Validity conditions of the hydrostatic approach for self-gravitating systems: a microcanonical analysis

Champion, Maxime; Alastuey, A.; Dauxois, Thierry; Ruffo, Stefano

doi:10.1088/1751-8113/47/22/225001

Cited by 8 publications

(18 citation statements)

References 44 publications

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“…The probability of such events is extremely low so that, in practice, the system remains in the metastable phase [8]. 7 Similar phase transitions are obtained if, instead of quantum particles, we consider classical particles and regularize the gravitational potential at short distances [25,[29][30][31] or take into account the finite size of the particles by considering a hard spheres gas [6,23,28,[32][33][34]. Even if the details of the phase transitions depend on the specific form of the small-scale regularization, the phenomenology of these phase transitions is relatively universal as described in [8].…”

Section: Introductionmentioning

confidence: 57%

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Models of dark matter halos based on statistical mechanics: The fermionic King model

2015

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article number: 123527International audienceWe discuss the nature of phase transitions in the fermionic King model which describes tidally truncated quantum self-gravitating systems. This distribution function takes into account the escape of high energy particles and has a finite mass. On the other hand, the Pauli exclusion principle puts an upper bound on the phase space density of the system and stabilizes it against gravitational collapse. As a result, there exists a statistical equilibrium state for any accessible values of energy and temperature. We plot the caloric curves and investigate the nature of phase transitions as a function of the degeneracy parameter in both microcanonical and canonical ensembles. We consider stable and metastable states and emphasize the importance of the latter for systems with long-range interactions. Phase transitions can take place between a "gaseous" phase unaffected by quantum mechanics and a "condensed" phase dominated by quantum mechanics. The phase diagram exhibits two critical points, one in each ensemble, beyond which the phase transitions disappear. There also exist a region of negative specific heats and a situation of ensemble inequivalence for sufficiently large systems. We apply the fermionic King model to the case of dark matter halos made of massive neutrinos. The gaseous phase describes large halos and the condensed phase describes dwarf halos. Partially degenerate configurations describe intermediate size halos. We argue that large dark matter halos cannot harbor a fermion ball because these nucleus-halo configurations are thermodynamically unstable (saddle points of entropy). Large dark matter halos may rather contain a central black hole resulting from a dynamical instability of relativistic origin occurring during the gravothermal catastrophe

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Section: Introductionmentioning

confidence: 57%

“…As a result, for µ ≫ 1, the solutions A and B have almost the same temperature (β A ≃ β B ) and the profiles A and B coincide outside of the nucleus (see Figs. [34][35][36]. This is why the branches A and B in the series of equilibria superimpose for µ → +∞ (see Fig.…”

Section: Density Profiles and Rotation Curves Of The Fermionic Kinmentioning

confidence: 99%

Models of dark matter halos based on statistical mechanics: The fermionic King model

2015

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“…Figure 7 shows the kurtosis for the distribution of the sum of M subsequent position variables as a function of M for both cases of regularization, with an energy per particle e = −0.7 such that the particles form a compact cluster. For both cases the kurtosis oscillates around the expected value for uncorrelated variables, indicating that the mean field description is still valid with a hard-core part in the potential, although a further study on the validity of the mean field approach for long-range interacting potentials with a short-range divergence is still in need [32]. is drawn for reference.…”

Section: B Hard-core Regularizationmentioning

confidence: 96%

Microcanonical Monte Carlo study of one dimensional self-gravitating lattice gas models

et al. 2017

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In this study we present a Microcanonical Monte Carlo investigation of one dimensional selfgravitating toy models. We study the effect of hard-core potentials and compare to those results obtained with softening parameters and also the effect of the geometry of the models. In order to study the effect of the geometry and the borders in the system we introduce a model with the symmetry of motion in a line instead of a circle, which we denominate as 1/r model. The hard-core particle potential introduces the effect of the size of particles and, consequently, the effect of the density of the system that is redefined in terms of the packing fraction of the system. The latter plays a role similar to the softening parameter in the softened particles' case. In the case of low packing fractions both models with hard-core particles show a behavior that keeps the intrinsic properties of the three dimensional gravitational systems such as negative heat capacity. For higher values of the packing fraction the ring the system behaves as the Hamiltonian Mean Field model and while for the 1/r it is similar to the one-dimensional systems. * marco@fis.unb.br 1 arXiv:1512.01391v1 [cond-mat.stat-mech] 4 Dec 2015

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“…It can be shown that the statistical mechanics approach gives exactly the same results as the thermodynamic approach in a proper thermodynamic limit where the number of particles N → +∞ keeping Λ = −ER/GM 2 and η = βGM m/R fixed [101]. We refer to [107][108][109][110] for rigorous mathematical results on this subject.…”

Section: Introductionmentioning

confidence: 98%

Caloric curves of classical self-gravitating systems in general relativity

Alberti,

Chavanis

2019

Preprint

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We determine the caloric curves of classical self-gravitating systems at statistical equilibrium in general relativity. In the classical limit, the caloric curves of a self-gravitating gas depend on a unique parameter ν = GN m/Rc 2 , called the compactness parameter, where N is the particle number and R the system's size. Typically, the caloric curves have the form of a double spiral. The "cold spiral", corresponding to weakly relativistic configurations, is a generalization of the caloric curve of nonrelativistic classical self-gravitating systems. The "hot spiral", corresponding to strongly relativistic configurations, is similar (but not identical) to the caloric curve of the ultrarelativistic self-gravitating black-body radiation. We introduce two types of normalization of energy and temperature in order to obtain asymptotic caloric curves describing respectively the cold and the hot spirals in the limit ν → 0. As the number of particles increases, the cold and the hot spirals approach each other, merge at ν S = 0.128, form a loop above νS = 0.1415, reduce to a point at νmax = 0.1764, and finally disappear. Therefore, the double spiral shrinks when the compactness parameter ν increases, implying that general relativistic effects render the system more unstable. We discuss the nature of the gravitational collapse at low and high energies with respect to a dynamical (fast) or a thermodynamical (slow) instability.

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Validity conditions of the hydrostatic approach for self-gravitating systems: a microcanonical analysis

Cited by 8 publications

References 44 publications

Models of dark matter halos based on statistical mechanics: The fermionic King model

Models of dark matter halos based on statistical mechanics: The fermionic King model

Microcanonical Monte Carlo study of one dimensional self-gravitating lattice gas models

Caloric curves of classical self-gravitating systems in general relativity

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