane phase remain nonzero for both @xmath120 and @xmath62 while both of the n@xmath2el order parameters vanish along the directions @xmath151 and @xmath62 . we also observe critical behavior near the transition line in both @xmath132 and @xmath128 . to begin with , we consider difficulties in the fss analysis near the transition between the two phases . in this analysis , we have adjusted the critical point @xmath152 and exponents @xmath65 and @xmath66 so that the data for @xmath153 , 48 , and 96 follows a universal function . the results are depicted in fig . [ fig.4 ] . near the haldane large-@xmath8 critical point . @xmath131 , @xmath125 , and @xmath127 represent @xmath154 . , width=283 ] in fig . [ fig.4](a ) , we observe a deviation from the universal function @xmath71 at @xmath8 , not far from @xmath100 . the appearance of this deviation depends on the system size and the direction @xmath76 . thus , it is not easy to determine the critical region around @xmath100 with finite - size data less than 100 sites in this case . despite this difficulty , we can choose input parameters @xmath152 , @xmath155 , and @xmath79 such that a universal function @xmath71 appears near the transition point . in fig . [ fig.4](a ) , the string correlation functions in the direction @xmath120 provide us with @xmath156 and @xmath157 . on the other hand , in fig . [ fig.4](b ) , the string correlation functions in @xmath158 give @xmath156 and @xmath159 . the estimate of the transition point @xmath152 for @xmath120 and that for @xmath158 agree with each other . this fact strongly suggests that the string correlation functions for the transverse and longitudinal directions reveal a common phase transition . we should note that @xmath132 and @xmath128 are clearly different quantities near the transition point , because there are differences in their exponents , for example @xmath160 and @xmath161 . our fss analysis gives @xmath157 and @xmath162 . we recall that the growth of the correlation length determines the critical behavior near the transition point from a general argument of the renormalization group concerning critical phenomena . in this framework , only a single characteristic length in a system shows critical behavior . the characteristic length must be the correlation length of the system . thus , the exponent of the correlation length should be unique for the order parameters . in this case , the correlation functions of the string order parameters along both @xmath120 and @xmath158 show critical behavior as shown by the fss analysis . from this argument , @xmath163 and @xmath164 should exhibit a serious finite - size effect , which we will examine and solve by gsprg analysis . we consider the case of @xmath165 in order to observe the finite - size effect . in fig . [ fig.5 ] we illustrate our results for the exponents @xmath166 , @xmath167 , @xmath168 , and @xmath169 determined by gsprg analysis . , ( b ) @xmath170 , and ( c ) @xmath171 on @xmath172 . @xmath80 is given by eq . ( [ eq.11 ] ) . the dotted curves in ( a ) and ( b ) are guides for the eyes . the dotted lines in ( c ) are linear fitting lines . the string correlation functions @xmath173 and @xmath174 as a function of @xmath77 are shown in the logarithmic scale in the inset figures of ( a ) and ( b ) , respectively . , width=283 ] in fig.[fig.5](a ) , we observe the critical - disordered boundary at @xmath175 . the critical - ordered boundary is also observed at @xmath176 . on the other hand , we obtain no boundaries defined in eqs . ( [ co - boundary1])-([cd - boundary2 ] ) in the case of @xmath177 . this fact suggests that the critical region for finite - size systems in our study is realized around @xmath177 with a narrow width . in order to confirm whether the width shrinks or not as the system sizes increase , we examine the relationship between @xmath88 and @xmath8 so that the case is on the boundary . we obtain some of the critical - disordered boundaries at @xmath178 , @xmath179 , and @xmath180 . we also obtain some of the critical - ordered boundaries at @xmath181 , @xmath182 , and @xmath183 . these results indicate that the critical region for a given @xmath88 is gradually narrower when @xmath88 increases although the expression of the relationship between @xmath88 and @xmath8 on the boundary is unknown in the present stage . it is reasonable to conclude that the critical region shrinks and goes to the transition point for the infinite - size system . when one can confirm whether the critical region between the two boundaries is sufficiently narrow or not , the width of the region should be regarded as an error coming from the maximum system size and the interval of @xmath8 in the performed calculations . in this work , thus , we conclude @xmath184 . note here that we can obtain the same critical point from @xmath185 in fig.[fig.5](b ) in the same manner . hereafter , we determine critical points with an error in this way . in order to confirm whether the critical behavior ( [ eq.8b ] ) or ( [ eq.10b ] ) appears or not in the original correlation functions , each string correlation function as a function of @xmath77 is shown in the logarithmic scale in inset figures . the finite - size string correlations for each direction clearly reveal a power - law decay behavior at the critical point @xmath156 . on the other hand , a behavior deviating from power - law decay appears in the cases of @xmath186 and @xmath187 in the ordered and disordered phases , respectively , as we have mentioned in [ sec : level3 - 3 ] . note here that a comparison with these insets shows that the system size dependence of the finite - size quantity ( [ eq.11 ] ) sensitively change near the transition point . we next observe the @xmath80 dependence of the finite - size exponents of @xmath168 and @xmath169 for @xmath165 and @xmath188 in fig.[fig.5](c ) . these two finite - size exponents , @xmath163 and @xmath164 , get gradually closer with increasing @xmath80 . in the limit @xmath112 , @xmath163 and @xmath164 appear to approach a single value @xmath1891.2 . this is consistent with the above argument on the unique characteristic length . consequently , the problem of the disagreement of @xmath163 and @xmath164 in the fss analysis occurs due to the finite - size effect and is resolved by gsprg analysis . we now consider the transition point @xmath152 for a fixed @xmath135 . in this case , many studies have reported various estimates for the boundary of the haldane phase , @xmath152 : @xmath190 in ref . @xcite , @xmath191 in ref . @xcite , @xmath192 in ref . @xcite , @xmath193 in ref . @xcite , @xmath194 in ref . @xcite , @xmath195 in ref . @xcite , and @xmath196 in ref . @xcite . among these works , only a single study @xcite was based on the analysis of the string order , although data from the numerical - diagonalization calculations in this study for small clusters might not be sufficient to show the transition point . recently , tzeng and yang @xcite investigated the fidelity susceptibility @xcite of the ground state by the dmrg method to detect quantum phase transitions for the system . this work examines only the information of the ground state , a feature that is shared with our present analysis . other works analyzed the structure of low - energy levels . from the present analysis , our estimate is @xmath197 , which we have obtained irrespective of @xmath120 or @xmath158 . although the estimates are all very close to each other , there are small differences between them even taking errors into account . the reason for these differences is not clear at present and should be resolved as a future issue . next , we consider the transition point @xmath152 for a fixed @xmath121 . the estimation of this point is suitable for checking the availability of our analysis procedure , because a relatively large exponent @xmath198 which is reported 2.38 by analysis of the energy level structure appears @xcite . several previous studies presented numerical data of the transition point as follows : @xmath199 in ref . @xcite , @xmath200 in ref . @xcite , @xmath201 in ref . all of these works examined the free energy near the critical point to determine the critical point . in particular , the recent study @xcite develops rapidly converging methods by using the differentiations of a quantity , which is derivative of the ground state energy with respect to a controlled parameter , as a function of @xmath4 . from the viewpoint of using only information in the ground state for detecting a quantum phase transition , our analysis and their analysis have a common policy . our estimate for @xmath202 is @xmath203 , and this estimate is also consistent with all previous reports . in accordance with the above results , we apply the procedure to estimate the critical behavior for other @xmath7 , confirming the @xmath7 dependence of @xmath204 and @xmath205 . the error of @xmath205 is estimated by @xmath206 . we illustrate our results in fig . [ fig.6 ] together with those of previous reports @xcite . transition line and ( b ) critical exponent @xmath207 . @xmath131 : evaluated value of x - component , @xmath208 : evaluated value of z - component , + : ref . @xcite , @xmath129 : ref . @xcite , @xmath209 : ref . the inset of ( b ) magnifies the data at @xmath210 to allow a clear comparison to distinguish the data . , width=283 ] our estimates of @xmath204 and @xmath205 are common for @xmath120 and @xmath158 within errors . our transition line is almost consistent with those of previous reports @xcite , in which the energy - level structure is analyzed . our estimates of @xmath198 also agree well with previous reports within errors . consequently , our gsprg analysis successfully captures the transition between the haldane phase and the large-@xmath8 phase . the correlation length exponent @xmath198 is known to be related to other critical exponents . in the gaussian transition , okamoto obtained the following relationship from the argument by the bosonization method : @xmath211 where @xmath212 is the exponent defined by @xmath213 at the transition point . note here that @xmath214 holds . to confirm the consistency between our estimate of @xmath198 and the decay of the n@xmath2el correlation function , we plot our @xmath215 at @xmath216 and @xmath217 as a function of @xmath77 on a logarithmic scale in fig . [ sxsx_cor ] . we clearly observe a linear behavior for large @xmath4 . we have added the dotted line @xmath218 with @xmath219 . from eq . ( [ okamoto_relation_nu_eta ] ) , this value of @xmath220 gives @xmath221 , which is consistent with our estimate shown in the inset of fig . [ fig.6 ] . this consistency also supports the scaling hypothesis that the growth of the unique correlation length determines all the critical behavior around the transition point . dependence of @xmath215 at @xmath216 and @xmath217 . the dotted line shows @xmath218 with @xmath219 . , width=283 ] in this subsection , we examine the transition from the haldane phase to the n@xmath2el phase . this transition is considered to be of ising type . we recall that in a transition of ising type , the exponent of the correlation length is @xmath222 when the system approaches the transition point . we have mentioned in the above that the longitudinal string order is nonzero in both of the haldane phase and the n@xmath2el phase and that the order does not reveal the critical behavior at the transition point . this means that the longitudinal string order is not appropriate for studying the haldane n@xmath2el transition . therefore , to study this transition we examine only the transverse string order . by gsprg analysis of this order , we determine the transition point @xmath223 for a given @xmath8 or the transition point @xmath152 for a given @xmath7 and the critical exponent @xmath198 near the transition point . we consider the case of @xmath224 . we illustrate our result for finite - size exponents @xmath225 and @xmath198 in fig . [ fig.7](a ) and ( b ) , respectively . and ( b ) @xmath226 for @xmath227 from our dmrg results for @xmath228 . the dotted curves in ( a ) are guides for the eyes . the dotted line in ( b ) is a linear fitting line applied to the data for large @xmath80 . ( c ) extrapolation procedure of the finite - size critical point @xmath229 for @xmath227 by the numerical - diagonalization method for @xmath230 . the numerical - diagonalization data for @xmath231 are new in this paper . the dotted line is the extrapolation line in ref . the broken curve is a guide for the eyes . , width=283 ] our estimates are @xmath232 and @xmath233 . our estimate of the transition point is different from that of @xmath234 reported in ref . @xcite . to find the reason for the difference between the two estimates , we have made numerical - diagonalization calculations of finite - size clusters up to @xmath235 under the periodic boundary condition and obtained the eigenenergies of the low - energy states . we have performed the same analysis as that in ref . @xcite and determined the finite - size critical point @xmath236 as @xmath7 at which the scaled energy gap does not depend on the system size for @xmath230 . the results are depicted in fig . [ fig.7](c ) . from our numerical data for @xmath237 , we successfully reproduce the results of ref . @xcite . on the other hand , we can observe that @xmath236 of @xmath238 gradually departs from the fitting line of the extrapolation in ref . our new data points approach our estimates from the string order by the dmrg calculations , as shown by the guide for the eyes denoted by the broken curve in fig . [ fig.7](c ) . this agreement suggests that the results from the numerical - diagonalization and dmrg calculations are consistent with each other if we accept the interpretation suggested by the broken curve . hence , careful extrapolation with respect to system size is required . the @xmath80 dependence of our new data appears exponential rather than polynomial . a similar @xmath80 dependence of @xmath239 was reported in ref . @xcite , in which calculations up to @xmath240 based on the multi - target dmrg method with an infinite - system algorithm were carried out under the periodic boundary condition . our result and ref . @xcite suggest that the absence of polynomial components does not depend on the values of the parameters of the system . it is important to be careful when a system - size extrapolation of an ising transition point is carried out by the prg analysis of the energy - level structure . we now compare estimates of the transition point between ref . @xcite and the present analysis . reference @xcite gives @xmath241 . from the present analysis of our data up to @xmath242 , we obtain @xmath243 for the transition point . our estimate , with a very small error , agrees excellently with the estimate in ref . @xcite . we now discuss our estimate of @xmath198 . our estimate @xmath233 is in good agreement with @xmath222 of the ising - type transition . this agreement also suggests that our analysis successfully captures the haldane n@xmath2el transition as well as the haldane large-@xmath8 transition . we can now summarize our results for the transition points @xmath152 for a given @xmath7 and the critical exponents @xmath198 between the haldane and the n@xmath2el phases from our dmrg data . the results are depicted in fig . [ fig.8 ] . el transition points . @xmath131 : our work , + : ref . @xcite , @xmath208 : ref . ( b ) haldane n@xmath2el critical exponent @xmath198 . the inset figure compares our @xmath198 with that of ref . width=283 ] figure [ fig.8](a ) shows that our estimates for the transition points are in good agreement with the results in ref . @xcite of the multi - target dmrg method and the results in ref . @xcite of the numerical diagonalizations . in fig . [ fig.8](b ) , our estimates for the exponent agree well with @xmath222 irrespective of @xmath7 . note here that the center values of our estimates , namely the extrapolated results , are much closer to @xmath222 than the results in ref . @xcite , although our errors are estimated to be larger . note also that the error in @xmath244 is quite large . the reason for this is considered to be that the curve of the haldane n@xmath2el transition points and that of the haldane large-@xmath8 transition points approach each other . a similar phenomenon appears when the central charge @xmath245 on the curve of the haldane large-@xmath8 transition points was estimated in ref . @xcite , in which the estimate of @xmath245 gradually deviates from @xmath246 around @xmath247 . in the report of tzeng and yang @xcite , the transition point and the critical exponent are given as @xmath248 , @xmath249 , respectively , from fidelity susceptibility analysis . our estimated values at the same point are @xmath250 , @xmath251 , which are more precise than the values of tzeng and yang . in this subsection , we examine the transition from the haldane phase to the @xmath96 phase . this transition is considered to be a bkt - type transition . we recall that in a bkt - type transition , the exponents @xmath252 and @xmath253 appear at the transition point and the exponent @xmath198 can not be defined because the correlation length grows exponentially . we consider the case @xmath254 and examine the magnitudes of the string order and the n@xmath2el order . we refer back to the behavior of orders characterizing the haldane phase , in which we have @xmath255 under the condition @xmath256 this means that the region @xmath257 is not in the haldane phase because the inequality ( [ inequality_str ] ) and eq . ( [ vanishing_neel ] ) can not both be satisfied at the same time assuming the inequality ( [ inequality_orders ] ) . however , it is not as easy to make a direct comparison of these quantities in the limit @xmath24 as for the inequality ( [ inequality_orders ] ) . we can instead compare the finite - size quantities @xmath258 and @xmath259 . recall that for @xmath260 , @xmath258 is smaller than @xmath259 when @xmath254 , whereas @xmath258 is larger than @xmath259 when @xmath261 . we have studied the system size dependence of this behavior ; our results are depicted in fig . [ fig.9 ] . . @xmath131 and @xmath127 represent @xmath138 and @xmath132 . , width=283 ] the behavior is clearly independent of system size . we can also confirm this independence irrespective of @xmath8 for cases between the haldane phase and the @xmath96 phase . our present results suggest the inequality ( [ inequality_orders ] ) and indicate that the haldane@xmath96 transition point satisfies @xmath262 . the finding is entirely consistent with previous works . thus , it is sufficient to consider the case of @xmath263 hereafter in examining the haldane@xmath96 transition . we now estimate @xmath264 by our gsprg analysis . we consider the case @xmath265 for @xmath263 . for this purpose , we examine the finite - size exponent @xmath266 , and estimate the critical - ordered boundary point @xmath267 given by eq . ( [ cd - boundary1 ] ) or eq . ( [ cd - boundary2 ] ) . our results are depicted in fig . [ fig.10 ] . . the dotted lines are the rigorous exponent values of the bkt transition : @xmath268 , @xmath269 . @xmath131 , + , @xmath127 , @xmath129 , and @xmath208 represent @xmath270 , 0.1 , 0.15 , 0.18 , and 0.2 , respectively . , width=302 ] we find that the critical - ordered boundary given by eq . ( [ cd - boundary2 ] ) appears when @xmath7 is 0.1 , 0.15 , 0.18 , and 0.2 , but it does not appear when @xmath7 is 0 . concerning with @xmath151-component of the string order , we find the boundaries at @xmath271 , @xmath272 , and @xmath273 . concerning with @xmath62-component of the string order , on the other hand , we have @xmath274 , @xmath275 , and @xmath276 as the boundaries . in the cases of both of the components , one can observe that @xmath90 grows when @xmath7 approaches @xmath270 . these phenomena lead to our result that @xmath264 is between @xmath270 and @xmath277 . for estimating the transition point more accurately , the critical - ordered boundary point is extrapolated to the limit @xmath278 . the results are depicted in fig . [ fig.11 - 5 ] . at @xmath265 as a function of the system size @xmath90 . results are shown for @xmath279 . the error is estimated from the difference between the results for @xmath280 and for @xmath279 . , width=283 ] since the leading dependence of @xmath281 on @xmath282 is unknown , we here choose the power @xmath282 so that the dependence is almost linear . we can successfully determine an appropriate value of the power for each @xmath120 and @xmath158 , although the @xmath120 and @xmath158 values differ from each other . a linear extrapolation gives @xmath283 from the transverse component and @xmath284 from the longitudinal component . here we determine the error as being the difference between the values obtained by the extrapolation and the finite - size critical point @xmath281 for maximum @xmath88 . both results suggest @xmath285 irrespective of the direction of the string order parameter , which is consistent with a previous report @xcite . next , we examine what type of transition this is . our finite - size exponents in fig . [ fig.10 ] at @xmath137 indicate @xmath286 and @xmath287 . these values agree well with the exponents of the bkt transition @xmath288 and @xmath269 . our results are also consistent with many previous works @xcite . therefore , our gsprg analysis applied to the string correlation functions is useful in capturing bkt transitions .

this quantity shows that the finite - size scaling sensitively changes at the critical point . our estimates of the transition point and the critical exponents , which are determined only by the ground - state quantities , are consistent with results obtained from the analysis of the energy - level structure . this work will assist in the development of a method to directly observe quantum phase transitions .

we have developed a numerical procedure to clarify the critical behavior near a quantum phase transition by analyzing a multi - point correlation function characterizing the ground state . this work presents a successful application of this procedure to the string order parameter of the chain with uniaxial single - ion anisotropy . the finite - size string correlation function is estimated by the density matrix renormalization group method . we focus on the gradient of the inversed - system - size dependence of the correlation function on a logarithmic plot . this quantity shows that the finite - size scaling sensitively changes at the critical point . the behavior of the gradient with increasing system size is divergent , stable at a finite value , or rapidly decreases to zero when the system is in the disordered phase , at the critical point , or in the ordered phase , respectively . the analysis of the finite - size string correlation functions allows precise determination of the boundary of the haldane phase and estimation of the critical exponent of the correlation length . our estimates of the transition point and the critical exponents , which are determined only by the ground - state quantities , are consistent with results obtained from the analysis of the energy - level structure . our analysis requires only the correlation functions of several finite sizes under the same condition as a candidate for the long - range order . the quantity is treated in the same manner irrespective of the kind of elements which destroy the order concerned . this work will assist in the development of a method to directly observe quantum phase transitions .

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rich groups and clusters of galaxies are immersed in hot ( @xmath0@xmath4@xmath5 k ) x - ray - emitting gas that constitutes a large fraction of their baryonic mass @xcite . radiative cooling of this gas , by virtue of its x - ray emission , should result in an inflow of relatively cool gas to the cluster center ; i.e. , a x - ray cooling flow @xcite . in the absence of any reheating , this flow is inferred to have mass - deposition rates ranging from @xmath0@xmath6 to @xmath0@xmath7 depending on the given cluster , and over a hubble time ( @xmath0@xmath8 ) should deposit @xmath0@xmath9 to @xmath0@xmath10 of relatively cool gas in the central cd ( giant elliptical ) galaxy ( e.g. , reviews by * ? ? ? * ; * ? ? ? numerous searches have been made for the predicted mass sink from x - ray cooling flows . these searches cover a broad range of temperatures , from ionized gas at temperatures of @xmath0@xmath11 ( e.g. , through the ovi line in the ultraviolet ; * ? ? ? * and references therein ) down to @xmath0@xmath12 ( e.g. , h@xmath13 , @xmath14}$ ] and @xmath15}$ ] lines in the optical ; * ? ? ? * and references therein ) , to neutral gas at temperatures @xmath16 in atomic hydrogen ( 21-cm line ; * ? ? ? * and references therein ) , hot molecular hydrogen ( near - ir vibrational lines ; * ? ? ? * and references therein ) , as well as cool molecular hydrogen ( traced using rotational lines of carbon monoxide at mm wavelengths ; * ? ? ? * ; * ? ? ? * and references therein ) . none of these searches have found gas at quantities anywhere near the abovementioned predicted levels ( prior to the era of the xmm - newton satellite as explained below ) in putative cooling - flow clusters ( e.g. , review by * ? ? ? * ; * ? ? ? * ) . over the past few years , observations of hot gas in galaxy clusters with the xmm - newton and chandra x - ray observatories have radically altered our concept of x - ray cooling flows . spectra taken with xmm - newton at high energy resolution and sensitivity indeed show a decrease in gas temperature towards the cluster center , but fail to reveal any detectable gas at temperatures below about one - third the bulk ambient temperature @xcite . these results provide no evidence for a cooling flow , and imply that any gas cooling to temperatures @xmath17@xmath18 has a mass - deposition rate at least ten times lower than that previously inferred . furthermore , images taken with chandra at high angular resolutions reveal that the x - ray gas at the centers of putative cooling - flow clusters is usually disturbed ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? x - ray cavities are commonly seen , spatially coincident with radio jets from the central galaxy where detectable ( * ? ? ? * and references therein ) , indicating that energetic particles injected from an active galactic nucleus ( agn ) are responsible for the observed disturbances . the work needed to inflate these x - ray cavities implies that the energy output of agns is more than sufficient to balance radiative losses from the x - ray gas , and can therefore greatly diminish if not quench the cooling flow @xcite . against this backdrop , in the last few years searches targeting putative strong cooling - flow clusters have become relatively successful at detecting massive amounts of cool molecular hydrogen gas as traced in carbon monoxide ( co ) at the centers of these clusters @xcite . about twenty such examples are now known , whereas earlier searches ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) detected co gas at the center of only one cluster , the perseus cluster @xcite . the earlier searches targeted relatively nearby clusters which , in the light of the downward revisions in mass - deposition rates , are now known to mostly have very weak if any cooling flows . on the other hand , the more recent surveys @xcite target more distant clusters with higher mass - deposition rates as inferred in the traditional picture of x - ray cooling flows . follow - up imaging where performed reveals that the molecular gas is usually located within a region of @xmath19 kpc coincident with the central galaxy @xcite . the inferred mass of molecular hydrogen gas spans the range @xmath0@xmath20@xmath9 , still much lower than that predicted in the traditional picture of x - ray cooling flows , but closer now to the revised picture given the current upper limits in mass - deposition rates . the amount of cool molecular gas far outweighs all other gas components detected at temperatures below @xmath0@xmath21 combined . these results leave open the possibility that x - ray cooling flows may deposit what is still a massive amount of cool gas compared with that normally present in galaxies ( especially elliptical or cd galaxies ) . a cooling flow , however , is not the only possible source of molecular or other relatively cool gas in cd galaxies . ram - pressure stripping of the interstellar medium of gas - rich galaxies by the hot intracluster medium , or cannibalisms of gas - rich galaxies by the cd galaxy , provide plausible if not more attractive alternatives ( e.g. , reviews by * ? ? ? * ; * ? ? ? * ) . unlike cooling flows , ram - pressure stripping is firmly established to occur in cluster galaxies ( e.g. , review by * ? ? ? * ) , and likewise mergers and cannibalisms in field galaxies ( e.g. , review by * ? ? ? indeed , cd galaxies presumably attained their present - day mass through repeated cannibalisms of cluster galaxies , or repeated merging of subclusters and galaxy groups before or during cluster virialization ( e.g. , see discussion in * ? ? ? * ) . in support of these arguments , a number of elliptical galaxies in the field , members of groups not recognized to have x - ray cooling flows , or those residing in but not at the centers of clusters have been detected in co with inferred molecular hydrogen gas masses of up to several @xmath0@xmath22 ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) . at least one of these galaxies , ngc 759 , resides in but not at the center of a putative cooling - flow cluster , abell 262 . ngc 759 has an inferred mass in molecular hydrogen gas of @xmath23 , at least two orders of magnitude higher than the upper limit placed on the mass of molecular hydrogen gas in the central cd galaxy , ngc 708 @xcite . these results clearly demonstrate that a cooling flow is not the only mechanism capable of depositing large quantities of molecular gas in cluster elliptical galaxies . at the present time , the available observations do not allow us to confidently discriminate between the different possible origins for the molecular ( or other relatively cool ) gas in cd galaxies . yet , naively , such a distinction should be possible simply from the observed spatial distribution and kinematics of the molecular gas . in the absence of any disturbances , the molecular gas deposited by a x - ray cooling flow should simply flow radially inwards along the gravitational potential of the cd galaxy . on the other hand , gas captured from a gas - rich galaxy is expected to orbit ( and hence exhibit a global rotation ) about the cd galaxy , reflecting the orbit ( or passage ) of the gas - rich galaxy around ( or through ) the cluster center or cd galaxy . here , we present a high angular - resolution co observation of the cd galaxy perseus a ( per a ; ngc 1275 ) that reveals for the first time an ordered spatial - kinematic pattern in its molecular gas . located at a comparatively close distance of @xmath074 mpc ( redshift @xmath24 , and assuming @xmath25 and @xmath26 ) , per a lies at the center of the perseus cluster ( abell 426 ) , the x - ray - brightest cluster in the sky . the radiative cooling time in the inner few tens of kpc of the perseus cluster is less than @xmath0@xmath27 , leading to a mass - deposition rate of a few @xmath28 in the absence of any heat input @xcite , the highest of any cluster within its distance . for over a decade , perseus a was the only cd galaxy in a putative cooling - flow cluster known to contain molecular gas , which together with its other peculiarities and relative proximity have made it the subject of intensive studies . this galaxy has been mapped with single - dish telescopes in the @xmath29 @xcite , @xmath30 @xcite , and @xmath31 @xcite transitions of co. the most recent map in co(2 - 1 ) by @xcite , which has the highest angular resolution and covers the widest area , shows that the molecular gas is elongated approximately east - west across the center of the galaxy . in agreement with previous single - dish maps , the molecular gas shows no apparent ordered spatial - kinematic pattern , with predominantly blueshifted velocities both east and west of the nucleus , and velocities near the systemic velocity immediately around the nucleus . the inferred mass of molecular hydrogen gas in per a is @xmath0@xmath1 ( fig . 4 of * ? ? ? * ) , far larger than that yet detected in field or non - cd cluster elliptical galaxies in the local universe ( e.g. , review by * ? ? ? * ) . the only previous inteferometric map of the molecular gas in per a was made in co(1 - 0 ) with the nobeyama millimeter array ( nma ) by @xcite . this map differs in a number of important respects to single - dish maps ( see discussion in * ? ? ? * ) , and bears little resemblence to that shown here in co(2 - 1 ) . we suspect that the co(1 - 0 ) interferometric map may be compromised by inaccurate bandpass calibration , as explained in the next section . the only other published attempt to image the molecular gas in per a with an interferometer was made by @xcite in co(2 - 1 ) with the iram plateau de bure interferometer ( pdbi ) , where virtually all the emission was resolved out . readers interested in the technical details of our observations and data reduction should now proceed to @xmath32 . those interested only in the results can skip ahead to @xmath33 . in @xmath34 we compare the observed properties of the molecular gas with predictions for capture from gas - rich galaxies , and in @xmath35 with predictions for accretion from a x - ray cooling flow . in @xmath36 , we discuss the implications of our results for the cooling flow in the perseus cluster . readers interested only in a concise summary of our results and interpretation can proceed directly to @xmath37 .

we have imaged in co(2 - 1 ) the molecular gas in ngc 1275 ( perseus a ) , the cd galaxy at the center of the perseus cluster , at a spatial resolution of kpc over a central region of radius kpc . per a is known to contain of molecular gas , which has been proposed to be captured from mergers with or ram - pressure stripping of gas - rich galaxies , or accreted from a x - ray cooling flow .

we have imaged in co(2 - 1 ) the molecular gas in ngc 1275 ( perseus a ) , the cd galaxy at the center of the perseus cluster , at a spatial resolution of kpc over a central region of radius kpc . per a is known to contain of molecular gas , which has been proposed to be captured from mergers with or ram - pressure stripping of gas - rich galaxies , or accreted from a x - ray cooling flow . the molecular gas detected in our image has a total mass of , and for the first time can be seen to be concentrated in three radial filaments with lengths ranging from at least 1.12.4 kpc all lying in the east - west directions spanning the center of the galaxy to radii of kpc . the eastern and outer western filaments exhibit larger blueshifted velocities with decreasing radii , whereas the inner western filament spans the systemic velocity of the galaxy . the molecular gas shows no signature of orbital motion , and is therefore unlikely to have been captured from gas - rich galaxies . instead , we are able to reproduce the observed kinematics of the two outer filaments as free - fall in the gravitational potential of per a , as would be expected if they originate from a x - ray cooling flow . indeed , all three filaments lie between two prominent x - ray cavities carved out by radio jets from per a , and closely resembles the spatial distribution of the coolest x - ray gas in the cluster core . the inferred mass - deposition rate into the two outermost filaments alone is roughly . this cooling flow can provide a nearly continuous supply of molecular gas to fuel the active nucleus in per a.

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to better understand the origin of the molecular gas in per a , we have imaged this galaxy in co(2 - 1 ) at an angular resolution of 3 ( spatial resolution of 1 kpc ) with the submillimeter array ( sma ) . single - dish maps with angular resolutions as high as 12 ( 4 kpc ) have previously shown that the molecular gas is concentrated in the east - west direction , and extends @xmath040 ( @xmath014 kpc ) in both directions from center . this gas shows no discernible ordered spatial - kinematic pattern , exhibiting blueshifted velocities both east and west of center , and redshifted velocities at or close to the center . our sma map ( figs . 1 and 2 ) , which covers a region of radius @xmath028 ( @xmath010 kpc ) centered on per a , reveals that : * the molecular gas extends to the edge of our field , and is concentrated primarily in three radial filaments with projected lengths ranging from at least 1.12.4 kpc spanning the galaxy center to 7.7 kpc . these filaments , along with several blobs , have a total mass in molecular gas of @xmath75 , with the three filaments alone containing @xmath0@xmath78 of the detected gas mass . * the bulk of the molecular gas detected ( i.e. , all three filaments and all except two blobs of molecular gas ) is aligned roughly east - west and lie between two x - ray cavities to the north and south of center . this gas is aligned approximately orthogonal to the axis of the radio jets from the agn in per a. * the two outer ( western and eastern ) filaments , and the other blobs of molecular gas , exhibit only blueshifted velocities . the velocities of both these filaments change linearly with radius to larger blueshifted velocities at smaller radii . neither these filaments nor the blobs are coincident with detectable silhouette dust , suggesting that they lie at a relatively large inclination to the plane of the sky on the far ( back ) side of per a. * the inner filament exhibits both blueshifted and redshifted velocities that straddle the systemic velocity of the galaxy . unlike the two outer filaments , the velocity of the inner filament does not change linearly with radius ; furthermore , this filament exhibits smaller blueshifted or larger redshifted velocities at smaller radii . it is not clear whether this filament is coincident with silhouette dust associated with per a. * all the molecular gas detected in the east - west direction is spatially coincident with h@xmath83 gas , often lying against or close to local h@xmath83 brightenings . where measured , specifically at the locations of the inner and western filaments , the velocities of the h@xmath83 gas are comparable with that of the molecular gas . the molecular gas also coincides spatially with a band of relatively cool x - ray gas lying between the two x - ray cavities . * the filaments are unlikely to have been captured from one or more gas - rich galaxies . gas captured in this manner should orbit and hence show a global rotation about the cd galaxy , as has hitherto been the case in all other elliptical galaxies that have been well mapped in co. * lying on the far ( back ) side of per a , the two outer filaments are therefore flowing radially inwards towards the center of the galaxy . the only known process that can naturally deposit gas in this manner is a x - ray cooling flow . * the velocity pattern of the two outer filaments can be easily reproduced as free fall in the gravitational potential of per a , with their outer tips lying @xmath01 kpc downstream from where the cooling gas first decouples from the x - ray gas . both filaments have a dynamical age of @xmath020 myrs , implying a total mass - deposition rate into these filaments of roughly @xmath0@xmath3 ( likely accurate to only a factor of a few ) . * the velocity pattern of the inner filament can not be explained with a simple model . we speculate that this filament likely traces gas settling into the gravitational potential well of per a , and perhaps corresponds ( in part ) to the outer regions of a putative hot molecular hydrogen gas disk with a radius of @xmath050 pc around the agn . despite the strong and widespread heating of the surrounding gas inferred from x - ray observations , our results provide the most direct evidence yet for a ( residual ) x - ray cooling flow in the perseus cluster . this cooling flow may provide a nearly continuous supply of fuel for the agn in per a , which in turn regulates the cooling flow . we thank a. c. fabian and j. s. sanders for kindly providing a fits file of the x - ray image , and c. j. conselice for a fits file of the h@xmath83 image , used in this paper . we thank the second of the two anonymous referees for suggesting changes that improved our presentation . y .- p . ao acknowledges the asiaa for supporting his stay as a visiting scholar , when much of this work was done . j. lim thanks jan vritlek and bill forman for useful discussions during a visit to the harvard cfa , and acknowledges a grant from the national science council of taiwan in support of this work . the submillimeter array ( sma ) is a collaborative project between the smithsonian astrophysical observatory and the academia sinica institute of astronomy & astrophysics of taiwan . lim , j. , leon , s. , combes , f. , & dinh - v - trung 2004 , in penetrating bars through masks of cosmic dust : the hubble tuning fork strikes a new note , ed . d. l. block , i. puerari , k. c. freeman , r. groess , & e. k. block ( dordrecht : kluwer ) , 783 mcnamara , b. r. , wise , m. w. , nulsen , p. e. j. , david , l. p. , carilli , c. l. , sarazin , c. l. , odea , c. p. , houck , j. , donahue , m. , baum , s. , voit , m. , oconnell , r. w. , & koekemoer , a. 2001 , , 562 , l149 cccccccc inner filament & @xmath148 & @xmath149 & @xmath0@xmath150 & @xmath151 & @xmath152 & @xmath153 & @xmath154 + western filament & @xmath155 & @xmath156 & @xmath0@xmath157 & @xmath158 & @xmath159 & @xmath160 & @xmath161 + w1 & @xmath162 & & @xmath0@xmath163 & @xmath164 & & @xmath165 & @xmath166 + eastern filament & @xmath167 & @xmath168 & @xmath0@xmath169 & @xmath170 & @xmath171 & @xmath172 & @xmath173 + e1 & @xmath174 & & @xmath0@xmath169 & @xmath175 & & @xmath176 & @xmath177 + e2 & @xmath178 & & @xmath0@xmath179 & @xmath159 & & @xmath180 & @xmath181 + n1 & @xmath182 & & @xmath0@xmath183 & @xmath184 & & @xmath185 & @xmath186 + s1 & @xmath187 & & @xmath0@xmath188 & @xmath189 & & @xmath190 & @xmath191 + @xcite . contour levels are plotted at -3 , 3 , 4 , 5 , 6 , 7 , @xmath192 ( root - mean - square noise level ; @xmath193 ) . no primary beam correction has been applied to these maps . the gray background corresponds to the integrated co(2 - 1 ) intensity after primary beam correction as shown in figure 2 . the position of the nuclear continuum source in per a is indicated by a cross . the synthesized beam is shown as an ellipse at the lower left corner of the top left panel , and has a size of @xmath44 and position angle @xmath46 . the filaments indicated in figure 2 are not uniformly bright in intensity along their lengths , and hence may not appear continuous in these channel maps.,width=585 ] , and color - coded map of the intensity - weighted co(2 - 1 ) mean velocity measured with respect to the systemic heliocentric velocity of @xmath194 @xcite as indicated by the right vertical bar . the full - width half - maximum of the sma primary beam is 55 ( 20 kpc ) , as indicated by the dotted circle . the integrated co(2 - 1 ) intensity has been corrected for the primary beam response . the map is centered on the active nucleus of per a ( @xmath195 , @xmath196 ) , which was detected in the continuum at the location indicated by a cross . the synthesized beam is shown as a filled ellipse at the lower left corner , and has size of @xmath44 with major axis at a position angle of @xmath46 . the inner , western , and eastern filaments , along with the features e1 , e2 , w1 , n1 , and s1 , are labeled as described in the text . , width=585 ] , ( b ) western filament along a position angle of @xmath197 , and ( c ) eastern filament along a position angle of @xmath198 as a function of velocity . contour levels are plotted at @xmath199 , 2 , 3 , 4 , 5 , 6 , and @xmath200 ( @xmath193 ) . positions correspond to offsets from the center of per a with negative values indicating west , and velocities are measured with respect to the systemic heliocentric velocity of @xmath194 @xcite . in panel ( b ) , the feature at positions @xmath201 and velocities @xmath202 corresponds to the inner filament . in panel ( c ) , the feature at a position of 26 and velocity of @xmath66 that is discontinous in velocity from the eastern filament corresponds to e1 ( fig . 2 ) , which is probably a separate structure as described in the text . ] @xmath116 so that it spans 4.27.4 kpc as indicated by the double - headed arrow . panel ( b ) shows the computed velocity profile of an object dropped from a radius of 12.2 kpc , and superposed the pv - diagram ( contours ; from fig . 4 ) of the eastern filament deprojected by an inclination of @xmath0@xmath117 so that it spans 8.111.3 kpc as indicated by the double - headed arrow . as can be seen , the computed velocity profile assuming a lower galaxy mass of @xmath114 ( solid curve ) better matches the observed pv - diagrams than the computed velocity profile for a galaxy mass of @xmath109 inferred from the luminosity of the galaxy and its estimated mass - to - light ratio as described in the text . ]

the molecular gas detected in our image has a total mass of , and for the first time can be seen to be concentrated in three radial filaments with lengths ranging from at least 1.12.4 kpc all lying in the east - west directions spanning the center of the galaxy to radii of kpc . the eastern and outer western filaments exhibit larger blueshifted velocities with decreasing radii , whereas the inner western filament spans the systemic velocity of the galaxy . the molecular gas shows no signature of orbital motion , and is therefore unlikely to have been captured from gas - rich galaxies . instead , we are able to reproduce the observed kinematics of the two outer filaments as free - fall in the gravitational potential of per a , as would be expected if they originate from a x - ray cooling flow . this cooling flow can provide a nearly continuous supply of molecular gas to fuel the active nucleus in per a.

we have imaged in co(2 - 1 ) the molecular gas in ngc 1275 ( perseus a ) , the cd galaxy at the center of the perseus cluster , at a spatial resolution of kpc over a central region of radius kpc . per a is known to contain of molecular gas , which has been proposed to be captured from mergers with or ram - pressure stripping of gas - rich galaxies , or accreted from a x - ray cooling flow . the molecular gas detected in our image has a total mass of , and for the first time can be seen to be concentrated in three radial filaments with lengths ranging from at least 1.12.4 kpc all lying in the east - west directions spanning the center of the galaxy to radii of kpc . the eastern and outer western filaments exhibit larger blueshifted velocities with decreasing radii , whereas the inner western filament spans the systemic velocity of the galaxy . the molecular gas shows no signature of orbital motion , and is therefore unlikely to have been captured from gas - rich galaxies . instead , we are able to reproduce the observed kinematics of the two outer filaments as free - fall in the gravitational potential of per a , as would be expected if they originate from a x - ray cooling flow . indeed , all three filaments lie between two prominent x - ray cavities carved out by radio jets from per a , and closely resembles the spatial distribution of the coolest x - ray gas in the cluster core . the inferred mass - deposition rate into the two outermost filaments alone is roughly . this cooling flow can provide a nearly continuous supply of molecular gas to fuel the active nucleus in per a.

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recently we have proposed @xcite that the 750gev - resonance@xcite - which now turned out to be only a statistcal fluctuation@xcite - were our long speculated and waited for bound state@xcite of 6 top + 6 anti top quarks . the very suggestive existence of the bound state as well as the in the present article to be presented `` calculations '' of the masses of the bound state and of a compositum of two of these bound states is heavily based on our the even longer ago speculated idea of a new principle , `` multiple point principle '' @xcite , causing restrictions between coupling constants and thus potentially serving as a candidate for solving fine tuning problems@xcite . this `` multiple point principle '' ( = mpp ) says , that there are several vacua with extremely small energy densities . we could also say , that it means that the universe - vacuum is just at some multiple point , where several phases can coexist , much like one at the triple point for water has coexistence of ice , fluid water , and vapor for a common set of intensive variables , pressure and temperature . there may be no real good derivation or argument for our multiple point principle in spite of the fact , that we and others have publiched some attempts to derive this principle @xcite , but all such arguments would have to involve some influence of the future on the passed , at least on the coupling constants , and that would make all such derivations of mpp suspicious . the reader should rather take some previous works - even _ pre_diction(s ) - as well as the results of the present work as _ empirical _ evindence for this new law of nature , the `` multiple point principle '' . the calculation to be presented below is indeed just a slightly renewed version of the calculation delivered in the appendices of our earlier article @xcite , in which it is heavily used , that there should exist a new vacuum degenerate in energy density with the present one and with an approximated structure , as if the s - particles(what we called our bound state , which so much happened to fit the by now digamma fluctuation called in its fashion f , that we shall call it f now ) were sitting as the carbon atoms in the diamond chrystal , as we shall review in section [ modelling ] . colin froggatt and i ended in these appendices@xcite with a mass 260 gev for the bound state , but we certainly did not believe our mass _ pre_diction 260 gev to be very accurate . for the trustworthiness of our whole story the recent work of larisa laperashvili , chitta das and myself @xcite relating the _ mass of _ the speculated _ bound state to _ the degree of instability/_negative energy density _ of the second minimum in the standard model higgs field effective potential calculted without inclusion of our bound state . the point is that in order to achieve just zero energy density ( as our multiple point principle requires ) for the vacuum represented by the second minimum the correction required is just getting right for the mass of the bound state f being in a range very close to 750 gev . we shall return to this work in the last subsection in the conclusion [ larisaetal ] . in the following section [ boundmpp ] we shall review our model of there existing an exceedingly strongly bound system of 6 top + 6 anti top quarks , and of our `` multiple point principle '' fine tuning the coupling constants , so that for instance a condensate of the bound state can fill the vacuum and cause a `` new vacuum '' with the energy density just finetuned to be again remarkably small , of the same order as say the astronomical observation of the energy density(= cosmological constant ) of the vacuum , in which we live . ( this astronomically observed cosmological constant is quite negligible compared to the energy densities of any significance for high energy physics parameters such the bound state mass or the higgs mass ) . a subsection [ mpp ] of this section [ boundmpp ] is assigned to our `` new law of nature'',``multiple point principle '' . in the next section [ modelling ] we then model in a very crude approximation and in a non - relativistic picture the just mentioned new vacuum ] in our model called the `` condensate vacuum '' as containing a bose - condensate of the f bound states by suggesting as a very crude approximation , that this vacuum has a system / a lattice of f(750 ) particles interacting with their neighbors contained in the vacuum . we take the `` atoms''= the f s in this lattice to interact in analogy with the carbon atoms in a diamond chrystal . in order to compare the interactions and the binding energies we ignore the effect , that when a top quark goes around /is bound to a swarm of with the same radius bound quarks and antiquarks , it only `` feels '' the force from about half the number of particles in the swarm . however , we argue in section [ accident ] , that the exchange of what we call `` eaten higgses '' , and which really is exchange of the longitudinal components of weak gauge bosons w and z , _ happens _ with help of gluons also just accidentally to cancel this effect . it is very important for the success of our whole picuture of bound states and a vacuum condensate numerically , that inside the bound state f as well as in the condensate vacuum the effective higgs - mass is appreciably lower than the higgs mass of 125 gev observed experimentally . since , however , the higgs field expectation value inside the bound state and inside the condensate vacuum is significantly lower than in the usual vacuum , the higgs self - interaction indeed cause a smaller higgs mass effectively in these places with many top and anti top around on the average . this deminished effective higgs mass is discussed in section [ effhiggsmass ] . in section [ potentialapproximation ] we then for simplicity make the very crude assumption of approximating the exponential factor @xmath0 in the higgs - yukawa - potential by a step - function , a @xmath1 meaning , that we put the higgs _ mass _ to zero for small distances , while we put the higgs _ yukawa potential _ to zero for large distances . next in section [ mass750 ] we `` calculate '' or rather very crudely estimate the mass of the bound state f _ from the requirement of the mpp assumption of the equality of the energy density of the `` condensate vacuum '' and the vacuum , we live in_. so our new principle mpp is really crucial for our mass prediction ! in section [ mass1c8 ] we also with the same picture discuss the at lhc actually first found possible resonance -of mass 1.8 tev - seen ( ? ) decaying into weak gauge bosons(it is very dobtful ) . we take this resonance to be composite from a couple of f s as very weakly suggested from the mass of the 1.8 tev ( we shall see combining the present work with our earlier work with laperashvili and das @xcite that an f - mass around 800 gev is called for ) possible particle being crudely twice that of f. a little problem for our interpretation of the 1.8 tev state this way may be its relatively small width observed . the problem is dicussed a bit in the subsection [ width ] . in section [ conclusion ] we review and comment our result . in the subsection [ larisaetal ] we summarize , that the value for the bound state estimated in the present article - developping the result of @xcite - and the value for the bound state needed for a quite different multiple point principle requirement coincides remarkably !

it is crucial to assume , that our since long speculated principle `` multiple point principle '' is true . this principle says : _ there are several vacua all having almost zero energy density_. further we make an approximation of the higgs yukawa potential essentially replacing the exponential in it by a step - function . ( speculative ) vacua occuring in the pure standard model .

we have long speculated , that 6 top + 6 anti - top quarks due to the realtively large size of the top - yukawa coupling would bind exceptionaly strongly by mainly higgs exchange . here we present a surprisingly simple `` calculation '' of the mass of this speculated bound state . even a possible resonance in scattering of two such bound states is speculated . for the `` calculation '' of the masses it is crucial to assume , that our since long speculated principle `` multiple point principle '' is true . this principle says : _ there are several vacua all having almost zero energy density_. further we make an approximation of the higgs yukawa potential essentially replacing the exponential in it by a step - function . the new result means that there are now two independent calls for our bound state having the mass around 750 gev required by our `` new law of nature '' the multiple point principle . it should be remarked that in our picture there is _ no new physics _ in the sense of new fundamental particles , but the `` multiple point principle '' is new in the sense of being not yet accepted . further we get the _ same _ mass within uncertainties as earlier but now from a completly different assumption , except for being from our `` multiple point principle '' . but the two masses are gotten from using _ different _ ( speculative ) vacua occuring in the pure standard model .

