Gravothermal Catastrophe: the dynamical stability of a fluid model
  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 be carried out also 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 to
understand the difference (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) lies in the
role of the detailed angular momentum in a collisionless system. Finally, we
briefly comment on the meaning of the Boltzmann entropy and its applicability
to the study of the dynamics of self- gravitating inhomogeneous gaseous
systems.
