EDP Sciences
Free access
Volume 401, Number 1, April I 2003
Page(s) 15 - 42
Section Cosmology
DOI http://dx.doi.org/10.1051/0004-6361:20021779

A&A 401, 15-42 (2003)
DOI: 10.1051/0004-6361:20021779

Gravitational instability of isothermal and polytropic spheres

P. H. Chavanis

Laboratoire de Physique Quantique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France
(Received 3 July 2002 / Accepted 19 November 2002)

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 connexion with a generalized thermodynamical approach 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.

Key words: stellar dynamics -- hydrodynamics -- instabilities -- gravitation

© ESO 2003