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we have presented an overly simple `` calculation '' leading to there being due to the strong top - yukawa coupling and under the assumtion of a finetuning ensuring a with the normal vacuum degenerate one with a condensate of bound states s = f of six top + six anti top , two `` resonances '' with masses respectively @xmath56 these results were obtained in the philosophy , that the coupling constants - especially say the top - yukawa - coupling @xmath9 - are by the new principle `` multiple point principle '' adjusted / finetuned to make the energy density of a condensate of f - particles - which _ we _ earlier caled s - particles - ( the bound states of 6 top + 6 anti top quarks ) have just the same energy density as the usual vacuum ( in which we live ) . that were to say , that the interaction between the f - particles in the condensate should be just so strong an attracktion between them , that the total energy ( density ) of the condensate just becomes zero ( relative to the normal vacuum ) . that is to say the binding between the neighboring f - states just equals the mass - energies of these f - states . if one therefore considers our good agreement of the masses as an evidence for the truth of the assumptions having been used , then there is a significant evidence for our long speculated `` multiple point principle '' ! it must , however , be admitted that the present very simplified `` calculation '' were based on a very crude treatment of the yukawa potential representing the higgs exchange between the f - particles , which is the ( main ) interaction between these f - particles in our picture . in fact we approximated higgs exchange by letting the higgs be effectively massless , when the top - antitop quarks are in relative orbits with atomic main quantum number n=1 , while we let the higgs potential be totally cut away for n=3 , 4 , ... . for the main quantum number n=2 we made the more complicated assumption of letting it be either as for a zero mass higgs or cut down to zero according to the surroundings , which influence the average higgs field . indeed we took for n=2 the higgs exchange force to be like for massless higgs inside the condensate vacuum , while we put the exchnage potential to be zero , when applied in the two - f - system identified with the 1.8 tev excess seen decaying into weak gauge bosons . thus more severe calculations are to be performed to truly settle , if our calculations are right . it should in this connection be stressed , that since our model is in principle _ only standard model _ extended with our multiple point principle used to restrict the coupling constants , one should in principle be able to calculate whatever one wants . with a relatively strong coupling @xmath9 being the very basis for the whole story there is though of course the complication of not having in principle the basis for perturbation theory . a recent work by larisa laperashvili , chitta das and myself@xcite , in which we have the f - resonance give a little correction to the mass of the higgs , that should be measured relative to the one associated with the running self coupling at the weak scale , improves the agreement with exoeriment of requirement of multiple point principle for yet a vacuum . indeed we have in our picture a third vacuum ( in addition to the usual one and the condensate vacuum with its f(750 ) s in it ) , namely one with a very high higgs field expection value . according to standard model caculations witout our bound state the high higgs field vacuum has a slightly _ negative _ energy density ( compared to the two other vacua ) . however , we find a little correction depending among on other quantities on the mass of the bound state . we found that this bound state mass put to 750 gev would fit wonderfully and consider , that this fact strongly supports the truth of mpp . in fact it turns out that the mass 750 gev for the bound state f is perfect for the correction of ours just to bring the energy density of the vacuum with the high higgs field expectation value from its otherwise slightly negative value to zero . this means that our multiple point pinciple using a quite third vacuum , namely one with a high higgs field expectation value of the order of @xmath57 gev , leads to a need for a particle - our bound state indeed - with a mass about the 750 gev also . this means that now , when the f(750 ) fluctuation digamma once so fashionable turned out being only a statistical fluctuation , then we would nevertheless from multiple point principle get _ two different and essentailly independent reasons for our bound state to have the mass near the value 750 gev_. that is to say we would then claim , well our bound state should be with a mass close to 750 gev . we have already two calculations of this mass in different ways , although both originating from the same principle mpp , but involving quite different data to fit . in fact larisa laperashvili et al . @xcite uses a corection due to the diagram in order to correct the running self coupling of the higgs @xmath58 corresponding to the observed higgs mass 125 gev to go from the value obtained by degrassi et al . @xcite of @xmath59 at the high field scale @xmath60 to the value very accurately zero requied by multiple point principle(=mpp ) . since bound state f is an extended object we must include a formfactor , when using it . defining a quantity @xmath61 denoting the radius of the bound state measured with top quark compton wave length @xmath62 as unit by : @xmath63 we obtain a theoretical estimate @xmath64 crudely confirmed by a slightly different estimate . the dominant diagram / correction - the first and quadratic of the diagrams on the figure just above - is @xmath65 where we have the estimated or measured values @xmath66 using the after all rather small deviation from perfect mpp @xmath67 and requiring it to be cancelled by the correction from the bound state we get the requirement @xmath68 where @xmath69 , @xmath70 , @xmath71 and the factor `` @xmath72 '' were taken in to approximate some neglected diagrams , as the next on the figure . if a nearer study should show that the next diagrams add up to roughly as much as the first one should include the factor @xmath73 to take into account the neglected feynman diagrams correcting the higgs self coupling . the solution w.r.t . the mass of the bound state @xmath74 gives @xmath75 the `` without the @xmath73 '' means what one shall do if the first diagram indeed dominates strongly . in this way we got even two calculations for the bound state mass - using in addition crude estimation - @xmath76 the agreement of the value `` 692 gev '' with the estimate(s ) from the completly different vacuum with the high higgs field `` 850gev '' or `` 710 gev '' is encourraging and a support of our `` multiple point principle '' ! if our numbers are taken as so convincing that our picute should be taken seriously then we would have the consequences : * we must take our `` multiple point principle '' as a true new physical law , even the mechanism behind it may not be clear . * we must accept that the standard model except for `` smaller '' deviations , that are too small to significantly modify the running of the higgs self coupling , is valid all the way to about @xmath77 gev . some see - saw neutrinos may be acceptable , as long as they do not couple too strongly to the higgs to influence the running of its sef coupling . otherwise it would be very accidentally that a pure standard model calculation would give so consisten results . + so there would not be much place for new physics except for the various resonances formed from the boud states , because we now have a new regime of strong interactions that can only be treated by non - perturbative methods . ( the suggestion for the 1.8 tev resonance is an example for how there can be more particles in such a new strong interaction regime ) * there should be seen sooner or laler bound state of the 6 top + 6 anti top with a mass not far from 800 gev . but even if it thus looks a bit sad w.r.t . much new physics , one should not forget that having our multiple point principle established would be a strong element of new physics , perhaps then of an a bit unexpected type .

we have long speculated , that 6 top + 6 anti - top quarks due to the realtively large size of the top - yukawa coupling would bind exceptionaly strongly by mainly higgs exchange . here we present a surprisingly simple `` calculation '' of the mass of this speculated bound state . the new result means that there are now two independent calls for our bound state having the mass around 750 gev required by our `` new law of nature '' the multiple point principle . it should be remarked that in our picture there is _ no new physics _ in the sense of new fundamental particles , but the `` multiple point principle '' is new in the sense of being not yet accepted . further we get the _ same _ mass within uncertainties as earlier but now from a completly different assumption , except for being from our `` multiple point principle '' .

we have long speculated , that 6 top + 6 anti - top quarks due to the realtively large size of the top - yukawa coupling would bind exceptionaly strongly by mainly higgs exchange . here we present a surprisingly simple `` calculation '' of the mass of this speculated bound state . even a possible resonance in scattering of two such bound states is speculated . for the `` calculation '' of the masses it is crucial to assume , that our since long speculated principle `` multiple point principle '' is true . this principle says : _ there are several vacua all having almost zero energy density_. further we make an approximation of the higgs yukawa potential essentially replacing the exponential in it by a step - function . the new result means that there are now two independent calls for our bound state having the mass around 750 gev required by our `` new law of nature '' the multiple point principle . it should be remarked that in our picture there is _ no new physics _ in the sense of new fundamental particles , but the `` multiple point principle '' is new in the sense of being not yet accepted . further we get the _ same _ mass within uncertainties as earlier but now from a completly different assumption , except for being from our `` multiple point principle '' . but the two masses are gotten from using _ different _ ( speculative ) vacua occuring in the pure standard model .

0808.3393

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four of the sb2 solutions shown in figures [ fig : sb2plots1 ] and [ fig : sb2plots2 ] depend on a single measurement of the secondary velocity , and another nine on only two measurements . consequently , many of the derived @xmath48 s , and the resulting @xmath6 s , have large uncertainties . figure [ fig : qvsqmin ] plots @xmath28 against the measured @xmath6 s to evaluate the plausibility of the measured values . as expected , @xmath6 is greater than or within @xmath56 of @xmath28 for all of the binaries , except vb 59 and h382 which are consistent with @xmath28to better than @xmath68 . both vb 59 and h382 have long periods and were observed at orbital phases where the velocity separation was small , resulting in low precision measurements of @xmath48 . however , we have two observations of each system at slightly different phases and the measured secondary velocities are consistent . therefore , we are confident that we are detecting the secondary in both of these systems . observations of vb 59 in @xmath69 and of h382 as soon as @xmath70 , when the orbital phases will have changed significantly , would further improve the sb2 solutions for these systems . the flux ratio , @xmath7 , measured by our cross - correlation routine offers an additional validation of each sb2 solution . figure [ fig : qvsalpha ] plots the @xmath7 measured for each binary , averaged over all observations , against the measured mass ratio . also shown are theoretical _ h_-band curves calculated from bcah for binaries with primary masses from 0.6@xmath11 to 1.2@xmath11 . two factors complicate a direct comparison between our measured flux ratios and the theoretical values . first , the small wavelength range of cshell spectra severely limits our ability to measure precise flux ratios because individual spectral lines vary only a small amount relative to each other with changing spectral type . considerably more accurate flux ratios can be measured with spectra covering a larger wavelength range , and thereby having many more spectral lines with differing dependencies on spectral type . second , the theoretical curves represent the integrated flux over the entire _ h_-band , of which our cshell spectra only sample @xmath71 . nonetheless , our measured values are well grouped along the curves . the two obvious outliers are l79 and vb 142 . we have only a single , low s / n observation of the long period binary l79 . our measured flux ratio is poorly constrained , varying significantly depending on the exact pair of templates used ; the uncertainty shown in the figure probably underestimates the actual uncertainty . however , our measured secondary velocity is well constrained , independent of the template pair , and we are confident that the secondary detection is real . vb 142 has a very small mass ratio , making the measurement of the companion particularly difficult ; [ vb142 ] addresses this system in detail . our infrared observations failed to detect the secondary in seven systems : vb 8 , vb 30 , vb 39 , h411 , l77 , l90 , and vb 114 . figure [ fig : qminhist ] shows the distribution of @xmath28 for the infrared sample binaries ; the systems not detected as sb2s are indicated by the hashed region . we expected that our sensitivity to binary companions would be incomplete for systems with the smallest mass ratios because these systems also have small flux ratios . however , several of the systems for which we did not detect the secondary have large @xmath28 . for three additional systems , vb 43 , l57 , and h509 , we did not detect the secondary in a subset of our observations . we address each of these ten systems below . vb 8 and vb 30 have rapidly rotating f - type primary stars and both have small @xmath28 , 0.15 and 0.19 , respectively . we observed both spectra in the infrared at multiple epochs , with orbital phases where the predicted velocity separation was large . we propose two possible explanations for our failure to detected these companions . the true value of @xmath6 may actually be close to @xmath28 . for a given mass ratio , the _ h_-band flux ratio of a binary decreases as the mass of the primary increases . because vb 8 and vb 30 have primaries more massive than those of a typical binary in our sample , their flux ratio s may be too small to detect the secondaries at the s / n of our spectra . alternatively , if the companions are also rotating rapidly , their spectral lines would be too broad to measure with cshell s limited wavelength coverage , even with high s / n observations . vb 114 and vb 39 have orbital periods of 4578 days and 5083 days , respectively . our observations of both systems occurred at orbital phases such that the primary velocities were near @xmath25 , and the predicted velocity separations were only a few @xmath29 . velocity measurements under such conditions are inherently difficult , and even had we detected the secondary components , the resulting @xmath48 s would be poorly constrained . vb 114 will have a more favorable orbital phase in @xmath122010 ; the phase of vb 39 will not improve until @xmath122013 . both have moderate @xmath28 , 0.44 for vb 39 and 0.29 for vb 114 , so the flux ratios should not impede in detecting these secondaries . h411 , l77 , and l90 fall towards the faint edge of the distribution shown in fig . [ fig : hmag ] , and our observations of these targets have s / n insufficient to detect their secondaries . h411 has a small @xmath28 , @xmath72 , which corresponds to a minimum h - band flux ratio of only a few percent , and is at the limit of our best observation of this binary , with s / n@xmath1250 . because h411 is faint , obtaining a spectrum with cshell that has better s / n would require many hours of integration ; such an observation could be carried out with a high resolution spectrometer at an @xmath73 m telescope in a relatively small amount of time . l77 has a large @xmath28 of @xmath74 and we expected to be sensitive to its secondary . however , our single observation of l77 has s / n@xmath1225 , and occurred at an orbital phase when the velocity separation was small . the orbit of this system is such that even had we detected the secondary , the resulting sb2 orbit would be largely unconstrained . l77 will be at a more favorable orbital phase in 2009 . l90 has @xmath75 ; we observed it on two occasions , each with s / n@xmath1250 . however , its long period and current orbital phase indicate a small velocity separation . this system will not be at a more favorable orbital phase until @xmath122011 . we did not detect a companion in our observations of vb 43 on 2005 sep 30 , l57 on 2005 nov 25 and 2006 feb 2 , and h509 on 2005 oct 2 . each of these observations were carried out at orbital phases corresponding to primary velocities near @xmath25 . the observation of vb 43 was compromised further by a low s / n , relative to our other observations of it . l57 has small @xmath24 and @xmath48 , which when combined with it s k2 primary spectral type make it a difficult target to observe with cshell : future observations would benefit from higher spectral resolution or a larger free spectral range . our four infrared observations of vb 142 provided good phase coverage , and included measurements near the maximum velocity separation and on both sides of the @xmath25-velocity . despite this , the sb2 solution that we derive is poorly determined and the residuals , @xmath76 , are large . we do not fully understand the reasons behind this poor solution , but we include it here for the following reasons . our observations , except for that on 2005 november 28 , return plausible velocities for the companion , albeit with large uncertainties . the 2005 november 28 observation occurred at phase @xmath77 , and with small velocity separation , so our inability to accurately measure the secondary in this spectrum is not surprising . the average @xmath7 that we measure for all of the observations , @xmath78 , is , however , much larger than that predicted by bcah ( figure [ fig : qvsalpha ] ) . to investigate this discrepancy we used our m - type template lhs2351 to introduce an additional spectrum into our observed vb 142 spectra from 2004 october 1 and 2005 february 22 . we added in this component with a `` true '' flux ratio , @xmath79 , ranging from 0.05 to 0.0001 , and , to avoid confusion with the actual vb 142 companion , at a radial velocity of @xmath80 . we then attempted to recover this signal with our correlation procedure and the set of templates used in the original vb 142 analyses , excluding lhs2351 . we recovered the lhs2351 spectrum at the proper velocity with @xmath79 as small as 0.0005 . however , the uncertainty of the measured velocity increased as @xmath79 decreased , and the measured flux ratio , @xmath81 became unreliable for @xmath82 . consider , for example , the case of lhs2351 introduced into the 2005 february 22 spectrum with a radial velocity of -20@xmath29 and @xmath83 . our correlation routine recovered this signal with a velocity of @xmath84 and @xmath85 . the larger than expected @xmath81 is consistent with the results obtained for the vb 142 companion , and may arise because our primary templates do not precisely match the vb 142 primary spectrum . for small flux ratios , the correlation routine tries to correct for this mismatch by scaling the primary using @xmath7 ; we have previously reported this behavior @xcite . our modeling with lhs2351 gives us confidence that we can detect a companion with a very small flux ratio . the @xmath6 that we derive for vb 142 , @xmath86 , is consistent with @xmath87 from the sb1 solution . whatever the true value of @xmath6 may be , our @xmath88 upper limit of @xmath89 is very small . our primary goal in this endeavor is to measure the binary mass ratio distribution for the hyades ( 1 ) : @xmath6 for vb 142 is sufficiently well determined for this purpose . of additional interest , the primary of vb 142 is a g5 star , and so a companion with @xmath2 could be a brown dwarf , which would be an important discovery in the hyades @xcite . while spectroscopic observations of an sb2 yield its dynamical mass ratio , they do not measure its orbital inclination and so alone they can not provide a dynamical measurement of the individual component masses . observations of the visual orbit measure the inclination and the total mass , and when combined with the mass ratio result in the individual masses . all of the binaries in our sample have components with a small angular separation and their visual orbits are not currently available . those with periods longer than a few hundred days are resolvable with adaptive optics imaging at a large aperture telescope . in the absence of visual orbits , we can still obtain good estimates of the individual masses if the distance is known . _ hipparcos _ measured the parallax of most of our sample binaries @xcite , and all have precise photometric measurements of their total flux from 2mass at j , h , and k. we combined these with our measured mass ratios and a theoretical mass - luminosity isochrone from bcah to calculate the individual component masses . we chose the bcah models for several reasons : they show a good , albeit not perfect , agreement with measured dynamical masses @xcite ; they include the effects of atmospheres , which are important in the low mass regime that applies to most of our secondaries ; and lastly , they are provided in a convenient form that specifies magnitudes in the standard photometric bands used by observers . we used the 625 myr isochrone , while noting that at such an old age the mass - luminosity relationship is mostly insensitive to age . table [ table : componentmasses ] lists the calculated component masses . the uncertainties given in table [ table : componentmasses ] include contributions from the parallax , photometry , and mass ratio ; they do not include any uncertainties from the bcah models . all of the 2mass j , h , and k photometric uncertainties are small , @xmath90 mag . because our binaries have small flux ratios , the precision with which we determine the primary masses is mostly dependent on the precision of the parallax measurements . the uncertainty for the secondaries strongly depends on the precision of the mass ratios . most of the primaries have masses determined to better than 10% , while some of the secondaries approach this level . _ hipparcos _ did not measure the parallax of vb 59 or l57 , so for these systems we used values reported in the tycho catalog , and the resulting uncertainties on both the primary and secondary masses are large . the parallaxes of h69 , h441 , and l79 have not been measured , so we estimated their primary masses directly from their spectral type and assumed an uncertainty of @xmath91 . the secondary masses then follow directly from our measured mass ratios . finally , the primary of vb 68 is more massive than the range covered by bcah , so for this system only we used the empirical isochrone determined by @xcite and note that the resulting masses are consistent with measured spectral types .

we combine our double - lined infrared measurements with well constrained orbital parameters from visible light single - lined observations to derive dynamical mass ratios . using these results , along with photometry and theoretical mass - luminosity relationships , our emphasis is on measuring these distributions , not on measuring precise orbital parameters for individual binaries .

we have observed a large sample of spectroscopic binary stars in the hyades cluster , using high resolution infrared spectroscopy to detect low mass companions . we combine our double - lined infrared measurements with well constrained orbital parameters from visible light single - lined observations to derive dynamical mass ratios . using these results , along with photometry and theoretical mass - luminosity relationships , we estimate the masses of the individual components in our binaries . in this paper we present double - lined solutions for 25 binaries in our sample , with mass ratios from . this corresponds to secondary masses as small as . we include here our preliminary detection of the companion to vb 142 , with a very small mass ratio of ; this indicates that the companion may be a brown dwarf . this paper is an initial step in a program to produce distributions of mass ratio and secondary mass for hyades cluster binaries with a wide range of periods , in order to better understand binary star formation . as such , our emphasis is on measuring these distributions , not on measuring precise orbital parameters for individual binaries .

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we have obtained high resolution infrared spectroscopy of 32 sbs in the hyades , whose sb1 orbital parameters have been measured by rps and dwl at the cfa , in order to detect their companions and thereby study the binary mass ratio distribution in this young cluster . we detected the companion in 25 of these systems . for these , we combined our results with the sb1 parameters to determine their solutions as sb2s . some of the sb2 solutions we report have low precision for @xmath48 . however , obtaining precise orbital parameters for individual systems was not our objective here . instead , our intent was to constrain the _ distribution _ of mass ratios in binaries with low mass companions , and our results are sufficient for this purpose . we also estimated the primary and secondary masses of our sample binaries using 2mass photometry , _ hipparcos _ parallax measurements , and our measured mass ratios . the mass ratios of the binaries with the most reliable sb2 solutions span the range from @xmath92 , corresponding to secondary masses as small as @xmath1 . we also detect a very low mass companion to vb 142 . the solution for its mass ratio is not yet reliable , but it appears to be @xmath89 at the @xmath88 level , and may represent the detection of a brown dwarf companion . the precision of our derived primary masses is limited by the uncertainties in the _ hipparcos _ parallax measurements . the secondary mass measurements , however , can be improved significantly by reducing the uncertainties on the measured mass ratios through additional infrared observations . direct observations of sample members as visual binaries would measure their orbital inclinations and total masses , and when combined with the spectroscopy would yield dynamical component masses . by utilizing the _ hipparcos _ distances , such measurements would contribute a test of the theoretical mass - luminosity relationships ( e.g. , * ? ? ? improving the sb2 solutions or measuring the visual orbits of our sample would require a significant commitment of observing time and analysis resources . the visual orbit mapping may require technological improvements in interferometry and adaptive optics techniques . the results presented here are an initial step in a program to produce distributions of mass - ratio and secondary mass for hyades cluster binaries with periods from a few days to a few thousand days . future papers in this series will combine our new determinations of mass ratios with available orbital solutions from other hyades binary surveys , including the the spatially resolved systems studied by @xcite , to present the mass ratio and secondary mass distributions for the cluster . we also intend to address more fully the set of hierarchical triple systems , for which , when combined with the speckle observations of @xcite , we have information on both the inner and outer orbits . we are grateful to dwl and rps for providing the cfa sb1 parameters and for numerous discussions that improved the manuscript . we also thank the referee for several educational suggestions concerning the secondary velocity precision . we thank l. prato for providing the nirspec observations , t. mazeh for suggesting the procedure used to estimate the velocity uncertainties , and the telescope operators and staff at the irtf for their support during our many observing runs . the authors are visiting astronomers at the infrared telescope facility , which is operated by the university of hawaii under cooperative agreement no . ncc 5 - 538 with the national aeronautics and space administration , science mission directorate , planetary astronomy program . cb is supported by an nrc research associateship award at nrl . basic research in infrared astronomy at nrl is supported by 6.1 base funding . the authors were supported at stony brook in part by nsf grants 02 - 05427 and 06 - 07612 . data presented herein were obtained at the w.m . keck observatory , which is operated as a scientific partnership among the california institute of technology , the university of california and the national aeronautics and space administration . the observatory was made possible by the generous financial support of the w.m . keck foundation . this research made use of the simbad database , operated at cds , strasbourg , france , data products from 2mass , which is a joint project of the university of massachusetts and ipac at the california institute of technology , funded by nasa and nsf , and the hipparcos and tycho catalogues , esa sp-1200 . the authors wish to extend special thanks to those of hawaiian ancestry on whose sacred mountain we are privileged to be guests . lcccccc vb 8 & 25102 & 03 59 40.49 & + 10 19 49.4 & f5 & 6.4 & 5.4 + vb 9 & & 04 00 39.54 & + 20 22 49.5 & g4 & 8.7 & 7.0 + l20 & 284163 & 04 11 56.22 & + 23 38 10.8 & k0 & 9.4 & 6.6 + h69 & & 04 12 21.44 & + 16 15 03.5 & m1 & 14.0 & 9.1 + vb 30 & 27397 & 04 19 57.70 & + 14 02 06.7 & f0 & 5.6 & 4.9 + l33 & 286770 & 04 22 25.69 & + 11 18 20.6 & k8 & 9.8 & 7.1 + vb 40 & 27691 & 04 22 44.17 & + 15 03 21.9 & g0 & 7.0 & 5.6 + vb 39 & 27685 & 04 22 44.78 & + 16 47 27.7 & g4 & 7.8 & 6.3 + vb 43 & 284414 & 04 23 22.85 & + 19 39 31.2 & k2 & 9.4 & 7.3 + vb 59 & 28034 & 04 26 05.86 & + 15 31 27.6 & g8 & 7.5 & 6.2 + vb 62 & 28033 & 04 26 18.50 & + 21 28 13.6 & f8 & 7.4 & 6.1 + h382 & 28068 & 04 26 24.61 & + 16 51 12.0 & g1 & 8.0 & 6.6 + h411 & 285828 & 04 27 25.34 & + 14 15 38.5 & k2 & 10.3 & 7.8 + l57 & 285766 & 04 27 58.96 & + 18 30 00.9 & k2 & 10.2 & 7.7 + vb 68 & 28294 & 04 28 23.40 & + 14 44 27.5 & f0 & 5.9 & 5.1 + vb 69 & 28291 & 04 28 37.21 & + 19 44 26.5 & g5 & 8.6 & 7.0 + h441 & 285806 & 04 28 50.81 & + 16 17 20.3 & k7 & 10.7 & 7.6 + vb 77 & 28394 & 04 29 20.55 & + 17 32 41.8 & f7 & 7.0 & 5.8 + h509 & 28634 & 04 31 37.10 & + 17 42 35.2 & k2 & 9.5 & 7.3 + h532 & 286839 & 04 32 25.65 & + 13 06 47.6 & k0 & 11.0 & 7.8 + vb 96 & 285931 & 04 33 58.54 & + 15 09 49.0 & k0 & 8.5 & 6.6 + l79 & & 04 34 10.73 & + 11 33 29.6 & k7 & 11.7 & 8.3 + l77 & & 04 34 49.76 & + 20 23 41.6 & k7 & 11.1 & 8.0 + vb 102 & 29310 & 04 37 31.98 & + 15 08 47.2 & g1 & 7.5 & 6.1 + l90 & 29896 & 04 43 15.70 & + 17 04 08.8 & k0 & 9.9 & 7.5 + vb 142 & 30246 & 04 46 30.39 & + 15 28 19.4 & g5 & 8.3 & 6.8 + vb 113 & 30311 & 04 46 45.58 & + 09 01 02.7 & f5 & 7.2 & 5.9 + vb 114 & 30355 & 04 47 37.57 & + 18 15 31.4 & g0 & 8.5 & 6.9 + vb 115 & 284787 & 04 48 42.12 & + 21 06 03.6 & g5 & 9.1 & 7.2 + vb 121 & 30738 & 04 50 48.54 & + 16 12 37.6 & f8 & 7.3 & 6.2 + vb 151 & 240692 & 05 05 40.38 & + 06 27 54.6 & k2 & 9.9 & 7.6 + bd+02 1102 & 40512 & 05 59 29.92 & + 02 28 34.2 & f5 & 7.8 & 6.7 + llccc vb 8 & 2004 oct 4 & 53282.967 & c & + & 2005 sep 30 & 53643.982 & c & + vb 9 & 2004 oct 2 & 53280.978 & c & @xmath93 + & 2004 oct 4 & 53282.993 & c & @xmath94 + l20 & 2004 oct 1 & 53279.959 & c & @xmath95 + & 2004 oct 2 & 53280.950 & c & @xmath96 + & 2004 oct 3 & 53282.148 & c & @xmath97 + & 2005 oct 10 & 53645.985 & c & @xmath98 + & 2005 oct 3 & 53647.112 & c & @xmath99 + h69 & 2004 oct 3 & 53282.999 & c & @xmath100 + & 2005 feb 22 & 53423.715 & n & @xmath101 + & 2006 feb 3 & 53769.734 & c & @xmath102 + vb 30 & 2004 oct 3 & 53282.035 & c & + & 2004 oct 4 & 53283.036 & c & + l33 & 2004 oct 3 & 53281.959 & c & @xmath103 + & 2005 oct 2 & 53646.018 & c & @xmath104 + & 2005 nov 26 & 53700.826 & c & @xmath105 + vb 40 & 2004 oct 1 & 53280.012 & c & @xmath106 + & 2004 oct 3 & 53282.123 & c & @xmath107 + & 2005 oct 2 & 53645.958 & c & @xmath108 + & 2005 oct 3 & 53647.020 & c & @xmath109 + vb 39 & 2005 nov 26 & 53700.897 & c & + & 2006 feb 2 & 53768.727 & c & + vb 43 & 2004 oct 3 & 53282.052 & c & @xmath110 + & 2005 feb 22 & 53423.754 & n & @xmath111 + & 2005 sep 30 & 53644.008 & c & + & 2005 nov 27 & 53701.755 & c & @xmath112 + vb 59 & 2005 nov 27 & 53701.813 & c & @xmath113 + & 2006 feb 2 & 53768.812 & c & @xmath114 + vb 62 & 2004 oct 1 & 53280.052 & c & @xmath115 + & 2005 nov 25 & 53699.778 & c & @xmath116 + & 2005 nov 28 & 53702.758 & c & @xmath117 + h382 & 2005 nov 28 & 53702.801 & c & @xmath118 + & 2006 feb 2 & 53768.746 & c & @xmath119 + h411 & 2004 oct 3 & 53282.078 & c & + & 2005 oct 2 & 53646.060 & c & + l57 & 2004 oct 3 & 53282.104 & c & @xmath120 + & 2005 nov 25 & 53699.828 & c & + & 2006 feb 2 & 53768.889 & c & + vb 68 & 2005 oct 3 & 53657.074 & c & @xmath121 + vb 69 & 2004 oct 1 & 53280.082 & c & @xmath122 + & 2005 sep 30 & 53644.039 & c & @xmath123 + & 2005 nov 27 & 53701.787 & c & @xmath124 + h441 & 2005 nov 28 & 53702.851 & c & @xmath125 + & 2006 feb 2 & 53768.845 & c & @xmath126 + vb 77 & 2004 oct 1 & 53280.010 & c & @xmath127 + & 2005 nov 30 & 53644.122 & c & @xmath128 + h509 & 2004 oct 2 & 53281.117 & c & @xmath129 + & 2005 oct 2 & 53646.099 & c & + & 2006 feb 2 & 53768.786 & c & @xmath130 + h532 & 2004 oct 2 & 53281.015 & c & @xmath131 + & 2004 oct 4 & 53283.055 & c & @xmath132 + & 2005 nov 26 & 53700.916 & c & @xmath133 + vb 96 & 2006 feb 3 & 53769.922 & c & @xmath134 + l79 & 2006 feb 3 & 53769.792 & c & @xmath135 + l77 & 2006 feb 3 & 53769.840 & c & + vb 102 & 2004 oct 2 & 53281.041 & c & @xmath136 + & 2005 sep 30 & 53644.068 & c & @xmath137 + & 2006 feb 2 & 53768.921 & c & @xmath138 + l90 & 2005 nov 25 & 53699.881 & c & + & 2006 feb 3 & 53769.889 & c & + vb 142 & 2004 oct 1 & 53280.118 & c & @xmath139 + & 2005 feb 22 & 53423.860 & n & @xmath140 + & 2005 oct 1 & 53645.099 & c & @xmath141 + & 2005 nov 28 & 53702.910 & c & @xmath142 + vb 113 & 2004 oct 2 & 53281.066 & c & @xmath143 + & 2005 oct 1 & 53645.061 & c & @xmath144 + vb 114 & 2005 nov 27 & 53701.930 & c & + vb 115 & 2004 oct 4 & 53283.082 & c & @xmath145 + & 2005 nov 27 & 53701.894 & c & @xmath146 + vb 121 & 2004 oct 1 & 53280.135 & c & @xmath147 + & 2004 oct 3 & 53282.134 & c & @xmath148 + & 2005 nov 28 & 53702.941 & c & @xmath149 + vb 151 & 2004 oct 4 & 53283.112 & c & @xmath150 + & 2005 oct 2 & 53646.135 & c & @xmath151 + & 2005 nov 25 & 53699.929 & c & @xmath152 + bd+02 1102 & 2004 oct 4 & 53283.136 & c & @xmath153 + & 2005 oct 1 & 53645.135 & c & @xmath154 + lcccccccccccc vb 9 & 5070 & 0.22 & 107 & 48747 & 36.87 & 2.74 & @xmath155 & @xmath156 & @xmath157 & @xmath158 & @xmath159 & @xmath160 + l20 & 2.394358 & 0.053 & 286.4 & 50553.507 & 40.86 & 66.96 & @xmath161 & @xmath162 & @xmath163 & @xmath164 & @xmath165 & @xmath166 + h69 & 128.114 & 0.062 & 337 & 49110.9 & 37.96 & 13.80 & @xmath167 & @xmath168 & @xmath169 & @xmath170 & @xmath171 & @xmath172 + l33 & 1044.9 & 0.250 & 295.5 & 48902 & 40.11 & 5.67 & @xmath173 & @xmath174 & @xmath175 & @xmath176 & @xmath177 & @xmath178 + vb 40 & 4.000177 & 0.0043 & 118 & 48353.24 & 37.920 & 39.88 & @xmath179 & @xmath180 & @xmath181 & @xmath182 & @xmath183 & @xmath184 + vb 43 & 589.76 & 0.619 & 304.7 & 50002.65 & 38.925 & 9.61 & @xmath185 & @xmath186 & @xmath187 & @xmath188 & @xmath189 & @xmath190 + vb 59 & 5724 & 0.975 & 224.2 & 51385 & 39.349 & 15.1 & @xmath191 & @xmath192 & @xmath193 & @xmath194 & @xmath195 & @xmath196 + vb 62 & 8.550647 & 0.212 & 41.0 & 49925.248 & 38.247 & 16.73 & @xmath197 & @xmath198 & @xmath199 & @xmath200 & @xmath201 & @xmath202 + h382 & 2657 & 0.682 & 248.4 & 48884.7 & 38.73 & 7.79 & @xmath203 & @xmath204 & @xmath205 & @xmath206 & @xmath207 & @xmath208 + l57 & 1911.3 & 0.486 & 94.1 & 49211.6 & 39.124 & 6.63 & @xmath209 & @xmath210 & @xmath211 & @xmath212 & @xmath213 & @xmath214 + vb 68 & 331.66 & 0.288 & 319 & 50290.4 & 40.00 & 11.19 & @xmath215 & @xmath216 & @xmath217 & @xmath218 & @xmath219 & @xmath220 + vb 69 & 41.6729 & 0.643 & 328.4 & 49443.176 & 38.993 & 7.03 & @xmath221 & @xmath222 & @xmath223 & @xmath224 & @xmath225 & @xmath226 + h441 & 7494 & 0.186 & 324 & 52730 & 40.44 & 3.62 & @xmath227 & @xmath228 & @xmath229 & @xmath230 & @xmath231 & @xmath232 + vb 77 & 238.86 & 0.200 & 132 & 48557.3 & 39.22 & 6.58 & @xmath233 & @xmath234 & @xmath235 & @xmath236 & @xmath237 & @xmath238 + h509 & 849.95 & 0.174 & 316.9 & 48643 & 39.553 & 6.35 & @xmath239 & @xmath240 & @xmath241 & @xmath242 & @xmath243 & @xmath244 + h532 & 1.484698 & 0.0035 & 267 & 48170.37 & 40.31 & 68.94 & @xmath245 & @xmath246 & @xmath247 & @xmath248 & @xmath159 & @xmath249 + vb 96 & 5100 & 0.664 & 310.4 & 50106 & 41.14 & 4.77 & @xmath250 & @xmath251 & @xmath252 & @xmath253 & @xmath254 & @xmath255 + l79 & 3688 & 0.765 & 341.8 & 48662.1 & 41.454 & 4.31 & @xmath256 & @xmath257 & @xmath258 & @xmath259 & @xmath260 & @xmath261 + vb 102 & 734.79 & 0.513 & 337.2 & 50015.8 & 40.192 & 3.92 & @xmath262 & @xmath263 & @xmath264 & @xmath265 & @xmath266 & @xmath267 + vb 142 & 975.7 & 0.675 & 271.9 & 50383.6 & 41.684 & 1.19 & @xmath268 & @xmath86 & @xmath269 & @xmath270 & @xmath271 & @xmath272 + vb 113 & 2429 & 0.327 & 294.1 & 51404 & 41.544 & 3.36 & @xmath273 & @xmath274 & @xmath275 & @xmath276 & @xmath277 & @xmath278 + vb 115 & 1208.2 & 0.480 & 129.1 & 50731.6 & 40.730 & 5.65 & @xmath279 & @xmath280 & @xmath281 & @xmath282 & @xmath283 & @xmath284 + vb 121 & 5.750872 & 0.361 & 42.0 & 49743.257 & 41.28 & 20.11 & @xmath285 & @xmath222 & @xmath286 & @xmath287 & @xmath288 & @xmath289 + vb 151 & 629.37 & 0.297 & 203.8 & 50544.0 & 42.167 & 5.22 & @xmath290 & @xmath291 & @xmath292 & @xmath293 & @xmath294 & @xmath295 + bd+02 1102 & 32.5121 & 0.344 & 228.7 & 51056.33 & 47.60 & 21.31 & @xmath296 & @xmath297 & @xmath298 & @xmath299 & @xmath300 & @xmath301 + lccccccccc l20 & 2.394357 & 0.057 & 279.2 & 43892.36 & 36.76 & 66.2 & @xmath302 & @xmath303 & g81 + vb 40 & 4.00050 & 0.060 & 13 & 22274.81 & 37.4 & 36.1 & @xmath304 & @xmath305 & s21 + vb 43 & 590.6 & 0.638 & 303.1 & 43512.9 & 39.81 & 9.91 & @xmath306 & @xmath307 & g85 + vb 62 & 8.55089 & 0.233 & 38.0 & 42588.22 & 38.77 & 16.46 & @xmath308 & @xmath309 & g78 + l57 & 1907 & 0.485 & 95 & 43470.5 & 40.23 & 6.83 & @xmath310 & @xmath311 & g85 + vb 69 & 41.6625 & 0.662 & 326.9 & 43650.67 & 39.81 & 7.28 & @xmath312 & @xmath313 & g85 + vb 77 & 238.87 & 0.242 & 127 & 43298 & 39.81 & 6.53 & @xmath314 & @xmath315 & g85 + h509 & 844.6 & 0.148 & 325 & 44413 & 40.32 & 6.20 & @xmath316 & @xmath317 & g85 + vb 121 & 5.75096 & 0.354 & 54.9 & 42192.06 & 42.74 & 19.70 & @xmath318 & @xmath319 & g78 + lcc vb 9 & @xmath320 & @xmath321 + l20 & @xmath322 & @xmath323 + h69 & @xmath324 & @xmath325 + l33 & @xmath326 & @xmath327 + vb 40 & @xmath328 & @xmath329 + vb 43 & @xmath330 & @xmath331 + vb 59 & @xmath332 & @xmath333 + vb 62 & @xmath334 & @xmath335 + h382 & @xmath336 & @xmath337 + l57 & @xmath338 & @xmath339 + vb 68 & @xmath340 & @xmath341 + vb 69 & @xmath342 & @xmath222 + h441 & @xmath343 & @xmath344 + vb 77 & @xmath345 & @xmath346 + h509 & @xmath347 & @xmath348 + h532 & @xmath349 & @xmath350 + vb 96 & @xmath351 & @xmath352 + l79 & @xmath343 & @xmath353 + vb 102 & @xmath354 & @xmath355 + vb 142 & @xmath356 & @xmath357 + vb 113 & @xmath358 & @xmath359 + vb 115 & @xmath360 & @xmath251 + vb 121 & @xmath361 & @xmath362 + vb 151 & @xmath363 & @xmath364 + bd+02 1102 & @xmath365 & @xmath366 +

we have observed a large sample of spectroscopic binary stars in the hyades cluster , using high resolution infrared spectroscopy to detect low mass companions . this corresponds to secondary masses as small as . this paper is an initial step in a program to produce distributions of mass ratio and secondary mass for hyades cluster binaries with a wide range of periods , in order to better understand binary star formation . as such

we have observed a large sample of spectroscopic binary stars in the hyades cluster , using high resolution infrared spectroscopy to detect low mass companions . we combine our double - lined infrared measurements with well constrained orbital parameters from visible light single - lined observations to derive dynamical mass ratios . using these results , along with photometry and theoretical mass - luminosity relationships , we estimate the masses of the individual components in our binaries . in this paper we present double - lined solutions for 25 binaries in our sample , with mass ratios from . this corresponds to secondary masses as small as . we include here our preliminary detection of the companion to vb 142 , with a very small mass ratio of ; this indicates that the companion may be a brown dwarf . this paper is an initial step in a program to produce distributions of mass ratio and secondary mass for hyades cluster binaries with a wide range of periods , in order to better understand binary star formation . as such , our emphasis is on measuring these distributions , not on measuring precise orbital parameters for individual binaries .

0907.4004

i

the interstellar medium is known to be inhomogeneous , consisting of various gaseous phases , from cool molecular clouds to tenuous million degree gas @xcite . a study of the interaction of a supersonic wind with a dense cloud is a problem with many astronomical applications , such as galactic winds , supernova remnants , and broad absorption line quasars , and has received much attention . in the past this interaction has been studied both analytically ( e.g. * ? ? ? * ; * ? ? ? * ) and numerically ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? over the last two decades , numerous two- and three- dimensional simulations have been performed . many early attempts assumed an adiabatic interaction ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , while later attempts have included radiative cooling ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . among the plethora of simulations reported in the literature , the effects of thermal conduction ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , magnetic fields ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , photoevaporation ( e.g * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and the presence of multiple clouds ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) have been considered . the wind / cloud interaction has also been investigated in the laboratory via laser experiments ( e.g. * ? ? ? * ; * ? ? ? * ) . in this paper , we report on our high resolution three - dimensional simulations of the interaction of a supersonic wind with a non - uniform radiative cloud . this work is motivated by our recent simulations of a starburst - driven galactic wind ( * ? ? ? * ; hereafter paper i ) , which showed that a optically emitting filament could be formed by the break - up and ram - pressure acceleration of a cloud into a supersonic wind . these simulations were three - dimensional , radiative , and incorporated an inhomogeneous disk that allowed us to study the interaction of a galactic scale wind with fractal clouds of disk gas . the interaction of a spherical cloud with a shock wave is often characterized by four evolutionary phases ( e.g. * ? ? ? * ; and references therein ) : 1 . an initial phase where the blast wave interacts with the cloud . a shock passes into the cloud , with another shock reflected into the surrounding medium . 2 . a phase of shock compression where the flow around the cloud converges on the axis at the rear . during this phase , the cloud begins to flatten , with its transverse size greatly reduced . a shock is also driven into the back of the cloud . the re - expansion phase where the shock transmitted into the cloud has reached the back surface and produces a strong rarefaction back into the cloud . this leads to expansion of the shocked cloud downstream . 4 . a final phase where the cloud fragments and is destroyed by hydrodynamical instabilities ( e.g. kelvin - helmholtz and rayleigh - taylor instabilities ) . @xcite performed an extensive series of two - dimensional simulations of an spherical adiabatic cloud interacting with a shock wave . they found that irrespective of the initial parameters , the cloud was destroyed within several cloud crushing times . @xcite confirm this result in their three - dimensional simulations . however , @xcite in a short letter , reported their two - dimensional study of the evolution a cloud in a radio galaxy cocoon . their simulations included the effects of radiative cooling and showed that merging of the front and back shocks leads to the formation of an elongated structure . this structure breaks - up into fragments which are not immediately destroyed . this increased ability for the cloud to survive has been reproduced by all studies that implement radiative cooling in their simulations . in addition , it has been shown that strong cooling in the cloud can cause a thin dense shell that acts to protect the cloud from ablation @xcite . thermal conduction can suppress the hydrodynamical instabilities that act to fragment a cloud @xcite , while the presence of a magnetic field has been shown to both hasten ( e.g * ? ? ? * ) and delay ( e.g. * ? ? ? * ; * ? ? ? * ) the cloud s destruction . more recently , @xcite performed three - dimensional simulations of the wind / cloud interaction that included the effects of radiative cooling , thermal conduction , and magnetic fields . they showed that in the presence of an ambient magnetic field , the effect of thermal conduction in stabilizing the cloud may be diminished depending on the alignment of the field . clearly the survival of a cloud interacting with a strong wind is a problem of significantly more complexity than indicated by the purely adiabatic scenario investigated by @xcite and others . in order to compare the results of our current study to those of our global model we exclude the thermal conduction , magnetic fields , or photoevaporation . however , we consider the possible effect of these phenomena on our results in [ missing ] . in this work , we further investigate the effects of radiative cooling on the survival of the cloud , by performing high @xmath1 pc resolution simulations of both a radiative and an adiabatic cloud , allowing us to perform a direct comparison between the two scenarios . symmetry is _ not _ assumed , with the entire cloud being modeled , in contrast to the strategy employed in many previous three - dimensional models . this allows us to fully investigate of the turbulent flow on the evolution of the cloud . in order to understand the effects of the cloud s structure on the wind / cloud interaction , we consider two different cloud geometries : a more realistic fractal cloud , similar to those that comprised the inhomogeneous disk in paper i , and the idealized case of a spherical cloud . the effect of the cloud s geometry on its evolution has been investigated before . @xcite considered the interaction of a shock wave with a spherical and two different prolate cloud geometries , each with a different alignment of the cloud s major axis . in addition , @xcite considered both spherical and elliptical cloud geometries . both studies show that the initial geometry of the cloud can alter the evolution of the cloud significantly . one of the most important results from paper i was our suggestion of a mechanism for the formation of the filaments seen in starburst - driven winds at optical wavelengths ( see * ? ? ? * ; for review ) . according to paper i the filaments are formed from clouds of disk gas that have been accelerated into the outflow by the ram - pressure of the wind . an important question that arises is : can the clouds survive being immersed in a hot supersonic wind long enough to form a filament and remain sufficiently cool to emit at optical temperatures ? or will they be heated and destroyed by hydrodynamical instabilities ? here we set out to answer this question . another significant result to arise from paper i is our proposal of four different mechanisms that would give rise to soft x - ray emission that is spatially correlated with the filamentary optical emission ; a major finding of recent _ chandra _ observations @xcite . our global simulations found that soft x - rays can arise from ( i ) mass - loading from ablated clouds , ( ii ) the intermediate temperature interface between the hot wind and cool filaments , ( iii ) bow shocks upstream of clouds accelerated into the outflow , and ( iv ) interactions between these bow shocks . the first two mechanisms involve the mixing of hot and cold gas , and are possibly caused by numerical diffusion in the simulations , and thus may not be physical . to investigate this possibility , we have performed a detailed resolution study of the wind / cloud interaction . the study also allows us to test the impact of the numerical resolution on the evolution of the cloud .

these simulations are motivated by our recent three - dimensional model of a starburst - driven galactic wind interacting with an inhomogeneous disk , which show that an optically emitting filament can be formed by the break - up and acceleration of a cloud into a supersonic wind . in this study we confirm the mechanism behind the formation of the h emitting filaments found in our global simulations of a starburst - driven wind . based on our resolution study

we have performed a series of three - dimensional simulations of the interaction of a supersonic wind with a non - spherical radiative cloud . these simulations are motivated by our recent three - dimensional model of a starburst - driven galactic wind interacting with an inhomogeneous disk , which show that an optically emitting filament can be formed by the break - up and acceleration of a cloud into a supersonic wind . in this study we consider the evolution of a cloud with two different geometries ( fractal and spherical ) and investigate the importance of radiative cooling on the cloud s survival . we have also undertaken a comprehensive resolution study in order to ascertain the effect of the assumed numerical resolution on the results . we find that the ability of the cloud to radiate heat is crucial for its survival , with a radiative cloud experiencing a lower degree of acceleration and having a higher relative mach number to the flow than in the adiabatic case . this diminishes the destructive effect of the kelvin - helmholtz instability on the cloud . while an adiabatic cloud is destroyed over a short period of time , a radiative cloud is broken up via the kelvin - helmholtz instability into numerous small , dense cloudlets , which are drawn into the flow to form a filamentary structure . the degree of fragmentation is highly dependent on the resolution of the simulation , with the number of cloudlets formed increasing as the kelvin - helmholtz instability is better resolved . nevertheless , there is a clear qualitative trend , with the filamentary structure still persistent at high resolution . the geometry of the cloud effects the speed at which the cloud fragments ; a wind more rapidly breaks - up the cloud in regions of least density . a cloud with a more inhomogeneous density distribution fragments faster than a cloud with a more uniform structure ( e.g. a sphere ) . we confirm the mechanism behind the formation of the h emitting filaments found in our global simulations of a starburst - driven wind . based on our resolution study , we conclude that bow shocks around accelerated gas clouds , and their interaction , are the main source of the soft x - ray emission observed in these galactic - scale winds .

