Gravitational instability of isothermal and polytropic spheres
نویسنده
چکیده
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.
منابع مشابه
Gravitational instability of polytropic spheres and generalized thermodynamics
We complete the existing literature on the structure and stability of polytropic gas spheres reported in the classical monograph of Chandrasekhar (1942). For isolated polytropes with index 1 < n < 5, we provide a new, alternative, proof that the onset of instability occurs for n = 3 and we express the perturbation profiles of density and velocity at the point of marginal stability in terms of t...
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