Gravothermal catastrophe: The dynamical stability of a fluid model

Abstract

A re-investigation of the gravothermal catastrophe is presented. By means of a linear perturbation analysis, we study the dynamical stability of a spherical self-gravitating isothermal fluid of finite volume and find that the conditions for the onset of the gravothermal catastrophe, under different external conditions, coincide with those obtained from thermodynamical arguments. This suggests that the gravothermal catastrophe may reduce to Jeans instability, rediscovered in an inhomogeneous framework. We find normal modes and frequencies for the fluid system and show that instability develops on the dynamical time scale. We then discuss several related issues. In particular, (1) for perturbations at constant total energy and constant volume, we introduce a simple heuristic term in the energy budget to mimic the role of binaries. (2) We outline the analysis of the two-component case and show how linear perturbation analysis can also be carried out in this more complex context in a relatively straightforward way. (3) We compare the behavior of the fluid model with that of the collisionless sphere. In the collisionless case the instability seems to disappear, which is at variance with the linear Jeans stability analysis in the homogeneous case. We argue that a key ingredient for understanding the difference lies in the role of the detailed angular momentum in a collisionless system. A spherical stellar system is expected to undergo the gravothermal catastrophe only in the presence of some collisionality, which suggests that the instability is dissipative and not dynamical. Finally, we briefly comment on the meaning of the Boltzmann entropy and its applicability to the study of the dynamics of selfgravitating inhomogeneous gaseous systems.

Galaxy clusters and structure formation in quintessence versus phantom dark energy universe

“…The system undergoes gravothermal catastrophe [17,18]. Note that recently, gravothermal catastrophe has been identified as similar to Jeans instability [57]. Returning to Figure 2, we see that for some even bigger radius, let call it the "reentrant radius", the equilibria are restored.…”

Emergence of extended Newtonian gravity from thermodynamics

“…Accordingly, the microscopic field energy density in Eq. ( 6) is also negative, implying that it is of the gravitational field [12][13][14] . Therefore, we set…”

Caloric curves of classical self-gravitating systems in general relativity

“…As before we consider the instability at E c in the MCE but we focus on a different dynamical model in which the temperature T (t) is uniform throughout the system but evolves with time so as to conserve the energy E. Specifically, we consider a self-gravitating gas (star) described by the Euler-Poisson equations [201,202] or a system of self-gravitating Brownian particles described by the Smoluchowski-Poisson equations [91,92] with an additional equation assuring the conservation of energy.…”

“…44 When E > E c the system settles on a stable equilibrium state in which the pressure gradient equilibrates the gravitational attraction. At E = E c , the equilibrium becomes unstable and the system undergoes a form of gravothermal catastrophe [91,92,201,202]. The system collapses because it is too cold (even if the temperature increases with time) so the thermal pressure cannot balance the gravitational attraction.…”