0907.4004

i

we have performed a series of three - dimensional simulations of the interaction of a supersonic wind with a radiative cloud . we consider two different cloud geometries ( i.e. fractal and spherical ) , which enable us to investigate the impact of the initial shape and structure of the cloud on its subsequent evolution . this work was motivated by the simulations of the formation of a starburst - driven galactic wind in a inhomogeneous interstellar medium , reported in paper i. the aim of this work is to investigate the possible survival mechanism of a cloud accelerated by a hot freely expanding wind . we also set out to determine the effect of the numerical resolution of the evolution of the cloud and the implied soft x - ray emission associated with the interaction . the results of this study are as follows : 1 . both the initial geometry and the density distribution of the cloud significantly affect its evolution . a cloud which has a more inhomogeneous distribution of density fragments more than a cloud with a more uniform structure ( e.g. a sphere ) . the wind more rapidly breaks the cloud apart in regions where it encounters the least density . 2 . a radiative cloud survives longer than an identical adiabatic cloud . this is a result of the lower degree of heating in the radiative cloud , which suppresses the transverse expansion seen in the adiabatic case . the radiative cloud experiences a lower degree of acceleration and has a higher relative mach number to the flow , diminishing the destructive effect of the kelvin - helmholtz instability . 3 . the number of fragments formed by the break - up of the cloud increases as a power law with increasing numerical resolution . this is a direct result of further resolving the kelvin - helmholtz instability , which grows more quickly at shorter wavelengths . the number of fragments formed increases down to the resolution of the simulation and will not converge . 4 . the calculated mass flux increases with numerical resolution . this is due to the turbulent nature of the stream and the increasing fragmentation of the cloud . high ( @xmath105 ) resolution and an adaptive mesh would be required for convergence to possibly occur . 5 . a radiative cloud fragments into numerous cool , small dense cloudlets . these cloudlets are entrained into the turbulent flow , forming an overall filamentary structure , with regions where the concentration of cloudlets is higher . the velocity of the cloudlets at 0.7 myr falls in the range of @xmath90 irrespective of resolution . the filamentary structure that is formed and the range of velocities found are in good agreement with optical observations of starburst - driven winds . thus , we confirm our conclusion from paper i , that h@xmath0 emitting filaments can be formed from clouds accelerated into a supersonic wind by the ram - pressure of the wind . there is little variation in the estimated soft x - ray luminosity of the radiative fractal cloud at all numerical resolutions considered , indicating that the x - ray emission is well resolved . soft x - ray emission arises primarily from the main bow shock , produced in the initial interaction , and from bow shocks produced upstream of fragments that are directly exposed to the wind . regions where these bow shock interact are strong x - ray emitters . we see little evidence that the mixing of hot and cold gas ( e.g. mass - loading and the boundary between the cool cloud material and the hot wind ) , contribute significantly to the x - ray emission . 9 . the ovi emission arises is the same vicinity as the h@xmath0 emission and has comparable emission weighted velocities , suggesting that the detection of ovi in an outflow may be indicative of cooling in the filaments . the ability for a cloud to radiate heat is crucial for it to survive immersed inside a hot , turbulent , supersonic wind . while effects such as thermal conduction and magnetic fields will have an effect on the clouds survival , without radiative cooling the cloud is quickly destroyed by the kelvin - helmholtz instability , with the cloud s material completely mixed into the surrounding stream . thus , for a model of the wind / cloud interaction to be realistic , radiative cooling certainly can not be neglected . through the results of this work and paper i , we have shown that an optically emitting filament is easily formed via the interaction of a cool , dense cloud and a hot , tenuous supersonic wind under the conditions typically found in a starburst wind . we also find soft x - ray emission that has a natural spatial relationship to the filamentary gas . a relationship also seen in chandra observations of these winds . clearly , the multiphase nature of the interstellar medium is crucial for the formation of the filaments in starburst winds and can help explain much of the optical and soft x - ray emission detected in these complex objects .

we have performed a series of three - dimensional simulations of the interaction of a supersonic wind with a non - spherical radiative cloud . we consider the evolution of a cloud with two different geometries ( fractal and spherical ) and investigate the importance of radiative cooling on the cloud s survival . we find that the ability of the cloud to radiate heat is crucial for its survival , with a radiative cloud experiencing a lower degree of acceleration and having a higher relative mach number to the flow than in the adiabatic case . the geometry of the cloud effects the speed at which the cloud fragments ; a wind more rapidly breaks - up the cloud in regions of least density . a cloud with a more inhomogeneous density distribution fragments faster than a cloud with a more uniform structure ( e.g. a sphere ) .

we have performed a series of three - dimensional simulations of the interaction of a supersonic wind with a non - spherical radiative cloud . these simulations are motivated by our recent three - dimensional model of a starburst - driven galactic wind interacting with an inhomogeneous disk , which show that an optically emitting filament can be formed by the break - up and acceleration of a cloud into a supersonic wind . in this study we consider the evolution of a cloud with two different geometries ( fractal and spherical ) and investigate the importance of radiative cooling on the cloud s survival . we have also undertaken a comprehensive resolution study in order to ascertain the effect of the assumed numerical resolution on the results . we find that the ability of the cloud to radiate heat is crucial for its survival , with a radiative cloud experiencing a lower degree of acceleration and having a higher relative mach number to the flow than in the adiabatic case . this diminishes the destructive effect of the kelvin - helmholtz instability on the cloud . while an adiabatic cloud is destroyed over a short period of time , a radiative cloud is broken up via the kelvin - helmholtz instability into numerous small , dense cloudlets , which are drawn into the flow to form a filamentary structure . the degree of fragmentation is highly dependent on the resolution of the simulation , with the number of cloudlets formed increasing as the kelvin - helmholtz instability is better resolved . nevertheless , there is a clear qualitative trend , with the filamentary structure still persistent at high resolution . the geometry of the cloud effects the speed at which the cloud fragments ; a wind more rapidly breaks - up the cloud in regions of least density . a cloud with a more inhomogeneous density distribution fragments faster than a cloud with a more uniform structure ( e.g. a sphere ) . we confirm the mechanism behind the formation of the h emitting filaments found in our global simulations of a starburst - driven wind . based on our resolution study , we conclude that bow shocks around accelerated gas clouds , and their interaction , are the main source of the soft x - ray emission observed in these galactic - scale winds .

1008.1058

i

the size distribution is one of the most fundamental properties of a planetesimal population . as the size of an object is primarily determined from its accretion and collisional disruption histories , the size distribution can reveal important information on the accretion and collisional history of that population ( for a recent example , see * ? ? ? unlike the closer populations such as the asteroid belt , whose proximity has allowed the accurate measurement of their size distributions ( see for example * ? ? ? * ; * ? ? ? * ) , the distance to the kuiper belt has prevented an equally detailed determination of its size distribution . observations thus far have demonstrated that for the kuiper belt as a whole , the size distribution for objects with diameters , @xmath4 km , is well described by a power - law . at some size @xmath5 km , the size distribution rolls - over to a shallower distribution @xcite . smaller than the roll - over , the size distribution appears to remain shallow to objects as small as @xmath6 km @xcite . while the accuracy of current measurements prevents a detailed modelling of the history of objects in the region , some insight has already been gained . the steepness of the large object size distribution implies that for this population , accretion was a short - lived phenomenon , likely not more than a few 100 myr @xcite . the paucity of the observed belt , and the existence of the largest known members demonstrates that the belt has undergone significant mass depletion , losing as much or more than 99% of its primordial mass @xcite . the existence of the roll - over at sizes larger than @xmath7 km suggests that the belt has undergone significant collisional comminution in a region of significantly increased density compared to today @xcite . as well , recent observations have suggested that the size distribution of those dynamically cold ( low inclinations and eccentricities ) kuiper belt objects is different than that of the dynamically hot ( large inclinations and eccentricities ) population @xcite . @xcite found that the size distribution of objects with inclinations , @xmath8 was steeper than the size distribution of objects with @xmath9 . @xcite found similar results showing that the cold population had a steeper slope than the mixed populations as a whole . this result implies that the hot and cold populations are genetically separate populations , that have significantly different accretion and evolution histories . the results of @xcite were drawn from samples of objects compiled from many different surveys . this practice was necessitated by available data . all surveys had either shallow limiting magnitudes and a large areal coverage , or vice - versa . the result was that most surveys did not have a sufficient range of objects for which the size distribution could be accurately measured from that survey alone . the practice of using data from multiple surveys opens the results to the possibility of being affected by calibration issues and variations in sky density which could lead to an incorrect measurement of the size distribution . when these effects were properly accounted for , @xcite found that these data could not be used to reliably test differences in subpopulations of the kuiper belt . here we present the results of a new kuiper belt survey . by virtue of the survey s design , a large number of objects were discovered and followed to determine their inclinations , over a range of sizes sufficient to measure the size distribution for the hot and cold population without the use of other surveys . in section [ sec : observations ] we present our observations , and our data reductions and discovery techniques . in section [ sec : analysis ] we present the analysis of our results , in section [ sec : discussion ] we discuss the implications of our results , and we end with concluding remarks in section [ sec : conclusions ] .

we have performed an ecliptic survey of the kuiper belt , with an areal coverage of 8.9 square degrees to a 50% limiting magnitude of , and have detected 88 kuiper belt objects , roughly half of which received follow - up one to two months after detection . using this survey data alone , we have measured the luminosity function of the kuiper belt , thus avoiding any biases that might come from the inclusion of other observations . as well , we discuss the similarities of the _ cold _ and _ hot _ populations with the size distributions of other planetesimal populations .

we have performed an ecliptic survey of the kuiper belt , with an areal coverage of 8.9 square degrees to a 50% limiting magnitude of , and have detected 88 kuiper belt objects , roughly half of which received follow - up one to two months after detection . using this survey data alone , we have measured the luminosity function of the kuiper belt , thus avoiding any biases that might come from the inclusion of other observations . we have found that the _ cold _ population defined as having inclinations less than has a luminosity function slope , and is different from the _ hot _ population , which has inclinations greater than and a luminosity function slope . as well , we have found that those objects closer than 38 au have virtually the same luminosity function slope as the _ hot _ population . this result , along with similar findings of past surveys demonstrates that the dynamically cold kuiper belt objects likely have a steep size distribution , and are unique from all of the excited populations which have much shallower distributions . this suggests that the dynamically excited population underwent a different accretion history and achieved a more evolved state of accretion than the cold population . as well , we discuss the similarities of the _ cold _ and _ hot _ populations with the size distributions of other planetesimal populations . we find that while the jupiter family comets and the scattered disk exhibit similar size distributions , a power - law extrapolation to small sizes for the scattered disk can not account for the observed influx of comets . as well , we have found that the jupiter trojan and _ hot _ populations can not have originated from the same parent popuation , a result that is difficult to reconcile with scattering models similar to the nice model . we conclude that the similarity between the size distributions of the _ cold _ population and the jupiter trojan population is a striking coincidence . kuiper belt centaurs trojan asteroids accretion

1008.1058

c

the observed luminosity functions imply size distribution slopes @xmath110 , @xmath111 , and @xmath112 for the _ cold _ , _ hot _ , and _ close _ populations . the consistency of the _ hot _ and _ close _ populations leaves us to consider the two populations together , implying a slope for the combined population of @xmath113 . though the results presented by @xcite and @xcite were possibly affected by sky density variations and calibration errors , we find similar conclusions , ie . , the _ cold _ population size distribution _ is _ steeper than the _ hot _ population size distribution . given the similarity in these repeated measurements of the kuiper belt luminosity function , the results stand confident . while over the magnitude range of our observations , both the _ hot _ and _ cold _ populations are well described by power - law models , other works have put into question whether the power - law behaviour extends to all brightnesses . the fact that the luminosity function of the _ tno _ population exhibits a roll - over at magnitudes @xmath114 is well accepted . the results of @xcite however , suggest that the power - law behaviour of the _ cold _ population breaks down for the brightest objects . specifically they find that at the bright - end , the _ cold _ population luminosity function has a steeper slope than at fainter magnitudes . similarly , @xcite suggests that the _ hot _ and _ cold _ populations are intimate mixtures of two primordial populations , one with a steep size distribution , and one with a shallow size distribution . in such a scenario , both populations should exhibit shallow slopes for the largest objects , then turn - up to a steeper slope for smaller objects , before finally breaking to a shallow slope at some size where collisional processing has dominated . to that end , we test the power - law behaviour of both the _ hot _ and _ cold _ populations . for the _ cold _ population , a simple extrapolation of the best - fit luminosity function suggests that the brightest object on the sky in this population should have a magnitude of @xmath115 . the entire low - latitude kuiper belt has been surveyed for objects to a limiting magnitude of @xmath116 @xcite , and the brightest known _ cold _ object has @xmath117 , nearly a full magnitude fainter . this observation confirms the results of @xcite . namely , that the power - law behaviour of the _ cold _ population luminosity function can not extend to the brightest targets . rather the power - law must be truncated . the exact behaviour can not be determined from the observations we present here . the suggestion by @xcite that the cold population size distribution will have a shallow slope for the largest objects , and a turn - up to the observed steep is excluded by this result . similarly , extrapolating the best - fit power - law luminosity function of the _ hot _ population suggests that this population is well described by a power - law to its brightest objects . indeed , when excluding the largest objects which are known to have different albedos than the objects observed here @xcite the absolute magnitude distribution of the biggest objects has a slope compatible with our observations @xcite . to test the exactness of a power - law requires combination of other survey data sensitive to the brightest _ hot _ members . as well this analysis should include modelling of the latitude distribution of the _ hot _ population . the fact however , remains that the _ hot _ population has a flat size distribution over all observable sizes . the behaviour of the _ hot _ population luminosity function at the faint end is uncertain ; the shallow slope of @xmath118 for @xmath119 is compatible with the lack of faint detections of the _ hot _ population in fainter surveys , eliminating the need for a break at the faint end . if however , the _ hot _ population slope is as steep as the upper limits of our confidence interval , a break at magnitudes fainter than @xmath120 is still required . the existence of a break in the _ hot _ population will only be confirmed by an off - ecliptic survey sensitive to objects with @xmath121 . the turn - up , as proposed by @xcite would produce an abundance of faint objects in our observed _ hot _ population . we can test this utilizing the anderson - darling statistic . we generate a fake _ hot _ subsample from a shallow power - law with the observed _ hot _ population slope that turns up to the best - fit observed slope of the _ cold _ population , @xmath122 , at some magnitude @xmath123 . we then fit a power - law to that sample , and calculate the anderson - darling statistic . this is repeated , and the probability of finding a statistic worse than the observations is calculated versus the value of @xmath123 . the strength of this test is weakened by the sparse sampling of high - latitude sources in our dataset . we still however , eliminate such a turn - up to the slope of the _ cold _ population for @xmath124 ( r ) at the 2@xmath125 level and @xmath126 at the 3-@xmath96 level . this is incompatible with the assertion of @xcite who suggest that the _ hot _ population should have the same slope as the _ cold _ population over an absolute magnitude range of @xmath127 , corresponding to r magnitudes , @xmath128 . the significance of the test results over the entire magnitude range however , prevents this result from being iron clad . clearly , the possibility of a turn - up ( or down ) must be tested from a survey which detects a large sample of high - latitude objects . the difference in size distribution slopes of the _ hot _ and _ cold _ populations suggest very different histories for these two groups . interestingly , the shallow slope of the _ hot _ distribution is compatible with a heavily collisionally processed population , either one that has reached collisional equilibrium , or in which the largest objects are fragments of even larger , disrupted primordial bodies @xcite . for collisional evolution to completely reshape the size distribution of the _ hot _ population would require extremely high collision rates , seemingly incompatible with plausible protoplanetary disk densities , and formation scenarios @xcite . rather it is likely that this slope is the result of the accretionary processes that formed the _ hot _ population . unlike the _ hot _ population , the steep slope of the _ cold _ population is entirely incompatible with a collisionally evolved distribution . this slope must be the result of accretionary processes as well . the shallower slope of the _ hot _ population , and the fact that the largest objects of the _ hot _ population are larger than those of the _ cold _ population , implies that the _ hot _ population achieved a more advanced stage of accretion than the _ cold _ population @xcite . the incompatibility of their slopes implies that these two populations underwent different accretion scenarios . it is possible , that the _ hot _ population underwent a longer duration of accretion than the _ cold _ population . to halt accretion for the _ cold _ population would require excitation and mass depletion with some yet unseen perturber beyond the outer edge of the kuiper belt . the past existence of one or more planetary embryos in the kuiper belt region is a possible source of this excitation , and has been proposed to explain some of the kuiper belt dynamical features @xcite . another possibility is that the _ hot _ population underwent accretion in a more dense region of the protoplanetary nebula . this would result in more rapid accretion than compared to the _ cold _ population , allowing the _ hot _ population to grow to larger sizes before the process was halted . under this scenario , the _ hot _ and _ cold _ populations could then have similar accretion timescales . as currently favoured formation scenarios suggest the _ hot _ population was scattered from a region closer to the sun than their current locations @xcite , where the protoplanetary disk might have been more dense , this scenario seems likely . however the _ hot _ and _ cold _ populations came about , their incompatible size distributions imply different accretion scenarios . once accretion was finished , these objects were excited and emplaced onto their current orbits , creating the architecture of the current kuiper belt . given the dynamically cold nature of the _ cold _ population , it seems plausible that this population formed in - situ . what ever the mechanism(s ) ultimately responsible for the belt , our results show that little mixing between the _ hot _ and _ cold _ populations has occurred . there is a striking similarity in the size distributions of the _ cold _ population , and the jupiter trojans . both have similarly steep slopes , ( @xmath129 and @xmath130 ) , and both exhibit breaks to shallower slopes at roughly the same object diameter @xcite . this result argues strongly against the trojan formation mechanism of the so - called nice model in which the trojan populations and the hot and cold kuiper belt populations are all scattered into their current regions from the same primordial disk population @xcite . if this scenario were true , @xcite has shown that over the magnitude range of our observations , the hot population should have the same slope as that observed for large jupiter trojans . using the anderson - darling statistic , we tested the probability of the _ hot _ sample being drawn from a luminosity function with the slope of the jupiter trojan luminosity function , @xmath131 . we found that the _ hot _ sample could not be drawn from the jupiter trojan population at greater than the 3-@xmath96 significance . as the size distributions of these two populations in the size range considered have not evolved significantly since they were emplaced in their current regions @xcite , we must conclude that the hot and jupiter trojan populations must have different progenator populations . this result and the lack of mixing between the hot and cold populations is difficult to reconcile with the nice model . it seems likely the hot , cold , and trojan populations formed by separate means . if this is true , the similarities between the cold and trojan populations are quite a coincidence . another similarity is seen between the _ hot _ population ( @xmath132 ) and the jupiter family comets , who exhibit a size distribution slope of @xmath133 albeit over a smaller size range , @xmath134 km @xcite . this resemblance is interesting as one likely source of jupiter family comets are scattered disk objects - members of the _ hot _ population - which have fallen into the inner solar system under gravitational perturbations from the gas - giants , suggesting that the scattered disk size distribution might be a power - law for @xmath135 km . we consider this possibility here . while the observations we present do not measure the size distribution of the scattered disk directly , the similarity in slopes between the _ hot _ and _ close _ subsamples implies that the scattered disk can not have a size distribution significantly different than that of the _ hot _ sample as a whole . additionally we can not determine the total number scattered disk objects from our observations . rather , we turn to other estimates which suggest that , if their size distribution is a power - law with slope of @xmath136 , then there are roughly @xmath137 scattered disk objects with @xmath138 km ( * ? ? ? * ; * ? ? ? * schwamb , personal communication ) . simulations by @xcite suggest that if the scattered disk is the sole source of the jupiter family comets , then there must be at least @xmath139 objects in that population to account for the current flux of jupiter family comets through the inner solar system , implying that either the scattered disk is not the sole source of the jupiter family comets , or that the extrapolation of a power - law to @xmath140 km is unreasonable ; it must be that the size distribution of scattered disk objects steepens significantly in the @xmath141 km range . further observations are required before this feature can be detected .

this suggests that the dynamically excited population underwent a different accretion history and achieved a more evolved state of accretion than the cold population . we find that while the jupiter family comets and the scattered disk exhibit similar size distributions , a power - law extrapolation to small sizes for the scattered disk can not account for the observed influx of comets . as well we conclude that the similarity between the size distributions of the _ cold _ population and the jupiter trojan population is a striking coincidence .

we have performed an ecliptic survey of the kuiper belt , with an areal coverage of 8.9 square degrees to a 50% limiting magnitude of , and have detected 88 kuiper belt objects , roughly half of which received follow - up one to two months after detection . using this survey data alone , we have measured the luminosity function of the kuiper belt , thus avoiding any biases that might come from the inclusion of other observations . we have found that the _ cold _ population defined as having inclinations less than has a luminosity function slope , and is different from the _ hot _ population , which has inclinations greater than and a luminosity function slope . as well , we have found that those objects closer than 38 au have virtually the same luminosity function slope as the _ hot _ population . this result , along with similar findings of past surveys demonstrates that the dynamically cold kuiper belt objects likely have a steep size distribution , and are unique from all of the excited populations which have much shallower distributions . this suggests that the dynamically excited population underwent a different accretion history and achieved a more evolved state of accretion than the cold population . as well , we discuss the similarities of the _ cold _ and _ hot _ populations with the size distributions of other planetesimal populations . we find that while the jupiter family comets and the scattered disk exhibit similar size distributions , a power - law extrapolation to small sizes for the scattered disk can not account for the observed influx of comets . as well , we have found that the jupiter trojan and _ hot _ populations can not have originated from the same parent popuation , a result that is difficult to reconcile with scattering models similar to the nice model . we conclude that the similarity between the size distributions of the _ cold _ population and the jupiter trojan population is a striking coincidence . kuiper belt centaurs trojan asteroids accretion

1008.1058

c

we have performed an ecliptic survey , and have detected 88 kuiper belt objects with magnitudes @xmath142 . a subset of these objects have received additional follow - up observations allowing us to accurately determine their inclinations and distances . using these data , we have measured the size distribution of the _ hot _ and _ cold _ subsamples , historically defined as those objects with inclinations above and below @xmath1 respectively . this measurement , which is independent of any previous observations has confirmed that the _ cold _ population has a much steeper luminosity function , with slope @xmath94 , than the _ hot _ population , with slope @xmath3 . the observed luminosity functions imply different size distributions for the _ hot _ and _ cold _ populations . the size distribution slopes of the the two subsamples are @xmath110 and @xmath111 . in addition , we have found that the _ close _ population , which is defined as those objects with heliocentric distance , @xmath143 have the same luminosity function slope as the _ hot _ subsample , demonstrating that these two share a similar size distribution . in addition , our findings suggest that the dynamical populations which make up both the _ hot _ and _ close _ populations must all have similar size distributions . the primary consequence of these findings is that the _ cold _ population , which consists primarily of cold classical kuiper belt objects , has a separate , and distinct accretion history from the _ hot _ population , requiring either potentially different accretion timescales for the two populations , or formation in different locations of the protoplanetary disk . these observations reveal the similarities in the size distributions between the subsamples of the kuiper belt and the jupiter family comets and trojans , suggesting a connection between the formation and subsequent evolution of the small body populations of the outer solar system .

we have found that the _ cold _ population defined as having inclinations less than has a luminosity function slope , and is different from the _ hot _ population , which has inclinations greater than and a luminosity function slope . as well , we have found that those objects closer than 38 au have virtually the same luminosity function slope as the _ hot _ population . , we have found that the jupiter trojan and _ hot _ populations can not have originated from the same parent popuation , a result that is difficult to reconcile with scattering models similar to the nice model .

we have performed an ecliptic survey of the kuiper belt , with an areal coverage of 8.9 square degrees to a 50% limiting magnitude of , and have detected 88 kuiper belt objects , roughly half of which received follow - up one to two months after detection . using this survey data alone , we have measured the luminosity function of the kuiper belt , thus avoiding any biases that might come from the inclusion of other observations . we have found that the _ cold _ population defined as having inclinations less than has a luminosity function slope , and is different from the _ hot _ population , which has inclinations greater than and a luminosity function slope . as well , we have found that those objects closer than 38 au have virtually the same luminosity function slope as the _ hot _ population . this result , along with similar findings of past surveys demonstrates that the dynamically cold kuiper belt objects likely have a steep size distribution , and are unique from all of the excited populations which have much shallower distributions . this suggests that the dynamically excited population underwent a different accretion history and achieved a more evolved state of accretion than the cold population . as well , we discuss the similarities of the _ cold _ and _ hot _ populations with the size distributions of other planetesimal populations . we find that while the jupiter family comets and the scattered disk exhibit similar size distributions , a power - law extrapolation to small sizes for the scattered disk can not account for the observed influx of comets . as well , we have found that the jupiter trojan and _ hot _ populations can not have originated from the same parent popuation , a result that is difficult to reconcile with scattering models similar to the nice model . we conclude that the similarity between the size distributions of the _ cold _ population and the jupiter trojan population is a striking coincidence . kuiper belt centaurs trojan asteroids accretion

1106.1927

r

optical cmds provide a powerful means of selecting likely _ chandra _ source counterparts and investigating their properties . for each of the 79 _ chandra _ sources within the half - mass radius , we checked the locations of all objects within the x - ray error circle in the cmds shown in figures [ f : cmd_cv ] and [ f : cmd_ab ] . objects that fell on the main sequence were considered to be unlikely counterparts , given the relatively low x - ray to optical flux ratio , @xmath16 , of most ms stars , in contrast to the ranges for chromospherically active binaries and cataclysmic variables . table [ t : counterparts ] summarizes the result of this counterpart search . plausible identifications were obtained for nearly all sources and are listed in this table , along with previous source designations , inferred object types , proper - motion information , and photometry . the only sources for which the error circle was empty are the quiescent low - mass x - ray binary ( qlmxb ) u24 @xcite , u104 , u106 , u111 , u113 , u119 , u121 , u122 , and u123 . in the case of u24 , there is a small `` blip '' near the center of the error circle in the stacked @xmath0 image , but it likely represents the combination of airy ring artifacts from two bright nearby stars . several other sources , u5 , u16 , u77 , and u84 , lie outside of the @xmath0 field and thus are difficult to classify , from these data , due to the lack of and color measurements . however , the u5 and u77 counterparts , v30 and v36 respectively , have been shown to be variable using ground - based photometry @xcite . @xcite classified v30 as an eclipsing binary that lies to the far red of the main sequence ( suggestive of it being a non - member ) . @xcite have recently classified v36 as a single - line spectropsopic binary . we have classified both of these stars as uncertain active binaries ( abs ) . u5 and u84 have very red @xmath17 colors , suggesting that their colors are likely very red as well , which supports an ab identification . table [ t : counterparts ] also gives a summary of the results of the proper - motion analysis , which indicates whether the object is consistent with being a cluster member , a field member , or neither , based on a comparison of its proper motion to the proper - motion distribution for stars of similar magnitude . based on the location of the proposed counterparts in the cmds ( or , in a few cases , based on ground - based detection of variability ) , we primarily assigned types of cataclysmic variable ( cv ) and chromospherically active binary ( ab ) . cvs were defined as being significantly to the blue of the ms and having significant excesses ( either relative to the ms or to the white dwarf sequence ) . abs were defined as lying within @xmath18 mag above the ms ( and thus within @xmath19 mag to the red of the ms ) and having small excesses ( @xmath20 mag ) , based on the previous analysis of abs in ngc 6397 by @xcite . in three cases where the only object in the error circle was an apparent ms star , u41 , u91 , and u112 , we note its presence in table [ t : counterparts ] . similarly , an apparent msto star is the only object present in the error circle for source u118 . we note that an ab with a low mass ratio and weak lines could look like a ms star in both cmds . two objects , u28 and u108 , were classified as background galaxies based on the extended appearance of their images . u28 resembles an edge - on spiral , while u108 has a more complex structure suggestive of interacting galaxies . the high x - ray to optical flux ratio of u28 ( see [ flux_ratio ] ) suggests that it is an active galactic nucleus ( agn ) . while the flux ratio of u108 was not determined , due to the complex nature of the optical image , it is clearly much lower than that of u28 . one possibility is that we are detecting x - ray emission from u108 that is produced by a galaxy collision . figure [ f : cmd_cv ] shows the location of the cv candidates in the cmds . there is a suggestion of an evolutionary sequence from young , bright cvs to old , faint ones . we return to this point in [ summary ] . the six brightest cvs mostly lie about 0.2 0.8 mag to the blue of the ms . the optical emission of the systems appears to be dominated by the secondary in the @xmath0 band , with a larger contribution from the disk in the @xmath1 band . the fairly high @xmath0-band flux indicates that the secondaries are relatively massive , @xmath21 , as inferred from the isochrones of @xcite . all of the bright cvs have substantial excesses relative to the ms ; these excesses generally increase with magnitude . the cv candidates 18 are numbered according to the scheme used in previous papers , as listed by @xcite . a prefix cv is used to designate each cv candidate . @xcite identify u28 as a cv ; however we find that this chandra source appears to be a galaxy . here we use the identification by @xcite of u60 as cv9 . cvs 1015 are newly identified in the present study ; @xcite assigned numbers for cvs 10 and 11 . we have numbered cvs 1215 based on optical luminosity within this group . the translation between _ chandra _ source numbers and cv numbers is given in table [ t : counterparts ] . there is a two magnitude gap between the bright cvs and the fainter cvs . just below this gap are two possible transitional objects , u7 and u61 , which lie between the white dwarf sequence and the main sequence . we note that the proper - motion data produce an unknown membership status for u61 , while u7 registers as consistent with membership . this leaves open the possibility that u61 is a background agn with an emission line that is shifted into the window . however , the image of the u61 counterpart does not show obvious evidence of extension . the fainter cv candidates , below u7 and u61 , lie in the vicinity of the wd cooling sequence . the optical fluxes for the faint cv candidates are clearly dominated by the contribution of the wd . the indices for these faint cvs nearly all lie at least 0.5 mag to the excess side of the wd clump , which is centered at about @xmath22 . this suggests that the faint cvs have a strong -emission core ( due to an accretion disk ) within the broad absorption lines of the wd continuum . this inferred spectroscopic property of the faint cvs appears to be generally consistent with those of the wz sge class of evolved cataclysmic variable @xcite . another possibility is that some of these objects are am cvn type double - degenerate systems , in which a low - mass he wd donor feeds a much more massive carbon - oxygen wd . such systems show no evidence of hydrogen lines in their spectra and instead have he i and sometimes he ii lines , which are typically in emission @xcite . am cvn stars could have evolved into contact from the known he wds in ngc 6397 , which have been shown to have ( detached ) heavy co wd companions @xcite . such an object should lie close to the main sequence in the @xmath23 cmd . possible candidate am cvn stars among the cv candidates reported here are u25 , u31 , u60 , u80 , and u83 . we note that most of the wd - like cv candidates cluster near a magnitude of @xmath24 , which corresponds to a @xmath25 , using the distance modulus determined by @xcite . we note that @xcite have reported a sharp peak ( `` spike '' ) near the period minimum ( @xmath26 ) in the period distribution of cvs selected from the sloan digital sky survey ( sdss ) . the average absolute magnitude for the cvs in the spike is @xmath27 . allowing for the difference in photometric band , this is reasonably close to the characteristic magnitude of the faint cvs in our study . this suggests that these faint cvs may well belong to the spike population , i.e. have periods in the vicinity of the period minimum . this could be tested by determining orbital periods for the faint cvs from suitable time - resolved photometry . @xcite find that of 33 cvs with orbital periods less than 86 min , 20 have spectra that are wd - dominated . in our sample , it appears that all seven faint cvs are wd - dominated . given the small sample size , it is not clear whether this represents a significant difference between faint field and faint cluster cvs . figure [ f : cmd_ab ] shows the location of the objects identified as ab stars in the cmds . we note that these objects sometimes lie near the edge of the ms in either the right or left panel , but deviate by a larger amount in the other panel . of the 42 ab counterparts listed in table [ t : counterparts ] , 26 are newly identified in our study . overall , the abs appear to form a relatively homogeneous binary sequence alongside the ms , presumably mostly differing in mass . @xcite have argued that these stars are likely by draconis stars and represent a hard binary population in ngc 6397 . in a large study of photometric variability in 47 tuc , @xcite found a substantial population of by draconis binaries , as well as w uma and other contact binaries , and eclipsing binaries . in addition to the likely by dra population , there are a number of counterparts that show a significantly different distribution in the cmd . these include the `` red straggler '' counterpart to u12 ( the millisecond pulsar ) and the similar counterpart to u18 , the blue - straggler counterpart to u70 , a group of five stars with very red colors , and a group of five stars with strong excesses . there are two stars in common between these latter two groups . the counterparts to u12 and u18 both have proper motions consistent with cluster membership . given their similar optical and x - ray properties , it appears likely that u18 is a msp @xcite . the counterpart to u70 , which registers as a proper - motion cluster member , has been identified as variable star v20 by @xcite . @xcite find that it is a double - line spectroscopic binary with a period of @xmath28 and a mass ratio of @xmath29 . the he wd candidate pc-5 @xcite , which has been previously suggested as a possible counterpart to u70 , lies well outside of the current error circle . the counterparts to u42 , u63 , u65 , u86 , and u92 differ strikingly from the typical abs , lying up to 1 mag to the red of the ms , and thus well above it . of these , the counterparts to u42 and u92 have been previously identified as optically variable stars @xcite , as confirmed here ( see [ variability ] and fig . [ f : variability ] ) ; the counterparts to u63 , u65 , and u86 are new identifications . the u92 counterpart ( v7 ) is classified as a w uma system by @xcite , while the u42 counterpart ( v26 ) is classified as an irregular variable by @xcite . u92 is consistent with the cluster proper - motion distribution . the proper - motion information available for u42 , u65 , and u86 produce an unknown membership status . these stars have proper motions that are well outside of the cluster distribution but they are also inconsistent with the field distribution . there is no proper - motion information for u63 . one reasonable possibility is that these stars are foreground active binaries superposed on the cluster , as discussed by @xcite in the case of u5 ( v30 ) . in this interpretation , the foreground binaries contain k / m type dwarfs with distance moduli that put them well above the cluster main sequence in the @xmath30 cmd . figure [ f : cmd_ab ] also shows several ab candidates that have larger than typical excesses ; these include the counterparts to u62 , u65 , u66 , u86 , and u120 . there is no proper - motion information available for u62 . the proper - motion information for u65 , u86 , and u120 produces an unknown membership status . u66 is consistent with the field proper - motion distribution . thus , the proper - motion information does not offer much assistance in determining whether these stars are likely cluster members . @xcite have drawn attention to two of the variable stars that we have identified as ab counterparts , v17 and v36 , which correspond to the sources u76 and u77 . these similar objects both lie close to the main - sequence turnoff in the cmd presented by @xcite . both objects are single - line spectroscopic binaries , in which the unseen primary is inferred to have a mass in excess of 1 . they suggest that these two objects are members of a class of dormant degenerate binaries which may have much larger peak x - ray luminosities . as an additional aid to the classification of sources , we have examined the x - ray to optical flux ratio , @xmath16 , where we take @xmath31 from @xcite and set @xmath32 . the latter conversion factor is computed from the _ hst _ flux calibration constants . the x - ray count to flux transformation assumes a power - law spectrum with a photon index of @xmath33 @xcite . the resulting flux ratio is plotted versus @xmath34 in fig . [ f : fx_fopt ] . the ratio is observed to be higher for accretional sources , such as cvs , lmxbs , and agns , than for chromospherically active binaries ( see e.g. * ? ? ? * who studied the _ chandra _ source distribution in m4 ) . consistent with this , fig . [ f : fx_fopt ] shows that the cv and ab candidates form two distinct groups with no overlap in flux ratio . the median flux ratio is about 500 times larger for the cvs than for the abs . within each group there is a broad range of the flux ratio , about a factor of 40 for the cvs and a factor of 100 for the abs . there is no apparent dependence of the flux ratio on @xmath34 over a range of more than three decades in @xmath34 for the cvs and nearly two decades for the abs . the apparent agn , u28 , has the highest flux ratio of all objects . the known millisecond pulsar , u12 , has a higher flux ratio than most of the abs and is about 40@xmath7 brighter in the x - ray than a typical ab . the object u18 , which has a similar optical counterpart to that of u12 , has even higher values of @xmath34 and @xmath16 . this supports the interpretation of u18 as a msp not yet detected at radio wavelengths @xcite . interestingly , the x - ray flux of cv5 ( u22 ) is considerably lower in the 2007 observations than in the previous 2002 observations ; the flux differs more than an order of magnitude . this gives cv5 the lowest @xmath16 value of all the cvs when the 2007 x - ray flux is used together with the 2004 - 05 optical flux . since the x - ray and optical fluxes were not measured contemporaneously , it is possible that cv5 typically has a flux ratio that is more consistent with the other bright cvs . we note that the x - ray flux of a bright cv typically drops during outburst ( e.g. * ? ? ? * ) , suggesting that cv5 may have been in outburst in 2007 . the objects u62 , u66 , and u86 , which lie among the abs with the four highest flux ratios , all have significantly larger excesses than the typical ab . it is not surprising that two measures of chromospheric activity , x - ray flux and flux , are correlated for these stars . since our dataset provides a 40-exposure time sequence of exposures , with four exposures per orbit , it was possible to investigate optical variability . the time sequence samples time scales shorter than about one hour ( the visibility period per _ hst _ orbit ) and also time scales from one month to one year . the analysis of variability is complicated by the presence of outliers in the time sequences , some of which represent photometric anomalies . we investigated several measures of variability and adopted the rms deviation about the mean of the magnitude measurements , computed using an iterative 3@xmath35 clip to reduce the impact of outliers . we plot @xmath36 versus mean magnitude in figure [ f : variability ] . this procedure results in a measure of variability that is most sensitive to orbital variability of binary systems , rather than large - amplitude fluctuations of cvs , given the outlier filtering . thus , we also investigated the total range of the magnitudes for each object and constructed light curves for each of the cv candidates in order to test for outburst behavior . as can be seen in fig . [ f : variability ] , most stars fall on a well - defined sequence of increasing @xmath36 with increasing magnitude . stars that lie significantly above this sequence generally show evidence for variability , although some of this scatter is likely due to photometric issues . we note that the mean trend of the variability index @xmath36 with mean @xmath37 magnitude differs for stars brighter than @xmath38 , for which @xmath36 increases from a minimum of about 0.003 mag to about 0.04 mag for the brightest stars plotted . this behavior for bright stars is due to saturation issues that increase in size with decreasing magnitude . we have plotted the positions of the previous and new chandra source counterparts in fig . [ f : variability ] . many of these counterparts show significant variability as measured by the @xmath35 of the time series . this group includes all of the bright cvs 16 : sources u10 , u17 , u19 , u21 , u22 , and u23 . of the newly identified faint cv counterparts , only u61 registers as clearly variable by this measure and u25 shows a possible slight variability . while the other faint cv candidates have @xmath36 values that are comparable in size to those of the bright cvs , these values are not significantly larger than those of other stars of similar magnitude . thus , the failure to detect statistically significant variability for the other faint cv counterparts may well be due to the decreasing sensitivity of the variability test with increasing magnitude . the total magnitude range for each of the six bright cvs was about 0.61.3 mag , which is less than the 25 mag amplitude for a dwarf nova outburst @xcite . source u21 ( cv4 ) had the largest amplitude ( 1.3 mag ) of these bright cvs , with a light curve that a high phase of about 50 days duration . source u61 ( cv12 ) displayed a total range of 2.3 mag . the faintest magnitude measurements , which contribute significantly to this large range , have a high degree of uncertainty . the light curve shows a clearly differentiated low state in the first half of the year of observation and a high state during the second half . the mean offset between these two states is about 1 mag and thus also falls short of a dwarf nova outburst . a number of the candidate ab counterparts also show evidence of variability , including six newly identified abs : sources u79 , u97 , and u114 , which show strong variability at the level of the six bright cvs ; sources u88 and u101 , which show moderate variability ; and source u103 , which shows slight evidence of variability . five previously identified ab counterparts , u14 , u18 , u42 , u70 , and u92 , show clear variability , and u76 and u81 show weaker evidence of variability . we note that u18 has a similar level of variability to the msp counterpart u12 , again suggesting that these are similar objects . we carried out a period - folding light curve analysis for the bright cvs 16 and the msp u12 . given the very unequal spacing of the data , it is difficult to determine a period ab initio , due to the high degree of aliasing . however , we were able to confirm the previously determined orbital periods obtained by @xcite and @xcite for cvs 1 and 6 , as well as that of u12 @xcite . we also see evidence for additional long - term variability for cvs 1 and 6 , at the level of a few tenths of a magnitude . we determined the cluster center by iterative centroiding in a 20 radius aperture using a sample of ms stars with magnitudes in the range @xmath39 . the resulting center of @xmath40 lies within about 1 of cv2 ( u19 ) . experimentation with the centroiding aperture size and the stellar sample definition indicates that the center position is uncertain by about 1 . we then determined the cumulative radial distributions of a number of stellar groups out to a radius of 100 , which is the approximate size of the central surface density cusp of ngc 6397 @xcite . figure [ f : radial ] shows the distribution functions for the stellar groups listed in the figure legend . as has been previously noted , the bright cvs in ngc 6397 show a strong central concentration relative to other stellar groups , including the fainter cvs . with the exception of cv6 , the five other bright cvs lie within 11 ( @xmath41 ) of the cluster center . in comparison , with the exception of u25 , the faint cvs lie at least 20 ( @xmath42 ) from the cluster center . we carried out kolmogorov - smirnov intercomparisons of the stellar samples defined in fig . [ f : radial ] . the comparison of each group to a msto sample , defined by @xmath43 , is given in table [ t : cored_pl_fits ] , where the probability , @xmath44 , of the two samples being drawn from the same parent distribution is listed . the bright cv and blue straggler ( bs ) samples both differ very significantly from the msto sample ( @xmath45 ) , while the overall cv and ab samples differ from the msto sample at the 4% level and 1% level , respectively . the bright and faint cv samples differ from each other at a significance level of 3% and the bright cv and ab samples differ at a level of 2% . lrcccccr msto & 1111 & 1.0 & @xmath46 & @xmath47 & @xmath48 & & + cv & 14 & @xmath49 & @xmath50 & @xmath51 & @xmath52 & 2.3 & 4.0% + bright cv & 6 & @xmath53 & @xmath54 & @xmath55 & @xmath56 & 2.9 & 0.07% + faint cv & 8 & @xmath57 & @xmath58 & @xmath59 & @xmath60 & 0.2 & 89% + ab & 36 & @xmath61 & @xmath62 & @xmath63 & @xmath64 & 2.6 & 1.1% + bs & 23 & @xmath65 & @xmath66 & @xmath67 & @xmath68 & 3.7 & 0.03% + in order to further investigate the spatial distribution of the _ chandra _ sources in ngc 6397 and the implications for object masses , we carried out maximum likelihood fits of what has been termed a `` generalized king model '' to the surface density distributions . this model can be described more generally as a `` cored power law , '' in that it has a smooth transition from an inner core region to an outer power law . it takes the form , @xmath69^{\alpha/2},\ ] ] with the core radius @xmath70 related to the scale parameter @xmath71 by , @xmath72 an `` analytic king model , '' which provides a good fit to the surface density profile of the turnoff - mass stellar group for a normal - core cluster ( e.g. 47 tuc ; * ? ? ? * ) , corresponds to @xmath73 and @xmath74 . since ngc 6397 has a central - cusp structure , due to its core - collapsed status , we expect that the turnoff - mass group will have a flatter power - law slope than @xmath75 @xcite . we performed a maximum - likelihood fit of eqn . [ eqn : cored_pl ] to a turnoff - mass group , defined by @xmath43 and radial offset within @xmath76 of the cluster center , to determine the best - fit values of @xmath77 and @xmath70 . we used nonlinear optimization to maximize the likelihood and bootstrap resampling to estimate the parameter uncertainties , as discussed by @xcite . the resulting best - fit parameter values are @xmath78 and @xmath79 . by fitting eqn . [ eqn : cored_pl ] to the surface density distributions of individual groups such as the cvs and abs , the characteristic masses of these objects can be estimated , as described by @xcite and @xcite . in order to do this , we adopt the approximation here that stellar groups with masses exceeding the turnoff mass are in approximate thermal equilibrium with the turnoff mass group and that the velocity dispersion of each mass group is approximately constant with radius within the central cusp region . this approach is motivated by fokker - planck simulations of post - collapse core oscillations which indicate that a cluster core spends a majority of the time near a maximally expanded state in which the more massive stellar groups are close to thermal equilibrium @xcite . more recent monte - carlo and n - body simulations suggest that the presence of primordial binaries may delay the gravothermal oscillation phase to well beyond a hubble time and that even clusters with an observationally core - collapsed designation such as ngc 6397 may still be in the binary burning phase @xcite . in any case , the assumption of thermal equilibrium among the most massive components in the central region of an evolved cluster is a useful starting point . in the thermal equilibrium approximation , the surface density profile for a mass group with mass @xmath80 is given by eqn . [ eqn : cored_pl ] with a slope parameter @xmath77 related to the turnoff - mass slope @xmath81 by @xmath82 where @xmath83 . thus , fitting this model involves just one free parameter , the mass ratio @xmath84 , as @xmath85 is determined by normalization and @xmath71 and @xmath81 are determined by the fit to the turnoff - mass group . table [ t : cored_pl_fits ] gives the results of maximum - likelihood fits of eqn . [ eqn : cored_pl ] to the turnoff mass stars , cvs , abs , and a comparison group of blue stragglers ( bss ) . the cumulative radial distributions for these groups and the model fits are shown in fig . [ f : radial ] . as can be seen from the table , the @xmath84 values for all of the groups exceed unity , indicating that the characteristic masses exceed the turnoff mass . for all cases other than the faint cvs , the excesses are significant at the 2@xmath35 or higher level . the groups with the strongest evidence for a mass significantly above the turnoff mass are the bright cvs ( @xmath86 ) and the bss ( @xmath87 ) . we note that the results of this analysis agree with the k - s comparison results given in the last column of the table . the inferred mass range for the bright cvs ( @xmath88 ) is consistent with a system made up of a heavy white dwarf ( e.g. @xmath89 ) with a main sequence secondary of mass @xmath90 . the inferred mass range for the faint cvs ( @xmath91 ) is consistent with a somewhat less massive white dwarf ( e.g @xmath92 ) and a secondary mass that has been whittled down to @xmath93 . in such a system , the optical flux would be dominated by the white dwarf , as observed here . we presume that the white dwarf in this case has been heated by the accretion process , since noninteracting heavy white dwarfs are too faint to detect due to the degree of cooling that has occurred over their long lifetimes . as discussed in [ source_types ] , an alternative interpretation is that some of the cvs are am cvn systems , in which the secondary is a he wd . in this case , the mass of the secondary would likely be about 0.20.3 @xcite . it is interesting to compare the white dwarf masses inferred here with those for field cvs . @xcite have recently determined a mass of @xmath94 for the wd in a field cv that lies above the period gap . @xcite have determined the masses of the wds in seven cvs that lie below period gap , with a resulting mean mass and standard deviation of @xmath95 . thus , given the uncertainty ranges in the cv masses inferred here , our results for likely wd masses are generally consistent with these measured wd masses .

we have searched for optical identifications for 79 _ chandra _ x - ray sources that lie within the half - mass radius of the nearby , core - collapsed globular cluster ngc 6397 , using deep hubble space telescope advanced camera for surveys wide field channel imaging in , , and . photometry of these images allows us to classify candidate counterparts based on color - magnitude diagram location . the 15 likely and possible cvs in ngc 6397 mostly fall into two groups : a brighter group of six for which the optical emission is dominated by contributions from the secondary and accretion disk , and a fainter group of seven for which the white dwarf dominates the optical emission . there are two possible transitional objects that lie between these groups . the faintest cvs likely lie near the minimum of the cv period distribution , where an accumulation is expected .

we have searched for optical identifications for 79 _ chandra _ x - ray sources that lie within the half - mass radius of the nearby , core - collapsed globular cluster ngc 6397 , using deep hubble space telescope advanced camera for surveys wide field channel imaging in , , and . photometry of these images allows us to classify candidate counterparts based on color - magnitude diagram location . in addition to recovering nine previously detected cataclysmic variables ( cvs ) , we have identified six additional faint cv candidates , a total of 42 active binaries ( abs ) , two millisecond pulsars ( msps ) , one candidate active galactic nucleus , and one candidate interacting galaxy pair . of the 79 sources , 69 have a plausible optical counterpart . the 15 likely and possible cvs in ngc 6397 mostly fall into two groups : a brighter group of six for which the optical emission is dominated by contributions from the secondary and accretion disk , and a fainter group of seven for which the white dwarf dominates the optical emission . there are two possible transitional objects that lie between these groups . the faintest cvs likely lie near the minimum of the cv period distribution , where an accumulation is expected . the spatial distribution of the brighter cvs is much more centrally concentrated than those of the fainter cvs and the active binaries . this may represent the result of an evolutionary process in which cvs are produced by dynamical interactions , such as exchange reactions , near the cluster center and are scattered to larger orbital radii , over their lifetimes , as they age and become fainter .

