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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2024

Phase transitions in self-gravitating systems and bacterial populations surrounding a central body

Résumé

We study the nature of phase transitions in a self-gravitating classical gas in the presence of a central body. The central body can mimic a black hole at the center of a galaxy or a rocky core (protoplanet) in the context of planetary formation. In the chemotaxis of bacterial populations, sharing formal analogies with self-gravitating systems, the central body can be a supply of ``food'' (chemoattractant). We consider both microcanonical (fixed energy) and canonical (fixed temperature) descriptions and study the inequivalence of statistical ensembles. At high energies (resp. high temperatures), the system is in a ``gaseous'' phase and at low energies (resp. low temperatures) it is in a condensed phase with a ``cusp-halo'' structure, where the cusp corresponds to the rapid increase of the density of the gas at the contact with the central body. For a fixed density $\rho_{*}$ of the central body, we show the existence of two critical points in the phase diagram, one in each ensemble, depending on the core radius $R_{*}$: for small radii $R_{*}R_{*}^{\rm CCP}$, there is no phase transition at all. We study how the nature of these phase transitions changes as a function of the dimension of space. We also discuss the analogies and the differences with phase transitions in the self-gravitating Fermi gas [P.H. Chavanis, Phys. Rev. E 65, 056123 (2002)].

Dates et versions

hal-04185196 , version 1 (22-08-2023)

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Pierre-Henri Chavanis, Julien Sopik, Clément Sire. Phase transitions in self-gravitating systems and bacterial populations surrounding a central body. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2024, 109 (1), pp.014118. ⟨10.1103/PhysRevE.109.014118⟩. ⟨hal-04185196⟩
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