Gravitational Phase Transitions in the Cosmological Many-Body System

Saslaw, William C.; Ahmad, Farooq

doi:10.1088/0004-637x/720/2/1246

Cited by 23 publications

(39 citation statements)

References 15 publications

(31 reference statements)

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“…This is that the integral is evaluated over a finite distance R 1 even though the gravitational force has an infinite range. The justification comes from the observation (Saslaw and Fang 1996) that the expansion of the Universe cancels the effect of the long range gravitational field for distances greater than R 1 so that the infinite range gravitational force has a finite effective range. The value of R 1 is thus the limit of the spatial integration where the expansion of the Universe cancels the gravitational mean field.…”

Section: The Three-component Partition Functionmentioning

confidence: 99%

“…These results have been used elsewhere (Wahid et al 2011) to derive the distribution function for fluctuations in particle number and to determine the conditions for application of quasi-equilibrium approximation. Ideas from the earlier work (Ahmad et al 2002(Ahmad et al , 2006a have been utilized to study the gravitational phase transition in the cosmological manybody systems (Saslaw and Ahmad 2010).…”

mentioning

confidence: 99%

“…The justification for quasi-equilibrium approximation has been discussed at length in the literature (Saslaw and Hamilton 1984;Saslaw et al 1990;Saslaw and Sheth 1993;Saslaw and Fang 1996;Saslaw 2000).…”

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confidence: 99%

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Spatial galaxy distribution function for a three-component system

Malik

Ali

Ahmad

2011

Astrophys Space Sci

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We derive the distribution function and the allied thermodynamic quantities for a system of galaxies with three mass species. A new clustering parameter b 3 that inherently takes into account the masses and the number of galaxies of each kind, emerges directly from the calculations. Our general conclusion is that the inclusion of the third component does not significantly effect the overall features of the distribution function.

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Section: The Three-component Partition Functionmentioning

confidence: 99%

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confidence: 99%

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Spatial galaxy distribution function for a three-component system

Malik

Ali

Ahmad

2011

Astrophys Space Sci

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“…For systems which are not virialized on all scales, the successively higher order energy integrals will make successively smaller contributions. Now incorporating the second term as well, we find [10] for the partition function Now incorporating the second term as well, we find [10] for the partition function…”

Section: Gm^mentioning

confidence: 98%

Statistical Mechanics of Infinite Gravitating Systems

Saslaw¹

2008

AIP Conference Proceedings

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The cosmological many-body problem was stated over 300 years ago, but its solution is quite recent and still incomplete. Imagine an infinite expanding universe essentially containing a very large number of objects moving in response to their mutual gravitational forces. What will be the spatial and velocity distributions of these objects and how will they evolve? This question fascinates on many levels. Though inherently non-linear, it turns out to be one of the few analytically solvable problems of statistical mechanics with long range forces. The partition function can be calculated. From this all the thermodynamic properties of the system can be obtained for the grand canonical ensemble. They confirm results derived independently directly from the first and second laws of thermodynamics. The behavior of infinite gravitating systems is quite different from their finite relations such as star clusters. Infinite gravitating systems have regimes of negative specific heat, an unusual type of phase transition, and a very close relation to the observed largescale structure of our universe. This last feature provides an additional astronomical motivation, especially since the statistical mechanics may be generalized to include effects of dark matter haloes around galaxies. Previously the cosmological many-body problem has mostly been studied using the BBGKY hierarchy (not so suitable in the non-linear regime) and by direct computer integrations of the objects' orbits. The statistical mechanics agrees with and substantially extends these earlier results. Most astrophysicists had previously thought that a statistical thermodynamic approach would not be applicable because: a) many-body gravitational systems have no rigorous equilibrium state, b) the unshielded nature of the long-range force would cause the partition function to diverge on large scales, and c) point masses would produce divergences on small scales. However, deeper considerations show that these are not significant difficulties. There remain many important questions for which we have only a very preliminary understanding. An example is to find the basin of attraction for initial states which are able to evolve into systems described by this gravitational partition function. It may well be that ideas and techniques developed for other types of statistical mechanical systems will help us answer these questions.

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“…Therefore, it has become reasonable to expect that a statistical mechanical description of cosmological many-body problem system is possible. An interesting feature of galaxy clustering can be observed (Saslaw and Ahmad 2010) when the value of the specific heat changes from positive to negative values and this occurs when the specific heat becomes zero. In general as clustering progresses, the scale and amplitude of correlation among particles increases.…”

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confidence: 99%

Gravitational clustering of galaxies: Derivation of two-point galaxy correlation function using statistical mechanics of cosmological many-body problem

Ahmad

Malik

Bhat

2016

Astrophys Space Sci

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We derive the spatial pair correlation function in gravitational clustering for extended structure of galaxies (e.g. galaxies with halos) by using statistical mechanics of cosmological many-body problem. Our results indicate that in the limit of point masses ( = 0) the two-point correlation function varies as inverse square of relative separation of two galaxies. The effect of softening parameter ' ' on the pair correlation function is also studied and results indicate that two-point correlation function is affected by the softening parameter when the distance between galaxies is small. However, for larger distance between galaxies, the two-point correlation function is not affected at all. The correlation length r 0 derived by our method depends on the random dispersion velocities v 2 1/2 and mean number densitȳ n, which is in agreement with N-body simulations and observations. Further, our results are applicable to the clusters of galaxies for their correlation functions and we apply our results to obtain the correlation length r 0 for such systems which again agrees with the data of N-body simulations and observations.

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Gravitational Phase Transitions in the Cosmological Many-Body System

Cited by 23 publications

References 15 publications

Spatial galaxy distribution function for a three-component system

Spatial galaxy distribution function for a three-component system

Statistical Mechanics of Infinite Gravitating Systems

Gravitational clustering of galaxies: Derivation of two-point galaxy correlation function using statistical mechanics of cosmological many-body problem

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