1106.1927

i

we have shown that with moderately deep @xmath1 , @xmath0 , and _ hst_-acs / wfc imaging , it is possible to identify and classify nearly all of the 79 currently detected _ chandra _ sources within the half - mass radius of ngc 6397 . our classifications are based on cmd location and are tested for consistency with expected ranges of the x - ray to optical flux ratio . in only a few cases was it not possible to classify the source , generally due to a lack of coverage in one filter . the vast majority of the sources in the cluster can be classified as either cataclysmic variables ( a total of 15 ) or active binaries ( a total of 42 ) . the x - ray to optical flux ratio for the cvs ( 0.2 6 ) substantially exceeds that for most of the abs ( @xmath96 ) . there is one previously known msp and one potential msp ; the latter classification is based on the similar photometric properties of the two objects . the proper - motion test for cluster membership produces an unknown status for many of the _ chandra _ source counterparts . this is largely a consequence of the short time baseline of 1.5 years between the two epochs of acs / wfc data used for determining proper motions . while the 1999 wfpc2 observations give a longer baseline , fewer stars are detected by the wfpc2 . thus , the proper - motion part of this study would benefit substantially from new _ hst _ observations of ngc 6397 with either the acs / wfc or the wfc3 . while it appears likely that the vast majority of the proposed counterparts are cluster members , proper - motion confirmation would be valuable . it would be particularly interesting to know how many of the atypical abs are cluster members . while it is likely that most are foreground stars , one of the very red ones has appears to be a member on the basis of our preliminary proper - motion measurements . the cv distribution in ngc 6397 has a bimodal character . we detect distinct bright and faint populations with only two possible transition objects . the optical emission of the six brightest cvs appears to be dominated by a relatively massive secondary , while that of the faint cvs appears to be dominated by the wd , with very little contribution from a very low - mass secondary . alternatively , some of the faint cvs may be am cvn systems , with a he wd secondary . the distribution of cvs in optical luminosity and color is consistent with expected cv evolution due to the effects of mass transfer and angular momentum loss . as cvs age and the secondary loses mass to the primary , the orbit tightens due to magnetic braking and ultimately gravitational wave radiation . in this picture , the bright cvs 16 represent young , recently formed systems , while the faint cvs represent old , highly evolved systems . while cvs can be born at any orbital period , depending on the nature of the secondary star , there is a bias for cvs formed in exchange interactions in collapsed cluster cores to have more massive secondaries and thus longer orbital periods than newly formed field cvs . this is both the result of mass segregation in the cluster , which may invert the mass function in the cluster core , and of the tendency for more massive stars to displace less massive ones in exchange interactions . thus , while it is possible for a faint cv to be a young system , we expect that the bulk of the faint cvs evolved from an earlier bright state . given the likely ongoing formation of cvs by dynamical processes in the central region of the cluster , it is plausible that we are observing a roughly equilibrium cv population in ngc 6397 . however , there remains a possibility that the current population of six bright cvs represents the result of a recent core collapse event that resulted in an enhanced production of cvs . in this case , the bright cvs would be overpopulous relative to the faint cvs . the six brightest cvs in ngc 6397 have a much more centrally concentrated spatial distribution than do either the fainter cvs or the abs . indeed , five of six bright cvs are located within about 2@xmath70 of the cluster center , while all but one of the fainter cvs lie outside of 4@xmath70 . this suggests that cvs are preferentially formed by dynamical processes within the core and surrounding region and migrate to larger radii as they age and undergo repeated scattering interactions that act to increase the typical size of their orbits in the cluster potential . since repeated strong interactions between compact binaries and other stars ultimately result in the ejection of the binaries from clusters , the lifetime of a compact binary in a cluster is extended if the amount of time it spends in the central region of the cluster is reduced . thus , it is reasonable to expect that long - lived cvs in globular clusters should generally be found outside of the densest regions . this is consistent with the spatial distribution of the cvs in ngc 6397 . , s. f. , becker , a. c. , haggard , d. , prieto , j. l. , knapp , g. r. , sako , m. , halford , k. e. , jha , s. , martin , b. , holtzman , j. , frieman , j. a. , garnavich , p. m. , hayward , s. , ivezi , . , mukadam , a. s. , sesar , b. , szkody , p. , malanushenko , v. , richmond , m. w. , schneider , d. p. , & york , d. g. 2008 , , 135 , 2108 , s. f. , haggard , d. , homer , l. , joshi , n. r. , margon , b. , silvestri , n. m. , szkody , p. , wolfe , m. a. , agol , e. , becker , a. c. , henden , a. , hall , p. b. , knapp , g. r. , richmond , m. w. , schneider , d. p. , stinson , g. , barentine , j. c. , brewington , h. j. , brinkmann , j. , harvanek , m. , kleinman , s. j. , krzesinski , j. , long , d. , neilsen , jr . , e. h. , nitta , a. , & snedden , s. a. 2005 , , 130 , 2230 , b. t. , dillon , m. , southworth , j. , thorstensen , j. r. , rodrguez - gil , p. , aungwerojwit , a. , marsh , t. r. , szkody , p. , barros , s. c. c. , casares , j. , de martino , d. , groot , p. j. , hakala , p. , kolb , u. , littlefair , s. p. , martnez - pais , i. g. , nelemans , g. , & schreiber , m. r. 2009 , , 397 , 2170 , d. , & hut , p. 2003 , the gravitational million - body problem : a multidisciplinary approach to star cluster dynamics ( the gravitational million - body problem : a multidisciplinary approach to star cluster dynamics , by douglas heggie and piet hut . cambridge university press , 2003 , 372 pp . ) , d. , lewin , w. h. g. , anderson , s. f. , baumgardt , h. , filippenko , a. v. , gaensler , b. m. , homer , l. , hut , p. , kaspi , v. m. , makino , j. , margon , b. , mcmillan , s. , portegies zwart , s. , van der klis , m. , & verbunt , f. 2003 , , 591 , l131 llrlllllcccl u5 & 17:40:54.531 @xmath9753:40:44.57 & 1.85 & v30 & 1 & ab ? & ? & & & 18.73 & 19.23 & outside of @xmath0 field + u7 & 17:40:52.832 @xmath9753:41:21.77 & 1.81 & cv10@xmath98 & 1 & cv & c & & 22.58 & 23.44 & 24.73 & + u10 & 17:40:48.978 @xmath9753:39:48.62 & 1.21 & cv6 , v13 & 1 & cv & c & c & 19.14 & 20.34 & 21.53 & + u11 & 17:40:45.781 @xmath9753:40:41.52 & 0.58 & cv7 & 1 & cv & ? & c & 23.65 & 24.26 & 25.88 & + u12 & 17:40:44.621 @xmath9753:40:41.60 & 0.42 & by - wf4 - 1 , v16 & 1 & msp & c & c & 16.25 & 17.43 & 18.99 & + u13 & 17:40:44.084 @xmath9753:40:39.17 & 0.33 & cv8 & 1 & cv & ? & c & 24.00 & 24.33 & 25.95 & + u14 & 17:40:43.328 @xmath9753:41:55.46 & 1.46 & v35 & 1 & ab & c & & 18.31 & 19.72 & 20.96 & + u15 & 17:40:42.910 @xmath9753:40:33.81 & 0.14 & by - pc-2 & 1 & ab & c & & 17.25 & 18.53 & 19.93 & + u16 & 17:40:42.636 @xmath9753:42:15.24 & 1.78 & & 1 & ? & ? & & & & 25.83 & outside of @xmath0 and @xmath1 fields + u17 & 17:40:42.651 @xmath9753:40:19.30 & 0.17 & cv3 , v33 & 1 & cv & c & c & 18.52 & 19.10 & 20.67 & + u18 & 17:40:42.606 @xmath9753:40:27.62 & 0.07 & by - pc-8 , v31 & 1 & msp & c & c & 16.10 & 17.51 & 18.73 & + u19 & 17:40:42.306 @xmath9753:40:28.70 & 0.02 & cv2 , v34 & 1 & cv & c & c & 18.87 & 20.02 & 21.03 & + u21 & 17:40:41.830 @xmath9753:40:21.37 & 0.13 & cv4 & 1 & cv & c & c & 19.82 & 20.94 & 21.82 & + u22 & 17:40:41.701 @xmath9753:40:29.00 & 0.07 & cv5 & 1 & cv & c & c & 20.15 & 21.50 & 22.04 & + u23 & 17:40:41.597 @xmath9753:40:19.30 & 0.18 & cv1 , v12 & 1 & cv & c & c & 17.88 & 18.93 & 20.25 & + u24 & 17:40:41.468 @xmath9753:40:04.43 & 0.42 & & 0 ? & qlmxb & & & & & & hint of detection in @xmath0 only + u25 & 17:40:41.237 @xmath9753:40:25.79 & 0.15 & cv13@xmath98 & 1 & cv ? & & & 23.48 & 23.44 & 26.01 & uncertain photometry + u28 & 17:40:38.904 @xmath9753:39:51.09 & 0.79 & & 1 & agn & ? & & 22.72 & 24.73 & 25.44 & + u31 & 17:40:34.202 @xmath9753:41:15.28 & 1.41 & cv11@xmath98 & 1 & cv & f & & 23.32 & 23.93 & 26.07 & + u41 & 17:40:45.008 @xmath9753:39:55.21 & 0.70 & & 1 & ms & c & c & 16.74 & 17.69 & 19.50 & only object in error circle + u42 & 17:40:43.059 @xmath9753:38:31.29 & 1.96 & v26 & 1 & ab & ? & & 15.52 & 17.47 & 18.20 & very red + u43 & 17:40:40.543 @xmath9753:40:22.79 & 0.26 & by - pc-4 & 1 & ab & c & c & 17.68 & 19.03 & 20.38 & + u60 & 17:40:47.807 @xmath9753:41:28.40 & 1.30 & cv9 & 1 & cv & c & c & 23.38 & 23.63 & 26.04 & + u61 & 17:40:45.223 @xmath9753:40:28.60 & 0.45 & cv12@xmath98 & 1 & cv ? & ? & & 22.08 & 23.19 & 24.19 & uncertain photometry + u62 & 17:40:30.422 @xmath9753:39:17.47 & 2.11 & & 1 & ab ? & & & 20.90 & 23.33 & 23.17 & uncertain photometry + u63 & 17:40:31.663 @xmath9753:38:46.36 & 2.31 & & 1 & ab ? & & & 18.15 & 20.39 & 20.72 & very red , moderate excess + u65 & 17:40:37.558 @xmath9753:39:17.85 & 1.36 & & 1 & ab ? & ? & & 18.72 & 21.27 & 21.11 & very red , large excess + u66 & 17:40:38.918 @xmath9753:38:49.80 & 1.71 & & 1 & ab ? & f & & 21.93 & 24.56 & 24.29 & red , large excess + u67 & 17:40:40.065 @xmath9753:40:16.59 & 0.37 & & 1 & ab & c & c & 19.34 & 21.17 & 22.00 & + u68 & 17:40:40.730 @xmath9753:38:32.63 & 1.95 & & 1 ? & ? & & & & & & marginal detection in @xmath0 only + u69 & 17:40:40.867 @xmath9753:40:17.17 & 0.27 & by - pc-5 & 1 & ab & c & c & 17.84 & 19.03 & 20.52 & + u70 & 17:40:41.693 @xmath9753:40:33.33 & 0.11 & v20 & 1 & ab , bs & c & c & 15.50 & 16.21 & 18.30 & + u73 & 17:40:42.681 @xmath9753:39:28.73 & 1.00 & & 1 & ab & c & c & 18.19 & 19.47 & 20.88 & + u75 & 17:40:43.666 @xmath9753:40:30.61 & 0.22 & & 1 & ab & c & & 19.71 & 21.78 & 22.32 & + u76 & 17:40:43.818 @xmath9753:41:16.32 & 0.83 & v17 & 1 & ab & c & c & 15.81 & 16.81 & 18.57 & + u77 & 17:40:44.125 @xmath9753:42:11.48 & 1.74 & v36 & 1 & ab ? & & & & & 24.21 & outside of @xmath0 field + u79 & 17:40:46.409 @xmath9753:40:04.05 & 0.75 & & 1 & ab & ? & & 19.82 & 21.98 & 22.41 & + u80 & 17:40:46.455 @xmath9753:41:56.50 & 1.60 & cv14@xmath98 & 1 & cv ? & & & 25.40 & 25.84 & 27.91 & weak detection + u81 & 17:40:46.481 @xmath9753:41:15.44 & 1.01 & v14 & 1 & ab & c & c & 18.62 & 20.27 & 21.29 & + u82 & 17:40:48.537 @xmath9753:39:39.53 & 1.25 & by - wf2 - 1 & 1 & ab & c & & 18.72 & 20.29 & 21.39 & + u83 & 17:40:49.615 @xmath9753:40:43.02 & 1.13 & cv15@xmath98 & 1 & cv ? & ? & ? & 26.22 & 27.18 & 28.56 & very faint + u84 & 17:40:54.807 @xmath9753:40:19.79 & 1.88 & & 1 & ab ? & ? & ? & & 17.27 & 18.23 & very red , outside of @xmath0 field + u86 & 17:40:37.473 @xmath9753:41:47.24 & 1.48 & & 1 & ab ? & ? & & 21.16 & 24.06 & 23.39 & very red , large excess + u87 & 17:40:42.877 @xmath9753:40:26.45 & 0.11 & by - pc-3 & 1 & ab & c & c & 17.46 & 18.69 & 20.14 & + u88 & 17:40:42.863 @xmath9753:40:23.43 & 0.13 & by - pc-1 , v19 & 1 & ab & c & c & 16.73 & 17.77 & 19.43 & + u89 & 17:40:43.613 @xmath9753:40:24.60 & 0.23 & & 1 & ab & c & c & 19.76 & 21.82 & 22.38 & + u90 & 17:40:41.779 @xmath9753:40:14.42 & 0.24 & by - pc-6 & 1 & ab & c & c & 18.45 & 19.88 & 21.11 & + u91 & 17:40:42.430 @xmath9753:40:41.65 & 0.22 & & 1 & ms & c & & 18.94 & 20.44 & 21.63 & only object in error circle + u92 & 17:40:43.916 @xmath9753:40:35.39 & 0.28 & by - wf4 - 2 , v7 & 1 & ab ? & c & c & 16.72 & 18.26 & 19.53 & very red , slight deficit + u93 & 17:40:42.393 @xmath9753:40:46.62 & 0.30 & & 1 & ? & & & & & 24.95 & uncertain photometry + u94 & 17:40:42.868 @xmath9753:40:49.07 & 0.36 & & 1 & ab & c & c & 18.88 & 20.58 & 21.53 & + u95 & 17:40:40.320 @xmath9753:40:44.58 & 0.38 & & 1 & ab ? & c & & 20.81 & 23.02 & 23.41 & ms color , excess + u96 & 17:40:39.097 @xmath9753:40:23.09 & 0.47 & v24 & 1 & ab & c & & 18.40 & 20.15 & 21.42 & + u97 & 17:40:43.918 @xmath9753:40:05.90 & 0.46 & & 1 & ? & c & & 20.90 & 22.88 & 23.56 & blue , normal + u98 & 17:40:40.994 @xmath9753:40:58.40 & 0.53 & & 1 & ab & c & & 19.18 & 21.09 & 21.82 & + u99 & 17:40:46.431 @xmath9753:40:30.40 & 0.63 & & 1 & ab & c & & 18.49 & 19.96 & 21.16 & + u100 & 17:40:38.201 @xmath9753:40:46.55 & 0.66 & & 1 & ab & c & & 20.81 & 23.14 & 23.40 & + u101 & 17:40:45.399 @xmath9753:41:01.40 & 0.73 & & 1 & ab ? & c & c & 18.48 & 19.94 & 21.19 & red , normal + u102 & 17:40:38.845 @xmath9753:39:43.12 & 0.90 & & 1 & ab & c & & 21.27 & 23.80 & 23.87 & + u103 & 17:40:35.698 @xmath9753:40:12.56 & 1.00 & & 1 & ab & c & & 19.26 & 21.05 & 21.93 & + u104 & 17:40:43.124 @xmath9753:39:29.04 & 1.01 & & 0 & & & & & & & empty error circle + u105 & 17:40:36.521 @xmath9753:41:07.85 & 1.06 & & 1 & ab & ? & & 19.78 & 21.84 & 22.37 & + u106 & 17:40:43.737 @xmath9753:39:17.52 & 1.21 & & 0 & & & & & & & empty error circle + u107 & 17:40:34.115 @xmath9753:40:17.01 & 1.21 & & 1 & ab & c & & 19.61 & 21.63 & 22.23 & + u108 & 17:40:52.099 @xmath9753:39:48.25 & 1.62 & & 1 & glx ? & & & & & & extended object + u109 & 17:40:52.728 @xmath9753:40:52.88 & 1.61 & & 1 & ab ? & c & c & 19.77 & 21.83 & 22.44 & red , normal + u110 & 17:40:33.455 @xmath9753:39:16.83 & 1.76 & & 1 & ab & c & & 19.92 & 22.04 & 22.53 & + u111 & 17:40:29.845 @xmath9753:40:26.99 & 1.82 & & 0 & & & & & & & empty error circle + u112 & 17:40:50.374 @xmath9753:39:06.00 & 1.84 & & 1 & ms & f & & 19.60 & 21.25 & 22.29 & only object in error circle + u113 & 17:40:42.764 @xmath9753:40:20.76 & 0.16 & & 0 & & & & & & & empty error circle + u114 & 17:40:43.469 @xmath9753:40:34.34 & 0.21 & & 1 & ? & c & & 19.49 & & 22.10 & uncertain photometry + u116 & 17:40:42.236 @xmath9753:40:19.97 & 0.18 & & 1 & ab & c & c & 18.18 & 19.49 & 20.88 & + u117 & 17:40:42.153 @xmath9753:40:25.56 & 0.14 & & 1 & ab & c & c & 16.82 & 17.84 & 19.55 & + u118 & 17:40:41.576 @xmath9753:40:15.88 & 0.05 & & 1 & msto & c & c & 15.60 & 16.60 & 18.34 & only object in error circle + u119 & 17:40:41.261 @xmath9753:40:19.35 & 0.22 & & 0 & & & & & & & empty error circle + u120 & 17:40:46.517 @xmath9753:40:15.64 & 0.21 & & 1 & ab ? & ? & ? & 21.09 & 23.70 & 23.39 & moderately red , large ha excess + u121 & 17:40:33.631 @xmath9753:39:34.96 & 0.68 & & 0 & & & & & & & empty error circle + u122 & 17:40:47.903 @xmath9753:39:24.83 & 1.55 & & 0 & & & & & & & empty error circle + u123 & 17:40:49.621 @xmath9753:38:45.93 & 2.04 & & 0 & & & & & & & empty error circle +

in addition to recovering nine previously detected cataclysmic variables ( cvs ) , we have identified six additional faint cv candidates , a total of 42 active binaries ( abs ) , two millisecond pulsars ( msps ) , one candidate active galactic nucleus , and one candidate interacting galaxy pair . of the 79 sources , 69 have a plausible optical counterpart . the spatial distribution of the brighter cvs is much more centrally concentrated than those of the fainter cvs and the active binaries . this may represent the result of an evolutionary process in which cvs are produced by dynamical interactions , such as exchange reactions , near the cluster center and are scattered to larger orbital radii , over their lifetimes , as they age and become fainter .

we have searched for optical identifications for 79 _ chandra _ x - ray sources that lie within the half - mass radius of the nearby , core - collapsed globular cluster ngc 6397 , using deep hubble space telescope advanced camera for surveys wide field channel imaging in , , and . photometry of these images allows us to classify candidate counterparts based on color - magnitude diagram location . in addition to recovering nine previously detected cataclysmic variables ( cvs ) , we have identified six additional faint cv candidates , a total of 42 active binaries ( abs ) , two millisecond pulsars ( msps ) , one candidate active galactic nucleus , and one candidate interacting galaxy pair . of the 79 sources , 69 have a plausible optical counterpart . the 15 likely and possible cvs in ngc 6397 mostly fall into two groups : a brighter group of six for which the optical emission is dominated by contributions from the secondary and accretion disk , and a fainter group of seven for which the white dwarf dominates the optical emission . there are two possible transitional objects that lie between these groups . the faintest cvs likely lie near the minimum of the cv period distribution , where an accumulation is expected . the spatial distribution of the brighter cvs is much more centrally concentrated than those of the fainter cvs and the active binaries . this may represent the result of an evolutionary process in which cvs are produced by dynamical interactions , such as exchange reactions , near the cluster center and are scattered to larger orbital radii , over their lifetimes , as they age and become fainter .

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deep multiwavelength surveys are progressively sheding light on the history of galaxy evolution since very high redshifts . from new surveys in the ultraviolet regime ( e.g. martin et al . 2005 ) to the latest ir , sub - millimetre and radio campaigns ( e.g. werner et al . 2004 ; dunlop 2005 ; condon et al . 2003 ) , the advent of numerous datasets is enhancing our understanding of when galaxies were formed and how they evolved through cosmic time . uv / optical observations can unveil the sources of stellar emission but are limited to detect unobscured systems , missing an important fraction of the galaxies with on - going star formation . ir and longer - wavelength surveys provide an unbiased way of studying star - forming systems , but are insensitive to galaxies with little or no dust content . near - ir observations , on the contrary , appear as one of the most suitable methods for making a complete census of galaxy populations , as they are sensitive to the stellar emission from both young and old galaxies , and are also relatively unaffected by the presence of dust . the rest - frame @xmath15 band is the most efficient tracer of the stellar mass content of the universe . recent studies of near - ir - selected galaxies allowed for a rapid progress in setting different constraints on the history of galaxy formation ( cimatti et al . 2002 ; daddi et al . 2003 ; caputi et al . 2004 ; caputi et al . 2005a ; among others ) and , in particular , on the evolution of the stellar mass content of the universe with redshift ( dickinson et al . 2003 ; fontana et al . 2004 ; glazebrook et al . 2004 ; caputi et al . 2005a ; drory et al . 2005 ) . it is now recognised that , although more than a half of the stellar mass has been formed at redshifts @xmath16 $ \sim$}}~}1.5 $ ] , near - ir - selected galaxies are already present before at least redshifts @xmath17 and contain a significant fraction of the stellar mass observed at redshift @xmath5 . however , one of the main problems of existing near - ir surveys is that , when sufficiently deep , they are usually restricted to small areas of the sky , making the results prone to large error bars due to cosmic variance . also , the lack of statistics prevents refined studies of galaxy evolution , where trends for different near - ir sub - populations can be individually investigated . the goods project ( giavalisco et al . 2004 ) is a public program of multiwavelength observations which is now close to completion . the data sets are kindly released to the astronomical community in a fully reduced mode . as part of the goods project , @xmath18 of the cdfs have been observed with the advanced camera for surveys ( acs ) on board the hubble space telescope ( hst ) in four passbands : @xmath3 , @xmath19 , @xmath20 and @xmath21 . in addition , the goods project includes deep near - ir imaging taken with the infrared spectrometer and array camera ( isaac ) on the ` antu ' very large telescope ( antu - vlt ) . a first release of the european southern observatory ( eso ) imaging survey ( goods / eis v0.5 release ) provided data in the @xmath22 , @xmath23 and @xmath24 bands for @xmath25 of the goods / cdfs field . in this sub - region , roche , dunlop & almaini ( 2003 ) selected a deep sample of extremely red galaxies ( ergs ) with @xmath26 ( vega ) , whose redshift distribution and luminosity evolution were studied by caputi et al . a detailed comparison of the properties of ergs with other @xmath2-selected galaxies was presented by caputi et al . ( 2005a ) . over the last year , however , new datasets have been made public within the goods project , increasing the coverage in wavelength and area of the goods / cdfs . the second goods / eis ( v1.0 ) release extends the deep @xmath22 and @xmath24 band imaging to @xmath1 of the goods / cdfs . also , the infrared array camera ( irac ) on board the spitzer space telescope imaged this field at @xmath27 , @xmath28 , @xmath29 and @xmath30 . the availability of these data allows one to map the rest - frame @xmath2-band light up to redshifts @xmath17 . in this work , we take advantage of the further wavelength and area coverage of the goods / cdfs , in conjunction with the information provided by the latest released spectroscopic and combo17 data , to set tighter constraints on the properties and evolution of @xmath2-selected galaxies . the layout of this paper is as follows . first , in section [ sec_sample ] , we present the sample selection and give details on the multiwavelength photometry . in section [ sec_redsh ] , we explain the technique we applied to construct an optimised redshift catalogue for our galaxy sample and show the resulting redshift distribution . in section [ sec_lf ] , we present the rest - frame @xmath2-band luminosity function ( lf ) for our sample of @xmath2-selected galaxies . in section [ sec_mass ] , we discuss several aspects of the evolution of different mass systems . in section [ sec_nearir ] , we explore additional hints from the study of the purely near - ir colours of our galaxies . finally , in section [ sec_conc ] we present some concluding remarks . we adopt throughout a cosmology with @xmath31 , @xmath32 and @xmath33 . a salpeter ( 1955 ) imf over stellar masses @xmath34 is assumed , unless where otherwise stated .

we have selected and analysed the properties of a sample of 2905 galaxies in of the great observatories origins deep survey ( goods ) chandra deep field south ( cdfs ) , to obtain further constraints on the evolution of-selected galaxies with respect to the results already obtained in previous studies .

we have selected and analysed the properties of a sample of 2905 galaxies in of the great observatories origins deep survey ( goods ) chandra deep field south ( cdfs ) , to obtain further constraints on the evolution of-selected galaxies with respect to the results already obtained in previous studies . we made use of the public deep multiwavelength imaging from the optical through the infrared ( ir ) bands , in conjunction with available spectroscopic and combo17 data in the cdfs , to construct an optimised redshift catalogue for our galaxy sample . we computed the-band lf and determined that its characteristic magnitude has a substantial brightening and a decreasing total density from to . we also analysed the colours and number density evolution of galaxies with different stellar masses . within our sample , and in contrast to what is observed for less massive systems , the vast majority (% ) of the most massive ( ) local galaxies appear to be in place before redshift . around% of the total assemble between redshifts and and most of them display extremely red colours , suggesting that plausible star formation in these very massive systems should mainly proceed in obscured , short - timescale bursts . the remaining fraction ( up to% ) could be in place at even higher redshifts , pushing the first epoch of formation of massive galaxies beyond the limits of current near - ir surveys . [ firstpage ] galaxies : evolution galaxies : formation galaxies : high - redshift galaxies : luminosity function , mass function

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with the goods project close to completion , in this work we have been able to set tighter constraints on the evolution of near - ir - selected galaxies in the goods / cdfs field . we took advantage of the latest available very deep and homogeneous multiwavelength photometry , in conjunction with the information provided by complementary spectroscopic programs and the combo17 campaign , to construct an optimised redshift catalogue for the @xmath0 galaxies in the goods - south field . based on this catalogue , we performed a detailed analysis of galaxy luminosity and mass evolution up to very high redshifts @xmath184 . the incorporation of the spitzer / irac data at @xmath185 and @xmath186 allowed us to compute rest - frame @xmath2-band luminosities and stellar masses with considerably smaller extrapolations than those applied in caputi et al . ( 2005a ) . in spite of this important difference , we note that most of the main conclusions obtained by caputi et al . ( 2005a ) have been confirmed by this work . the addition of irac data did not produce any overall change in the derived galaxy luminosities and stellar masses . other authors also have concluded that the use of irac data produced a minor impact on the derived galaxy stellar masses , when other shorter optical / near - ir multiwavelength data are also available ( e.g. shapley et al . 2005 ) . from the modelling of the evolution of the @xmath2-band luminosities , we determined that the characteristic magnitude @xmath93 of the rest - frame @xmath2-band lf significantly brightens from redshifts @xmath5 to @xmath98 . this is simultaneously produced with a decrease in the total density of objects , so we conclude that the @xmath2-band lf has both a substantial luminosity and density evolution with redshift . the characteristics of this evolution reveal some important aspects of the sequence of galaxy formation . for instance , that most of the brightest galaxies are assembled at high redshifts ( @xmath89 $ \sim$}}~}1 $ ] ) , while the creation of a substantial number of intermediate - to - low luminosity objects might continue down to low redshifts ( although the latter will need to be confirmed by future deeper surveys , which have direct access to low - luminosity objects at high redshifts ) . we have also studied the very high stellar - mass end ( @xmath132 ) of galaxy evolution . we found that most of these very massive systems in our sample have been formed in the @xmath187-period of time between redshifts @xmath141 and @xmath148 , although a significant fraction ( up to @xmath13% ) appear to have been in place before redshift @xmath122 . very recently , from the cross - correlation of our @xmath0 galaxy sample with the spitzer/@xmath51 galaxies in the same field , caputi et al . ( 2005b ) found that the most - intense star - forming galaxies at redshifts @xmath188 are mainly massive ( @xmath189 ) galaxies . this is also the main epoch of flourish of submillimetre galaxies ( chapman et al . 2005 ) , which presumably are progenitors of the most massive local galaxies ( e.g. stevens et al . thus , this period appears to be critical to understand the formation and evolution of the bulk of the most massive systems present in the local universe . theoretical models of galaxy formation in their current status are not completely able to account for all of these results . several different clues have been proposed in recent works to try to improve the agreement of the models with the data at high redshifts , including e.g. the effects of qso and supernova feedback ( granato et al . 2004 ; cirasuolo et al . 2005 ) , the adoption of an alternative imf ( baugh et al . 2005 ) or the use of hydrodynamical models ( nagamine et al . however , the discrepancies are not produced by the specific recipes used by theoretical models to account for star formation , but seem to lie at the more fundamental level of hierarchical model predictions . hierarchical models do not seem to be able to reproduce the whole of observational properties from the local universe to high redshifts . a likely alternative to this problem is the invalidity of a universal imf when deriving stellar masses from the observed luminosities . a definitive comprehension of the main epoch of very massive galaxy formation , as well as the determination of the initial distribution of stars in these systems , still constitutes a major challenge from both the observational and theoretical points of view .

we made use of the public deep multiwavelength imaging from the optical through the infrared ( ir ) bands , in conjunction with available spectroscopic and combo17 data in the cdfs , to construct an optimised redshift catalogue for our galaxy sample . we computed the-band lf and determined that its characteristic magnitude has a substantial brightening and a decreasing total density from to . assemble between redshifts and and most of them display extremely red colours , suggesting that plausible star formation in these very massive systems should mainly proceed in obscured , short - timescale bursts . the remaining fraction ( up to% )

we have selected and analysed the properties of a sample of 2905 galaxies in of the great observatories origins deep survey ( goods ) chandra deep field south ( cdfs ) , to obtain further constraints on the evolution of-selected galaxies with respect to the results already obtained in previous studies . we made use of the public deep multiwavelength imaging from the optical through the infrared ( ir ) bands , in conjunction with available spectroscopic and combo17 data in the cdfs , to construct an optimised redshift catalogue for our galaxy sample . we computed the-band lf and determined that its characteristic magnitude has a substantial brightening and a decreasing total density from to . we also analysed the colours and number density evolution of galaxies with different stellar masses . within our sample , and in contrast to what is observed for less massive systems , the vast majority (% ) of the most massive ( ) local galaxies appear to be in place before redshift . around% of the total assemble between redshifts and and most of them display extremely red colours , suggesting that plausible star formation in these very massive systems should mainly proceed in obscured , short - timescale bursts . the remaining fraction ( up to% ) could be in place at even higher redshifts , pushing the first epoch of formation of massive galaxies beyond the limits of current near - ir surveys . [ firstpage ] galaxies : evolution galaxies : formation galaxies : high - redshift galaxies : luminosity function , mass function

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r

the rmf+bcs minimizations with nl - sv1 give rise to a prolate and an oblate solution for most of the nuclei . we show the quadrupole deformation @xmath64 for the lowest energy state ( ground state ) for all the isotopic chains in figures [ fig : fig1](a)- [ fig : fig1](j ) . a large number of nuclei in these chains assume a prolate shape in the ground state . this is especially the case in the region of neutron number @xmath76 . typically , these nuclei exhibit a prolate deformation of @xmath77 . for the isotopic chains of no @xmath78 , rf @xmath79 and sg @xmath80 , there is a transition from a prolate shape to an oblate shape at @xmath81 . beyond @xmath7 , nuclei assume an oblate shape in the ground state for these isotopic chains ( see figs . [ fig : fig1](a)@xmath82 [ fig : fig1](d ) ) . the magnitude of the oblate deformation decreases as the neutron number increases above @xmath7 , which approaches a vanishing value as the neutron number @xmath6 arrives . in the vicinity of @xmath6 , nuclei exhibit a spherical shape . such a feature has been commonly predicted by several relativistic as well as non - relativistic theories , whereby @xmath6 constitutes a major magic number in the region of superheavy nuclei . values for isotopes of the elements @xmath83 obtained with nl - sv1 . the results with frdm are shown for comparison.,scaledwidth=100.0% ] as one goes to the heavier elements above sg @xmath80 , one can visualize that the tendency of prolate shapes in the range of neutron numbers @xmath84 continues for heavier superheavy elements as well . the point of shape transition from prolate to oblate seems to be shifting to a higher neutron number . for instance , for hs ( @xmath85 ) the prolate to oblate transition occurs at @xmath86 . for the isotopic chain ds ( @xmath87 ) the shape transition point advances to @xmath88 . however , for @xmath9 and above , the transition point falls back to @xmath86 and below it . for instance , for @xmath89 and @xmath90 , the shape transition occurs at @xmath91 and @xmath7 , respectively . similarly , the shape transition point for @xmath1 falls back to @xmath92 . thus , the number of nuclei which exhibit an oblate shape below the neutron number @xmath6 increases steadily in going from @xmath9 to @xmath1 . as far as the spherical shape for @xmath6 nuclei is concerned , it is exhibited by all the isotopic chains from @xmath0 to @xmath1 . this is reminiscent of a magic shell character for the neutron number @xmath93 . the general feature of shape transition from prolate to oblate in the region of @xmath94 prevails for all the isotopic chains considered in this study . we have made a comparison of nl - sv1 deformations with those predicted by the macroscopic - microscopic mass formula frdm . for the isotopic chains @xmath95 , the frdm exhibits a predominantly prolate shape for the neutron numbers @xmath84 . this feature is very similar to that predicted by nl - sv1 . the frdm shows a shape transition from prolate to an oblate shape at the neutron number @xmath96 for the chains @xmath97 . there is only a single nuclide exhibiting an oblate shape in frdm at @xmath96 for these chains , beyond which all the nuclei assume a spherical shape for the isotopic chains of @xmath95 in the frdm predictions , in contrast to nl - sv1 . the oblate deformation for @xmath86 nuclei in this region amounts to @xmath98 in the frdm . this is unlike nl - sv1 , where a significant number of nuclei exhibit a moderately deformed oblate shape until the supposedly magic number @xmath6 arrived at . for the isotopic chains @xmath99 , the behaviour of frdm for deformation properties is rather uneven . for the region of the lower neutron numbers , some nuclei in these chains show a moderately prolate shape , whereas a few others exhibit a small prolate deformation . this is followed by a shape transition to an oblate deformation at @xmath7 , followed by a spherical shape in going to higher neutron numbers . that nuclei in the vicinity of @xmath6 are predominantly spherical in frdm points to the hypothesis that @xmath6 maintains its magicity even for heavier superheavy elements in frdm . the mass formula extended thomas - fermi with strutinsky integral ( etf - si ) @xcite was obtained to fit experimental masses of more than 1600 nuclei from all over the periodic table . the etf - si , due to its partly microscopic structure , has found broader acceptance for nuclear physics applications . it predicts binding energies and deformations of nuclei over a broad range of masses quite well . here we compare the ground state deformations obtained with nl - sv1 with those predicted by etf - si . the quadrupole deformations @xmath64 are compared for the given isotopic chains in figs . [ fig : fig2](a)@xmath82[fig : fig2](j ) . figs . [ fig : fig2](a)@xmath82[fig : fig2](d ) show that etf - si deformations are in good agreement with the nl - sv1 values from @xmath26 to @xmath100 for the elements from ds ( @xmath0 ) to hs ( @xmath85 ) . for ds ( @xmath87 ) , the agreement between nl - sv1 and etf - si is good up to @xmath101 ( see fig . [ fig : fig2](e ) ) . a constrasting picture with the etf - si is that for neutron numbers @xmath100 and above , it shows a strong divergence from the nl - sv1 predictions . etf - si does not exhibit a prolate to oblate transition as do nl - sv1 and frdm predictions . in constrast , etf - si predicts a constant and a large value of @xmath102 for nuclei in the range of @xmath103 for the isotopic chains of @xmath97 . for the heavier elements @xmath104 , etf - si predicts a nearly constant value @xmath102 for all the neutron numbers @xmath105 . values for the isotopes of the elements @xmath83 obtained with nl - sv1 are compared with etf - si predictions.,scaledwidth=100.0% ] etf - si predicts a spherical shape of nuclei in the vicinity of @xmath6 for the elements @xmath106 . this feature of etf - si is similar to that of frdm . however , for @xmath89 , etf - si bypasses the spherical shape for @xmath6 . on the other hand , for several isotopic chains etf - si predicts a shape transition from spherical to a strongly prolate shape at @xmath107 ( see figs.[fig : fig2](b)@xmath82 [ fig : fig2](g ) ) . for @xmath87 and @xmath9 , nuclei with two neutrons below and two neutrons above @xmath6 exhibit a spherical shape , whereas for @xmath10 there is only one nuclide i.e , @xmath6 that shows a spherical shape . it s neighbours on both sides , assume a prolate shape in etf - si . this is indicative of a decrease in the shell strength at @xmath6 with etf - si . this point is supported by a deformed shape taken by the @xmath6 nuclide for @xmath89 ( see fig . [ fig : fig2](h ) . ) with etf - si . whilst etf - si values for @xmath90 and @xmath1 are not known , the aforesaid diminishing of @xmath6 shell strength points to an erosion of a possible @xmath6 magicity for the heaviest superheavy elements from @xmath89 to @xmath1 with etf - si . obtained with nl - sv1 for @xmath83 and @xmath2.,scaledwidth=90.0% ] a summary of quadrupole deformation @xmath64 in the ground state of superheavy nuclei with nl - sv1 obtained in this work is shown in the fig [ fig : fig3 ] . the nuclei denoted by the red colour indicate a prolate ground state . an oblate ground state is shown by the green colour . spherical nuclei are indicated by yellow . as seen in fig . [ fig : fig3 ] , nuclides with @xmath108 for almost all the isotopic chains exhibit a prolate shape . on the other hand , nuclides with @xmath109 exhibit an oblate shape until a spherical shape appears for nuclei close to @xmath6 . there is a little exception here in that for she with @xmath85 to @xmath9 , a few nuclides above @xmath7 continue to exhibit a prolate shape . this indicates an intrusion of prolate shape into the domain of oblate shapes as indicated in the middle of the figure . nuclei in the vicinity of @xmath6 are predominantly spherical as shown by the yellow blocks . in a few cases and especially for @xmath0 , nuclei two neutrons below and two neutrons above @xmath6 assume a spherical shape . as shown by the picture , @xmath6 acts as a major magic number in the neutron - rich region for all the she with @xmath83 . as we will see in the single - particle levels , the neutron number @xmath6 remains as a major magic number . also we will see that in the rmf theory with nl - sv1 , the proton number @xmath1 is also a magic number . the combination @xmath1 and @xmath6 seems to act as double closed shell in the rmf theory . nuclides above @xmath6 show a prolate ( red ) region for a few lighter she . however , for heavy she with @xmath85 , nuclides above @xmath6 are predominantly oblate ( green ) as shown in the fig . [ fig : fig3 ] . thus , a significant region below as well as above @xmath6 lends itself to an oblate deformation . the phenomenon of shape co - existence in the region of deformed nuclei arises due to interplay of deformed single - particle levels . splittings and alignment of deformed single - particle levels leads often to ground states with a prolate and an oblate shape nearly degenerate in energy . for practical purposes , when the two minimum energy states are within @xmath1101 mev , the two states are said to be shape co - existent . exhibiting the shape - coexistence in the lagrangian model nl - sv1.,scaledwidth=95.0% ] we show in figs . [ fig : fig4](a)@xmath82[fig : fig4](j ) nuclides which exhibit a shape co - existence with nl - sv1 . looking at the figures one can see that a large number of nuclides exhibit the shape co - existence for the superheavy chains . the nuclides in isotopic chains from @xmath0 ( no ) to @xmath9 show a common pattern of shape co - existence between prolate and oblate shapes for the region of neutron numbers @xmath111 to @xmath112 . whilst for @xmath0 and @xmath113 shape co - existence is limited to neutron numbers @xmath114 to @xmath96 , for @xmath115 to @xmath9 the region of shape co - existence extends to neutron number @xmath116 . whereas for the lighter neutron numbers there is a prolate - oblate shape co - existence for elements @xmath0 to @xmath9 , there is a shape co - existence of spherical - oblate shapes for @xmath116 isotones from @xmath117 . this indicates a softer nature of @xmath6 shell closure even for the lighter superheavy elements . several nuclides with @xmath118 , also exhibit a spherical - oblate shape co - existence for the isotopic chains @xmath119 . figures [ fig : fig4](g)- [ fig : fig4](j ) show the shape co - existence for heavier superheavy elements from @xmath10 to @xmath1 . unlike the picture for superheavy elements @xmath95 , the shape co - existence in the lighter neutron region is reduced significantly for @xmath120 . only a few nuclides below @xmath88 exhibit a prolate - oblate shape co - existence . for @xmath10 and @xmath89 , several nuclides exhibit a spherical - oblate shape co - existence for neutron numbers @xmath121 . interestingly , @xmath122 nuclide for @xmath89 shows a spherical - oblate shape co - existence . this indicates a softening of the shell effects for @xmath6 for @xmath89 . the superheavy elements @xmath90 and @xmath1 exhibit the shape co - existence rather scarcely i.e , only two isotopes @xmath92 and @xmath7 show a prolate - oblate shape co - existence . in the rest of the neutron region , there is no shape co - existence for the heaviest superheavy elements with @xmath90 and @xmath1 this may imply that the shell strength at @xmath6 has picked up for these chains and that a readjustment of the deformed single - particle levels does not lend to degenerate shapes in the ground state . a summary of the shape co - existence in superheavy nuclei is illustrated in fig . [ fig : fig5 ] . the brown squares depict a shape co - existence between a prolate and an oblate shape , whereas the blue squares represent a shape co - existence between a spherical and an oblate shape . as the figure shows , the phenomenon of prolate - oblate shape co - existence pervades the region from @xmath92 to @xmath88 . for the lighter elements this shape co - existence lies in the neutron region 170 - 178 . the lower boundary of this region gradually shifts to higher neutron numbers @xmath87 is reached . as one moves above @xmath87 , the region shifts gradually towards lower neutron numbers again . from @xmath10 to @xmath1 , however , there are fewer cases of the prolate - oblate shape co - existence . apparently , the region of prolate - oblate shape co - existence as shown by the brown colour is symmetric about @xmath87 . in addition , there are a few more cases of prolate - oblate shape co - existence for higher neutron numbers near n@xmath123 . the region of spherical - oblate shape co - existence lies near @xmath6 . the neutron number @xmath6 being a major magic number , the ground - state of nuclides with @xmath6 is spherical as seen earlier . for almost all the isotopic chains there is no shape co - existence ( empty squares ) at @xmath6 , with the exception of @xmath89 . only for @xmath89 , there is a spherical - oblate shape co - existence at @xmath6 . this is due to an erosion of the magicity of @xmath6 for @xmath89 . nuclides with @xmath116 show a spherical - oblate shape co - existence as shown by blue squares . nuclides with @xmath124 and @xmath125 also exhibit a spherical - oblate shape co - existence for several isotopic chains . the fact that nuclides just below and above @xmath6 display a spherical shape co - existence indicates that @xmath6 is not such a strong magic number . this can be constrasted with other magic numbers in the periodic table which exhibit robustness . there are rarely occasions of a shape - coexistence or even a deformation in the direct vicinity of a major magic number especially when one is not very far from the line of @xmath69-stability . superheavy nuclei especially those associated to @xmath6 do not fall in this category and are deemed to be in a region far from the stability line . therefore , mellowing of the shell strength of @xmath6 is not unexpected . 0.1 cm magic numbers in nuclei are characterized by a large shell gap between the last single - particle level of the magic number and the next single - particle level above it . this results in a larger value of 2-neutron separation energy @xmath126 for a nucleus with 2-neutrons more than the magic number . consequently , the major magic numbers exhibit a characteristic kink in @xmath126 values all over the periodic table . thus , the difference @xmath127 at the magic neutron number @xmath128 reflects its shell gap . its magnitude is a measure of the shell strength . for the isotopes of @xmath0 to @xmath1 with neutron numbers ranging from @xmath26 to @xmath27.,scaledwidth=62.0% ] with a view to visualize as to whether there are possible shell closures in neutron numbers for superheavy nuclei , we have computed @xmath126 values for all the isotopic chains . using the binding energies of neighbouring isotopes , s@xmath129 is defined as , @xmath130 the @xmath126 values for the isotopic chains considered in this work are shown in fig . [ fig : fig6 ] . the values correspond to the lowest energy state ( ground state ) obtained with rmf+bcs minimization using the force nl - sv1 . as expected , the @xmath126 values show a decreasing trend in going to nuclei with higher neutrons . the @xmath126 values show a rather monotonous decrease in going from @xmath131 to @xmath132 with a slight kink - like structure in the neighbourhood of @xmath133 and @xmath134 . due to significant changes in deformation properties of nuclei near @xmath135 and @xmath136 , there is much more structure in the @xmath126 values . for the isotopes of elements @xmath0 to @xmath1 , with neutron numbers ranging from @xmath131 to @xmath92 . ( b ) s@xmath129 values for @xmath92 to @xmath27.,scaledwidth=80.0% ] in order to visualize the structure in the @xmath126 values , we have split fig . [ fig : fig16 ] into two parts which are shown in fig . [ fig : fig7 ] . in fig . [ fig : fig17 ] ( a ) the @xmath126 values for @xmath137 are shown . the higher neutron part with @xmath138 is shown in fig . [ fig : fig7 ] ( b ) . one can notice a slight kink at @xmath139 for several isotopic chains . a kink like structure is visible for @xmath140 . this structure diminishes for @xmath90 and @xmath1 . the structure at @xmath139 is compatible with a deformed shell gap predicted by non - relativistic macroscopic - microscopic approaches @xcite . one can also notice a slight kink at @xmath134 . thus , there seems to exist a few pockets of presumably deformed shell gaps at @xmath133 and @xmath134 . however , there are no signatures of any strong magic number in the region @xmath137 . fig . [ fig : fig7 ] ( b ) shows structures in @xmath126 values at @xmath141 172 , 178 and 184 . the behaviour of @xmath126 values in the neutron region @xmath138 is far from monotonous . however , for the lighter superheavy elements , there is very little structure at @xmath142 except for @xmath0 and 104 . for the heavier elements with @xmath143 , the kink at @xmath135 shows a slightly upward trend . a kink like structure in this region indicates a possible @xmath135 deformed shell gap for superheavy elements . a combination of @xmath142 and @xmath144 might lend itself to a structure akin to a double shell closure . the region near @xmath145 is full of structural effects as can be seen in fig . [ fig : fig7 ] ( b ) . a kink in the @xmath126 values can be seen clearly at @xmath6 in several isotopic chains with @xmath146 . thus , for the lighter superheavy elements nl - sv1 predicts a shell closure at @xmath6 as indicated by the kink . for the deformed rmf+bcs calculations with nl - sv1 , a sharp decrease in the s@xmath129 values at @xmath6 is indicative of a shell closure which is consistent with that with nl - sh @xcite . for she above @xmath147112 the kink and the structure at @xmath6 is reduced significantly . thus , for the heaviest she , @xmath126 values do not give an unambiguous indication of a shell closure at @xmath6 .

the region of study spans nuclides with neutron numbers . it is shown that a large number of nuclides exhibit the phenomenon of shape - coexistence over a significant region of the superheavy elements . shape coexistence of a prolate and an oblate shape is prevalent in nuclides far below , whilst nuclei in the vicinity of tend to show a shape coexistence between a spherical and an oblate shape . it is shown that the neutron number acts akin to a magic number in the deformed region . it is suggested that the combination and has the potential of being a doubly magic number in the superheavy region .

we have studied properties and shell structure of the superheavy elements from to within the framework of the rmf theory . the region of study spans nuclides with neutron numbers . the lagrangian model nl - sv1 with the inclusion of the vector self - coupling of the-meson has been employed in this work . we have performed rmf + bcs calculations for an axially deformed configuration of nuclei . the ground - state binding energies , single - particle properties and quadrupole deformation of nuclei have been obtained from the mean - field minimizations . two - neutron separation energies , values and-decay half - life have been evaluated . it is shown that a large number of nuclides exhibit the phenomenon of shape - coexistence over a significant region of the superheavy elements . shape coexistence of a prolate and an oblate shape is prevalent in nuclides far below , whilst nuclei in the vicinity of tend to show a shape coexistence between a spherical and an oblate shape . the shell structure and 2-neutron separation energies obtained with the rmf theory reinforce the neutron number as a major magic number . it is shown that the neutron number acts akin to a magic number in the deformed region . it is suggested that the combination and has the potential of being a doubly magic number in the superheavy region .

