Gravothermal instability of anisotropic selfgravitating gas spheres  Singular equilibrium solution
Abstract
A reinvestigation of linear perturbation theory is presented which examines the hydrostatic readjustment of an isolated selfgravitating gas sphere to a redistribution of energy. Such a model describes a stellar system by the common equations of gas in hydrostatic equilibrium but with the effect of the anisotropic velocity distribution on the pressure gradient. The total variation of the Boltzmann entropy resulting from a perturbation of the system caused by a redistribution of heat (i.e., rms kinetic energy of the stars) is calculated for anisotropic solutions to first order, as well as to second order for the isotropic equilibrium. The extremized eigenfunctions which represent the entropy and anisotropy perturbation functions exhibit gravothermal behavior in the central region where heat is removed. It is also found that the anisotropy readjusts nonthermally, in the sense that the system departs from isotropy although the total entropy increases.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 September 1991
 DOI:
 10.1093/mnras/252.2.177
 Bibcode:
 1991MNRAS.252..177S
 Keywords:

 Equilibrium Equations;
 Gas Dynamics;
 Gravitational Effects;
 Thermal Instability;
 Anisotropy;
 Hydrostatics;
 Kinetic Energy;
 Perturbation Theory;
 Astrophysics