Gravitational instability of isothermal and polytropic spheres

Details Gravitational instability of isothermal and polytropic spheres Gravitational instability of isothermal and polytropic spheres

2002-07-03

arxiv.org/abs/astro-ph/0207080v4

Astron.Astrophys. 401 (2003) 15

Astronomy and Astrophysics

Astrophysics

Submitted to A&A

Scientific paper

10.1051/0004-6361:20021779

We complete previous investigations on the thermodynamics of self-gravitating systems by studying the grand canonical, grand microcanonical and isobaric ensembles. We also discuss the stability of polytropic spheres in the light of a generalized thermodynamics proposed by Tsallis. We determine in each case the onset of gravitational instability by analytical methods and graphical constructions in the Milne plane. We also discuss the relation between dynamical and thermodynamical stability of stellar systems and gaseous spheres. Our study provides an aesthetic and simple approach to this otherwise complicated subject.

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