0908.2678

i

we have studied the structure of superheavy nuclei within the framework of the relativistic mean - field theory . the region of superheavy elements from @xmath0 to @xmath1 has been explored . the isotopic chains of the superheavy elements encompassing the neutron number from @xmath26 to @xmath27 have been investigated . the lagrangian model nl - sv1 with the inclusion of the vector self - coupling of the @xmath3-meson has been employed . rmf calculations for a large number of nuclides in the isotopic chains of superheavy elements have been performed by taking an axially symmetric deformed configuration . the binding energies , deformation properties and single - particle levels have been obtained from rmf+bcs minimizations . nuclides in general are found to possess a moderate oblate or a prolate deformation . on the other hand , nuclei in the vicinity of the neutron number @xmath6 display a spherical shape . display of a spherical shape for all the isotopic chains indicates an inclination of @xmath6 being toward a potential magicity . it is shown that nuclei in the region of superheavy elements exhibit the phenomenon of shape co - existence . a large number of nuclei much below @xmath6 exhibit a shape co - existence between a prolate and an oblate shape . this is specially the case for the isotopic chains from @xmath0 to @xmath10 . some isotopic chains exhibit a shape - coexistence between a spherical and an oblate shape especially those in the vicinity of @xmath6 . the shape - coexistence in nuclei is demonstrated by the potential energy landscapes obtained for a few nuclei . the @xmath4 values and the corresponding @xmath5-decay half - lives were obtained using the ground - state binding energies . the @xmath5-decay half - lives @xmath161 demonstrate clearly that in the vicinity of @xmath6 nuclides have a significantly larger @xmath161 as compared to their neighbours . this is again a strong indicator of the magicity of the neutron number @xmath6 . two - neutron separation energies of nuclides were calculated using the results with nl - sv1 . the @xmath126 values exhibit a small kink near @xmath182 and @xmath7 . this suggests that the neutron number @xmath182 and @xmath7 have a larger shell gap than their neighbours . in comparison , a strong kink in @xmath126 values at @xmath6 is a clearest indication of a major shell gap at @xmath6 . the single - particle levels obtained with the lagrangian model nl - sv1 show that there exist shell gaps at neutron numbers @xmath7 and @xmath6 . whilst @xmath7 can not be construed as a major magic number as displayed by a mild kink in @xmath126 values , the neutron number @xmath6 does behave as a major magic number in the neutron - rich region . evidently , the magicity of @xmath6 is demonstrated succintly by a large shell gap at @xmath6 seen in the single - particle levels . this picture of the magicity of n=184 in the rmf theory is consistent with the predictions in the density - dependent skyrme hartree - fock approach and also with the previous studies performed within the rmf theory using the conventional model of the nonlinear scalar self - couplings . thus , our study with the lagrangian model nl - sv1 with the vector self - coupling of @xmath3 meson reinforces the magic character of the neutron number @xmath6 . albeit , a decrease in the shell gap at @xmath6 in going towards @xmath1 implies a weakening of the shell strength in approaching the extreme end of the periodic table . whilst a combination of @xmath6 in conjuction with @xmath160 in the vicinity of 120 produces nuclei which have impractically large number of neutrons , the combination of the neutron number @xmath7 and @xmath1 does lie within the domain of feasibility . our study shows that this combination is suggestive of a double magicity . thus , synthesis of superheavy elements heavier than @xmath89 with neutron number close to @xmath7 should be susceptible to an extra stability rendered by the apparent magic nature of @xmath1 and @xmath7 .

the lagrangian model nl - sv1 with the inclusion of the vector self - coupling of the-meson has been employed in this work . the ground - state binding energies , single - particle properties and quadrupole deformation of nuclei have been obtained from the mean - field minimizations . the shell structure and 2-neutron separation energies obtained with the rmf theory reinforce the neutron number as a major magic number .

we have studied properties and shell structure of the superheavy elements from to within the framework of the rmf theory . the region of study spans nuclides with neutron numbers . the lagrangian model nl - sv1 with the inclusion of the vector self - coupling of the-meson has been employed in this work . we have performed rmf + bcs calculations for an axially deformed configuration of nuclei . the ground - state binding energies , single - particle properties and quadrupole deformation of nuclei have been obtained from the mean - field minimizations . two - neutron separation energies , values and-decay half - life have been evaluated . it is shown that a large number of nuclides exhibit the phenomenon of shape - coexistence over a significant region of the superheavy elements . shape coexistence of a prolate and an oblate shape is prevalent in nuclides far below , whilst nuclei in the vicinity of tend to show a shape coexistence between a spherical and an oblate shape . the shell structure and 2-neutron separation energies obtained with the rmf theory reinforce the neutron number as a major magic number . it is shown that the neutron number acts akin to a magic number in the deformed region . it is suggested that the combination and has the potential of being a doubly magic number in the superheavy region .

0911.2212

i

this is a continuing study of the narrow - line region ( hereafter nlr ) of the seyfert galaxy ngc4151 using data obtained with the gemini near - infrared integral field spectrograph ( nifs ) . the data comprise spectra of the inner@xmath12pc@xmath13 , at a spatial resolution of@xmath14pc at the galaxy , covering the wavelength range@xmath15@xmath16 m at a spectral resolving power r@xmath17 . in a previous paper ( * ? ? ? * hereafter paperi ) we have used these data to map the nlr intensity distributions of @xmath18 emission lines , as well as their ratios . the main results were the distinct flux distributions and physical properties observed for the ionised , molecular and coronal gas . the ionised gas is co - spatial with the ionisation bi - cone observed in the optical ] emission at position angle ( hereafter pa)@xmath19 @xcite , and seems to trace the outflow along the bi - cone @xcite . in the inner region , the nir ionised - gas emission extends beyond the borders of the cone , which does not have a sharp apex as noted also by @xcite . the h@xmath20 molecular gas intensity distribution , on the other hand , avoids the region of the bi - cone and seems to originate in the galaxy disc , while the coronal gas emission is barely resolved . in another recent work @xcite , we have studied the unresolved nuclear continuum showing that its origin is emission by hot dust within @xmath44pc from the nucleus as expected from the dusty torus postulated by the unified model @xcite . the origin of this structure is probably a dusty wind that originates in the outer parts of the accretion disk . this wind is probably clumpy , as suggested by recent models @xcite , and necessary in order to allow the escape of radiation along the equatorial plane of the bi - cone in order to ionize the gas and produce the observed flux maps of paperi . in the present paper we use the nifs data to map the nlr kinematics of ngc4151 . although many papers have been devoted to such a study , most of them are based on long - slit spectroscopy obtained in the optical with the hubble space telescope ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the present study was performed in the near - ir , a waveband which is less affected by dust , and using integral field spectroscopy , which allows a full two - dimensional ( hereafter 2d ) coverage of the nlr kinematics . with our data and analysis we aim to examine previous claims of acceleration of the gas along the nlr , quantify the mass outflow rate and the corresponding feedback power , as well as investigate the origin of the nlr gas . as ngc4151 harbors the closest bright agn , its nlr is one of the best suited for this type of study . our approach for the analysis of the nlr kinematics of ngc4151 is as follows . first we map the centroid velocity and velocity dispersion of the ionised , molecular and coronal gas , obtained from fits to the emission - line profiles and compare our results with those of previous studies . then we use an alternative approach to map the nlr kinematics , made possible by integral field spectrographs : a `` velocity tomography '' of the emitting gas , obtained by slicing the line profiles in velocity bins of@xmath21kms@xmath6 , producing channel maps which provide a clearer view of the velocity distribution in the different gas phases . we have grouped the channel maps together in a sequence of velocity bins , generating movies which can be recovered at the authors website.thaisa/ifu_movies/ngc4151 ] we adopt in this paper the same distance to ngc4151 as in paperi:@xmath22mpc , corresponding to a scale at the galaxy of@xmath23pcarcsec@xmath6 @xcite . the paper is organised as follows . in [ data ] we provide a quick description of the data , in [ results ] we present the centroid velocity and velocity dispersion measurements , in [ tomography ] we present the emission - line `` tomography '' , in [ discussion ] we discuss our results , in [ feed ] we estimate the mass outflow rate along the nlr and compare with the mass accretion rate and in [ conclusion ] we present our conclusions .

we have used the gemini near - infrared integral field spectrograph ( nifs ) to map the gas kinematics of the inner 200pc of the seyfert galaxy ngc4151 in the z , j , h and k bands at a resolving power and spatial resolution ofpc . the ionised gas emission is most extended along the known ionisation bi - cone at position angle pa=60240 , but is observed also along its equatorial plane .

we have used the gemini near - infrared integral field spectrograph ( nifs ) to map the gas kinematics of the inner 200pc of the seyfert galaxy ngc4151 in the z , j , h and k bands at a resolving power and spatial resolution ofpc . the ionised gas emission is most extended along the known ionisation bi - cone at position angle pa=60240 , but is observed also along its equatorial plane . this indicates that the agn ionizes gas beyond the borders of the bi - cone , within a sphere with radius around the nucleus . the ionised gas has three kinematic components : ( 1 ) one observed at the systemic velocity and interpreted as originating in the galaxy disk ; ( 2 ) one outflowing along the bi - cone , with line - of - sight velocities between and 600kms and strongest emission atkms ; ( 3 ) and another component due to the interaction of the radio jet with ambient gas . the radio jet ( at pa=75255 ) is not aligned with the nlr , and produces flux enhancements mostly observed at the systemic velocity , suggesting that the jet is launched close to the plane of the galaxy ( plane of the sky ) . the mass outflow rate , estimated to bemyr along each cone , exceeds the inferred black hole accretion rate by a factor of . this can be understood if the narrow - line - region ( nlr ) is formed mostly by entrained gas from the circumnuclear interstellar medium by an outflow probably originating in the accretion disk . this flow represents feedback from the agn , estimated to release a kinetic power ofergs , which is only.3% of the bolometric luminosity of the agn . there is no evidence in our data for the gradual acceleration followed by gradual deceleration proposed by previous modelling of the [ oiii ] emitting gas . our data allow the possibility that the nlr clouds are accelerated close to the nucleus ( within 0 pc ) after which the flow moves at essentially constant velocity (kms ) , being consistent with nir emission arising predominantly from the interaction of the outflow with gas in the galactic disk . the molecular gas exhiibits distinct kinematics relative to the ionised gas . its emission arises in extended regions approximately perpendicular to the axis of the bi - cone and along the axis of the galaxy s stellar bar , avoiding the innermost ionised regions . it does not show an outflowing component , being observed only at velocities very close to systemic , and is thus consistent with an origin in the galaxy plane . this hot molecular gas may only be the tracer of a larger reservoir of colder gas which represents the agn feeding . [ firstpage ] galaxies : nuclei , galaxies : active , galaxies : seyfert , galaxies : kinematics , galaxies : jets , galaxies : individual ( ngc4151 )

0911.2212

c

in the centroid velocity maps for the ionised gas emission ( fig.[f - doublevel ] ) , the lowest velocities are observed at the nucleus , while the highest are observed away from the nucleus . this is the case for ngc4151 and also for 6 other seyfert galaxies for which we have recently obtained kinematic data with the ifu of the gemini multi - objetct spectrograph ( gmos ) @xcite . the channel maps , on the other hand , show a different behavior : the highest velocities are usually observed at the nucleus @xcite . in the case of ngc4151 , blueshifts of @xmath76kms@xmath6 in ] and ] are observed at the nucleus and in a narrow region along the bi - cone axis extending from the nucleus almost to the outer edge of the nlr ( figs . [ f - chmsiii ] and [ f - chmfeii ] ) . lower velocity blueshifted gas appears to fill the bi - cone and extend into the region of the radio jet near the systemic velocity . a similar structure is seen in redshifted gas with the emission at moderate redshifts appearing to fill the receding bi - cone . emission at the highest redshifts of @xmath77kms@xmath6 occurs at the nucleus and in a localised region @xmath0 0@xmath109 to the ne of the nucleus that is offset from the bi - cone axis . this morphology differs from that of the highest velocity blueshifted gas and may simply reflect the clumpy nature of the nlr emission . we attribute the difference between the kinematics probed by the centroid velocity and channel maps to the fact that the centroid velocity probes the brightest emission , while the channel maps also probe fainter emission ( in the wings of the line profiles ) . in the vicinity of the nucleus the brightest component is the one originating in the galactic disc , while away from the nucleus the brightest component is the outflowing one . as a consequence , the centroid velocities show an apparent increase in velocity outwards , that mimics acceleration along the nlr . in the channel maps we see high velocity gas at the nucleus , showing that the outflow does not leave the nucleus at zero velocity . we interpret this high velocity gas as an outflowing wind from the agn or ambient gas more directly interacting with this wind . as this highest velocity gas moves away from the nucleus , it pushes and accelerates the gas from the disc . the small amount of high velocity gas thus transfers momentum to a large reservoir of low velocity gas from the disc , causing the observed emission - line profiles and velocity structure along the bi - cone . this scenario is consistent with the one proposed by @xcite who , after verifying the failure of various wind models to reproduce the observed outflows in ngc4151 , suggested that the interaction of an outflowing nuclear wind with the ism could explain the observed velocity profile . some of the previous studies of the nlr of ngc4151 have suggested that there is no relation between the radio jet and the bi - conical outflow @xcite . the distinct orientations of the two outflows do support distinct origins for them : the radio jet ( oriented at pa@xmath475@xmath3 ) originates in the funnel of the accretion disc , while the bi - conical outflow originates further out , probably still in the accretion disc . the disc should also be warped , in order to produce a wind with a distinct orientation ( pa=60@xmath3 ) from that of the radio jet . the channel maps of figs . [ f - chmsiii ] , [ f - chmfeii ] and [ f - chmbrg ] confirm that the flux distributions at high velocities show no relation with the radio jet . but at velocities close to systemic the flux distributions become oriented along the radio axis instead of along the bi - cone . in addition , a comparison between the channel maps for velocities close to systemic and the contours of the radio map reveals line flux enhancements at the locations of radio knots . our proposed interpretation is that the radio jet has been launched close to the plane of the galaxy , and does interact with the circumnuclear gas pushing it out approximately along the plane and introducing the flux enhancements mostly due to gas density enhancement which are observed at velocities close to systemic . the observed flux enhancements could also be due to extra ionization by shock - induced x - rays in the nlr clouds interacting with the jet . recent chandra x - ray observations of the nlr of ngc4151 @xcite have shown extended emission along the nlr with x - ray flux enhancements in association with radio knots . they show that the radio - jet parameters are only consistent with the x - ray flux beeing due to thermal emission associated with the radio jet . the presence of shock heating is supported by the results of paperi , namely the increase of the [ feii]1.257/[pii ] line ratio to values larger than @xmath42 in association with the radio knots . values larger than @xmath42 imply the presence of fast shocks to destroy dust grains and release the fe . we also find , in paperi , a high temperature ( 16 000k ) in the flux - enhanced regions , as derived from the [ feii ] line ratios , in agreement with this scenario . in the channel maps , the relation of the gas emission with the radio jet seems also to be strongest for ] , as can be observed in fig . [ f - chmfeii ] : at velocities from @xmath78 to @xmath79kms@xmath6 , there is enhanced ] emission at the locations of most radio knots . there seems also to be an association between a `` flared structure '' to the sw observed in the radio map with the line emission at velocities of up to @xmath80kms@xmath6 . this suggests that the radio jet has been deflected towards the line - of - sight at this location . some spatial association between optical and radio emission in the nlr of ngc4151 has also been observed by @xcite . comparing high resolution radio images to an hst ] image , they found a number of bright ] clouds that seem to bound a number of knots observed in the radio image , which they interpret are due to shocks of the radio jet with the circumnuclear ism as the jet moves through the nlr and encounters gas clouds . @xcite studied the ] kinematics of the nlr of the prototypical seyfert 2 galaxy , ngc1068 , using a long - slit spectrum obtained at pa 202 with stis on hst . they found a distribution of line centroid velocities along the slit that resembled a `` figure of eight '' , with prominent high - velocity redshifted and blueshifted emission clumps and relatively few low - velocity clouds at intermediate distances from the nucleus . this distribution led them to infer a highly inclined conical geometry for the nlr of ngc1068 , with the emission arising from clouds outflowing radially along the cone walls . the cloud outflow velocities increase approximately linearly with radial distance on both sides of the nucleus to @xmath81kms@xmath6 at distances of @xmath82arcsec from the nucleus , and then decline back to zero by @xmath83arcsec . @xcite were forced to hypothesise a gradual acceleration of the nlr clouds over @xmath84pc followed by gradual deceleration to @xmath85pc to account for this velocity structure . @xcite used a more extensive set of stis spectra to develop this model for ngc1068 further . @xcite applied the same model to stis spectra of the nlr of ngc4151 . the nlr of ngc4151 is far less inclined to the line of sight than ngc1068 @xcite infer @xmath86 compared to @xmath87 for ngc1068 so radial flows along the cone walls do not separate as cleanly into high - velocity redshifted and blueshifted structures . consequently , the fit to the ngc4151 data is less compelling than for ngc1068 . @xcite revisited the ngc4151 nlr kinematics by fitting a similar model to spectra from five adjacent stis slit positions . their comprehensive analysis provides strong evidence that the nlr of ngc4151 is inclined by @xmath88 to the line of sight , with a hollow bi - conical outflow occupying cone half - angles between @xmath89 and @xmath90 . @xcite conclude that the outflow along the walls of the bi - cone is best reproduced with a velocity law : @xmath91 valid for distances @xmath92 from the nucleus up to a turnover point at @xmath93pc ( @xmath94 ) , from where the gas starts to decelerate and reaches the systemic velocity at @xmath95pc ( @xmath96 ) . the sw side of the bi - cone is tilted toward us , as illustrated in fig . [ f - geom ] . in this geometry and orientation , we view the nucleus just outside the outer wall , at an angle of @xmath97 with respect to the nearest part of the sw cone . this geometry and orientation has led to the idea that we see ngc4151 as a seyfert 1 galaxy because the blr can be viewed directly through a clumpy medium defining the cone walls . the angle between the bi - cone axis and the normal to the galaxy disk is @xmath98 @xcite , and thus , for a total opening angle of the bi - cone of @xmath99 , one side of the cone exits the galactic disk steeply , with the outer wall making an angle of 87@xmath3 with the galaxy plane , while the other outer wall leaves the plane at only 21@xmath3 , impacting a larger area of the disk ( for a typical scale height for the disc of several tens of pc ) , as illustrated in fig.[f - geom ] . @xcite argue that the intersection of the cone with the disc produces the observed geometry of the extended narrow - line region as shown by @xcite . if we now inspect our centroid velocity maps of fig . [ f - doublevel ] and fig.[f - pv ] in light of the geometry proposed by @xcite , we conclude that , in most regions where we see two velocity components , there is always one component at the systemic velocity plus an outflowing component in blueshift to the sw and in redshift to the ne . we attribute the systemic velocity component to emitting gas from the galaxy disc , in which case we are led to the conclusion that the agn ionizes a region of the galaxy disc comparable in extent to that of the outflowing gas emission we detect along the bi - cone axis ( @xmath415 , or @xmath4100pc ) and somewhat less extended perpendicular to it ( @xmath41 , or @xmath465pc ) . blueshifted components are observed to the sw at @xmath100kms@xmath6 and at higher velocities of up to @xmath5kms@xmath6 ( fig.[f - doublevel ] for ] and fig.[f - pv ] ) . we interpret the component with blueshifts @xmath100kms@xmath6 at the position labelled _ d _ in fig.[f - doublevel ] , together with the single component surrounding it ( region _ e _ in fig.[f - doublevel ] ) , as originating in the back surface of the sw cone . in the bottom part of the region we labelled _ c _ in fig.[f - doublevel ] , we observe a few points with higher blueshifts of up to @xmath5kms@xmath6 ( see also fig.[f - pv ] ) . these components probably originate in the front part of the sw cone , which we see at a small angle ( @xmath97 ) and thus with a large velocity component along the line - of - sight . there is less emission from this front part of the sw cone than from the back , and our hypothesis to explain this is that the cone walls are formed by gas entrained from the galaxy disk . the front wall is thus likely to be comprised of more tenuous gas than the back wall , as there is less gas to be entrained at high angles to the galactic disk . redshifted components are observed to the ne at somewhat lower velocities than to the sw ( region labelled _ b _ in fig.[f - doublevel ] ) . this can be seen more clearly in fig.[f - pv ] : there is a sequence of redshifts of up to @xmath60kms@xmath6 , which can be attributed to the front of the ne cone and then some higher redshifts of up to 400500kms@xmath6 , which can be attributed to the back of the ne cone . in fig.[f - doublevel ] , there is more emission from gas at the highest redshifts than emission from gas at the highest blueshifts . this result , together with the lower redshifts to the ne than blueshifts to the sw , suggest that the ne cone has its axis somewhat tilted towards the line of sight , instead of being aligned with the axis of the sw cone . this tilt would allow us to see more of the back wall of the ne cone and would result in lower observed velocities for both its front and back walls . in the model proposed by @xcite , the nlr gas first accelerates up to @xmath4100pc from the nucleus and then decelerates , analogous to their successful model for ngc1068 . while it is appealing in terms of agn unification for ngc1068 and ngc4151 to be fit with a similar model , neither our centroid velocity maps of figs.[f - doublevel ] and [ f - pv ] nor the ] kinematic data for ngc4151 unambiguously point to this interpretation . the gradual acceleration over the inner @xmath101pc and then deceleration required by the model remain unexplained . @xcite noted that radiative and magnetic acceleration from the region of the accretion disk both accelerate gas on length scales of the order of the launch radius , so winds driven by these mechanisms should reach their terminal velocities by @xmath102pc from the central source , not the @xmath103pc required by the model fits to the data . thermal winds also fail in this regard @xcite . dynamical models including various acceleration and deceleration mechanisms have been developed @xcite . while these models fail to identify the acceleration mechanism , they do demonstrate that gravitational forces alone can not produce the required deceleration , while drag forces from the interaction of nlr clouds with a diffuse , hot , x - ray - emitting ambient medium could be responsible . the difficulty in identifying a suitable wind acceleration mechanism leads to the question of whether some of the nlr kinematics are due to gradual global wind acceleration or whether they result from the local interaction of an already accelerated wind with its ambient medium , as we have proposed above on the basis of the channel maps . this scenario has been proposed by @xcite , who realised that the interaction of an outflowing nuclear wind with the ism could reproduce the apparent acceleration of the nlr following the works of @xcite and @xcite . these authors showed that a protostellar hydromagnetic wind expanding into the surrounding gas produces a bipolar outflow with velocity proportional to the distance to the star until a maximum radius beyond which the gas starts to decelerate . in order to be able to compare our data with those of previous works ( e.g. @xcite , @xcite ) , we have built position - velocity diagrams ( hereafter pv diagrams ) , which are shown in fig . [ f - pv2siii ] for the ] emission line . these diagrams were obtained from the @xmath104-band nifs data cube by extracting @xmath105arcsec wide pseudo - slit spectra oriented at pa@xmath55 ( which is the orientation of the bi - cone axis ) , offset from the nucleus perpendicular to the pseudo - slit direction by between @xmath106 ( along pa@xmath107 ) and @xmath108 ( along pa@xmath109 ) in steps of @xmath110 . the ] diagrams are plotted both on a logarithmic scale ( top of fig . [ f - pv2siii ] ) to reveal the faint emission structure and on a linear scale ( bottom ) to show the regions with strongest emission . while qualitatively similar to previous long - slit ] spectra ( e.g. fig . 2 of * ? ? ? * ) , the ] diagrams seem to show less emission at velocities exceeding @xmath111kms@xmath6 . in particular , high - velocity ] clouds a and b in @xcite ( near @xmath112kms@xmath6 and @xmath113 ) are not apparent in our data . in part , this could be due to the poorer spatial resolution obtained with nifs+altair at short near - infrared wavelengths . as with the ] line , most of the ] emission occurs at velocities below @xmath114kms@xmath6 . the central diagrams of fig . [ f - pv2siii ] can be compared directly with the ] slit spectrum shown in fig . 2 of @xcite . the ] spectra are much less structured than the ] spectra , presumably due to poorer spatial resolution and consequent lower sensitivity to faint emission . nevertheless , the two emission lines show a similar overall appearance along the central slit with blueshifted emission near @xmath115kms@xmath6 extending from @xmath116 to @xmath1173 from the nucleus towards pa@xmath118 ( sw , bottom of fig.[f - pv2siii ] ) , emission at the systemic velocity near the nucleus , and some redshifted emission near @xmath119kms@xmath6 extending to @xmath120arcsec from the nucleus towards pa@xmath55 ( ne , top of fig.[f - pv2siii ] ) . the off - nucleus pv diagrams in fig . [ f - pv2siii ] have a similar overall structure , but show that the @xmath115kms@xmath6 component is present in all negative offsets up to the slit at @xmath1218 . of note is the fact that the velocity of this emission remains approximately constant over its full extent . the brightest @xmath122kms@xmath6 emission is only clearly apparent towards pa@xmath55 along the cone axis ( i.e. , in the upper part of the central panel of fig . [ f - pv2siii ] ) . some aditional emission from this component can be observed along the slits with positive offsets at fainter levels and at larger distances from the nucleus . the systemic velocity component is prominent in the upper section ( ne ) of pseudo - slits with negative offsets and in the lower sections ( sw ) of pseudo - slits having positive offsets , and originates in circumnuclear gas from the galaxy plane . [ f - pvfeii ] shows the corresponding pv diagrams for the ] 1.644 line . the emission in the central pseudo - slit corresponds closely to the brightest ] emission in fig . 2 of @xcite , but the high - velocity extensions of the ] clumps are much less prominent in our ] data . although the major velocity components apparent in the ] line are also apparent in ] , the higher spatial resolution achieved at this longer wavelength helps to reveal sharper structures than in fig . [ f - pv2siii ] . on the other hand , the structures seen in the ] emission can also in part be attributed to enhancements associated with the radio jet , as observed in the channel maps . the component near @xmath115kms@xmath6 is comprised of several clumps and extends to only @xmath1235 along the central pseudo - slit towards pa@xmath118 , but reaches @xmath124arcsec at large negative , and possibly also positive , slit offsets i.e. , in the extreme left and right panels of fig . [ f - pvfeii ] . clouds with velocities @xmath125kms@xmath6 are observed at @xmath126arcsec along the central slit and closer to the nucleus along the @xmath110 and @xmath127 offset slits . emission with velocities up to @xmath128kms@xmath6 is apparent at slit offsets of @xmath129 and @xmath130 . the systemic - velocity component is restricted to the nucleus in the central slit , but extends to nearly @xmath131arcsec along the @xmath130 to @xmath132 offset slits and to nearly @xmath133arcsec along the @xmath129 and @xmath134 offset slits . however , the systemic - velocity emission at negative slit offsets to the left in fig . [ f - pvfeii ] is dominated by a further bright clump near @xmath133arcsec approximately east of nucleus , in the vicinity of the receding radio lobe . overall the impression from the ] data is of roughly constant redshifted velocities towards pa@xmath55 and blueshifted velocities towards pa@xmath118 with an additional systemic - velocity component originating in the galaxy disc and associated with the radio jet . the role of the geometry and projection effects on the observations can best be evaluated via modelling . in this section , we compare our data with models with and without acceleration along the nlr . we begin by testing the model proposed by @xcite on the basis of the optical ] emission obtained with stis , namely of an inclined hollow cone with radial outflow along the cone walls that is characterised by linear acceleration followed by linear deceleration @xcite . our 3d kinematic data allow us to test this model against both channel maps and pv diagrams through multiple pseudo - slits in ways that were not available to previous authors . we begin by presenting both these views for the model parameters of @xcite in figs . [ f - daspv ] and [ f - daschm ] . as our data cover essentially the entire region of acceleration in the models , emission from decelerating gas beyond the velocity maximum has been suppressed in fig [ f - daschm ] . . ] the @xcite model predictions differ in several ways from the near - infrared emission - line data . first , the high velocity gas just to the sw and ne of the nucleus predicted by the models ( fig . [ f - daspv ] ) and seen in ] is less conspicuous in our data . it is seen in our data only in the log plots for ] , where the faint emission gets enhanced ( top panel of fig.[f - pv2siii ] ) . we also see little evidence of acceleration and deceleration in the near - infrared data , which mostly show sequences at constant velocities from the nucleus all the way out . even in the deep ] pv diagrams , gas up to @xmath135arcsec from the nucleus in the lower half of these diagrams extending to pa@xmath118 is still moving at blueshifted velocities of @xmath100kms@xmath6 , with similar but smaller redshifted velocities in the upper half of the diagrams . another significant difference between the model and the near - infrared pv data is that the model predicts that pseudo - slits offset from the nucleus will show no emission near the slit centre fig . [ f - daspv ] . this is the equatorial region away from the nucleus and between the two oppositely - directed cone `` lobes '' . most of the actual emission at off - nucleus slit positions arises in this region that is excluded by the model c.f . , fig . [ f - pvfeii ] . there is also emission at zero velocity mainly observed in the ] pv diagram which is not included in the model . finally , the model predicts that the channel maps should show ridges of emission perpendicular to the cone axis at high positive and negative velocities fig . [ f - daschm ] . this morphology arises because outflowing material in the hollow cone essentially emits from an annular region perpendicular to the cone axis convolved with other orientation factors . in contrast , the channel maps in figs . [ f - chmsiii ] and [ f - chmfeii ] show that the highest - velocity emission is confined to positions close to the cone axis , and is possibly extended along the cone axis towards the nucleus . we now investigate modifications to the hollow - cone , radial - outflow model that attempt to address the above differences . the simplest modification is to hypothesise that the cone wall that is steeply inclined to the plane of the sky does not emit strongly in near - infrared lines . this could occur because this cone wall is more inclined to the galactic disk . as discussed in sec . [ centroid ] , under the hypothesis that the cone walls are formed by gas entrained from the galaxy disk , this wall is likely to be comprised of more tenuous gas , as there is less gas to be entrained at high angles to the galactic disk . this modification removes the high - velocity components in fig.[f - daspv ] . to this , we then add an illustrative systemic - velocity component that is aligned with the radio jet and an arbitrary galactic disk component . the radio - jet component is modeled as a central nuclear component plus two clumps offset e - w from the nucleus by 1 . each clump is assumed to be at the systemic velocity of the galaxy . the galaxy component has a gaussian intensity profile and is assumed to be at the systemic velocity . the presence of this component is suggested both by the zero velocity component in the centroid velocity maps fig . [ f - doublevel ] and by the channel maps , which show strong emission at zero velocities ( figs . [ f - chmsiii ] and [ f - chmfeii ] ) . the resulting pv diagrams are shown in fig.[f - modpv ] . the pv diagrams in fig.[f - modpv ] do not provide a perfect fit to the data ( in particular to the highest spatial resolution ] data in fig.[f - pvfeii ] ) . however , they serve to illustrate the following points : firstly , the emission from the cone ( blue regions in fig.[f - modpv ] ) is a better fit to the data in the linear plots ( showing the strongest emitting gas ) if only the section of the cone wall closest to the plane of the sky , and hence closest to the galactic disk , is included . this may be due to interaction of the nlr gas in the cone wall with the galactic disk , possibly by the entrainment of disk material into the nlr outflow . given that this material is moving in a direction closer to the plane of the sky , we are less sensitive to its true velocity so can not make strong claims about the length scale on which it is accelerated . fig.[f - modpv ] is drawn for the gradual acceleration and subsequent deceleration proposed by @xcite . however , the data permit virtually any velocity law , including constant velocity outflow , on the length scales to which they are sensitive . the second point illustrated by fig.[f - modpv ] is that emission from gas interaction with the radio jet is significant . this is modeled as nuclear and off - nuclear clumps , but in reality other emitting gas forms a bridge between the main clumps and the nucleus . this is seen in the channel maps shown in fig.[f - chmfeii ] . finally , the galaxy component at systemic velocity reproduces the data at pa=60@xmath3 for pseudo - slits at negative offsets and at pa@xmath136for pseudo - slits at positive offsets , supporting the presence of a disc component , as concluded also from the centroid velocity maps of fig.[f - doublevel ] . simulated channel maps are shown in fig.[f - modchm ] . these only approximately reproduce the data presented in fig.[f - chmfeii ] . in particular , two separated emission clumps aligned perpendicular to the cone axis are predicted from the cone walls at high - redshifted and high - blueshifted velocities while only a single clump near the cone axis is actually seen in the data . .[f - modchm ] ] finally , we have considered a truncated hollow conical outflow at a constant velocity of @xmath137kms@xmath6 , as we could not see acceleration or deceleration in our data . as in the previous model , we add the radio jet and galactic disk component . the resulting position - velocity diagrams are shown in fig . [ f - modconstpv ] . the fit to the observed constant velocity sequence at @xmath100kms@xmath6 for ] ( fig.[f - pv2siii ] ) along the slit passing through the nucleus and the ones with negative offsets are improved by this model . the disc component at zero velocity reproduces emission observed at the nucleus and along pa@xmath138 ( positive position in the panels of fig . [ f - pv2siii ] ) and pa@xmath139 ( to the left in fig . [ f - pv2siii ] ) , as well as less extended emission along pa@xmath140 ( negative positions in fig . [ f - pv2siii ] ) and pa@xmath141 ( to the right in fig . [ f - pv2siii ] ) . the high velocity sequences predicted by the models although not conspicuous in the linear pv diagrams of ] ( bottom panel of fig.[f - pv2siii ] ) are observable in the log pv diagrams ( upper panel of fig.[f - pv2siii ] ) , due to its faint emission . these high velocity sequences and are due to the front wall of the approaching cone and far wall of the receeding cone . we point out that this short high velocity sequence as predicted by the constant velocity model seems to be adequate to reproduce also the high velocity gas observed in ] ( fig . 2 of @xcite ) . nevertheless , this model did not improve the fit for pseudo - slits offset by more than @xmath127 from the nucleus , which still do not show emission near the slit centre in the model . in addition , these pseudo - slits show velocity sequences that decrease with increasing distance from the nucleus . in order to improve the fit , new geometries should be considered . for example , a flow that is not conical , but in the form of a bowl as observed in planetary nebulae and in recent nifs observations of ngc1068 @xcite . simulated channel maps are shown in fig . [ f - modconstchm ] . these maps are an improvement relative to the previous model for velocity channels between @xmath142kms@xmath6and @xmath143kms@xmath6 , but show double structures for velocities between @xmath144kms@xmath6and @xmath145kms@xmath6 , which are not seen in the data . for the highest velocities , a small triangular structure is seen , while the data show only clumps near the cone axis . this discrepancy can also be attributed to possible deviations from a bi - conical geometry and to very weak emission from the wall of the bi - cone that is most inclined . ( see text ) . the orientation and velocity bins are as for fig.[f - pv2siii ] . [ f - modconstchm ] ] the modelled integrated emission - line map is similar for the three models discussed above . we show in fig . [ f : mod_int ] the map obtained for the modified @xcite model . a comparison with fig . [ f : feii_int ] shows that it provides a reasonable reproduction of the data , taking into account that one should add the contribution of gas from the galaxy plane to the modelled emission . @xcite identified blueshifted ] emission with velocities up to @xmath146kms@xmath6 in the ngc1068 nlr @xmath147pc ne of the nucleus . this is the region attributed to the highest radial outflow velocities in the gradual acceleration model . many of these knots are linked kinematically to more massive and slower - moving clumps located closer to the nucleus . @xcite identify these knots as ablation flows from disintegrating molecular clouds that are being photoionised and radiatively accelerated by the agn . @xcite detected faint , high - velocity ] emission with radial velocities up to @xmath148kms@xmath6 in stis slitless spectra of ngc4151 . the high - velocity emission was shown to arise in high - excitation ionised gas , and has velocity dispersions in excess of @xmath149kms@xmath6 @xcite , which is also consistent with an origin in an ablation flow . near - infrared ] emission arises in conditions similar to the optical ] emission , and can thus be formed in tenuous fully ionised gas experiencing a high local ionisation parameter . but then , why do we see less ] than ] emission ? either we lack the sensitivity to detect faint high - velocity emission , or this emission is not present . in order to investigate this , version 8.0 of the photoionisation code cloudy , last described by @xcite , was used to calculate the ratio of ] to ] for nlr clouds with a range of densities . the ionisation parameter was set to @xmath150 for a gas density of @xmath151@xmath152 and then varied inversely with the gas density to simulate clouds with different densities being illuminated by the same radiation field . such a situation would occur if the low - velocity ] is emitted at the front face of a dense nlr cloud and the high - velocity ] emission arises in an associated low - density ablation flow . the resulting emission - line ratios are plotted in fig . [ f - ratio ] where it can be seen that ] / ] increases from @xmath153 at densities typical of nlr clouds to @xmath154 at densities @xmath155 @xmath152 that might be typical of an ablation flow . the values at high densities are typical of the integrated line ratios observed in seyfert galaxies nlrs ( e.g. , * ? ? ? the strength of ] falls sharply to lower densities while the strength of ] is largely unchanged . the reason for this dependence on ionisation parameter is that sulphur exists predominantly as ] at typical nlr densities , but as ] and higher species in more highly excited low - density regions . in contrast , the higher ionisation potential of ] ( 54.9 ev compared to 35.1 ev for ] and 47.2 ev for ] ) means that ] survives better in highly excited regions . the lower intensity of ] in low - density irradiated regions makes it more difficult to detect a low - density ablation flow in ] emission than in ] emission . this combined with the lower strehl ratio and consequent poorer image quality achieved by adaptive optics systems at short near - infrared wavelengths probably account for our inability to detect more high - velocity gas in ngc4151 . there is little evidence in our near - infrared data for the gradual acceleration followed by gradual deceleration proposed by @xcite based on ] kinematics . no viable physical mechanism has been identified for such a gradual acceleration . a possible explanation is that the high - velocity ] emission does not represent the bulk motion of the outflow . rather , this could be low - density material ablated from nlr clouds that we observe outflowing at @xmath4250kms@xmath6 and are accelerated much closer to the agn . this is consistent with the low surface brightness of the high - velocity , low - density emission in ] and with the prominence of near - infrared emission formed on the sides of the outflow closer to high - density gas in the galactic disk .

this indicates that the agn ionizes gas beyond the borders of the bi - cone , within a sphere with radius around the nucleus . the ionised gas has three kinematic components : ( 1 ) one observed at the systemic velocity and interpreted as originating in the galaxy disk ; ( 2 ) one outflowing along the bi - cone , with line - of - sight velocities between and 600kms and strongest emission atkms ; ( 3 ) and another component due to the interaction of the radio jet with ambient gas . the radio jet ( at pa=75255 ) is not aligned with the nlr , and produces flux enhancements mostly observed at the systemic velocity , suggesting that the jet is launched close to the plane of the galaxy ( plane of the sky ) . the mass outflow rate , estimated to bemyr along each cone this can be understood if the narrow - line - region ( nlr ) is formed mostly by entrained gas from the circumnuclear interstellar medium by an outflow probably originating in the accretion disk . there is no evidence in our data for the gradual acceleration followed by gradual deceleration proposed by previous modelling of the [ oiii ] emitting gas . our data allow the possibility that the nlr clouds are accelerated close to the nucleus ( within 0 pc ) after which the flow moves at essentially constant velocity (kms ) , being consistent with nir emission arising predominantly from the interaction of the outflow with gas in the galactic disk . it does not show an outflowing component , being observed only at velocities very close to systemic , and is thus consistent with an origin in the galaxy plane . this hot molecular gas may only be the tracer of a larger reservoir of colder gas which represents the agn feeding .

we have used the gemini near - infrared integral field spectrograph ( nifs ) to map the gas kinematics of the inner 200pc of the seyfert galaxy ngc4151 in the z , j , h and k bands at a resolving power and spatial resolution ofpc . the ionised gas emission is most extended along the known ionisation bi - cone at position angle pa=60240 , but is observed also along its equatorial plane . this indicates that the agn ionizes gas beyond the borders of the bi - cone , within a sphere with radius around the nucleus . the ionised gas has three kinematic components : ( 1 ) one observed at the systemic velocity and interpreted as originating in the galaxy disk ; ( 2 ) one outflowing along the bi - cone , with line - of - sight velocities between and 600kms and strongest emission atkms ; ( 3 ) and another component due to the interaction of the radio jet with ambient gas . the radio jet ( at pa=75255 ) is not aligned with the nlr , and produces flux enhancements mostly observed at the systemic velocity , suggesting that the jet is launched close to the plane of the galaxy ( plane of the sky ) . the mass outflow rate , estimated to bemyr along each cone , exceeds the inferred black hole accretion rate by a factor of . this can be understood if the narrow - line - region ( nlr ) is formed mostly by entrained gas from the circumnuclear interstellar medium by an outflow probably originating in the accretion disk . this flow represents feedback from the agn , estimated to release a kinetic power ofergs , which is only.3% of the bolometric luminosity of the agn . there is no evidence in our data for the gradual acceleration followed by gradual deceleration proposed by previous modelling of the [ oiii ] emitting gas . our data allow the possibility that the nlr clouds are accelerated close to the nucleus ( within 0 pc ) after which the flow moves at essentially constant velocity (kms ) , being consistent with nir emission arising predominantly from the interaction of the outflow with gas in the galactic disk . the molecular gas exhiibits distinct kinematics relative to the ionised gas . its emission arises in extended regions approximately perpendicular to the axis of the bi - cone and along the axis of the galaxy s stellar bar , avoiding the innermost ionised regions . it does not show an outflowing component , being observed only at velocities very close to systemic , and is thus consistent with an origin in the galaxy plane . this hot molecular gas may only be the tracer of a larger reservoir of colder gas which represents the agn feeding . [ firstpage ] galaxies : nuclei , galaxies : active , galaxies : seyfert , galaxies : kinematics , galaxies : jets , galaxies : individual ( ngc4151 )

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in this paper , we have presented the results of our multi - epoch phase - referencing observations with vera over 18 months of an h@xmath0o maser source in the galactic star - forming region ngc 281 west , associated with a fragmenting superbubble @xmath196 pc above the perseus spiral arm . the primary results are summarized as follows : 1 . we detected a trigonometric parallax of [email protected] mas , corresponding to a distance of [email protected] kpc to ngc 281 . our parallactic distance agrees well with the photometric distance of [email protected] kpc derived by guetter & turner ( 1997 ) , allowing for improved study of the absolute magnitutudes of high - mass ob stars , and resolved the large distance discrepancy of ngc 281 from previous photometric and kinematic studies . we revised the absolute proper motions of the h@xmath0o maser features measured in sato ( 2007 ) , and using our new determination of the parallactic distance , we derived more precisely the velocity component of the ngc 281 region @xmath197 km s@xmath4 perpendicular to the galactic plane . this yields a timescale of @xmath182 myr and kinectic energy of the region to be @xmath134 ergs in the direction perpendicular to the plane . we demonstrated the 3d structure and expansion of the ngc 281 superbubbles in comparison of our parallactic distance to ngc 281 with the parallactic distance derived by moellenbrock ( 2007 ) for another h@xmath0o maser source , iras 00420 + 5530 in the superbubble . our new parallactic distance revealed the structure of the superbubble @xmath2650 pc in size parallel to the galactic disk and with a shape slightly elongated along the disk or spherical , but not vertically elongated in the @xmath187 direction . therefore , the superbubble expansion may be confined to the disk , possibly due to the magnetic field of the disk . we suggested a new possible interpretation of an expanding molecular ring parallel to the galactic plane in the longitude - velocity diagram by megeath ( 2002 , 2003 ) . in either interpretation , the ring center , i.e. the likely origin of the superbubble lies at @xmath118 . the velocity deviation of the superbubble from the galactic rotation is estimated to be @xmath183 km s@xmath4 inward the galactic rotation and toward the sun from our proper motion measurements and from the longitude - velocity diagram , which might be due to velocity jumps over a spiral shock in the perseus spiral arm . we also estimated the velocity component and timescale of the ring expansion to be @xmath198 km s@xmath4 and @xmath199 myr , respectively , parallel to the galactic plane , which are in good agreement with those independently estimated for the direction perpendicular to the galactic plane , @xmath197 km s@xmath4 and @xmath182 myr . the kinetic energy estimate of the region parallel to the plane is @xmath148 ergs , and the total kinetic energy of both perpendicular and parallel to the plane is then estimated to be @xmath149 ergs , requiring multiple supernovae . we are deeply grateful to the referee dr . felix j. lockman for his invaluable comments and suggestions that improved both scientific discussions and presentation of the manuscript . we would like to thank dr . mark j. reid for his tremendous help with carefully reading and improving the manuscript and for his insightful comments on scientific issues . we are very grateful to prof . kohji tomisaka for illuminating and insightful discussions . we also greatly appreciate the optical image for figure 1 that was kindly provided by dr . travis a. rector and the national optical astronomy observatory ( noao ) . we wish to thank all the support staff at vera for their efforts and continuous support for our observations . m. sato gratefully acknowledges financial support by a research fellowship from the japan society for the promotion of science ( jsps ) for young scientists . this research has made use of the simbad database , operated at cds , strasbourg , france and of nasa s astrophysics data system . megeath , s. t. , biller , b. , dame , t. m. , leass , e. , whitaker , r. s. , & wilson , t. l. 2002 , in asp conf . 267 , hot star workshop : the earliest stages of massive star birth , ed . p. a. crowther ( san francisco : asp ) , 257 moellenbrock , g. a. , claussen , m. j. , & goss , w. m. 2007 , in proc . iau symposium 242 : astrophysical masers and their environments , ed . j. m. chapman & w. a. baan ( cambridge : cambridge univ . press ) , 168

we have used the japanese vlbi array vera to perform high - precision astrometry of an ho maser source in the galactic star - forming region ngc 281 west , which has been considered to be part of a 300-pc superbubble . we successfully detected a trigonometric parallax of 0.355.030 mas , corresponding to a source distance of 2.82.24 kpc . the source distance as well as the absolute proper motions were used to demonstrate the 3d structure and expansion of the ngc 281 superbubble , pc in size parallel to the galactic disk and with a shape slightly elongated along the disk or spherical , but not vertically elongated , indicating the superbubble expansion may be confined to the disk .

we have used the japanese vlbi array vera to perform high - precision astrometry of an ho maser source in the galactic star - forming region ngc 281 west , which has been considered to be part of a 300-pc superbubble . we successfully detected a trigonometric parallax of 0.355.030 mas , corresponding to a source distance of 2.82.24 kpc . our direct distance determination of ngc 281 has resolved the large distance discrepancy between previous photometric and kinematic studies ; likely ngc 281 is in the far side of the perseus spiral arm . the source distance as well as the absolute proper motions were used to demonstrate the 3d structure and expansion of the ngc 281 superbubble , pc in size parallel to the galactic disk and with a shape slightly elongated along the disk or spherical , but not vertically elongated , indicating the superbubble expansion may be confined to the disk . we estimate the expansion velocity of the superbubble as km s both perpendicular to and parallel to the galactic disk with a consistent timescale of myr .

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objects were identified to be m ( or early l ) dwarf main - sequence stars . two objects were found to be best fit by early l dwarf templates @xcite . both of these objects are red enough to be outside of the color range shown in figures [ vibv ] and [ izvi ] with @xmath48 and @xmath49 . deep infrared observations of these two objects will be required to confirm that they are l dwarfs . nicmos observations of the hudf did not detect these objects in either the j or h bands . all other very red objects are best fit using m dwarf templates . the broad spectral features of m dwarfs listed in table [ table2 ] were well fitted using m dwarf @xcite templates , and for objects brighter than @xmath1 mag we believe the identification to be secure . + because these late - type sources can be seen to great distances , they can be used to probe the structure of the galactic disk and halo as traced by the lowest - mass stellar components of these populations . this was explored using monte carlo mass function ( mf ) simulations based on those developed by @xcite . assuming power - law representations of the mf , dn / dm @xmath50 m@xmath51 , for masses 0.005 to 0.2 m@xmath52 , luminosity ( lf ) and effective temperature ( t@xmath53 ) distributions were created using evolutionary models from @xcite over the range 100 @xmath54 t@xmath53 @xmath54 4000 k. for all simulations , @xmath55 was fixed at 1.13 for @xmath56 @xcite but allowed to vary between 0.51.5 for @xmath57 ; number densities are normalized to the empirical value at 0.1 m@xmath52 from the 8 pc sample @xcite . two separate populations were simulated : a disk population with a flat age distribution spanning 10 myr to 10 gyr ( the majority of sources have age greater than 1 gyr ) , and a halo population with uniformly sampled ages between 9 - 10 gyr and a relative number density of 0.25% @xcite . the resulting bolometric lfs were converted to @xmath58 ( cousins ) lf s using a polynomial fit to empirical data ( spanning @xmath59 ; i.e. , m4 to t8 ) from @xcite and @xcite . note that this fit is based on measurements for solar metallicity field dwarfs , and may not be appropriate for a subsolar metallicity halo subdwarf population . apparent @xmath58-band distributions were determined by first assuming a constant density population out to a limiting magnitude m@xmath60 = 27.5 ( taking into account the difference between hudf ab - magnitudes and vega magnitudes from the empirical data ) and then applying a correction for the vertical distribution of sources . for the disk population , we assumed a density distribution @xmath61 @xcite , where @xmath62 , @xmath63 is the source distance , @xmath64 is the galactic latitude of the hudf , and @xmath65 is the 1/e disk scale height , assumed to range between 200 and 500 pc . for the halo population , a galactocentric oblate spheroid distribution as given in @xcite was assumed , using the values derived there and an axial ratio q = c / a = 0.7 . figure [ mlf2 ] presents the results of these simulations in the form of cumulative number distributions as a function of magnitude down to the limiting magnitude of our sample . these distributions show that variations in the disk scale height are far more pronounced than those from the different mf s assumed , and this analysis is limited to the former parameter . the cumulative distribution of the six dwarfs in table [ table2 ] with spectral types m4 and later ( consistent with the mass constraints of the simulations ) is also shown . the observed distribution matches that of the @xmath66 disk simulation very well , particularly out to @xmath67 mag where the halo population makes negligible contribution . because the simulated distributions are rather sensitive to the disk scale height , particularly at fainter apparent magnitudes , one can conservatively constrain @xmath65 to @xmath68100 pc assuming poisson uncertainties . this is in good agreement with the estimate of @xmath69 from @xcite which was computed using acs hudf parallel fields i - drops . for @xmath70 mag , the observed distribution is slightly greater than the disk population alone but does not increase as sharply as the combined disk+halo distribution . indeed , the shape of the observed number distribution implies few if any halo stars in the hudf down to @xmath7 mag , consistent with the lack of significant proper motion sources in this sample . this suggests that either the number density ratio of halo to disk stars , or the adopted axial ratio for the halo density distribution , or both , may be smaller than assumed here . with no late - type halo subdwarf detections in this sample , we can not usefully constrain these possibilities . objects brighter than @xmath7 were individually examined and distances were estimated under various assumptions of what the exact nature of each object might be : ( 1 ) a main sequence star ; ( 2 ) a young white dwarf ; ( 3 ) an old white dwarf . the reddest objects , which are all well - fitted by m - and - later type templates , as well as the few extra - galactic objects identified in section [ qso ] were excluded from this analysis . the remaining objects were all initially considered to potentially be white dwarfs . + assuming that an object is a white dwarf , one can use the measured @xmath71 color of that object ( table [ table1 ] ) and the cooling curves of @xcite ( after accounting for passbands and zeropoints differences ) , to derive an absolute band magnitude , an age , and a distance to that object . as shown in figure 2 of @xcite , blue white dwarfs can either be young , hot objects ( @xmath72 , t @xmath73k , @xmath74 mag ) or older , cooler , intrinsically dimmer ones ( age @xmath75 10 gyr , t @xmath76 , @xmath77 mag ) . this results in several white dwarf distance estimates for each object . + proceeding via a process of elimination , the distinction between main sequence stars , young white dwarfs , old white dwarfs , and disk or halo white dwarfs is possible . assuming that a star is a main sequence star , which is intrinsically much more luminous than a white dwarf , can cause the distance estimate for that object to be unreasonably large . assuming that a star is a young white dwarf ( @xmath78 ) implies that this object is less likely to be part of the galactic halo since the latter is composed of much older objects . also , and based on the lack of proper motion detection discussed in section [ pmm ] , one can define an upper limit to the tangential velocity ( @xmath79 ) of each object once its distance is determined . the motion of an object moving by more than 0.18 hudf pixel ( 0.027 / yr ) should have been detected at the @xmath4 significance level as discussed in section [ pm ] . as discussed above , objects in the galactic halo are expected to have velocities around 100 - 200 km / s . even if projection effects should result in lower values of @xmath80 , one would expect at least some of them to have @xmath80 values larger than 30 - 60 km / s . a final clue to help narrow down the nature of a particular object is provided by the fact that an object that is nearby would suffer from a significant , easily measurable , parallax during the 73 days interval between epoch 1 and epoch 2 observations . calculating the parallax vector for the hudf exposures shows that an object 30 pc away would produce a parallax of about 0.060 or 2 hudf pixel between epoch 1 and epoch 2 observations . objects that are closer than 200 pc are therefore expected to produce a parallax that would be detected at more than @xmath4 level . + examining table [ table4 ] , objects 4322 , 4839 , 7768 , 9020 are unlikely to be main - sequence stars as this would make them very distant objects . the magellanic stream @xcite is too far away from the hudf to possibly explain the existence of main - sequence stars at such large distances . objects 1147 , 3166 , and 5921 which do not ( this is true of all objects listed in table [ table4 ] ) have measurable parallax or proper motion , are not likely to be white dwarfs . being either young or old white dwarfs would place these two objects less than 200 pc away and would have resulted in measurable parallax in the hudf image stacks . another object unlikely to be a white dwarf is object 9230 which was observed to have a fainter , unresolved companion 0.5 away . this companion , for which we have no grapes spectrum , has a band magnitude of @xmath81 mag and the colors @xmath82 mag . based on these colors , this object should be an early m dwarf that is @xmath83 away . this places both object 9230 and its companion at the same distance ( within error bars ) . the likelihood of any two stars being within 0.5 in the hudf , and at nearly the same distance , is very small ( @xmath84 ) and these two objects are likely to be part of a binary system , with object 9230 being a k type main - sequence star . independently of this , object 9230 can not be an old white dwarf since this would place this object at distance of 34 pc where its parallax motion would have been very easily detected . + four objects ( 4322 , 4839 , 7768 , 9020 ) remain as white dwarf candidates . using a simple 1/@xmath85 @xcite analysis , the white dwarf number density in the direction of the hudf can be computed . the detection of 4 white dwarfs in the hudf implies a local density of @xmath86 . the upper and lower limits on the density are computed using old or young white dwarfs respectively , while the errors reflect the large uncertainties in the intrinsic luminosities of young and old white dwarfs ( @xmath87 mag ) . note that this estimate is actually not affected by whether or not object 9230 was included as a hudf white dwarf . the contribution of this object to the 1/@xmath85 is negligible . for comparison , @xcite previously determined the local white dwarf density to be @xmath88 , while @xcite found a value of @xmath89 , and @xcite derived a density of white dwarfs in the thick disk of @xmath90 . the white dwarf density derived here is consistent with most of the previous density estimates . properly determining the disk and halo membership of the 4 white dwarfs identified in the hudf will be needed before a stronger conclusion can be made . re - observing the hudf field in the band in 1.5 years would allow ( assuming that a 0.18 hudf pixel shift corresponds to a @xmath4 level detection ) one to unambiguously detect the proper motion of halo white dwarfs with @xmath91 km / s at distances up to 1000 pc . + the above density estimate assumed that all four hudf white dwarfs were galactic disk objects . could some of these objects be in the galactic halo ? at least two of these objects ( 4839 , 7768 ) have @xmath92 values that are lower than 60 km / s . the probability that this is caused by a projection effect is under 10% ( assuming a relatively low velocity of @xmath93 km / s for halo objects ) . the last two white dwarfs listed in table [ table4 ] ( 4322 , 9020 ) are at slightly larger distances which average to 583 pc , and more importantly have larger values of @xmath92 . the average distance of these objects still seems a bit low for objects which would be part of a galactic halo whose density increases all the way up to 7 kpc @xcite , while white dwarfs with absolute magnitudes of @xmath94 mag @xcite should be detected all the way out to 1000 pc . unless these objects are intrinsically much dimmer , one would expect the average distance to these two objects to be larger than 583 pc and much closer to our limit of 1000pc . the @xmath92 values inferred for objects 4322 and 9020 , while higher than those of objects 4839 and 7768 , fall substantially short of expected typical halo velocities . the probability of observing each of the objects with the @xmath92 values listed in table [ table4 ] is between 1420% . as a group , the probability that objects 4322 and 9020 are halo objects is under 3% . similarly , the hypothesis that all 4 detected white dwarfs in the hudf are halo rather than disk objects is excluded at the 99.9986 % level . overall , the distances to the four white dwarf candidates identified here is more consistent with them being part of a galactic thick disk . @xcite derived a disk scale height of 400600 pc using a study of low velocity white dwarfs . this value was somewhat larger than previous estimates of 250350 pc but it is interesting to note that the m - dwarf disk scale height derived in section [ mdwarfs ] , as well as the distance estimates of the white dwarfs listed in table [ table4 ] all appear to agree with this value . + it would be interesting to attempt to set an upper limit on the halo white dwarf density based on the finding of up to two white dwarfs in the hudf . under this assumption , the upper limit to the galactic halo white dwarf density is computed to be @xmath95 . this result is consistent with the previous work of @xcite using the combined observations of the hubble deep fields north and south ( @xmath96 ) . + a population ii halo white dwarf population that is older than 12 - 13 gyr would have remained undetected here ( an intrinsically fainter than @xmath97 mag white dwarf population would also help explaining the low average distances of the white dwarfs listed in table [ table4 ] ) . as discussed above , the white dwarfs identified in this work are more likely to be within the galactic thick disk . it is to be noted that @xcite recently observed a disproportionately large fraction of disk to halo white dwarfs in the hubble deep field north ( hdf - n ) . @xcite found no evidence of any white dwarfs with tangential velocities larger than 30 km / s down to @xmath98 mag and the authors concluded that the blue objects they saw were all part of the galactic disk . similarly , the hudf observations presented here successfully identified 4 white dwarf candidates with @xmath99 mag in the hudf , none very likely to be in the galactic halo while 23 detection would have been expected to be consistent with previous studies . + while dynamical studies of the galaxy predict the dark matter white dwarf density as high as @xmath100 ( assuming that 100% of the dark matter halo mass is in the form of @xmath101 white dwarfs ) , the failure to detect a significant population of high velocity white dwarfs in the hudf points to a dark matter halo devoid of a significant white dwarf population . following the methodology of @xcite , one can estimate the amount of dark matter halo mass that is probed by the hudf images , and directly compute the fraction of the dark matter halo mass that could be contained in a white dwarf population . assuming a white dwarf absolute @xmath102 magnitude of 17.0 mag@xcite and a limiting magnitude of @xmath1 mag , the maximum probed distance is 1000 pc . in the corresponding volume , and in the direction of the hudf , the included dark matter halo mass is 3 @xmath103 . a population of dark matter halo white dwarfs could possibly have remained undetected in this study for several reasons : ( 1 ) the method used in this paper may be inefficient at properly identifying halo white dwarfs in table [ table4 ] . in this case , if one assumes that the hudf contains 4 halo white dwarfs ( @xmath28 ) , these would account for @xmath104 , a significant fraction of the expected dark matter halo mass . this would however increase the ratio of halo to disk white dwarfs to unrealistically high levels ( i.e. @xmath105 ) , and would assume that all the white dwarfs seen in the hudf are from the dark matter halo and not from the pop ii halo , which is highly unrealistic . the lack of proper motion detections also makes this scenario unlikely ; ( 2 ) white dwarfs do not contribute significantly to the galactic dark matter halo mass . from microlensing experiements towards the magellanic clouds , the contribution of machos to dark matter has been estimated to be anywhere between 20% to less than 2% ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) . furthermore , @xcite showed how an increased thick disk scale height of 400 - 600 pc makes it unlikely that white dwarfs could be the macho objects ; ( 3 ) white dwarfs could contribute significantly to the mass of the galactic dark matter halo but are too faint to be detected in this study . @xcite showed that an increase in the age of the white dwarf halo population from 10 gyr to 16 gyr is expected to reduce the number of white dwarf detection ( down to @xmath106 ) by a factor of 7 . the lack of high velocity white dwarf detections in the hudf puts upper limits on the contribution of an hypothetical white dwarf population to the galactic dark matter halo . based on the brightest objects in the hudf for which we have spectra ( i.e. @xmath28 ) , if the dark matter halo is as old as about 12 gyr @xcite then dark matter halo white dwarfs with @xmath107 ( @xmath108 ) contribute less than 20% to the dark matter . if the age of the dark matter halo is 10 gyr , white dwarfs ( @xmath109 ) contribute less than 2% to the dark matter . the possibility that there is a large population of faint white dwarfs that has remained unidentified in this study and which would account for a significant fraction of the dark matter halo can be investigated a little further . recall that in section [ qso ] , 14 sources with ( @xmath44 ) and blue ( @xmath46 , @xmath47 ) colors were identified . not all of these sources were expected to be bona - fide stars and some are likely to be extra - galactic sources , but as discussed in section [ test ] , it is estimated that 95% of the stars in the hudf were properly identified , so that this number should be considered to be an upper limit on the number of faint starts in the hudf . following the same methodology used above , but now using a limiting magnitude of @xmath110 , the hudf images probe through 79 @xmath103 of the dark matter halo . even under the extreme assumption that all 14 unresolved candidates in the udf are high velocities white dwarfs , this implies that , when reaching down to = 29.5 , faint white dwarfs in the galactic dark matter halo contributing less than 10% to the total dark matter halo mass for a dark matter halo age of 12 gyr . future observations of the hudf would allow more sensitive measurements of the proper motion of these faint objects ( section [ disk ] ) . setting tighter constraints on the maximum tangential velocities of these faint hudf unresolved objects would allow to exclude some of these objects from high velocity white dwarfs and would allow to further lower the maximum fraction of the dark matter halo mass that could be accounted for by white dwarfs .

the local white dwarf density is computed to be as high as . based on observations taken 73 days apart no high velocity white dwarfs were identified in the hudf , and all four candidates appear more likely to be part of the galactic thick disk . the lack of detected halo white dwarfs implies that , if the dark matter halo is 12 gyr old , white dwarfs account for less than 10% of the dark matter halo mass .

we identified unresolved source candidates in the hubble ultra deep field , down to . unresolved objects were identified using a parameter , which measures the deviation from the curve - of - growth of a point source . extensive testing of this parameter was carried out , including the effects of decreasing signal - to - noise and of the apparent motions of stars , which demonstrated that stars brighter than could be robustly identified . low resolution grism spectra of the objects brighter than identify m and later stellar type dwarfs , 2 candidate l - dwarfs , qsos , and 4 white dwarfs . using the observed population of dwarfs with spectral type m4 or later , we derive a galactic disk scale height of for m and l stars . the local white dwarf density is computed to be as high as . based on observations taken 73 days apart , we determined that no object in the field has a proper motion larger than 0.027/year ( detection limit ) . no high velocity white dwarfs were identified in the hudf , and all four candidates appear more likely to be part of the galactic thick disk . the lack of detected halo white dwarfs implies that , if the dark matter halo is 12 gyr old , white dwarfs account for less than 10% of the dark matter halo mass .

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a systematic search for unresolved objects in the hudf identified objects with @xmath110 mag . using the grapes spectra of these objects , objects with @xmath28 mag were spectroscopically identified , including m and later dwarfs ( including 2 unconfirmed l dwarf candidates ) , and qsos . the m dwarf luminosity function of m4 and later - type stars was computed and compared to predictions based on monte - carlo simulations . assuming a simple analytical model of the galactic disk , the number of detected m dwarfs was shown to be large enough to constraint the scale height of the m and l dwarf galactic disk to be @xmath111 . out of 8 stars that were found to not be m or later - type stars , four stars were determined to be old white dwarf candidates . not a single object was found to have a proper motion that is larger than 0.027/year making them likely galactic thick disk objects . further imaging of the hudf , using a time span larger than 1.5 year would provide more sensitive proper motion measurements . more sensitive proper measurements are required to positively place unresolved objects in the galactic disk or halo . it would also allow to search for high tangential velocity objects amongst the 14 fainter ( @xmath44 ) unresolved sources identified in the hudf . excluding halo membership of objects down to @xmath0 based on proper motion measurements would further constraint the maximum white dwarf contribution to the dark matter halo mass . the currently available observations of the hudf , spanning 73 days , show the absence of a significant population of high velocity white dwarfs down to @xmath7 , and a relatively small number of unresolved , faint blue sources in the field down to @xmath0 . this is interpreted as a consequence of white dwarfs accounting for less than 10% of the dark matter halo , assuming that the dark matter halo is 12 gyr old . we would like to thank i. n. reid for helpful discussions . this work was supported by grant go -09793.01-a from the space telescope science institute , which is operated by aura under nasa contract nas5 - 26555 . afonso c. et al . 2003 , a&a , 404 , 145 alcock , c. , et al . 2000 , apj , 542 , 281 allen , c. w. 2000 , astrophysl quantities 4th ed . ( athlone press , london ) , p388 beckwith s. , et al . 2004 , in preparation bertin , e. arnouts , s. 1996 , a&as , 117 , 393 burgasser , a. j. , kirkpatrick , j. d. , liebert , j. & burrows , a. 2003 , apj , 594 , 510 burgasser , a. j. 2004 , apjs , in press ( astro - ph/0407624 ) burrows , a. et al . 1997 , apj , 491 , 856 chaboyer , b. , demarque , p. , kernan , p.j . , krauss , l.m . j. 494:96 - 110 chiba , m. & beers , t. c. , aj , 199 , 2843 cohen , s. h. , ryan , r. e. , hathi , n. , windhorst , r. a. , koekemoer , a. , xu , c. , pirzkal , n. , malhotra , s. & strolger , l. 2004 , apj in preparation dahn , c. c. et al . 2002 , aj , 124 , 1170 digby , a. p. , hambly , n. c. , cooke , j. a. , reid , i. n. , & cannon , r. d. 2003 , mnras , 344 , 583 evans , n. w. , belokurov , v. 2004 , in press ( astroph/0411222 ) fruchter , a. s. hook , r. n. 2002 , pasp , 114 , 144f gates , i. e. & gyuk , g. 2001 , apj , 547 , 786 gates , i. e. et al . 2004 , in press ( astroph/0405566 ) giavalisco , h. c. et al . 2004 , apj , l93 golimowski , d. a. et al . 2004 , aj , 127 , 3516 harris , h. c. et al . 2001 , apj , 549 , l109 harris , h. c. et al . 2003 , aj , 126 , 1023 hansen , b. m. s. , et al . 2002 , aj , 574 , l155 ibata , r. a. , richer , h. b. , gilliland , r. l. & scott , d. 1999 , apj , 524 , l95 ibata , r. a. , irwin , m. , bienaym , o. , scholz , r. & guibert , j. 2000 , apj , 532 , l41 kawaler , s. , d. 1996 , aj , l61 kilic , m. , von hippel , t. , mndez , r. a. & winget , d. e. 2004 , apj , 609 , 766 kirkpatrick et al . 2000 , aj , 120 , 447 liebert , j. , dahn , c. , c. & monet , d. g. 1988 , apj , 332 , 891 majewski , s. r. , siegel , m. h. , 2002 , apj , 569 , 432 mathewson , d. , s. & ford , v. , l. 1984 , iaus , 108 , 125 mndez , r. a. , minniti , d. , de marchi , g. , baker , a. & couch , w. j. 1996 , mnras , 283 , 666 mndez , r. a. & minniti , d. 2000 , apj , 529 , 911 mndez , r. a. 2002 , a&a , 395 , 779 oppenheimer , b. r. , hambly , n. c. , digby , a. p. , hodgkin , s. t. & and saumon , d. 2001 , science , 292 , 698 pirzkal n. , et al . 2004 , apjs , 154 pickles , a. j. 1998 , pasp , 110 , 863 reid , i. n. & majewski , s. r. 1993 , apj , 409 , 635 reid , i. n. et al . 1999 , apj , 521 , 613 reid , n. & hawley , s. l. 2000 , new light on dark stars ( chichester : praxis ) reid , i. n. , sahu , k. , c. & hawley , s. l. 2001 , apj , 559,942 reid , i. n. , ara&a , 43 , in press richer , h. b. , hansen , b. , limongi , m. , chieffi , a. , straniero , o. & fahlman , g. c. 2000 , apj , 529 , 318 robin , a. c. , reyl , c. , derrire , s. & picaud , s. 2003 , a&a , 409 , 523 ryan , r. e. , hathi , n. p. , cohen , s. h. , & windhorst , r. a. , apj in preparation sahu , k. c. 2003 , space telescope science institute symposium series , vol . 15 , cambridge university press , p. 14 - 23 ( astro - ph/0302325 ) sahu , k. c. 1994 , nature , 370 , 275 schlegel , d. j. , finkbeiner , d. p. & davis , m. 1998 , apj , 500 , 525 schmidt , m. 1968 , apj , 151 , 393 tinney , c. g. , reid , i. n. & mould , j. r. 1993 , apj , 414 , 254 xu , c. et al . 2004 , apjs , in preparation cccccccccc 19 & 53.1623248 & -27.8269460 & 26.58 & 1.91 & 1.01 & 0.30 & 0.015 & 0.004 + 366 & 53.1753062 & -27.8198904 & 29.99 & 2.20 & 3.05 & 1.27 & 0.009 & 0.030 + 443 & 53.1583988 & -27.8189953 & 31.25 & 0.86 & 3.47 & 1.51 & 0.016 & 0.028 + 834 & 53.1648156 & -27.8143652 & 27.67 & 2.35 & 2.00 & 0.76 & 0.013 & 0.011 + 911 & 53.1460739 & -27.8123237 & 25.21 & 2.09 & 1.80 & 0.65 & 0.007 & 0.002 + 1147 & 53.1834639 & -27.8067589 & 19.58 & -0.16 & 0.52 & 0.13 & 0.091 & 0.002 + 1343 & 53.1398080 & -27.8100295 & 27.36 & -0.23 & -0.14 & -0.04 & 0.045 & 0.046 + 2150 & 53.1767483 & -27.7996684 & 22.60 & 1.99 & 1.43 & 0.80 & 0.147 & 0.003 + 2368 & 53.1676057 & -27.8037923 & 29.07 & 1.18 & 0.08 & -0.20 & 0.046 & 0.050 + 2457 & 53.1616105 & -27.8027738 & 26.98 & 1.91 & 0.98 & 0.30 & 0.004 & 0.008 + 2977 & 53.1726388 & -27.8006672 & 27.94 & -0.18 & -0.21 & 0.18 & 0.042 & 0.049 + 3166 & 53.1583425 & -27.7949215 & 20.80 & 0.96 & 0.80 & 0.37 & 0.086 & 0.007 + 3561 & 53.1483050 & -27.7977856 & 29.24 & 1.98 & 0.91 & 0.24 & 0.018 & 0.012 + 3794 & 53.1474097 & -27.7965561 & 28.89 & 2.14 & 0.98 & 0.29 & 0.010 & 0.007 + 3940 & 53.1498728 & -27.7961691 & 27.06 & -0.48 & -0.21 & -0.18 & 0.033 & 0.038 + 4120 & 53.1839107 & -27.7954147 & 28.04 & 0.03 & 0.12 & 1.31 & 0.023 & 0.012 + 4322 & 53.1349058 & -27.7944480 & 26.83 & 0.06 & -0.06 & -0.07 & 0.067 & 0.043 + 4643 & 53.1848922 & -27.7933971 & 31.73 & 1.52 & 0.74 & 0.25 & 0.019 & 0.050 + 4839 & 53.1883621 & -27.7923200 & 27.22 & 1.20 & 0.40 & 0.07 & 0.018 & 0.015 + 4945 & 53.2003709 & -27.7898451 & 25.06 & 2.06 & 1.74 & 0.67 & 0.020 & 0.013 + 5317 & 53.1257144 & -27.7904647 & 29.06 & 0.49 & -0.00 & -0.30 & 0.045 & 0.039 + 5441 & 53.1625253 & -27.7896458 & 27.81 & 1.75 & 1.27 & 0.39 & 0.016 & 0.019 + 5921 & 53.1322881 & -27.7828516 & 20.57 & 0.77 & 1.19 & 0.51 & 0.094 & 0.070 + 5992 & 53.1498432 & -27.7874448 & 27.52 & 1.63 & 0.69 & 0.16 & 0.014 & 0.005 + 6334 & 53.1782000 & -27.7861688 & 27.71 & -0.27 & -0.16 & -0.18 & 0.049 & 0.049 + 6442 & 53.1416300 & -27.7856726 & 28.16 & -0.19 & 0.04 & -0.07 & 0.044 & 0.030 + 6461 & 53.1984259 & -27.7848674 & 26.80 & 1.77 & 1.00 & 0.30 & 0.010 & 0.010 + 6620 & 53.1428439 & -27.7849376 & 31.27 & 3.19 & 0.25 & -0.14 & 0.041 & 0.049 + 6732 & 53.1784892 & -27.7840395 & 25.73 & 1.13 & -0.04 & 0.01 & 0.010 & 0.022 + 7113 & 53.1707114 & -27.7826303 & 30.83 & 2.49 & 0.65 & 0.20 & 0.026 & 0.024 + 7194 & 53.1860335 & -27.7822207 & 26.91 & -0.12 & -0.13 & -0.06 & 0.048 & 0.045 + 7357 & 53.1692789 & -27.7813943 & 27.93 & 0.10 & -0.21 & -0.16 & 0.024 & 0.031 + 7525 & 53.1318579 & -27.7820076 & 28.70 & 2.22 & 1.08 & 0.30 & 0.011 & 0.007 + 7768 & 53.1472186 & -27.7714786 & 27.12 & 1.66 & 0.68 & 0.20 & 0.014 & 0.005 + 7894 & 53.1831085 & -27.7802451 & 27.46 & 0.03 & -0.15 & -0.12 & 0.047 & 0.039 + 8081 & 53.1580838 & -27.7701503 & 27.92 & -0.32 & -0.40 & -0.30 & 0.038 & 0.020 + 8157 & 53.1649526 & -27.7736713 & 30.85 & 2.16 & 0.40 & 0.07 & 0.042 & 0.039 + 8186 & 53.1867094 & -27.7735490 & 27.72 & -0.13 & -0.14 & -0.34 & 0.044 & 0.029 + 9006 & 53.1853179 & -27.7799976 & 27.46 & -0.05 & -0.07 & 0.24 & 0.039 & 0.024 + 9020 & 53.1685421 & -27.7805214 & 27.00 & 0.28 & -0.01 & -0.16 & 0.025 & 0.034 + 9212 & 53.1485421 & -27.7701387 & 25.50 & 1.82 & 0.96 & 0.29 & 0.011 & 0.003 + 9230 & 53.1580164 & -27.7691869 & 21.18 & 0.76 & 0.38 & 0.10 & 0.037 & 0.007 + 9331 & 53.1638484 & -27.767128 & 27.95 & 2.20 & 1.84 & 0.67 & 0.025 & 0.005 + 9351 & 53.1781506 & -27.7691241 & 26.21 & 2.03 & 1.32 & 0.42 & 0.015 & 0.004 + 9397 & 53.162852 & -27.7671662 & 21.44 & 0.26 & 0.11 & 0.02 & 0.043 & 0.033 + 9959 & 53.1611698 & -27.7555109 & 29.12 & 2.42 & 0.91 & 0.29 & 0.022 & 0.021 + ccccccc 19 & m1-m2 & no & @xmath112 & @xmath113 & 3.129 & 2.529 + 366 & l0-l1 & no & @xmath114 & @xmath115 & 3.750 & 3.150 + 443 & l0-m6 & no & @xmath116 & @xmath117 & 4.274 & 3.674 + 834 & m4-m5 & no & @xmath118 & @xmath119 & 3.258 & 2.658 + 911 & m4-m5 & no & @xmath118 & @xmath120 & 2.818 & 2.218 + 1147 & f6-f8 & no & @xmath121 & @xmath122 & 2.142 & 1.542 + 1343 & a0-k7 & yes & @xmath123 & @xmath124 & 3.713 & 3.113 + 2150 & m3-m4 & no & @xmath125 & @xmath126 & 2.315 & 1.715 + 2368 & o9-m6 & yes & @xmath127 & @xmath128 & 3.774 & 3.174 + 2457 & m0-m1 & no & @xmath129 & @xmath130 & 3.209 & 2.609 + 2977 & a0-m4 & yes & @xmath131 & @xmath132 & 3.818 & 3.218 + 3166 & k4-k5 & no & @xmath133 & @xmath134 & 2.164 & 1.564 + 3561 & m0-m1 & no & @xmath129 & @xmath135 & 3.647 & 3.047 + 3794 & m0-m1 & no & @xmath129 & @xmath136 & 3.544 & 2.944 + 3940 & o5-m3 & yes & @xmath137 & @xmath138 & 3.702 & 3.102 + 4120 & gal & yes & & & & + 4322 & a7-k5 & no & @xmath139 & @xmath140 & 3.548 & 2.948 + 4643 & a0-m6 & yes & @xmath141 & @xmath142 & 4.237 & 3.637 + 4839 & g5-k2 & no & @xmath143 & @xmath144 & 3.400 & 2.800 + 4945 & m4-m5 & no & @xmath145 & @xmath146 & 2.796 & 2.196 + 5317 & a0-m6 & yes & @xmath147 & @xmath148 & 3.910 & 3.310 + 5441 & m2-m3 & no & @xmath149 & @xmath150 & 3.407 & 2.807 + 5921 & k4-k5 & no & @xmath133 & @xmath151 & 2.155 & 1.555 + 5992 & k7-m0 & no & @xmath152 & @xmath153 & 3.373 & 2.773 + 6334 & f8-l0 & yes & @xmath154 & @xmath155 & 3.791 & 3.191 + 6442 & a0-g5 & yes & @xmath156 & @xmath157 & 3.865 & 3.265 + 6461 & m0-m1 & no & @xmath129 & @xmath158 & 3.202 & 2.602 + 6620 & b8-m4 & yes & @xmath159 & @xmath160 & 3.812 & 3.212 + 6732 & gal & no & & & & + 7113 & g8-k0 & yes & @xmath161 & @xmath162 & 3.861 & 3.261 + 7194 & o5-k5 & yes & @xmath163 & @xmath164 & 3.601 & 3.001 + 7357 & o9-m5 & yes & @xmath165 & @xmath166 & 3.760 & 3.160 + 7525 & m1-m2 & no & @xmath167 & @xmath168 & 3.491 & 2.892 + 7768 & k5-k7 & no & @xmath169 & @xmath170 & 3.286 & 2.686 + 7894 & b8-k7 & yes & @xmath171 & @xmath172 & 3.680 & 3.080 + 8081 & o5-a3 & yes & @xmath173 & @xmath174 & 3.843 & 3.243 + 8157 & gal & yes & & & & + 8186 & b0-k7 & yes & @xmath175 & @xmath176 & 3.764 & 3.164 + 9006 & b9-a3 & yes & @xmath177 & @xmath178 & 3.697 & 3.097 + 9020 & f0-f2 & no & @xmath179 & @xmath180 & 3.540 & 2.940 + 9212 & m0-m1 & no & @xmath129 & @xmath181 & 2.929 & 2.329 + 9230 & k2-k3 & no & @xmath182 & @xmath183 & 2.279 & 1.679 + 9331 & m5-m6 & no & @xmath184 & @xmath185 & 3.345 & 2.745 + 9351 & m1-m2 & no & @xmath186 & @xmath187 & 3.031 & 2.431 + 9397 & gal & no & & & & + 9959 & m0-m1 & no & @xmath129 & @xmath188 & 3.535 & 2.935 + 1147 & ms f6-f8 & 3.7 - 4.0 & @xmath189 & & & f6-f8 + 1147 & young wd & 14.0 - 15.0 & 110 @xmath68 24 & 1.4 - 3.9 & 14.1 & & + 1147 & old wd & 17.4 - 18.3 & 24 @xmath190 5 & 10.3 - 12.1 & 3.0 & & + 3166 & ms k4-k5 & 6.8 - 7.1 & @xmath191 & & & k4-k5 + 3166 & young wd & 14.8 - 15.8 & 80@xmath190 18 & 2.5 - 5.7 & 10.2 & & + 3166 & old wd & 17.2 - 18.2 & 27 @xmath68 6 & 9.9 - 11.5 & 3.5 & & + 4322 & ms a7-k5&2.3 - 7.1 & @xmath192 & & + 4322 & young wd & 12.1 - 13.1 & @xmath193 & 0.4 - 1.4 & 1545.6 & + 4322 & old wd & 17.5 - 18.4 & 590 @xmath68 126 & 10.7 - 12.9 & 75.5 & disk or halo & @xmath194 + 4839 & ms g5-k2 & 5.0 - 6.3 & @xmath195 & & + 4839 & young wd & 12.5 - 13.5 & @xmath196 & 1.1 - 3.3 & 885 . & disk & @xmath197 + 4839 & old wd & 17.4 - 18.3 & 417 @xmath68 88 & 10.4 - 12.3 & 53.4 & disk or halo & @xmath198 + 5921 & ms k4-k5 & 6.8 - 7.1 & @xmath199 & & & k4-k5 + 5921 & young wd & 14.5 - 15.5 & @xmath200 & 1.9 - 4.7 & 11.9 & & + 5921 & old wd & 17.3 - 18.2 & @xmath201 & 10.1 - 11.7 & 3.3 & & + 7768 & ms k5-k7 & 7.1 - 7.6 & @xmath202 & & & + 7768 & young wd & 14.5 - 15.5 & @xmath203 & 1.9 - 4.7 & 160.2 & disk & @xmath204 + 7768 & old wd & 17.3 - 18.2 & 345 @xmath68 70 & 10.1 - 11.7 & 44.1 & disk or halo & @xmath205 + 9020 & ms f0-f2 & 2.7 - 3.6 & @xmath206 & & + 9020 & young wd & 13.3 - 13.3 & @xmath207 & 0.5 - 1.6 & 793.9 & + 9020 & old wd & 17.5 - 18.4 & 576 @xmath68 123 & 10.7 - 12.9 & 73.7 & disk or halo & @xmath208 + 9230 & ms k2-k3 & 6.3 - 6.7 & @xmath209 & & & k2-k3 + 9230 & young wd & 13.6 - 14.6 & 187 @xmath68 41 & 1.1 - 3.2 & 23.9 & & + 9230 & old wd & 17.5 - 18.4 & 32 @xmath68 7 & 10.4 - 12.3 & 4.0 & & + ( green ) and @xmath39 ( red ) values for the hudf objects . the stellarity index was defined ( see section [ sindexsec ] ) so that higher values correspond to objects which are increasingly resolved in the images . we selected unresolved objects fainter than @xmath210 mag to be unresolved if @xmath2110.05 , and @xmath2110.15 for brighter objects which are saturated.[fig1],width=480 ] values for the brightest objects in the field . each object appears 10 times in this figure , with increasingly lower signal to noise ( increasingly darker dots ) . the observed increase in values as a function of magnitude at @xmath212 mag is similar to the one observed in figure [ fig1 ] where the real distribution of the values from the hudf objects is shown . this demonstrates the robustness of to distinguish between point sources and extended objects down to faint magnitudes . at fainter magnitudes , images of stars become increasingly dominated by noise which tends to increases the measured values of . the same test was performed in the band and yielded an identical behavior . [ fig2],width=480 ] mag and @xmath217 mag . solid red squares are m dwarfs . empty red squares are the two l dwarf candidates . solid green triangles represent the non m or l dwarfs stars which could be main - sequence stars . the empty blue circles are white dwarf candidates ( table [ table4 ] ) . the solid yellow circles represent the qsos . [ vbv],width=480 ] , unresolved , spectroscopically identified objects in the hudf . m and l dwarfs are shown using red squares with photometric error bars . main - sequence stars are shown in green thick circles . extra - galactic objects , including those dimmer than @xmath1 mag , are shown using large blue stars . the 5 white dwarf candidates are shown using large blue crosses . pickles main - sequence objects are also shown using small black circles . the ( - ) locations of the o , a , f , g , k , and m stellar type are shown for reference . hot white dwarfs are shown in large blue squares . cool white dwarfs ( ( 3000k , 4000k , 5000k ) , * ? ? ? * ) are shown using labeled , empty circles . finally , the solid black line shows the qso track , from redshift of z=4.0 ( top right ) to z=0.1 ( bottom left)[vibv],width=480 ] values of 200 , 300 , 400 and 500 pc ( bottom curves to top curves respectively ) . for each value of @xmath65 , mass functions corresponding to @xmath218 and 1.5 are shown ( solid and dashed lines respectively ) . the observed hudf distribution is shown using a solid black line which is best fit by a disk with a scale height of @xmath219 while reasonably excluding values of @xmath65 = 200,300 , and 500.[mlf2],width=480 ]

we identified unresolved source candidates in the hubble ultra deep field , down to . low resolution grism spectra of the objects brighter than identify m and later stellar type dwarfs , 2 candidate l - dwarfs , qsos , and 4 white dwarfs . using the observed population of dwarfs with spectral type m4 or later , we derive a galactic disk scale height of for m and l stars . , we determined that no object in the field has a proper motion larger than 0.027/year ( detection limit ) .

we identified unresolved source candidates in the hubble ultra deep field , down to . unresolved objects were identified using a parameter , which measures the deviation from the curve - of - growth of a point source . extensive testing of this parameter was carried out , including the effects of decreasing signal - to - noise and of the apparent motions of stars , which demonstrated that stars brighter than could be robustly identified . low resolution grism spectra of the objects brighter than identify m and later stellar type dwarfs , 2 candidate l - dwarfs , qsos , and 4 white dwarfs . using the observed population of dwarfs with spectral type m4 or later , we derive a galactic disk scale height of for m and l stars . the local white dwarf density is computed to be as high as . based on observations taken 73 days apart , we determined that no object in the field has a proper motion larger than 0.027/year ( detection limit ) . no high velocity white dwarfs were identified in the hudf , and all four candidates appear more likely to be part of the galactic thick disk . the lack of detected halo white dwarfs implies that , if the dark matter halo is 12 gyr old , white dwarfs account for less than 10% of the dark matter halo mass .

1301.1135

c

from our knowledge , the model we developed in this paper is the first model that accounts for both stylized facts of market prices microstructure ( including random time arrival of price moves , discrete price grid , high frequency mean reversion , correlation functions behavior at various time scales ) and the stylized facts of market impact ( mainly the concave / relaxation characteristic shape of the market impact of a meta - order ) . analytical closed formula can be obtained for most of these stylized facts . not only it allows us to reveal ( through the estimations of the different kernels ) the dynamics involved between trade arrivals and price moves , but it also allows us to estimate the entire market impact profile from anonymous market data . as far as trade and price dynamics are concerned , we have provided evidence of a power - law behavior of the kernels @xmath377 and @xmath378 and that the model is close to instability ( i.e. @xmath379 is smaller but close to 1 ) . this suggests the existence of some self - similarity properties in the order - book dynamics and sharply contrasts with the usual exponential kernels used in former parametric hawkes modeling in finance . the cross - kernels associated with impact of trade on prices ( @xmath380 ) and feed - back ( @xmath381 ) are well localized in time ( i.e. of `` impulsive nature '' ) . thus , upward ( resp . downward ) price moves are mainly impacted by trades on the ask ( resp . bid ) side . in turn , positive ( resp . negative ) mid - price variations imply an increase of the trading intensity on the bid ( resp . ask ) side . besides these important points , qualitative arguments showed that , provided @xmath382 and @xmath383 , the long memory puzzle `` of the order flow raised by bouchaud et al . @xcite can be addressed without any fine tuning of the model parameters : trades naturally appear as long - range correlated over a wide range of lags while price variations are almost uncorrelated . moreover , the same kind of arguments can explain the concave ( ' ' square - root " law ) / relaxation typical market impact shape and an almost vanishing permanent impact . let us first point out that the model , as is , can be used as a stochastic price replayer " using as an input the true market order arrivals in place of the stochastic process @xmath17 . this allows one to replay " the price of a given historical period and , for instance , using it as an input price for any algorithm designed to estimate or manage a risk . in this paper , we have presented the most basic form of the model . it can be seen as a building block for more elaborate models depending on what it is meant to be used for . there are many ways for extensions . let us just go through some of them we have already developed or we are still working on . for instance , it would be important to have a model which not only takes into account the arrival times of the market orders but their volumes too . this is a pretty easy extension since it can be done within the framework of marked hawkes processes for which straightforward extensions of all computations presented in this paper can be obtained . in the simplest form , one could use i.i.d . volumes @xmath384 for the market orders : at any time @xmath10 a market order arrives ( @xmath385 or @xmath386 ) a volume @xmath384 is chosen randomly ( using a given law ) . in its simplest form the new model consists in replacing the projection of on the last two components by @xmath387 where @xmath75 is a function that describes how the volume impacts the price . it basically corresponds to what is generally referred into the literature by the instantaneous impact function " . in order to go further into the understanding of the underlying dynamics of the order - book , a very natural extension of the model , consists in using more dimensions in order to take into account limit / cancel orders . thus , for instance , one way would be to introduce a new point process @xmath388 where @xmath389 ( resp . @xmath390 ) is incremented by 1 whenever a limit order arrives at the best ask ( resp . best bid ) or a cancel order arrives at best bid ( resp . best ask ) . one would then need to introduce the different kernels that account for the influence of @xmath391 on @xmath15 and @xmath49 and the kernels that account for the influence of @xmath15 and @xmath49 on @xmath391 itself . the estimation procedure of the kernels can follow the exact same procedure described in section [ sec : estimation ] . along the same line , i.e. , by adding new dimensions to the 4d - hawkes model presented in this paper , one could quantify the impact of a given exogenous news on the market order flow or directly on the price by estimating the corresponding kernel . or , alternatively , one could consider a multi - agent models ( e.g. , adding 2 dimensions for each agent ) and model / estimate the influence of a given agent on another one or on all the anonymous agents ( as @xmath392 does in ) . these extended framework would open the door to precise estimations and obvious interpretations in order to get better insights into to full order book dynamics .

we introduce a multivariate hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level . it allows one to account for both stylized facts of market prices microstructure ( including random time arrival of price moves , discrete price grid , high frequency mean reversion , correlation functions behavior at various time scales ) and the stylized facts of market impact ( mainly the concave - square - root - like / relaxation characteristic shape of the market impact of a meta - order ) . moreover , it allows one to estimate the entire market impact profile from anonymous market data .

we introduce a multivariate hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level . our model is a point process mainly characterized by 4 kernels associated with respectively the trade arrival self - excitation , the price changes mean reversion the impact of trade arrivals on price variations and the feedback of price changes on trading activity . it allows one to account for both stylized facts of market prices microstructure ( including random time arrival of price moves , discrete price grid , high frequency mean reversion , correlation functions behavior at various time scales ) and the stylized facts of market impact ( mainly the concave - square - root - like / relaxation characteristic shape of the market impact of a meta - order ) . moreover , it allows one to estimate the entire market impact profile from anonymous market data . we show that these kernels can be estimated from the empirical conditional mean intensities . we provide numerical examples , application to real data and comparisons to former approaches .

cond-mat0203232

r

evolving random graphs have recently attracted attention , see e.g. refs @xcite and references therein . this interest is mainly motivated by concrete problems related to the structure of communication or biological networks . experimental data are now available in many contexts @xcite . in these examples , the asymmetry and the evolving nature of the networks are likely to be important ingredients for deciphering their statistical properties . it is however far from obvious to find solvable cases that would possibly account for some relevant features of , say , the regulating network of a genome . although biology has strongly influenced our interest in evolving networks , the model we solve is not based on realistic biological facts but it nevertheless incorporates asymmetry and chronological order . understanding such simple evolving graphs may help understanding biological networks , at least by comparison and opposition . we were initially motivated by the study of the yeast genetic regulatory network presented in ref.@xcite . the authors studied in and out degree distributions and discovered a strong asymmetry : a single gene may participate to the regulation of many other genes the law for out - degrees seems to be large , but each genes is only regulated by a few other genes the law for in - degrees seems to have finite moments . this is why we consider oriented evolving random graphs in the sequel . a biological interpretation for the asymmetry is that the few promoter - repressor sites for each gene bind only to specific proteins , but that along the genome many promoter - repressor sites are homologous . however , this does not predict the precise laws . an understanding of the same features from a purely probabilistic viewpoint would be desirable as well . the recent experimental studies dealt with global statistical properties of evolving graphs , i.e. when the evolving network is observed at some fixed time with the ages of different vertices and edges not taken into account . there are simple experimental reasons for that : to keep track of the ages would in many cases dramatically reduce the statistics , and in other cases this information is even not available . our second motivation is a better understanding of the local - in - time statistical properties of evolving networks . this helps dating or assigning likely ages to different structures of the networks . as we shall later see , the global analysis , which is like a time average , gives a distorted view of the real structure of the networks . we shall present a detailed analysis of local - in - time features in our model . the model we study is the natural evolving cousin of the famous erds - renyi random graphs @xcite . starting from a single vertex at time @xmath0 , a new vertex is created at each time step so that at time @xmath1 , the size of the system , i.e. the number of vertices , is @xmath1 , and new oriented edges are created with specified probabilistic rules . a tunable parameter @xmath2 ranging from @xmath3 to @xmath4 describes asymptotically the average number of incoming edges on a vertex . precise definitions are given in the next section . our main results are the following : from very simple rules , we see an asymmetry emerging . the global in and out degree distributions are different . we also compute the local profiles of in and out degree distributions , and comment on the differences . we make a detailed global analysis for the structure and sizes of the connected components . we use generating function methods to write down a differential equation that implies recursion relations for the distribution of component sizes , see eqs.([cdiff],[crecur ] ) . a salient global feature of the model is a percolation phase transition at a critical value of the average connectivity . below this value , no single component contains a finite fraction of the sites in the thermodynamic limit , i.e. in the large @xmath1 limit . however , a slightly unusual situation occurs in that below the transition the system contains components whose sizes scale like a power of the total size of the graph , see eq.([eq : grosclu ] ) . correspondingly , the probability distribution for component sizes has an algebraic queue , see eq.([asympk ] ) , and its number of finite moments jumps at specific values of the average connectivity . above the transition , this probability distribution becomes defective , but its decrease is exponential , see eq.([pklarge ] ) . the transition is continuous . close to the threshold , the fraction of sites in the giant component the percolation cluster has an essential singularity , see eq.([eq : pof ] ) . we argue that this result is universal , with the meaning used in the study of critical phenomena . the essential singularity at the percolation threshold had already been observed numerically by @xcite in a different model which we show to be in the same universality class as ours for the percolation transition , and computed analytically for another class of models in @xcite . we then turn to the study of local - in - time profiles of connected components . guided by a direct enumeration based on tree combinatorics , we show that they satisfy recursion relations , and we give the first few profiles ( isolated vertices , pairs , triples ) explicitly . the profile of the giant component is given by a differential equation , from which we extract the singularity in the far past and the critical singularity in the present see eqs([eq : rho_0],[eq : rho_1 ] ) . in particular the giant component invades all the time slices of the graph above the transition . one strange feature of profiles , which would deserve a good explanation , is that in several instances the formal parameter involved in generating functions for global quantities is simply traded for the relative age to obtain interesting local - in - time observables , see eqs.([eq : young],[ddiff ] ) . we have compared our analytical results with numerical simulation whenever possible . while polishing this paper , we became aware of @xcite , whose goals overlap partly with ours . when they can be compared , the results agree

we introduce a new oriented evolving graph model inspired by biological networks . a node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes . the distribution of component sizes decreases algebraically with a continuously varying exponent depending on the average connectivity . we also present a thorough analysis of aging properties . michel bauer and denis bernard service de physique thorique de saclay ce saclay , 91191 gif sur yvette , france

we introduce a new oriented evolving graph model inspired by biological networks . a node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes . this leads to a statistical asymmetry between incoming and outgoing edges . we show that the model exhibits a percolation transition and discuss its universality . below the threshold , the distribution of component sizes decreases algebraically with a continuously varying exponent depending on the average connectivity . we prove that the transition is of infinite order by deriving the exact asymptotic formula for the size of the giant component close to the threshold . we also present a thorough analysis of aging properties . we compute local - in - time profiles for the components of finite size and for the giant component , showing in particular that the giant component is always dense among the oldest nodes but invades only an exponentially small fraction of the young nodes close to the threshold . michel bauer and denis bernard service de physique thorique de saclay ce saclay , 91191 gif sur yvette , france

1605.03462

i

hydrodynamical simulations of structure formation have convincingly demonstrated that the forest is an excellent probe of the underlying dark matter distribution , tracing the cosmic web of large scale structure on scales @xmath9@xmath10 comoving mpc ( cmpc ) along the line of sight @xcite . detailed comparison of intergalactic absorption line observations to simulations at @xmath11 have placed constraints on the matter power spectrum @xcite , the ionisation and thermal state of the intergalactic medium @xcite , the coldness of cold dark matter @xcite , and the baryon acoustic oscillation scale @xcite . in the forthcoming decade , thirty metre class telescopes equipped with high resolution ( @xmath12 ) echelle spectrographs , coupled with huge numbers of low - to - moderate resolution spectra ( @xmath13@xmath14 ) obtained with proposed large scale quasar surveys with the _ _ william herschel telescope enhanced area velocity explorer _ _ ( weave ) and the _ _ dark energy spectroscopic instrument _ _ ( desi ) , will open up new vistas on the high redshift intergalactic medium ( igm ) probed by the forest . these facilities and surveys will enable access to fainter , more numerous background quasars , and will probe the igm transverse to the line of sight with densely packed background sources . critical to all these programmes are high fidelity models of the igm . these are required for forward modelling the observational data and facilitating ( model - dependent ) constraints on quantities of cosmological and astrophysical interest . a drawback of existing hydrodynamical simulations of the igm is their narrow dynamic range , which translates to simulation volumes of @xmath15@xmath16 due to the requirement of resolving structures with @xmath17 @xcite and spatial scales of @xmath18 @xcite . this requirement is problematic when simulating correlations in the igm on large scales , analysing the properties of absorption systems around rare , massive haloes , and correcting for the lack of large scale power in small simulation volumes . convergence at the @xmath19 per cent level in the forest power spectrum requires gas particle masses of @xmath20 and volumes @xmath21 to correctly capture the relevant large scale modes @xcite . in addition to achieving a sufficient dynamic range , it is important to assess how faithfully the hydrodynamical simulations reproduce the observational properties of the forest . although the overall agreement between high resolution spectroscopic data at @xmath22 and hydrodynamical simulations is astonishingly good , several discrepancies have been highlighted over the last few decades . these include absorption line velocity widths in the simulations which are too narrow @xcite , underdense gas that may be significantly hotter than typically assumed in the models @xcite , and too few absorption lines in the simulations with column densities @xmath23 @xcite . in this work , we revisit these issues while introducing a new set of state - of - the - art hydrodynamical simulations of the igm the sherwood simulation suite performed with a modified version of the parallel tree - pm smoothed - particle hydrodynamics ( sph ) code p - gadget-3 , an updated and extended version of the publicly available gadget-2 @xcite . these are some of the largest hydrodynamical simulations of the forest performed to date , in volumes @xmath0@xmath24 with up to @xmath25 ( 17.2 billion ) particles . other recent simulations similar in scale include forest models performed with the eulerian nyx hydrodynamical code @xcite , as well as the illustris @xcite and eagle simulations @xcite . the sherwood simulations are similar in terms of volume and resolution to the forest simulations presented by @xcite , but employ a different hydrodynamics algorithm and explore a wider array of model parameters including warm dark matter and galactic outflows . illustris and eagle performed with the moving mesh code arepo @xcite and a modified version of p - gadget-3 , respectively have more sophisticated sub - grid treatments for gas cooling , star formation and feedback , but are performed at lower mass resolution . the highest resolution sherwood runs furthermore stop at @xmath26 , whereas illustris and eagle have been performed to @xmath27 . the sherwood simulations are designed to fulfill a broad range of roles , including studying the igm during hydrogen reionisation at @xmath28 , constraining the matter power spectrum with the forest at @xmath29 , mapping three dimensional structure in the igm with multiple quasars at @xmath30 and examining the properties of the low redshift forest at @xmath31 . a subset of these models have already been compared to metal line observations approaching reionisation at @xmath32 @xcite and to the forest in an ultra - high signal - to - noise spectrum ( @xmath33 per pixel ) of quasar he0940@xmath341050 at @xmath35 ( rorai et al . 2016 , submitted ) . in this work the first in a series of papers we provide an overview of the simulations and undertake a comparison to high resolution observations of absorption at column densities @xmath36 over the redshift range @xmath22 , where observational data are readily accessible with optical spectroscopy . our goal is not to advocate for a `` best fit '' set of model parameters in this work . rather , we instead report the differences and agreements between our simulations and observational data . for a comprehensive set of reviews on this topic , we also refer the interested reader to @xcite , @xcite and @xcite . this paper is structured as follows . we first describe the simulations in section [ sec : method ] . in section [ sec : results ] we compare the simulations to a wide variety of observational data , including the distribution and power spectrum of the transmitted flux , the column density distribution function and the distribution of absorption line velocity widths . we summarise and present our conclusions in section [ sec : conclude ] . the appendix contains numerical convergence tests . we assume the cosmological parameters @xmath37 , @xmath38 and @xmath39 throughout @xcite and refer to comoving and proper distance units with the prefixes `` c '' and `` p '' respectively .

these are performed in volumes comoving , span almost four orders of magnitude in mass resolution with up to 17.2 billion particles , and employ a variety of physics variations including warm dark matter and galactic outflows . an uncertain correction for continuum placement bias is required to match the distribution and power spectrum of the transmitted flux , particularly at . finally , the temperature of intergalactic gas in the simulations may be slightly too low at and a flatter temperature - density relation is required at , consistent with the expected effects of non - equilibrium ionisation during reionisation . [ firstpage ] methods : numerical - intergalactic medium - quasars : absorption lines

we introduce a new set of large scale , high resolution hydrodynamical simulations of the intergalactic medium : the sherwood simulation suite . these are performed in volumes comoving , span almost four orders of magnitude in mass resolution with up to 17.2 billion particles , and employ a variety of physics variations including warm dark matter and galactic outflows . we undertake a detailed comparison of the simulations to high resolution , high signal - to - noise observations of the forest over the redshift range . the simulations are in very good agreement with the observational data , lending further support to the paradigm that the forest is a natural consequence of the web - like distribution of matter arising in cosmological models . only a small number of minor discrepancies remain with respect to the observational data . saturated absorption lines with column densities at are underpredicted in the models . an uncertain correction for continuum placement bias is required to match the distribution and power spectrum of the transmitted flux , particularly at . finally , the temperature of intergalactic gas in the simulations may be slightly too low at and a flatter temperature - density relation is required at , consistent with the expected effects of non - equilibrium ionisation during reionisation . [ firstpage ] methods : numerical - intergalactic medium - quasars : absorption lines

1605.03462

c

in this work we introduce a new set of large scale , high resolution hydrodynamical simulations of the igm the sherwood simulation suite . we perform a detailed comparison to high resolution ( @xmath196 ) , high signal - to - noise ( @xmath197 ) observations of the forest over the redshift range @xmath3 . our conclusions are as follows : * the observed effective optical depth at @xmath5 and @xmath198 is overpredicted by the recent @xcite ionising background model ( see also * ? ? ? . the photo - ionisation rate , @xmath199 , in the @xcite model must be increased by @xmath200 $ ] per cent at @xmath201 $ ] in our reference 40 - 2048 simulation , corresponding to @xmath202\times 10^{-12}\rm\,s^{-1}$ ] , in order to match the effective optical depth evolution described by eq . ( [ eq : taueff ] ) . an in depth analysis of the photo - ionisation rate that includes systematic uncertainties is presented in @xcite . * the observed transmitted flux pdf from @xcite and @xcite at @xmath64 is not recovered correctly in the simulations at @xmath58 . this is most likely due to the uncertain effect of star formation and galactic outflows , which increase the incidence of saturated ( @xmath4 ) absorption lines , as well as the detailed signal - to - noise properties of the spectra @xcite . the observed pdf at @xmath62 furthermore still lies systematically below the mock data , although we find it is generally within the @xmath59 uncertainty we estimate from the models ( see also * ? ? ? this agreement may be improved for models with hotter underdense gas @xcite . a recent analysis of an ultra - high resolution quasar spectrum by rorai et al . ( 2016 , submitted ) is consistent with this possibility . * we find that star formation and galactic winds have the largest impact on the forest at redshifts @xmath203 ( see also * ? ? ? * ; * ? ? ? * ) . when compared to simulations optimised for forest modelling which simply convert all gas with @xmath169 and @xmath204 into stars , the @xcite star formation and winds sub - grid model produces a greater incidence of saturated absorption systems and increases the transmitted flux power spectrum on large scales . at @xmath205 , however , this has little impact on the forest . * the effect of later reionisation ( and hence less pressure smoothing ) and the suppression of small scale power by a warm dark matter thermal relic has a large impact on the forest at @xmath6 . decreasing the pressure smoothing scale acts on the pdf and power spectrum in the opposite direction to warm dark matter . it produces more pixels with @xmath206 in the pdf , and increases the power spectrum at scales @xmath100 . this indicates it should be possible to constrain the integrated thermal history during reionisation using the line of sight forest power spectrum at high redshift @xcite . * mock forest spectra extracted from hydrodynamical simulations are in better agreement with the observed pdf and power spectrum if a correction for the uncertain continuum normalisation is applied . the continuum is typically placed too low on the observed spectra , and the correction varies from a few per cent at @xmath26 to as much as @xmath119 per cent at @xmath108 ( see also * ? ? ? this changes the shape of the pdf at @xmath63 and increases the power spectrum on all scales . * the observed scatter in the mean transmitted flux @xcite is in reasonable agreement with the simulations at @xmath52 . however , this quantity is sensitive to the continuum placement on the simulated spectra . increasing ( decreasing ) the continuum level decreases ( increases ) the scatter in the mean transmission . variations in this correction may explain the broader scatter in the data at @xmath135 relative to the simulations . * the simulations are in good agreement with the cddf of forest absorbers presented by @xcite at @xmath30 . the only discrepancies are that the simulations underpredict the number of weak lines with @xmath207 , and ( at @xmath90 only ) underpredict the incidence of saturated absorption lines with @xmath208 . we suggest the former may be due to unidentified metals and the detailed signal - to - noise properties of the data , whereas the latter agreement is improved ( but not resolved ) by including a sub - grid model for star formation and galactic winds . * the observed distribution of absorption line velocity widths @xcite is in good overall agreement with the simulations at @xmath90 and @xmath7 , although absorption lines with @xmath209 are underpredicted by the models . this difference is likely due to the presence of unidentified narrow metal lines in the observational sample . at @xmath7 , the simulations slightly overpredict the number of lines with @xmath210@xmath172 . this suggests the simulations may be slightly too cold at @xmath7 , possibly due to additional non - equilibrium heating not included in the simulations @xcite . * the lower cut - off in the @xmath155@xmath180 distribution for lines with @xmath211 measured by @xcite and reanalysed by @xcite at @xmath8 is in broad agreement with our reference simulation , which has a temperature at mean density of @xmath191 at this redshift . however , a slightly lower value ( by @xmath212@xmath194 ) for the slope of temperature - density relation assumed in the models at this redshift , @xmath192 , may provide better agreement with the observational data at @xmath8 . we stress , however , that forest absorption lines at @xmath52 typically probe mildly overdense gas . hot gas may still persist at @xmath195 while still allowing consistency with the lower envelope of the @xmath155@xmath180 plane for absorption lines at @xmath8 ( see rorai et al . 2016 , submitted ) . overall , we conclude the sherwood simulations are in very good agreement with a wide range of forest data at @xmath213 . these results lend further support to the now well established paradigm that the forest is a natural consequence of the web - like distribution of matter arising in cosmological models . however , a number of small discrepancies still remain with respect to the observational data , motivating further observational and theoretical investigation . we suggest that in the short - term , improved measurements of the power spectrum and pdf at @xmath135 using larger , high resolution data sets , and tighter constraints on the slope of the temperature - density relation at @xmath214 will be particularly beneficial .

we introduce a new set of large scale , high resolution hydrodynamical simulations of the intergalactic medium : the sherwood simulation suite . we undertake a detailed comparison of the simulations to high resolution , high signal - to - noise observations of the forest over the redshift range . the simulations are in very good agreement with the observational data , lending further support to the paradigm that the forest is a natural consequence of the web - like distribution of matter arising in cosmological models . only a small number of minor discrepancies remain with respect to the observational data . saturated absorption lines with column densities at are underpredicted in the models .

we introduce a new set of large scale , high resolution hydrodynamical simulations of the intergalactic medium : the sherwood simulation suite . these are performed in volumes comoving , span almost four orders of magnitude in mass resolution with up to 17.2 billion particles , and employ a variety of physics variations including warm dark matter and galactic outflows . we undertake a detailed comparison of the simulations to high resolution , high signal - to - noise observations of the forest over the redshift range . the simulations are in very good agreement with the observational data , lending further support to the paradigm that the forest is a natural consequence of the web - like distribution of matter arising in cosmological models . only a small number of minor discrepancies remain with respect to the observational data . saturated absorption lines with column densities at are underpredicted in the models . an uncertain correction for continuum placement bias is required to match the distribution and power spectrum of the transmitted flux , particularly at . finally , the temperature of intergalactic gas in the simulations may be slightly too low at and a flatter temperature - density relation is required at , consistent with the expected effects of non - equilibrium ionisation during reionisation . [ firstpage ] methods : numerical - intergalactic medium - quasars : absorption lines

0904.0505

i

experiments on , where @xmath7 is na , rb , or k , show a wide range of strongly correlated phases.@xcite , in particular , has attracted much attention following the discovery of superconductivity when water is intercalated into the system.@xcite the phase diagram , with doping @xmath8 , shows many interesting phases,@xcite including a ` curie - weiss metal ' , a type antiferromagnetism ( ferromagnetic layers stacked antiferromagnetically ) and an ` insulating ' phase seen only at @xmath9 . the latter phase is particularly puzzling as many probes [ including resistivity,@xcite optical conductivity,@xcite and angle resolved photoemission spectroscopy ( arpes)@xcite ] suggest that it is insulating , however , shubnikov - de haas oscillations are also observed,@xcite suggesting the state is metallic . the aims of this paper are to present a simple variational theory of , where @xmath7=na , rb , or k , and to attempt to reconcile these seemingly contradictory experiments . in the co atoms form a triangular lattice and the simplest model of the band structure , a single band triangular lattice with nearest neighbour hopping only , gives good agreement with arpes experiments on .@xcite the doping of the system is controlled by the concentration of @xmath7 ions , @xmath8 , with the single band being half filled at @xmath10 and filled at @xmath11 . however , the @xmath7 ions order so as to minimise the mutual coulomb repulsion.@xcite therefore , the coulomb potential due to the @xmath7 ions is different at different co atoms and , because the @xmath7 ions are ordered , this gives rise to an ordered arrangement of potentials at the vertices of the triangular lattice . thus an effective hamiltonian for is the ionic hubbard model.@xcite in addition to the interest in the ionic hubbard model is of significant interest in its own right . the ionic hubbard model on half filled bipartite lattices has attracted interest because it undergoes a transition from a mott insulator to a band insulator.@xcite furthermore , away from half filling and on frustrated lattices the ionic hubbard model shows a subtle interplay between charge and spin ordering and metallic and insulating phases.@xcite the hamiltonian of the ionic hubbard model is @xmath12 where @xmath0 is the hopping amplitude between nearest neighbour sites only , @xmath13 is the effective on - site coulomb repulsion between two electrons , @xmath14 is the site energy , @xmath15 annihilates ( creates ) an electron on site @xmath16 with spin @xmath17 and @xmath18 . previous studies of this model on frustrated lattices included both analytical and numerical studies of zigzag ladders,@xcite dynamical mean field theory ( dmft ) studies on infinite dimensional fcc@xcite and two - dimensional triangular lattices@xcite and exact diagonalisation on small triangular lattices.@xcite a more extensive discussion of previous work on the ionic hubbard model is given in ref . however , here we aim to provide a simple variational description that captures as much of the strongly correlated physics of this model as possible . the wide range of numerical techniques , described above , that have been applied to the ionic hubbard model have not , previously , been complemented by a commensurate effort to develop simple variational approaches . the history of the theory of strongly correlated electrons shows that progress has often been made when accurate numerical techniques are combined with such variational calculations . therefore , our theory , which can be straightforwardly generalised to other potential arrangements , lattices , fillings , etc . , is complementary to the previous numerical work . in many different na ordering patterns are seen at different values of @xmath8,@xcite and each of these correspond to a different @xmath19.@xcite in principle , each of these different @xmath19 correspond to a different hamiltonian . therefore , for simplicity and definiteness , we specialise to the hamiltonian relevant to @xmath9 . this model has two sublattices with different site energies , @xmath20 for a - sites and @xmath21 for b - sites,@xcite and with the sublattices arranged in stripes as shown in fig . [ fig : unit - cells]b . thus the hamiltonian is @xmath22 where @xmath23 annihilates ( creates ) an electron with spin @xmath17 in an orbital centred on site @xmath16 belonging to sublattice @xmath24 and @xmath25 indicates that the sum is over nearest neighbours on the appropriate sublattices only . hamiltonian ( [ ham ] ) is a natural instance of hamiltonian ( [ ham1 ] ) for initial study on both theoretical and experimental grounds . experimentally , the behaviour of , particularly , is very different from that of with @xmath8 either a little larger or smaller than @xmath26 . further , many of the phenomena observed at @xmath9 seem to have a natural explanation in terms of the ionic hubbard model.@xcite we have previously studied the quarter - filled ionic hubbard model with a stripe potential by exactly diagonalising small clusters.@xcite we found a complicated interplay between the charge and spin degrees of freedom and between insulating and metallic states . we also found that these calculations provide a possible framework for understanding a wide variety of experiments on , , and . however , the most interesting regime ( i.e. , @xmath27 , see section [ sect : natheory ] ) , in terms of its relevance to experiments , is also the most challenging to investigate theoretically . this provides additional motivation to investigate the simpler mean - field theory presented below . comparison between our mean - field theory and these exact diagonalisation calculations will be made , where possible , below . the rest of this paper is organised as follows . in the remainder of this introduction we briefly review the most pertinent experiments on and previous theories aimed at explaining these measurements . in section [ sect : formal ] we give the formal details of our theory and derive a set of self - consistency equations for the ground state . in section [ sect : numeric ] we report the results of numerical solutions of these equations and compare our results with experiments on and previous theoretical studies of the triangular lattice ionic hubbard model . in section [ sect : conc ] we draw our conclusions . in appendix [ sect : non - int ] we describe the band structure of the model ( [ ham ] ) for non - interacting electrons . there has been far less experimental work on or than . therefore , in this section , we focus mainly on experiments on . the brief review below brings out two particular puzzles that theory needs to explain about the ground state . the first is how it is some properties are consistent with a metallic ground state and that others are more consistent with an insulating ground state . the second puzzles concerns how it is that the ground state has a large magnetic moment but a small amount of charge ordering . measurements of the relaxation rates for @xmath28co nmr found two distinct co sites , consistent with a charge ordered state.@xcite however , the authors noted that the degree of charge disproportionation is rather small . more recent @xmath28co and @xmath29na nmr measurements find no signature of differences in the charge state of the cobalt ions at the two distinct sites,@xcite suggesting that all the co atoms are in the charge state co@xmath30 , where @xmath31 gives an upper bound on the extent of charge ordering.@xcite this is in contrast , to the case of @xmath32 or 0.75 for which nmr clearly detecting a charge disproportionation.@xcite high resolution neutron crystallography detects small differences in co - o bond lengths , and an analysis based on bond valence sums , is consistent with a charge order of @xmath33.@xcite very recent nmr measurements were able to detect a very small charge ordering along the co(1 ) chains , below 51 k,@xcite but the authors do not discuss the magnitude of the difference in charge between two sublattices . as the temperature decreases the intralayer resistivity increases monotonically . no feature is seen at the magnetic ordering temperature ( 88 k , see below ) . above 51 k , it is weakly temperature dependent with values of a few m@xmath34 cm,@xcite characteristic of a `` bad '' or incoherent metal which does not have well - defined quasi - particle excitations.@xcite below 51 k , the resistivity increases significantly , consistent with an activated form with energy gap of about 10 mev.@xcite although , it is usually stated that the transition at 51 k is a `` metal - insulator '' transition , we stress that it is really above 51 k is a bad metal and below 51 k the experimental evidence is not all consistent with the claim that is an insulator ( see section [ sect : metal ] ) . applying hydrostatic pressure causes the resistivity to decrease and the temperature where the resistivity becomes activated to increase . above about 13 gpa the resistivity has a metallic temperature dependence.@xcite in contrast , for @xmath8=0.75 is metallic at ambient pressure but becomes insulating above about 23 gpa . resistivity measurements found that the charge gap apparent from the resistivity was suppressed by magnetic fields parallel to the layers , larger than about 35 t , with hysteresis between 15 and 40 t , at low temperatures.@xcite a field perpendicular to the layers does not suppress the `` insulating '' state.@xcite the thermopower and hall coefficient have small and weakly temperature dependent positive values above 100 k.@xcite however , they change sign near 88 k , obtain large negative values below 50 k , and then decrease towards zero at low temperatures . the latter is distinctly different from the behaviour of conventional semiconductors and insulators , for which the thermopower and hall constant both diverge as the carrier density vanishes with decreasing temperature . quasi - particle features are only observed in angle resolved photoemission spectroscopy ( arpes ) below about 150 k and reveal a fermi surface consistent with a hole - like band for a tight - binding model on the triangular lattice with an effective hopping integral of @xmath35 mev,@xcite about six times smaller than that predicted by lda calculations . a gap begins to open up over the fermi surface below about 60 k , and has a magnitude of about 6 - 11 mev at 10 k.@xcite measurements of the frequency dependence of the conductivity show no evidence of a drude peak , consistent with the bad metal behaviour , seen in the static transport quantities.@xcite below about 100 k there is a loss of spectral weight at frequencies below about 100 @xmath36 , consistent with the opening of a charge gap . this leads to a peak in @xmath37 at @xmath38 @xmath36.@xcite in comparison for na@xmath39coo@xmath40 , with @xmath8 away from 0.5 , a drude peak is present at low temperatures and the total spectral weight of the optical conductivity scales with @xmath41.@xcite shubnikov - de haas oscillations are observed in the field range of 15 - 30 t.@xcite a fast fourier transform of the oscillatory part of the conductivity has peaks at frequencies of 150 t and 40 t. these frequencies correspond to pockets with cross - sectional areas of 0.25 % and 0.06 % of the area of the undistorted hexagonal brillouin zone ( cf . figure 1d ) . the effective mass associated with these orbits are ( in units of the free electron mass ) @xmath42 and @xmath43 , respectively . these measurements are extremely surprising given the range of other evidence suggesting that has an insulating ground state . muon spin rotation ( @xmath44sr ) experiments first saw evidence for magnetic order below about 86 k , and slight effects at 50 k and 30k.@xcite below 88 k , there is a splitting of nmr lines , consistent with the development of commensurate antiferromagnetic order.@xcite the change in the resistivity from a bad metal to an activated behaviour at 51 k has little effect on the magnetic state . elastic neutron scattering also detects long - range antiferromagnetic order below 88 k , with a magnetic moment of @xmath45 per magnetic cobalt ion.@xcite the authors interpret this order in terms of alternating rows of magnetic co@xmath46 and non - magnetic co@xmath47 ions . ( i.e. , complete charge order ) . however , we stress that the observation of such magnetic order does not require charge ordering to be present . simple classical arguments suggest the magnetic moment should be less than @xmath48 where @xmath49 is the average number of electrons on the @xmath50 sublattice . hence , the charge disproportionation observed in the crystallography experiments discussed above , would imply a moment of about @xmath51 , about one quarter of the observed value . both the bulk magnetic susceptibility and the knight shift are weakly temperature dependent , with a peak around 300 k , and a magnitude of about 5 @xmath52 emu / mol.@xcite this suggests an antiferromagnetic exchange between magnetic ions of order a few hundred kelvin . at other values of @xmath8 in , the ordering of sodium ions has been found to be important for the existence of various ordered phases.@xcite no insulating state is seen in the corresponding misfit cobaltates,@xcite which supports the claim that na - ordering is necessary for the insulating state . furthermore , cooling a material at different rates found that the presence of sodium ordering can drive an additional magnetic phase transition at @xmath53 and 0.85.@xcite choy _ et al_. @xcite considered an extended hubbard model that included the coulomb interaction between electrons on neighbouring sites , @xmath54 , but neglected the na - ordering and the ` ionic ' term in eq . ( [ ham ] ) . they argued that @xmath54 stabilises a charge ordered state and considered an effective low - energy hamiltonian for this charge ordered state . by fine tuning the parameters in their effective hamiltonian choy _ et al_. were able to reproduce the observed temperature dependence of the resistivity and the hall coefficient . lee _ et al_. @xcite have studied via lda+u calculations that allow for the effects of na - ordering . they find a first order metal - charge ordered insulator transition as @xmath13 is increased . the charge disproportionation and the opening of the gap both occur at a single phase transition in this weak coupling theory . we have reported exact diagonalisation calculations for hamiltonian ( [ ham ] ) of finite lattices.@xcite these studies suggested that , for parameters relevant to , the system is a covalent insulator , with little charge disproportionation and a small gap @xmath55 , rather than a charge ordered insulator , with strong charge disproportionation and a gap @xmath56 . this prediction is consistent with the experimental measurements of the charge disproportionation.@xcite further , these calculations predict a gap of the same order of magnitude as in seen in the arpes@xcite and the resistivity,@xcite predict the large moment seen in neutron scattering,@xcite and reproduce the main features seen in the optical conductivity.@xcite zhou and wang@xcite also studied a model that incorporates the effects of na - ordering within the gutzwiller approximation and found it could explain many of the experimental observations . there has been significantly less work on and . lee and pickett@xcite have reported lda calculations for and compared these with equivalent calculations for . they found that the @xmath57 band is rather narrower in than and that the fermi surface is more complicated in as there are several small pockets along the @xmath58-@xmath59 line . they speculated that these pockets , some of which are quite well nested near the @xmath58 point , may lead to enhanced magnetic tendencies in . clearly an important question is : what parameters in hamiltonian ( [ ham ] ) correspond to the various possible choices of @xmath7 in ? various atomistic calculations that address this question have been presented for @xmath7=na , but for other @xmath7 there are not yet suitable estimates . calculations@xcite on small clusters of give @xmath60 ev , @xmath61 ev , and @xmath62 ev . for bulk the lda yields @xmath63 ev @xcite and @xmath64 ev @xcite , and electrostatic ewald calculations give @xcite @xmath65 ev . furthermore , coo@xmath40 , which is described by hamiltonian ( [ ham ] ) at half filling with @xmath66 , is observed to be a strongly correlated metal rather than a mott insulator.@xcite this suggests that @xmath67 , where @xmath68 is the critical value for formation of a mott insulator on the triangular lattice.@xcite hence , realistic parameters for may be in the range @xmath69 , and @xmath70 . the negative sign of @xmath0 is natural if the hopping between co sites is dominated by the contribution from hopping via an intermediate o site . to leading order this gives @xmath71 , where @xmath72 is the direct hopping between a co atom and a neighbouring o atom , @xmath73 is the energy of an electron in a @xmath74 orbital centred on a co atom , and @xmath75 is the energy of an electron in a @xmath76 orbital centred on an o atom ( note that one expects that @xmath77 ) .

we study the paramagnetic phases of this theory at three quarters filling , where it is a model of , , and . we compare our results with exact diagonalisation calculations and experiments on , and discuss the relevance of our results to and . we propose a resolution of seemingly contradictory experimental results on . many experiments suggest that there is a charge gap , yet quantum oscillations are observed suggesting the existence of quasiparticle states at arbitrarily low excitation energies .

we introduce a strongly correlated mean - field theory of the ionic hubbard model on the triangular lattice with alternating stripes of site energy using barnes - coleman slave bosons . we study the paramagnetic phases of this theory at three quarters filling , where it is a model of , , and . this theory has two bands of fermionic quasi - particles : one of which is filled or nearly filled and hence weakly correlated ; the other is half - filled or nearly half - filled and hence strongly correlated . further results depend strongly on the sign of the hopping integral , . the light band is always filled for , but only becomes filled for for , where is the difference in the site energies of the two sublattices . a metal charge transfer insulator transition occurs at for and for . in the charge transfer insulator complete charge disproportionation occurs : one sublattice is filled and the other in half filled . we compare our results with exact diagonalisation calculations and experiments on , and discuss the relevance of our results to and . we propose a resolution of seemingly contradictory experimental results on . many experiments suggest that there is a charge gap , yet quantum oscillations are observed suggesting the existence of quasiparticle states at arbitrarily low excitation energies . we argue that the heavy band is gapped while the light band , which contains less than 1 charge carrier per 100 unit cells , remains ungapped .

0904.0505

i

we have presented a mean - field slave boson theory of the ionic hubbard model on the triangular lattice with alternating stripes of site energy . this model has two bands : one of which is weakly correlated and nearly filled or filled , the other is nearly half - filled or half - filled and hence strongly correlated . the results depend strongly on the sign of @xmath0 . the light band is always filled for @xmath1 , but only becomes filled at @xmath193 for @xmath3 . a metal - charge transfer insulator transition occurs at larger ( 5.0 for @xmath1 and 8.0 for @xmath3 ) , when complete charge disproportionation occurs and one sublattice is filled and the other in half filled . we have also proposed a speculative picture of . in particular , we have argued that the observed quantum oscillations arise from quasiparticles in the bonding band , but these are not seen in the zero field resistivity and several other experiments because the low density of charge carriers in the bonding band mean that the metallic bonding band is not able to ` short circuit ' the incoherent / insulating antibonding band . calculations beyond the mean field slave boson calculations , which we have presented above , will be required to test this picture . another important avenue for future work will be to allow for magnetic ordering in the theory as this may improve the degree of agreement with experiments and allow one to compare with other experiments such as nmr@xcite and neutron scattering.@xcite

we introduce a strongly correlated mean - field theory of the ionic hubbard model on the triangular lattice with alternating stripes of site energy using barnes - coleman slave bosons . this theory has two bands of fermionic quasi - particles : one of which is filled or nearly filled and hence weakly correlated ; the other is half - filled or nearly half - filled and hence strongly correlated . further results depend strongly on the sign of the hopping integral , . charge transfer insulator transition occurs at for and for . in the charge transfer insulator complete charge disproportionation occurs : one sublattice is filled and the other in half filled .

we introduce a strongly correlated mean - field theory of the ionic hubbard model on the triangular lattice with alternating stripes of site energy using barnes - coleman slave bosons . we study the paramagnetic phases of this theory at three quarters filling , where it is a model of , , and . this theory has two bands of fermionic quasi - particles : one of which is filled or nearly filled and hence weakly correlated ; the other is half - filled or nearly half - filled and hence strongly correlated . further results depend strongly on the sign of the hopping integral , . the light band is always filled for , but only becomes filled for for , where is the difference in the site energies of the two sublattices . a metal charge transfer insulator transition occurs at for and for . in the charge transfer insulator complete charge disproportionation occurs : one sublattice is filled and the other in half filled . we compare our results with exact diagonalisation calculations and experiments on , and discuss the relevance of our results to and . we propose a resolution of seemingly contradictory experimental results on . many experiments suggest that there is a charge gap , yet quantum oscillations are observed suggesting the existence of quasiparticle states at arbitrarily low excitation energies . we argue that the heavy band is gapped while the light band , which contains less than 1 charge carrier per 100 unit cells , remains ungapped .

1105.3388

i

in the today s world full of crypto algorithms , one may wonder what makes a block cipher attractive . in the authors opinion , the answer to the question is one word : elegance . if something looks nice , then there is a big chance that it is also good . an elegant specification makes it easier to memorize . memorability makes it easier to realize and to analyze , that allows for fruitful cryptanalytic results , leading to deeper understanding which , in turn , makes greater confidence in the algorithm . the elegance comprises the following features : * few algebraic operations . using of many operations results in hardly - tractable and possibly undesirable interactions between them . * simple and regular key schedule . a complex key schedule , which effectively adds another , unrelated , function to the cipher , results in hardly - tractable and possibly undesirable interactions between the functions . idea , a secure block cipher designed by xuejia lai and james l. massey @xcite is an example of elegance . besides being elegant with an efficient choice and arrangement of algebraic operations , it is elegant for some more features : * the use of incompatible group operations , where _ incompatible _ means there are no simple relations ( such as distributivity ) between them . the incompatibility eliminates any exploitable algebraic property thus makes it infeasible to solve the cipher algebraically . * the use of modular multiplication . multiplication produces huge mathematical complexity while consuming few clock cycles on modern processors . it thus greatly contributes to security and efficiency of the cipher . however , idea uses multiplication modulo the fermat prime @xmath8 which does not exist for @xmath9 or @xmath7 , making it not extendable to machine word lengths nowadays . furthermore , its key schedule is rather irregular due to the rotation of the primary key . skipjack , a secure block cipher designed by the u.s . national security agency @xcite , is another example of elegant design . besides being elegant with an efficient , simple and regular key schedule , it is elegant for one more feature : the use of two ciphers an outer cipher , or _ wrapper _ , consisting of first and last rounds , and an inner cipher , or _ core _ , consisting of middle rounds . the terms `` core '' and `` wrapper '' were introduced in the design rationale of a structural analogous of skipjack : the block cipher mars @xcite . mars s designers justify this two - layer structure by writing that it breaks any repetitious property , it makes any iterative characteristic impossible , and it disallows any propagation of eventual vulnerabilities in either layer to the other one , thus making attacks more difficult . the wrapper is primarily aimed at fast diffusion and the core primarily at strong confusion . as claude e. shannon termed in his pioneer work @xcite , _ diffusion _ here refers to the process of letting each input bit affect many output bits ( or , equivalently , each output bit be affected by many input bits ) , and _ confusion _ here refers to the process of letting that affection very involved , possibly by doing it multiple times in very different ways . if a cipher is seen as a polynomial map in the plaintext and the key to the ciphertext , then the methods of diffusion and confusion can be described as the effort of making the polynomials as complete as possible , i.e. such that they contain virtually all terms at all degrees . approach is very evident in the structure of skipjack ( see figure [ fig : the - full - cipher-2 ] ) . skipjack ( as opposed to mars ) was moreover sought elegant as the wrapper there is , in essence , the inverse function of the core . however , skipjack uses an s - box that renders it rather slow , hard to program in a secure and efficient manner , and not extendable to large machine word lengths , as such . this article describes an attempt to combine the elegant idea of using incompatible and complex machine - oriented algebraic operations in idea with the elegant structure of skipjack into a scalable and tweakable block cipher called nsabc nice - structured algebraic block cipher . nsabc is scalable . it is defined for every even word length _ w_. it encrypts a 4__w__-bit text block under a 5__w__-bit key , thus allows scaling up with 8-bit increment in block length and 10-bit increment in key length . nsabc is tweakable . it can use an easily changeable 4__w__-bit parameter , called _ tweak _ @xcite , to make a unique version of the cipher for every block encrypted under the same key . included in the specification is a formula for changing the tweak . nsabc makes use of entirely the overall structure of skipjack , including the key schedule , and only replaces the internal 4-round feistel structure of skipjack with another structure . the new structure consists of two rounds of the binary operation @xmath10 , that encrypts a text word _ x _ using a key word _ z _ and a key - dependent word _ e_. the operation @xmath11 is derived from an algebraic group over _ w_-bit words taking @xmath12 as the unit element , so it is also capable of decrypting by means of the inverse element of _ z _ in the group . the two rounds are separated by an exclusive - or ( xor ) operation that modifies the current text word by a tweak word . nsabc is put in public domain . as it bases on skipjack , eventual users should be aware of patent(s ) that may be possibly held by the u.s . government and take steps to make sure the use is free of legal issues . we ( the designers of nsabc ) are not aware of any patent related to other parts of the design . the rest of the article is organized as follows . section 2 defines operations and notations . section 3 specifies the cipher . section 5 gives numerical examples . section 4 suggests some implementation techniques . section 6 concludes the article . source code of software implementations are given in the appendices .

the skipjack s internal 4-round feistel structure is replaced with a-bit , 2-round cascade of a binary operation that permutes a text word under control of a key word . the operation , similarly to the multiplication in idea , bases on an algebraic group over-bit words , so it is also capable of decrypting by means of the inverse element of in the group . the cipher utilizes a secret-bit tweak an easily changeable parameter with unique value for each block encrypted under the same key that is derived from the block index and an additional-bit key .

we introduce nsabc/ nice - structured algebraic block cipher using-bit word arithmetic , a-bit analogous of skipjack with-bit key . the skipjack s internal 4-round feistel structure is replaced with a-bit , 2-round cascade of a binary operation that permutes a text word under control of a key word . the operation , similarly to the multiplication in idea , bases on an algebraic group over-bit words , so it is also capable of decrypting by means of the inverse element of in the group . the cipher utilizes a secret-bit tweak an easily changeable parameter with unique value for each block encrypted under the same key that is derived from the block index and an additional-bit key . a software implementation for takes circa 9 clock cycles per byte on x86 - 64 processors .

1112.1469

i

quantum theory is generally formulated relative to a given causal structure . this is the case both in quantum field theory , where the spacetime metric is given from the beginning , and in the operational framework of quantum information , where protocols and computations consist in sequences of operations performed at different times . relative to the given causal structure , quantum theory has to satisfy the _ causality principle _ @xcite , stating that the probability of a measurement outcome at a given time be independent of the choice of operations performed at later times . the causality principle forbids any form of signalling from the future to the past : a sender in the future can not deterministically transfer the state of his system to a receiver in the past . however , it is easy to imagine situations where the state of a system is transferred from the future to the past _ with some probability _ , without leading to signalling . this is what happens , for example , if we eliminate the communication of classical data in the original quantum teleportation protocol @xcite : the receiver in the past ( say , alice ) can prepare a maximally entangled state and the sender in the future ( say , bob ) can perform a bell measurement on the state to be teleported together with half of the entangled state , as in fig . [ fig : originaltele ] . ( color online ) probablilistic teleportation from the future to the past . today alice prepares a maximally entangled two - qubit state @xmath3 of the ancilla and the output system , while tomorrow bob performs a measurement on the ancilla and his input qubit . the measurement has four possible outcomes , for one of which ( here denoted by @xmath4 ) successful teleportation will occur . with probability @xmath5 alice obtains bob s input state today . however , she will not know whether teleportation has been successful until bob performs his measurement and communicates the outcome . ] in this way , upon observing the right measurement outcome , bob will know that the state has been teleported successfully to the past , and alice will not need to perform any correction operation on the output . of course , to know that teleportation has succeeded , bob needs to wait until he sees the outcome of the bell measurement . however , the important fact here is that , even before the measurement is performed , one half of the entangled state is already ready to be used by alice in a quantum circuit : alice can perform any desired computation on her system , and in the end , if teleportation is successful , bob will know that alice s computation has been performed on the input state he provided in the future . conditionally to the occurrence of the right outcome , everything behaves as though the input state has travelled from the future to the past through an ideal quantum channel . note that this fact is not in contradiction with causality : the probability of teleportation is small enough that no signal can be sent from bob to alice . we will refer to the above use of probabilistic teleportation as a _ probabilistic simulation of the identity channel from the future to the past_. the idea of probabilistic teleportation as a simulated time - travel was originally proposed by bennett and schumacher in an unpublished work @xcite , and , more recently , by svetlichny @xcite . in different terms , this idea also appeared implicitly in the context of the graphical language of categorical quantum mechanics @xcite , where the reinterpretation of probabilistic teleportation as information flow from the future to the past follows from a stretching of wires in the basic teleportation diagram . interestingly , similar ideas also appeared in the work of horowitz and maldacena @xcite in the context of black hole evaporation , as an attempt to reconcile the unitarity of the black hole @xmath6-matrix with hawking s semiclassical arguments ( see also the discussion by gottesmann and preskill @xcite ) . recently , the role of probabilistic teleportation in simulating closed timelike curves has been further explored by lloyd _ et al _ in refs . @xcite . in particular , ref . @xcite reports an experiment that uses probabilistic teleportation to simulate a quantum computation within a closed timelike curve . de silva , galvao and kashefi @xcite showed that some patterns in measurement - based quantum computation can be interpreted as deterministic simulations of closed timelike curves . all the works mentioned so far focused on the use of teleportation for the probabilistic simulation of an ideal quantum channel from the future to the past . however , there are many interesting scenarios where one needs to consider the simulation of more general quantum channels . for example , suppose that we have @xmath0 identical copies of a the same state and that we want to teleport just one copy to the past . does the probability of success increase with the number if input copies ? and , if it does , what is the the asymptotic value of the success probability in the limit @xmath7 ? to answer these questions we have to address the probabilistic simulation of channels that trace all systems but one . in this paper we will address the general problem of the probabilistic simulation of a given channel from the future to the past , showing how the causality principle determines the maximum probability of success . to find the maximum probability we will optimize over all generalized teleportation schemes where a bipartite state is prepared and the input of the channel is jointly measured along with half of the bipartite state , so that , for a particular outcome , the desired channel is simulated , as in fig . [ genchan ] . ( color online ) probabilistic simulation of a given quantum channel from the future to the past via a generalized teleportation scheme . the output system and an ancilla are first prepared in a bipartite state @xmath3 . when the input becomes available , the input state and the ancilla are measured jointly . for a particular measurement outcome @xmath4 the simulation will be successful : the effective transformation from input to output will be proportional to the desired quantum channel , with proportionality constant @xmath8 equal to the probability of successful simulation . ] the spirit of this work is similar to the spirit of the early works on the optimal cloning of non - orthogonal quantum states @xcite : in that case , one knew from the no - cloning theorem @xcite that it is impossible to produce perfect copies of the input state and the goal was to find the optimal physical process that approximates the impossible cloning transformation . in our case , we know from causality that it is impossible to have a channel that deterministically transfers information from the future to the past and our goal is to find the optimal process that achieves the desired channel with maximum probability of success . in the same way in which the study of optimal cloning shed light on the process of copying information in the quantum world , we expect that the study of optimal simulations of channels to the past will shed light the interplay between causal structure and quantum information flow . the main message of this paper is that the maximum probability of simulating a quantum channel from the future to the past is a decreasing function of the amount of information that the channel can transmit . this general feature will be illustrated in several examples . first , we will consider ideal classical channels ( those that perfectly transmit the states of an orthonormal basis ) and , second , ideal quantum channels ( those that perfectly transmit all states of a given quantum system ) . in the first case we find the maximum probability @xmath9 where @xmath10 is the dimension of the hilbert space , while in the second case we find @xmath11 which is exactly the probability of the outcome that does not require correction operations in the original teleportation protocol @xcite . we will then focus on the probabilistic simulation of measure - and - prepare channels , which are a class of channels that transmit only classical information . in this case , we will find that the maximum probability of success is at least equal to the probability @xmath12 for a classical channel with the same output hilbert space . the exact value of the probability of success will be computed in two relevant cases of measure - and - prepare channels : the channel associated to the optimal estimation of a pure state , and the universal not channel @xcite . finally , we will analyze in detail the case of trace channels , sending @xmath0 copies of a given pure state to @xmath1 copies of the same state , and the case of universal cloning channels @xcite , sending @xmath0 copies of a pure state to @xmath13 optimal approximate copies . in both cases we find that the maximum probability of success is given by @xmath14 where @xmath10 is the dimension of the one - particle hilbert space and the superscript in @xmath15 reminds that we are restricting ourselves to the symmetric subspaces , in which the @xmath0 input copies and the @xmath16 output copies of the given pure state live . in the particular case of @xmath17 eq . ( [ gennmbound ] ) yields the value @xmath18 which increases with the number of input copies , starting from @xmath19 and reaching the classical value @xmath20 in the asymptotic limit @xmath7 . this result has to be contrasted with the classical scenario , where having more input copies of a pure state can not lead to any improvement : since classical pure states can be perfectly cloned , there is no difference in having more input copies . the convergence of the probability of success to the classical value @xmath12 will be explained as a consequence of the convergence of the trace channel to a measure - and - prepare channel @xcite . concerning the probability @xmath21 in eq . ( [ gennmbound ] ) , it is also worth noting that it is symmetric in @xmath0 and @xmath16 : in other words , the probability of successful simulation for a trace channel from @xmath0 to @xmath22 copies is equal to the probability of successful simulation for a universal cloning channel from @xmath16 to @xmath23 copies . we will explain the symmetry of the probabilities as a consequence of a _ time - reversal duality _ between trace and universal cloning . as we anticipated , the message emerging from our results is that the maximum probability for a given channel is a decreasing function of the amount of information that the channel can transmit : the smallest value @xmath24 corresponds to the identity channel , while measure - and - prepare channels have probability @xmath25 , and the erasure channels @xmath26 ~ \rho_0 $ ] have probability @xmath27 . we will also make the connection more quantitative , providing a set of _ statistical information bounds _ , stating that the probability of success in the simulation of a channel is upper bounded by the inverse of the amount of information that the channel can transmit . the amount of information will be quantified here as the maximum payoff that two parties can achieve in a communication game . the structure of the paper is the following : in section [ sec : general ] we present the general method and , in particular , the _ causality bound _ , a necessary and sufficient condition for the existence of a probabilistic simulation with probability @xmath8 . then , we will analyze the probabilistic simulation of several channels : sections [ sec : ideal ] , [ sec : measprep ] , and [ sec : opttele ] will focus on ideal classical and quantum channels , on measure - and - prepare channels , and on partial trace channels from @xmath0 to @xmath28 copies , respectively . section [ sec : opttele ] will also discuss the case of universal cloning channels from @xmath0 to @xmath29 copies , exploiting the existence of a time - reversal duality between partial trace channels and cloning channels . finally , in section [ sec : summary ] we will derive the statistical information bound and use it to explain the asymptotic behaviour of the maximum probability for partial trace and cloning channels . the conclusions of the paper are drawn in section [ sec : conclusion ] .

we introduce the study of quantum protocols that probabilistically simulate quantum channels from a sender in the future to a receiver in the past . we illustrate this dependence in several examples , including ideal classical and quantum channels , measure - and - prepare channels , partial trace channels , and universal cloning channels . for the simulation of partial trace channels , similar results are found for universal cloning channels from copies to approximate copies , exploiting a time - reversal duality between universal cloning and partial trace .

we introduce the study of quantum protocols that probabilistically simulate quantum channels from a sender in the future to a receiver in the past . the maximum probability of simulation is determined by causality and depends on the amount and type ( classical or quantum ) of information that the channel can transmit . we illustrate this dependence in several examples , including ideal classical and quantum channels , measure - and - prepare channels , partial trace channels , and universal cloning channels . for the simulation of partial trace channels , we consider generalized teleportation protocols that take input copies of a pure state in the future and produce output copies of the same state in the past . in this case , we show that the maximum probability of successful teleportation increases with the number of input copies , a feature that was impossible in classical physics . in the limit of asymptotically large , the probability converges to the probability of simulation for an ideal classical channel . similar results are found for universal cloning channels from copies to approximate copies , exploiting a time - reversal duality between universal cloning and partial trace .

1406.0767

i

consider the following situation . alice writes a message to bob consisting of the numbers of several bank accounts to which bob has to send some money . she writes in a hurry ( she just got to know that the transfers are urgent if they do not want to pay delay punishment , but currently she has little time ) . therefore her characters are not very well legible , so bob may misread some numbers . however , there are some rules for the possible mistakes , e.g. , a @xmath0 may be thought to be a @xmath1 but never a @xmath2 . this relation between the possible digits need not be symmetric : it is possible that a @xmath3 is sometimes read as a @xmath2 but a @xmath2 may not be decoded as a @xmath3 . these rules of possible confusions are known both by alice and by bob . as alice is aware of the possibility that bob misread her message , later in the day she sends another message to bob , the goal of which is to make bob certain whether he read ( decoded ) the first message correctly or not . if he did he can transfer the money with complete confidence that he sends it to the right accounts . if he did not he will know that he does not know the account numbers correctly and so he better wait and pay the punishment than transfer the money to the wrong place . the second message will be received by bob correctly for certain , but it uses an expensive device , e.g. , alice sends it as an sms from another country after she has arrived there . ( now we understand why she was in a hurry : she had to arrive to the airport in time . ) for some reason , every character sent from this foreign country costs a significant amount of money for her . so she wants to send the shortest possible message that makes it sure ( here we insist on zero - error ) that bob will know whether his decoding of the original handwritten message was error - free or not . the problem is to determine the best rate of communication over the second channel as the length of the original message received tends to infinity . in section [ sec : dil ] we describe the abstract communication model for this scenario and show that the best achievable rate is a parameter of an appropriate directed graph . we will see that this parameter of a directed graph is a generalization of the parameter ( of an undirected graph ) called witsenhausen rate . ( this means that we also obtain a new interpretation of witsenhausen rate . ) in section [ sec : bounds ] we investigate the relationship with other graph parameters . these include sperner capacity and the dichromatic number . the former is a generalization of shannon s graph capacity @xcite to directed graphs . though originally defined to give a general framework for some problems in extremal set theory ( see @xcite ) , sperner capacity also has its own information theoretic relevance , see @xcite . the dichromatic number is a generalization of the chromatic number to directed graphs introduced in @xcite . using the above mentioned relations we determine our new parameter for some specific directed graphs . in section [ sec : comp ] we consider a compound channel type version of the problem parallel to @xcite . in section [ sec : extr ] some connections to extremal set theory are pointed out . in section [ sec : ambit ] we will consider the setup where the requirement is more ambitious and we want that alice s second ( the error - free but expensive ) message make bob able to decode the original message with zero - error . ( that is , he will know the message itself not only the correctness or incorrectness of his original decoding of alice s handwriting . ) we will see that this setting leads to the witsenhausen rate of an undirected graph related to the problem . this gives a further new interpretation of witsenhausen rate . all logarithms are meant to be of base @xmath4 .

this scenario leads to the definition of a digraph parameter that generalizes witsenhausen s zero - error rate for directed graphs . we investigate this new parameter for some specific directed graphs and explore its relations to other digraph parameters like sperner capacity and dichromatic number . keywords : zero - error , graph products , sperner capacity , dichromatic number , witsenhausen rate

we investigate a communication setup where a source output is sent through a free noisy channel first and an additional codeword is sent through a noiseless but expensive channel later . with the help of the second message the decoder should be able to decide with zero - error whether its decoding of the first message was error - free . this scenario leads to the definition of a digraph parameter that generalizes witsenhausen s zero - error rate for directed graphs . we investigate this new parameter for some specific directed graphs and explore its relations to other digraph parameters like sperner capacity and dichromatic number . when the original problem is modified to require zero - error decoding of the whole message then we arrive back to the witsenhausen rate of an appropriately defined undirected graph . keywords : zero - error , graph products , sperner capacity , dichromatic number , witsenhausen rate

1401.4702

i

dispersive coupling of a quantum system to a mechanical or electromagnetic cavity mode has been attracting much attention recently . the coupling provides a means for quantum nondemolition measurement of the occupation number of the mode or of the populations in the energy levels of the system @xcite . the underlying read - out mechanism is the shift of the mode frequency or the system transition frequency , which depends on the state populations of the system or the mode , respectively . in the dispersive regime , a measurement erases information about the quantum phase , but does not cause transitions between energy levels . however , such transitions can happen due to coupling to a thermal reservoir , and also if the mode and/or the system are modulated by external fields . it is well understood that , through dispersive coupling , thermal interstate transitions cause decoherence @xcite . much less is known about the effects of periodic modulation and the interplay of the modulation and dephasing due to the coupling to a thermal reservoir . in this paper we address these problems . we consider a mode @xmath0 ( a harmonic oscillator ) coupled to a dynamical system @xmath1 . the mode and the system are also coupled to separate thermal reservoirs and can be modulated by periodic fields . the couplings and the modulation are assumed weak in the sense that the coupling energy is small compared to the interlevel energy spacing . in other words , the widths of the energy levels and the rabi energies are small compared to the level spacing . the modulation is assumed to be nearly resonant and will be described in the rotating wave approximation ( rwa ) . in distinction from the celebrated jaynes - cummings model @xcite , here the level spacings of the mode and the system are significantly different . for a dispersive @xmath2 coupling the major effect is not energy exchange , but rather it is the change of the level spacing depending on the state population , which occurs already in the first order in the coupling constant . semiclassically , this situation can give rise to multistability in the response to a modulating field as follows . for given modulating field parameters , the combined system may self - consistently support either large amplitude forced vibrations of mode @xmath3 , with the effective mode frequency tuned into good resonance with the driving field via the dispersive coupling , or small amplitude vibrations with an effective mode frequency far from resonance with the driving field . in each case , the vibration amplitude of mode @xmath3 sets the transition frequencies of the system @xmath1 . if system @xmath1 is modulated itself , this determines its quasi - steady - state level occupations . through the dispersive coupling , these level occupations tune the oscillator frequency into or out of resonance with the driving field , leading to the self - consistent mean - field multi - stability , see fig . [ fig : hysteresis ] . of the mode ( the squared mode amplitude is @xmath4 , where @xmath5 and @xmath6 are the mode mass and frequency , respectively ) . the abscissa shows the reduced squared modulation amplitude @xmath7 . both the mode and the system are resonantly modulated . in the rotating wave approximation , the model is described by eqs . ( [ eq : h_rwa1 ] ) , ( [ eq : liouville_osc ] ) and ( [ eq : bloch ] ) . the ratio of the relaxation rate of the two - level system @xmath8 to the relaxation rate of the mode @xmath9 is 30 ; the reduced amplitude of the field modulating the two - level system is @xmath10 . the reduced detunings of the modulating fields from the transitions frequencies of the mode and the system are , respectively , @xmath11 and @xmath12 . the reduced strength of the dispersive coupling is @xmath13 . the inset refers to @xmath14 , in which case the system does not show tristability . the unstable states are shown by dashed lines . the black vertical dashed line shows the modulation field used in fig . [ fig : graphic_solution ] below . ] the mean - field theory describes the semiclassical multistability of the system , but does not account for the role of _ fluctuations_. classical and quantum fluctuations unavoidably come along with relaxation as a consequence of coupling to a bath . in multistable systems , fluctuations cause interstate switching , _ even at zero temperature_. interestingly , where the dispersive coupling is weak , there is obviously no multistability ; however , where it is strong there is also no multistability , because the switching rate becomes comparable to the relaxation rate , and then the very notion of multistability becomes meaningless . in what follows we find the appropriate range of the coupling strength . we provide a general formulation of a mean - field theory and a theory of the switching rates in the important case where the typical relaxation time @xmath15 of the system @xmath1 is much smaller than the relaxation time @xmath16 of the mode . formally , the dispersive coupling hamiltonian @xmath17 is a function of a mode operator @xmath18 and a system operator @xmath19 , which commute with the isolated mode and system hamiltonians , respectively , in the absence of modulation . for example , @xmath18 can be the occupation number of the mode , @xmath20 , where @xmath21 and @xmath22 are the lowering and raising operators , while , if the dynamical system is a spin in a static magnetic field @xmath23 , @xmath24 can be the spin operator @xmath25 . this form of coupling assures that @xmath26 is independent of time in the interaction representation . for illustration , we consider a mode coupled to a two level system ( tls ) , each modulated by its own nearly - resonant field ( with @xmath27 ) : @xmath28 here @xmath29 , where @xmath30 are pauli operators which act on the tls . for nearly - resonant modulations , the detunings @xmath31 and @xmath32 of the modulation frequencies from the transition frequencies @xmath6 and @xmath33 are small compared to the transition frequencies themselves , and to their difference : @xmath34 . the condition on @xmath35 in particular justifies the approximation where only dispersive coupling is taken into consideration . the simplest form of the dispersive coupling of a mode and a tls is @xmath36 , which we now consider . we switch to the interaction representation using the unitary transformation @xmath37 . disregarding the fast - oscillating ( counter - rotating ) terms proportional to the modulation amplitudes @xmath38 , in the spirit of the rwa , we write the transformed hamiltonian @xmath39_{rwa}$ ] as @xmath40 with @xmath41 model ( [ eq : h_rwa1 ] ) describes , in particular , the dispersive coupling of a cavity mode to a two - level atom in cavity qed or to an effectively two - level josephson junction in circuit qed , which has been studied in many experiments , see e.g. refs . and references therein . more generally , @xmath26 may take on a more complicated form . in particular , the coupling does not have to be linear in @xmath20 . similarly , when system @xmath1 has more than two levels , the coupling hamiltonian may involve more complicated combinations of system operators as well . we will generally characterize the energy of dispersive coupling by a parameter @xmath42 , even where the coupling has a form different from @xmath43 in eq . ( [ eq : h_rwa1 ] ) ; we assume @xmath44 . in order to describe the dynamics in the presence of dissipation , we consider the density matrix @xmath45 of the coupled mode and system . assuming markovian dynamics in slow time , i.e. on times long compared to @xmath46 , we can write the equation of motion for @xmath45 in the interaction representation in the form : @xmath47.\ ] ] here , @xmath48 and @xmath49 are liouville operators , or superoperators , cf . ref . ; they describe , respectively , the dynamics of the mode and the system coupled to their thermal reservoirs but isolated from each other . below we will calculate the density matrix in the basis where operators @xmath50 and @xmath24 are diagonal . importantly , @xmath45 must remain hermitian through its evolution via eq . ( [ eq : rho__schematic ] ) . as a consequence , for any operator of the mode and the system @xmath51 , @xmath52 this condition applies also to @xmath48 and @xmath49 taken separately . in the frequently used model of dissipation where coupling of the mode to a thermal reservoir is taken to be linear in the operators @xmath53 , to the leading order in this coupling we have@xcite : @xmath54 + i[\rho,{\tilde h}_{_m}],\end{aligned}\ ] ] where @xmath55^{-1}$ ] is the mode planck number and @xmath56 is the decay rate . we note that eq . ( [ eq : liouville_osc ] ) is not limited to describing ohmic dissipation ; in the microscopic derivation it is assumed that @xmath57 and @xmath58 , and that the time is slow , cf . ref . . we assume that the renormalization of the parameters of the mode due to the coupling to the thermal reservoir has been incorporated into the parameter values . a simple form of relaxation for the two - level system is described via bloch equations . in this case operator @xmath59 in eq . ( [ eq : rho__schematic ] ) has the same form as @xmath60 , except that ( i ) the friction coefficient @xmath56 should be replaced by the parameter @xmath61 that gives the reciprocal lifetime of the two - level system , @xmath62 $ ] , where @xmath63 is the planck number ; ( ii ) operators @xmath21 and @xmath22 in the dissipation term should be replaced by @xmath64 and @xmath65 , respectively , with @xmath66 , and ( iii ) hamiltonian @xmath67 should be replaced with @xmath68 . further , we incorporate additional trasverse relaxation through a term @xmath69 in @xmath70 . to build intuition before the more technical discussion , we now provide a heuristic semi - quantitative picture of the adiabatic mean - field multistability for dispersive coupling to a tls ; the justification and the applicability conditions follow from the general analysis in sec . [ sec : mean_field ] below . suppose that the mode is in a state @xmath71 with @xmath72 . for the mode in this state , the detuning of the effective tls transition frequency from the driving field frequency is given by @xmath73 , as seen from eqs . ( [ eq : hamiltonian_rotating_frame ] ) and ( [ eq : h_rwa1 ] ) . in the adiabatic approximation we solve for the dynamics of the two - level system assuming that this frequency detuning is independent of time . using the well - known result for this problem , see e.g. ref . , we obtain the mean value of @xmath25 for a given value of @xmath74 : @xmath75^{-1}\nonumber\\ & & \gamma = \gamma_{_s}(2\bar n_{_s}+1 ) + \gamma_{\perp } , \quad \delta\omega_{_s}(m)=\delta\omega_{_s } -vm,\end{aligned}\ ] ] where @xmath76 is the decay rate of the spin components @xmath77 . through the interaction term @xmath78 in eqs . ( [ eq : hamiltonian_rotating_frame ] ) and ( [ eq : h_rwa1 ] ) , the average tls population difference @xmath79 acts back on the mode , changing its frequency by @xmath80 . importantly , the mode frequency depends on its degree of excitation , @xmath74 . such dependence is characteristic for nonlinear modes . here it comes from the resonant pumping of the tls . in turn , the typical values of @xmath74 in the stable mode state determine the detuning of the tls from the forcing @xmath81 that modulates it , @xmath82 , thus determining @xmath79 . the mutual tuning of the mode and the two - level system to resonance leads to multistability of the compound system . indeed , the stationary state mean occupation number of a resonantly modulated harmonic oscillator is given by the familiar expression @xmath83 $ ] . given the dependence of the mode frequency on its degree of excitation , @xmath74 , one might expect to find a self - consistency relation for the stationary state of the form : @xmath84 ^ 2\}.\ ] ] the resulting system of nonlinear equations ( [ eq : bloch ] ) and ( [ eq : naive_m ] ) can have multiple solutions . an example is the dependence of the squared mode vibration amplitude ( equal to @xmath85 , for a unit mode mass ) on the modulation strength , which is shown in fig . [ fig : hysteresis ] . in fact , the quantity plotted is the mean - field value of the `` center of mass '' variable @xmath86 of the quasi - stationary wigner distribution over the occupation numbers @xmath74 of the mode ; it is given by eq . ( [ eq : stationary_states ] ) , which for the considered model coincides with eq . ( [ eq : naive_m ] ) and justifies the above qualitative arguments . for the chosen parameters the mode can have up to three stable states at a time . in the mean - field picture where quantum and classical fluctuations are neglected ( see sec . [ sec : fluctuations ] for the role of fluctuations ) , this tristability is revealed by a hysteresis pattern with multiple switching between stable branches with the varying control parameter ( here , the driving strength ) . the onset of multistability can be understood from the graphical solution of eqs . ( [ eq : bloch ] ) and ( [ eq : naive_m ] ) , illustrated in fig . [ fig : graphic_solution ] . the solid lines on this figure show the resonant dependence of the reduced population difference of the tls ( see caption ) on the `` center of mass '' occupation number of the mode @xmath87 . it is given by eq . ( [ eq : bloch ] ) with @xmath74 replaced by @xmath87 . the resonance is a consequence of the tls frequency detuning @xmath88 being linear in @xmath87 . the dashed line shows the resonant dependence of the scaled squared amplitude of the modulated mode @xmath87 on the mode frequency . note that there is always an odd number of intersections ; for the blue and green curves it is equal to 1 and the intersection occurs for small @xmath87 outside the range shown in the figure . the corresponding regime corresponds to the single stable state of the modulated compound system . the case of 3 intersections corresponds to bistability , whereas 5 intersections correspond to tristability . the understanding of this pattern comes from the analysis of the bifurcation curves in sec.[subsec : multistability ] . as a function of the average occupation number of the mode @xmath89 ; for convenience , instead of @xmath79 we plot the reduced frequency shift @xmath90 counted off from @xmath91 . the dependence of @xmath79 on @xmath87 is resonant , which corresponds to the tuning of the two - level system in resonance with the modulating field by varying the mode occupation number . the blue , green , and red solid curves correspond to @xmath92 and 24 in eq . ( [ eq : bloch ] ) . other parameters are the same as in fig . [ fig : hysteresis ] . the dashed line shows the resonant response @xmath93 of a _ linear _ mode with eigenfrequency @xmath94 , cf . ( [ eq : naive_m ] ) ; here we use @xmath95 as a variable and find @xmath87 for a given @xmath95 and for @xmath96 ; such @xmath97 corresponds to the long - dash vertical line in fig . [ fig : hysteresis ] . the points show the solutions of eqs . ( [ eq : bloch ] ) and ( [ eq : naive_m ] ) ; the small-@xmath87 intersections of the dashed line with the blue and green solid lines occur for smaller @xmath98 and are not shown . ] the possibility of bistability of the response of a mechanical mode to resonant modulation in the situation where the mode is coupled to another system ( a massive classical particle diffusing along the mechanical resonator ) was considered earlier @xcite . such coupling is similar to dispersive coupling , as the diffusion changes the mode frequency and is in turn affected by the vibrations . however , in contrast to ref . , the analysis below is fully quantum , it is general as it is not limited to a specific coupling mechanism , the mean - field predictions are different ( for example , tristability ) , and most importantly , the class of systems to which the results refer is much broader . the rest of the paper is organized as follows . in sec . [ sec : adiabatic ] we develop equations of motion for the mode density matrix , and introduce the adiabatic approximation which allows a dominant and tractable part of the coupled set of equations to be isolated . then in sec . [ sec : mean_field ] we consider the semiclassical limit of large mode vibration amplitude , and derive mean field equations which govern the stationary state vibration amplitudes and phases of the mode . the mean field equations capture the multistability of the system and its critical slowing - down near bifurcation points in parameter space . in sec . [ sec : fluctuations ] we study fluctuations and switching between the mean - field metastable states , induced by random transitions of system @xmath1 through the @xmath99 coupling . finally , in sec . [ sec : conclusions ] we summarize our main conclusions and discuss the relevance for various experimental systems of current interest .

we focus on the regime where the relaxation rate of the system greatly exceeds that of the mode , and develop a quantum adiabatic approach for analyzing the dynamics . semiclassically , the dispersive coupling leads to a mutual tuning of the mode and system into and out of resonance with their modulating fields , leading to multistability . in the important case where the system has two energy levels and is excited near resonance , the compound system can have up to three metastable states .

we investigate a resonantly modulated harmonic mode , dispersively coupled to a nonequilibrium few - level quantum system . we focus on the regime where the relaxation rate of the system greatly exceeds that of the mode , and develop a quantum adiabatic approach for analyzing the dynamics . semiclassically , the dispersive coupling leads to a mutual tuning of the mode and system into and out of resonance with their modulating fields , leading to multistability . in the important case where the system has two energy levels and is excited near resonance , the compound system can have up to three metastable states . nonadiabatic quantum fluctuations associated with spontaneous transitions in the few - level system lead to switching between the metastable states . we provide parameter estimates for currently available systems .

0706.0211

m

the context for our study is the model of the spatial distribution of massive halos and the galaxies that inhabit them provided by the millennium simulation @xcite . this is a collisionless dark matter simulation performed in a periodic cube @xmath20mpc ( comoving ) on a side , using @xmath21 particles for a cosmology with parameters @xmath22 . mock galaxies , with luminosities and colors , are generated by post - processing the dark matter halo merger trees with a semi - analytic prescription for the gas dynamics and feedback . for details , see @xcite . in particular , our version is that described in detail in @xcite , however with the updated dust prescription of @xcite which better models dust extinction at higher redshifts . we focus our cluster finding investigation on local confusion , projections on spatial scales @xmath23 of a target halo that will , at these redshifts , be barely resolved by photometric redshifts of the next - generation surveys ( des , cfht - ls , pan - starrs1 , kids , snap , lsst ) . ( although the scales these surveys might resolve are comparable to the box size considered here , these surveys are not necessarily using only the rs method described in this paper . ) we use the simulated galaxy and halo catalogues at three fixed epochs given by redshifts @xmath24 , @xmath12 and @xmath13 . these values span much of the expected redshift range of interest for a survey such as the rcs . halos in the simulation are found by using a friends - of - friends algorithm @xcite and galaxy membership is determined based on this . the friends - of - friends linking length ( 0.2 times the mean interparticle spacing ) can link objects into one large halo which by eye look to be smaller components , we note below where our results show signs of this effect . halo masses are given in terms of @xmath25 ( denoted as @xmath26 henceforth ) , the mass enclosed within a radius interior to which the mean density is 200 times the critical density at that epoch . at our redshifts there were 1268 , 805 and 426 halos with @xmath27 and 113 , 47 and 19 halos with @xmath28 . for the red sequence search , the sdss @xmath29 and @xmath7 filters , which bracket the 4000 angstrom break for approximately @xmath30 , are employed . at the highest redshift , we also considered @xmath31 band , our results for this case are described at the end of 4 ; results below will be given for @xmath18 unless stated otherwise . [ fig : redseq ] shows that a red sequence in @xmath18 vs. @xmath7 exists in rich ms halos over the range of redshifts probed . we use galaxies above @xmath32 , corresponding to @xmath7-magnitudes of @xmath33 , 21 and 22 at redshifts @xmath34 , @xmath12 and @xmath13 , and yielding samples of 942313 , 1005469 and 1054711 galaxies , respectively . the top panels show contours of the full , magnitude - limited population while lower panels show the color - magnitude behavior of galaxies in halos with 8 or more members . taking galaxies within the inner @xmath35mpc of the centers of the latter sample , we fit a linear relation in the @xmath18 vs. @xmath7 plane . following @xcite , we throw out @xmath36 outliers and iterate the fit to find the slope and intercept of the red sequence . the width of the red sequence is set to enclose 90% of the full massive halo galaxy sample . the distance , @xmath15 , is taken perpendicular to the red sequence line in the color - magnitude space . of these galaxies , the red sequence widens and for high redshift slightly increases the contamination from projection under study here . ] table [ tab : zchange ] lists the slopes , intercepts , and widths of the red sequence for all three redshifts . the red sequence color - magnitude relation is a weak function of halo mass or richness , so the parameters are not particularly sensitive to the choice of halos with 8 or more members . defining the red sequence using the ms galaxy population itself means that our color cuts are optimally tuned to the content of the ms massive halos . with observations , one derives color cuts using the color - magnitude data of a target subset of galaxies , such as the approaches used by @xcite and @xcite . comparing the simulation results to observations , it appears that the mock red sequence has the wrong tilt and is slightly wider than observed . we experimented with `` tightening '' the red sequence by moving the galaxy colors closer to the best - fit line , but such a procedure did not have a large effect on our conclusions so we present our results using colors as provided . we wish to use projections of each proper time output to create finite redshift segments of a full sky survey . starting with the coeval ms galaxy samples , we introduce passive color and magnitude evolution into spatial projections to mimic the behavior of a light - cone population . the color evolution with redshift is based on an instantaneous bruzual - charlot ( bc ) burst at @xmath37 and shown for @xmath18 in fig . [ fig : colorchange]a . for comparison , we show the average ( slightly bluer ) color of the ms red sequence galaxies for our three redshifts . the ms red sequence galaxies are expected to be bluer than the bc model , since their stars were not formed in a single burst at high redshift . the ms galaxies are also bluer than bcg s in the sdss @xcite . we use this simple bc model to define piecewise constant color gradients , @xmath38 , along the line of sight , shown by the solid line segments in fig.[fig : colorchange]a . we define a @xmath7 magnitude gradient analogously . foreground and background color - magnitude evolution are modeled separately , with parameters given in table [ tab : zchange ] . fainter galaxies may evolve into the @xmath7 magnitude cut because of the change in observed magnitude with redshift . to catch these potential interlopers , we employ galaxy catalogues half a magnitude fainter in @xmath7-band than required by the unevolved red sequence cuts . note that the applied color gradient becomes progressively shallower at higher redshift . the assumed degree of color and magnitude evolution is key since it controls the redshift filtering power of the red sequence . to foreshadow one of our main results , fig . [ fig : colorchange]a illustrates how the color evolution determines the line - of - sight path length probed by the red sequence color range . the dashed regions in fig . [ fig : colorchange]a are centered at the average color of the red sequence galaxies at each redshift and are bounded vertically by the approximate range of color of the red sequence . they are bounded horizontally by the redshift extents of the comoving @xmath39 sightline available within the ms volume . at @xmath24 , the evolutionary color gradients are strong enough that projected red sequence galaxies will shift out of the target color range before the @xmath39 ms boundary is reached , but this is not quite the case at @xmath40 and @xmath13 . fig.[fig : colorchange]b further illustrates how the imposed color evolution acts as a redshift filter . taking the color and magnitude of each galaxy and our line of sight gradients , fig.[fig : colorchange]b shows the fraction of these galaxies remaining on the red sequence as a function of line - of - sight distance . such galaxies will still be potential members of a cluster centered at the origin . a more narrowly peaked distribution indicates a smaller fraction of galaxies available for inclusion via projection during cluster finding . as can be seen , the fraction of galaxies remaining within the red sequence cut at large distances from the origin increases with redshift ; the red sequence selects a longer path along line of sight at higher redshift . the other source of contamination is galaxies that are shifted into the red sequence by the change in observed color . the number density of these galaxies , normalized by the number of red sequence galaxies at the central redshift , is shown by the light lines in fig.[fig : colorchange]b . except for the most distant part of the box at @xmath24 , this number is relatively small . our use of a uniform color change with redshift for all galaxies is not strictly correct for all galaxy types . however , blue star forming galaxies change in observed color much more slowly with redshift than in this model , so to be shifted erroneously into our red sequence color cut , these galaxies are required to be at significantly higher redshift than the cluster . since they would then lie outside of our 500 @xmath41 mpc box , they are not included in our analysis . the strongest contribution to interloper candidates is from galaxies which have colors within our red sequence color cut even though they are far from the central galaxy along the line of sight . our algorithm defines clusters as circular regions , centered on a bright galaxy , with red - sequence sky surface density equal to a multiple @xmath42 of the mean value at the redshift of interest . this approach is analogous to the spherical overdensity method used to define the halo masses . for target centers , we work in descending order through a list of red - sequence galaxies ranked ( brightest to dimmest ) by apparent @xmath7-band magnitude . this ranking is motivated by a desire to find the rare , high mass halos first , then work down the mass function to more common objects . around a potential cluster center , a radially - sorted list of red sequence neighbors is used to define a mean galaxy number density profile as a function of transverse separation . we use the periodic boundaries of the ms to recenter the simulated volume on each candidate center . the volume extends @xmath43mpc in front and behind , and galaxy colors are adjusted , linearly with distance in the projected direction , as described above . starting with the 8 nearest neighbors , ( to avoid shot noise problems in tracing the cluster profiles at small radii ) , we work outward in radius @xmath44 until the the number of galaxies @xmath45 fails to satisfy the overdensity criterion @xmath46 here @xmath47 is the mean sky surface density of red sequence galaxies in the ms , including the effects of the applied observed color evolution along the projected dimension . if the overdensity criterion is not satisfied for 8 galaxies , the object is discarded , if @xmath45 meets or exceeds a minimum of 8 galaxies , then this cluster is added to the output list . all members are then recorded and removed from the remaining list of potential cluster centers . times the average red sequence ( background ) density , @xmath48 in our case . the approximate change of radius with richness can be read off from eq.[eqn : codefn ] . note too that our cluster - finding algorithm traces galaxy overdensities to radii which can potentially reach greater than 1 @xmath41 mpc . this algorithm increases the survey sensitivity to truly extended structures , but may also increase the cross - section for interlopers relative to algorithms which search for clusters only on a limited , smaller scale ; however , a fixed aperture richness based cluster finder performed significantly more poorly . ] note that area overlap of clusters is allowed , so that a single galaxy can belong to more than one cluster ( 6 - 7% of the galaxies end up in more than one cluster at the lowest 2 redshifts , dropping to @xmath49 at higher redshifts ; in contrast , galaxies only belong to one ms halo ) . to boost statistics , we make three projections of the simulated volume along its principal axes . the choice of @xmath42 is discussed below . the sensitivity of survey purity and completeness to the choice of @xmath42 is further explored in the appendix . the clusters found by the search algorithm can be linked back to the dark matter halos in the simulation using their respective lists of galaxy members . a perfect algorithm would be complete with respect to halos and have no false positives , no clusters that appear rich on the sky but are actually several less rich systems aligned along the line - of - sight . in addition , the halo and cluster richnesses would agree . a perfect algorithm would therefore recover the intrinsic distribution of halo mass @xmath26 as a function of red sequence galaxy richness @xmath45 . this distribution is shown in the top panels of fig . [ fig : ngalm200 ] . at all redshifts , a mean , red sequence richness of @xmath50 above our @xmath7-magnitude limit corresponds to a @xmath51 halo . when fit ( throwing out 3-@xmath52 outliers several times ) above a minimum of 8 members , we find that mass scales with red sequence richness as @xmath53 , with @xmath54 , @xmath55 and @xmath55 at @xmath56 , @xmath12 and @xmath13 respectively . the mass intercepts are @xmath57 , @xmath58 and @xmath59 and there are @xmath60 4100 , 2900 , and 1300 @xmath61 halos at these redshifts , respectively . note that red sequence richness is a fairly noisy tracer of mass ; the rms level of scatter is @xmath62 or higher above the richness cut of @xmath63 ( a detailed discussion of scatter in richness vs. mass can be found in @xcite ) . the richness we use in finding the clusters may not be the best richness to use for getting the cluster mass ( e.g. galaxy counts within some aperture might be useful after the clusters are found , for finding the clusters themselves we found a fixed aperture performed significantly worse ) . some observational surveys for galaxy overdensities account for projections of foreground / background galaxies via a statistical subtraction of the expected number of projected galaxies , calculated from random non - cluster pointings . our cluster richness estimator , @xmath64 , does not include such a correction ; our overdensity requirement means that approximately @xmath65 of the galaxies are from the background . for each cluster identified in projection , we list all halos contributing one or more of its member galaxies . the quality of the cluster detection is measured by the top - ranked matched fraction , @xmath66 , defined as the fraction of cluster members coming from the halo that contributes the plurality of the cluster s red sequence galaxies . we define two classes , _ clean _ and _ blended _ , based on whether the plurality is or is not the majority of the cluster s membership , @xmath67 we assign to each cluster the mass of its top - ranked halo found through member - matching . if two ( or more ) halos contribute the same number of galaxies , and are both top - ranked , we take the most massive .

we investigate halo mass selection properties of red - sequence cluster finders using galaxy populations of the millennium simulation ( ms ) . a clear red sequence exists for ms galaxies in massive halos at redshifts , and we use this knowledge to inform a cluster - finding algorithm applied to projections of the simulated volume . at low redshift ( ) , we find that of the clusters found have galaxy membership dominated by a single , real - space halo , and that are blended systems for which no single halo contributes a majority of a cluster s membership . at ,

we investigate halo mass selection properties of red - sequence cluster finders using galaxy populations of the millennium simulation ( ms ) . a clear red sequence exists for ms galaxies in massive halos at redshifts , and we use this knowledge to inform a cluster - finding algorithm applied to projections of the simulated volume . at low redshift ( ) , we find that of the clusters found have galaxy membership dominated by a single , real - space halo , and that are blended systems for which no single halo contributes a majority of a cluster s membership . at , the fraction of blends increases to , as weaker redshift evolution in observed color extends the comoving length probed by a fixed range of color . other factors contributing to the increased blending at high- include broadening of the red sequence and confusion from a larger number of intermediate mass halos hosting bright red galaxies of magnitude similar to those in higher mass halos . our method produces catalogs of cluster candidates whose halo mass selection function , , is characterized by a bimodal log - normal model with a dominant component that reproduces well the real - space distribution , and a redshift - dependent tail that is broader and displaced by a factor lower in mass . we discuss implications for x - ray properties of optically selected clusters and offer ideas for improving both mock catalogs and cluster - finding in future surveys . cosmology : clusters of galaxies , large scale structure

0706.0211

r

an ideal cluster catalog would be _ pure _ , _ complete _ and _ unbiased _ with respect to halos . a perfectly _ pure _ sample would have no accidental projections ; all the galaxies of any chosen cluster would be common members of a single , dark matter halo . a perfectly _ complete _ sample would be one for which each halo in the survey volume appears once , and only once , in the list of clusters . finally , an _ unbiased _ cluster catalog would contain clusters that reproduce the mean mass - richness relation defined by halos . in this section , we consider these issues , both in the context of setting our circular overdensity threshold and in the results obtained . we will see that high levels of purity and completeness are achieved , and that the cluster samples are nearly unbiased . ( many definitions of purity and completeness exist in the literature , we describe and compare several of them in the appendix , and detail our definitions as we use them below . ) the cluster catalogs produced by the search algorithm depend on the value of the number density threshold @xmath42 . choosing too high a value will pick out only the cores of the richest halos , resulting in a catalog that is pure and complete at very high masses , but is otherwise incomplete . picking too low a value will extend the search into the periphery of halos , leading to a catalog that , although complete across a wide range of masses , suffers from impurities due to blending multiple halos into a single cluster . our choice of @xmath68 and @xmath69 for clusters provides samples that are highly complete for @xmath70 halos . [ fig : ffound ] shows a measure of completeness , the fraction of halos assigned as top - ranged matches to clusters with @xmath61 . the completeness is very high for halos with intrinsic @xmath70 , but it drops considerably for lower - richness halos . more halos are missed at higher redshift , and these tend to have extended , filamentary shapes suggestive of recent ( or imminent ) merging . at higher redshift , the major merger rate increases , leading to a higher fraction of disturbed halos . keeping the cluster richness fixed at @xmath69 in order to define whether a halo is found or not ( completeness ) , samples derived with higher values of @xmath42 will be more pure ( have fewer blends ) but less complete , and vice - versa for samples constructed with lower @xmath42 . further quantitative discussion on purity and completeness can be found in the appendix . fig.[fig : nofn ] shows that , at each redshift , the value @xmath68 produces a cluster catalog with a richness function , @xmath71 , that matches well that of the underlying halo population . averaging the three projections , there are @xmath72 and @xmath73 clusters with @xmath74 at @xmath24 , 0.69 and 0.99 , respectively . these values compare well to the ms halo counts of 4098 , 2926 , 1290 for @xmath74 . the scatter from the average of cluster numbers between different lines of sight is less than a percent at @xmath24 and less than four percent at @xmath75 . the good match in number counts does not imply that the algorithm is perfect . in fact , the typical number of halos contributing to an @xmath76 cluster is @xmath77 . the second and fifth richest clusters found at @xmath24 illustrate the range of behavior in clean and blended clusters . figure [ fig : z041c12 ] shows projected positions and color - magnitude information for sky patches centered on the two clusters . the second richest cluster has 212 members contributed by 21 different halos . members of one of the most massive halos at that epoch , @xmath78 , comprise @xmath79 of the cluster members . the remaining members come from 20 other halos , including some lying in the foreground . a small number of members are contributed by halos in the background . the fifth richest cluster , with 175 members , presents a very different case . its most massive contributing halo has a mass @xmath80 , which contributes almost all of its own galaxies but only 35% of the cluster s members ( @xmath81 ) . a total of 53 other halos also contribute , many lying close ( within @xmath82 ) in the foreground or background . although much richer than most of the halos considered , these two examples illustrate the essential projection problem that is causing the blends ; both sets of galaxies appear to be reasonable clusters in the x - y plane . in the next two sections the statistics of the clean and blended clusters , and their features , will be discussed in more detail . the mass selection function is an important ingredient for cosmological tests with optical cluster surveys ( @xcite , @xcite ) . [ fig : ngalm200 ] ( bottom ) shows the relationship between the observed richness of a cluster and the mass of its top - ranked halo ( see [ sec : match ] ) . circles show clean clusters while small crosses show blends . at each redshift , the clean cluster population displays a power law mean relation remarkably similar to that of the underyling halo population . the slopes of the relations agree at the few percent level ; the values for halos ( clean clusters ) for @xmath74 are 1.07 ( 1.04 ) , 1.10 ( 1.06 ) , 1.10 ( 1.15 ) from low to high redshift , respectively . the intercepts at @xmath83 also agree at the few percent level , and could be further fine - tuned by introducing small changes to the search threshold @xmath42 at each redshift . at all redshifts , the circular overdensity algorithm is effective at identifying the mean richness - mass behavior of the underlying halo population . the dispersion in the observed cluster sample is larger than for halos , due to failure modes of the search algorithm . at fixed observed richness , blending creates a tail to low masses while fragmentation of large halos into multiple clusters introduces a high mass tail . [ fig : mlike ] shows estimates of the conditional halo mass distribution , @xmath8 , derived from cross - sections of the joint likelihood data in fig . [ fig : ngalm200 ] in richness ranges @xmath84 at redshifts @xmath85 , respectively . this choice gives a constant average halo mass , @xmath86 , at all three redshifts . the cluster likelihoods ( shaded in the figure ) are compared with the halo distributions for the same richness ranges , shown by solid lines . the top row shows all clusters , while the middle and bottom rows separate the samples into clean and blended systems , respectively . raw counts rather than normalized likelihoods are shown to give the number of objects . at @xmath56 , more than @xmath3 of clusters in the chosen richness range have their dominant underlying halo contributing at least half of the galaxies . the mass distribution of the found clusters matches well the underlying halo mass likelihood . at higher redshift , the correspondence between halos and clusters weakens somewhat ; the number of blends more than doubles , from @xmath87 at @xmath56 to @xmath6 at @xmath88 . the blended systems contribute a low mass tail to the halo mass likelihood . for the distributions , the central mass of the clean clusters remains at @xmath89 at all 3 redshifts , while the central mass of the blends drops , from @xmath90 at @xmath24 to @xmath91 . thus the ratio of central masses between the clean and blended clusters also increases with redshift . our classification of clean _ versus _ blended clusters is based on a somewhat arbitrary cutoff of @xmath92 in member fraction . figure [ fig : f1hcum ] provides a more complete picture by plotting the cumulative fraction of clusters that have top - ranked halo member fraction @xmath93 . here the same observed cluster richness limits as in fig . [ fig : mlike ] are used . cutting at @xmath94 , the vertical line , gives the clean fractions quoted in fig . [ fig : mlike ] . analogues for other definitions of `` clean fraction '' in terms of @xmath66 can be read off as well . there is a clear trend with redshift , with clusters at @xmath88 being less well - matched to halos than those at @xmath56 . the median value of @xmath66 tells a similar story , decreasing from @xmath95 at @xmath56 to @xmath96 at @xmath88 . blending is clearly increasing at larger redshift . going to a higher central mass gives similar trends , e.g. centering on a richness corresponding to a average @xmath97 halo mass at all redshifts gives a clean fraction of 90% at redshift 0.41 which decreases to 76% at redshift 0.99 for the same @xmath42 as above ( @xmath42 can be increased for higher richness to improve both numbers but the increase of blends at high redshift remains ) . there are several effects which cause an increasing incidence of blends at higher redshift . firstly , the change of observed color with distance is weaker , and secondly , the red sequence is wider , so the color - magnitude cut selects galaxies from a thicker slice along the line of sight . these seem to be the strongest causes and were illustrated in fig.[fig : colorchange ] . another way of seeing the effect of color / magnitude evolution is to remove it entirely at @xmath24 ; the background level then increases and the contrast between the clusters and the background declines . lowering @xmath42 to obtain the same number of clean clusters at the fixed mass range of fig . [ fig : mlike ] , we find that the level of blends increases to @xmath98 , very close to what is seen at @xmath99 . similarly , to increase the clean fraction , one can impose the @xmath24 color evolution on the @xmath75 population . in this case , however , the number of non - red sequence galaxies brought into the red sequence through our evolution increases strongly , limiting the degree to which blends can be reduced . a third contributing factor is that , at earlier times , the mass function is steeper , causing the number of possible interloper halos per target halo ( of mass @xmath100 , for example ) to grow at high redshift . the increase in intermediate - mass halos is also enhanced because the central galaxy magnitude is less well correlated with host halo mass at @xmath88 than at low redshift . over time , central galaxies in massive halos grow and brighten via mergers , leading to a stronger correlation between @xmath7magnitude and halo mass . our cluster finding algorithm works in descending order of luminosity . at low redshift , the luminosity sorting corresponds well to a sorting in halo mass but , at high redshift , more low mass systems are mixed into the range of central galaxy magnitude occupied by high mass halos . as these factors are fairly generic , as expected , the trend toward more blends at @xmath88 appeared in all the cases we considered : changing definition and tightness of the red sequence , changing @xmath64 cuts and changing the spherical overdensity requirement . for a wide range of density cuts and modeling choices the blends have roughly half the mass of the clean matches at @xmath24 , and this mass scale declines at higher redshift .

the fraction of blends increases to , as weaker redshift evolution in observed color extends the comoving length probed by a fixed range of color . other factors contributing to the increased blending at high- include broadening of the red sequence and confusion from a larger number of intermediate mass halos hosting bright red galaxies of magnitude similar to those in higher mass halos .

we investigate halo mass selection properties of red - sequence cluster finders using galaxy populations of the millennium simulation ( ms ) . a clear red sequence exists for ms galaxies in massive halos at redshifts , and we use this knowledge to inform a cluster - finding algorithm applied to projections of the simulated volume . at low redshift ( ) , we find that of the clusters found have galaxy membership dominated by a single , real - space halo , and that are blended systems for which no single halo contributes a majority of a cluster s membership . at , the fraction of blends increases to , as weaker redshift evolution in observed color extends the comoving length probed by a fixed range of color . other factors contributing to the increased blending at high- include broadening of the red sequence and confusion from a larger number of intermediate mass halos hosting bright red galaxies of magnitude similar to those in higher mass halos . our method produces catalogs of cluster candidates whose halo mass selection function , , is characterized by a bimodal log - normal model with a dominant component that reproduces well the real - space distribution , and a redshift - dependent tail that is broader and displaced by a factor lower in mass . we discuss implications for x - ray properties of optically selected clusters and offer ideas for improving both mock catalogs and cluster - finding in future surveys . cosmology : clusters of galaxies , large scale structure

0706.0211

c

with the advent of wide field imagers , optical searches have become a powerful way to compile large samples of high redshift clusters . key to these techniques is the use of multi - color information to reduce the line - of - sight contamination that plagued earlier , single filter , observations @xcite . two - filter information provides only limited redshift filtering , and this paper begins to explore the questions of what types of objects are selected by such techniques , and how this selection evolves with redshift . we use a simple circular overdensity search algorithm on local sky projections of the galaxy population of the millennium simulation , tuned using knowledge of the red sequence present in simulated halos with eight or more galaxies brighter than @xmath130 in the @xmath7-band . the free parameter , the density contrast @xmath42 , is tuned to maximize both purity and completeness , and the choice @xmath68 produces a number of clusters as a function of galaxy richness that is close to the underlying richness function of halos . we find that essentially all clusters have some degree of projected contamination ; a cluster of optical richness @xmath45 typically has red sequence members from @xmath131 halos along the line - of - sight . in the large majority of cases , the contamination is not dominant , and most of a cluster s members are associated with a single , massive halo . a minority are highly blended cases in which projected contamination is dominant , and no single halo contributes a majority of the cluster s members . we find an increased fraction of blends with redshift . although several factors contribute , the most important factor appears to be weaker evolution in the observed color of red sequence galaxies with increasing redshift . this effectively increases the path length searched by the red sequence color cut , leading to a larger cross section for accidental , line - of - sight projections . in addition , at higher redshift , the number of @xmath132 halos relative to a @xmath105 halo is larger , and the central galaxy red magnitudes at these mass scales are more similar . the blends add a low - mass tail to the halo mass selection function for clusters of fixed optical richness . for our found clusters with optical richness targeting @xmath133 halos , we expect that @xmath134 of these systems would be underluminous in x rays by a factor of two at @xmath24 , growing to @xmath98 underluminous by a factor closer to three at @xmath75 . the scatter in individual x ray luminosities for the complete set of clusters is expected to be large , @xmath135 at high redshift , and there is considerable overlap in the distributions of @xmath136 expected for clean and blended clusters . it should be noted that , observationally , high redshift low - luminosity systems are also likely have lower signal to noise . the galaxy number density profiles are slightly shallower for blends than for clean clusters , and a matched spatial filter approach may help identify and eliminate the former . since some fraction of halos , those undergoing mergers especially , will also be spatially extended , careful study of the effect of spatial filtering on halo completeness is needed . alternatively , instead of decreasing the number of blends in searches , our findings here suggest modeling the mass likelihood @xmath8 as a bimodal log - normal distribution , with the fraction of blends , and the location and width of that component , included as nuisance parameters . this expected bimodal distribution can be incorporated into error estimates for cluster number counts as a function of redshift , for instance , along with other expected errors ( such as the 5 - 10% scatter associated with red sequence associated redshifts @xcite ) . understanding the detailed color / magnitude trends within galaxy clusters is key to refining red sequence cluster finding and improving its success rate . fortunately , data sets in hand or on the way , combined with rapidly improving modeling methods , will lead to improvements in our understanding of high redshift colors and their evolution . this work will be driven largely by survey - specific mocks current examples are the 2mass @xcite , the deep2 survey@xcite , the 2dfgrs @xcite and the sdss @xcite and such efforts will be necessary for mining the rich science provided by existing and future high redshift cluster surveys . we thank the anonymous referee for many helpful comments and suggestions . jdc thanks a. albrecht , m. brodwin , c. fassnacht , r. gal , j. hennawi , a. von der linden , l. lubin , g. de lucia , s. majumdar , t. mckay , n. padmanabhan , e. rozo , r. stanek and d. weinberg for helpful discussions and/or questions and the galileo galilei institute , the santa fe cosmology summer workshop , and the aspen center for physics for hospitality during the course of this work and the opportunity to present these results , and lbl for support . aee thanks j. annis and t. mckay for conversations and acknowledges support from nasa grant nag5 - 13378 , from nsf itr aci-0121671 , and especially from the miller institute for basic research in science at uc , berkeley . mw thanks charles lawrence for conversations . djc wishes to thank both the aspen center for physics and the department of physics at the university of michigan for hospitality , and acknowledge support from nsf grant ast507428 . mw acknowledges support from nasa and ee acknowledges support from nsf grant ast-0206154 . the millennium simulation was carried out by the virgo supercomputing consortium at the computing centre of the max- planck society in garching ; semi - analytic galaxy catalogues are publicly available at http://www.mpa - garching.mpg.de / millennium/.

our method produces catalogs of cluster candidates whose halo mass selection function , , is characterized by a bimodal log - normal model with a dominant component that reproduces well the real - space distribution , and a redshift - dependent tail that is broader and displaced by a factor lower in mass . we discuss implications for x - ray properties of optically selected clusters and offer ideas for improving both mock catalogs and cluster - finding in future surveys .

we investigate halo mass selection properties of red - sequence cluster finders using galaxy populations of the millennium simulation ( ms ) . a clear red sequence exists for ms galaxies in massive halos at redshifts , and we use this knowledge to inform a cluster - finding algorithm applied to projections of the simulated volume . at low redshift ( ) , we find that of the clusters found have galaxy membership dominated by a single , real - space halo , and that are blended systems for which no single halo contributes a majority of a cluster s membership . at , the fraction of blends increases to , as weaker redshift evolution in observed color extends the comoving length probed by a fixed range of color . other factors contributing to the increased blending at high- include broadening of the red sequence and confusion from a larger number of intermediate mass halos hosting bright red galaxies of magnitude similar to those in higher mass halos . our method produces catalogs of cluster candidates whose halo mass selection function , , is characterized by a bimodal log - normal model with a dominant component that reproduces well the real - space distribution , and a redshift - dependent tail that is broader and displaced by a factor lower in mass . we discuss implications for x - ray properties of optically selected clusters and offer ideas for improving both mock catalogs and cluster - finding in future surveys . cosmology : clusters of galaxies , large scale structure

cond-mat0604238

c

we summarize our key results concerning the stability of stripe phases in the nickelates . we investigated this problem using two hubbard models the realistic model for @xmath0 electrons , and the ddh model which frequently serves as the simplest approach to the orbital degeneracy . @xcite it is quite encouraging that the ddh model gives already diagonal stripe phases as the most stable structures , in contrast to the nondegenerate hubbard model where the vertical ( horizontal ) stripes are found in the hf approximation . however , one finds half - filled bc stripes in the ddh model , and it is only in the realistic @xmath0 model for doped nickelates that one observes a generic tendency to promoting filled stripes over the half - filled ones . as an example of this behavior , we give the free energies of filled and half - filled stripe phases found within both ( @xmath0 and ddh ) models for @xmath201 doping in table [ tab : fez0 ] . first of all , one finds that the energies of bc phases are considerably lower for the realistic model of @xmath0 band due to the higher kinetic energy gains which result from the off - diagonal hopping.@xcite most importantly , for the parameters relevant to lsno used for the data of table [ tab : fez0 ] , one finds that the dbc phase has the lowest energy , _ i.e. _ , indeed experimentally observed _ filled _ diagonal stripes . in contrast , the sc stripe phases with unpolarized dw sites and large double occupancies have much higher energies , and the best of them is not diagonal , but vertical ( horizontal ) one . we also note that even though the ddh model with two equivalent orbitals clearly favors diagonal dws , it stabilizes instead of filled the _ half - filled _ diagonal phases . cccccc & & & model & phase & filled & half - filled & filled & half - filled @xmath0 & bc & * 2.5508 * & 2.5759 & 2.5629 & 2.5756 & sc & 2.7815 & 3.2615 & * 2.7012 * & 3.0729 ddh & bc & 2.8172 & * 2.8135 * & 2.8395 & 2.8354 as in the cuprates , the coexisting charge and magnetic order in diagonal stripe phases in the nickelates is a result of the compromise between the kinetic and magnetic energies the magnetic energy is gained in the af domains , and the kinetic energy is gained mainly along the dws . the bc stripes are favored as then the magnetic energy can be gained ( table [ tab : fez0 ] ) not only in the af domains , but also on the dw magnetic sites . finally , when the dws are filled , more kinetic energy is gained in the @xmath0 model while then the off - diagonal hopping is allowed . altogether , this mechanism shows little sensitivity to the small crystal field splitting . for moderate values of the latter it tends to eliminate stripe phases entirely rather than promoting one stripe phase over another one . in spite of the remarkable success of the present study which gave stable diagonal stripe phases , one has to admit that the predicted electronic properties show some difference to the experimental ones . in fact , our systematic studies of stripe phases completed within the relevant model for @xmath0 orbitals , where several phases separated by different lattice spacing varying from @xmath187 to @xmath235 were considered , have revealed that the optimal stripe filling in the true ground state is slightly less ( @xmath236 hole / ni depending on the crystal field splitting ) than the experimental value of one hole per ni ion . this concerns the entire low doping regime , @xmath237 , where @xmath19 . there may be a few reasons of this discrepancy . first of all , one has to realize that in a multiband model with oxygen orbitals included explicitly the holes would be doped primarily to oxygen orbitals , screening the local moments at ni sites,@xcite in analogy to zhang - rice singlets in the cuprates.@xcite an insulating ground state could then result from oxygen distortions by the peierls mechanism . thus , we argue that the present results could be further improved within a realistic model including not only two @xmath0 orbitals with different hopping elements , but also orbital polarization at oxygen sites . second , it may be expected that the stripe filling will be somewhat changed due to the electron correlation effects beyond the hf approximation used here . we believe that the present work provides a good starting point for future studies of the correlation effects . in summary we have analyzed the stripe formation in the doped nickelates in the realistic model with degeneracy of @xmath0 orbitals , using large clusters . the results obtained with this model were compared with the widely used doubly degenerate hubbard model . even though in both models the distance between the dw is inversely proportional to the doping , the most stable diagonal stripes are found to differ markedly from one model to the other one . in the @xmath0 model , the stripes are filled and nearly insulating , as observed experimentally in a series of layered nickelates . in contrast , in the ddh model they are half - filled and metallic . these latter stripe phases are reminiscent of the stripes observed experimentally in largely doped cuprates . these differences have their roots in the different structure of intersite hopping terms . as the ddh model is closer to @xmath153 than to @xmath0 hopping matrix elements , one might expect that doped insulators with @xmath153 orbital degrees of freedom , as in vanadates or in ruthenates , would promote different stripe phases than those observed in the nickelates . we thank k. rociszewski for insightful discussions . m.r . acknowledges support from the european community under marie curie program number hpmt2000 - 141 . this work was supported by the polish ministry of science and education under project no . 1 p03b 068 26 , and by the ministre franais des affaires etrangres under polonium 09294vh .

in contrast , for the doubly degenerate hubbard model the most stable stripes are somewhat reminiscent of the cuprates , with half - filled atoms at the domain wall sites . this difference elucidates the crucial role of the off - diagonal hopping terms for the stripe formation in lasrnio .

we investigate the electron density distribution and the stability of stripe phases in the realistic two - band model with hopping elements between orbitals at ni sites on the square lattice , and compare these results with those obtained for the doubly degenerate hubbard model with two equivalent orbitals and diagonal hopping . for both models we determine the stability regions of filled and half - filled stripe phases for increasing hole doping in the range of , using hartree - fock approximation for large clusters . in the parameter range relevant to the nickelates , we obtain the most stable diagonal stripe structures with filling of nearly one hole per atom , as observed experimentally . in contrast , for the doubly degenerate hubbard model the most stable stripes are somewhat reminiscent of the cuprates , with half - filled atoms at the domain wall sites . this difference elucidates the crucial role of the off - diagonal hopping terms for the stripe formation in lasrnio . the influence of crystal field is discussed as well .