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Astron. Astrophys. 355, 564-572 (2000)

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Dynamical stability for the gravitational evolution of a homogeneous polytrope

C. Ringeval  * and S. Bouquet

Commissariat à l'Énergie Atomique, Centre d'étude de Bruyères-le-Châtel, DAM/DIF, Département de Physique Théorique et Appliquée, Service de Physique des Plasmas et Électromagnetisme, 91680 Bruyères-le-Châtel, France

Received 19 July 1999 / Accepted 3 January 2000


The dynamic stability of the spherical gravitational evolution (collapse or expansion) for a homogeneous polytropic gas with any exponent [FORMULA], is studied using the lagrangian formalism. We obtain the analytical expression for density perturbations at the first order.

In the case [FORMULA], the Jeans' criterion is easily generalized to a self-similar expanding background. The collapsing case is found to be always unstable. The stability of density modes obtained for [FORMULA] does not introduce any conditions on the wavelength perturbation, but only a criterion on the polytropic index. As a result, stability is obtained for an expanding gas provided [FORMULA], and for a collapsing one, for [FORMULA].

Key words: stars: formation – hydrodynamics – instabilities – accretion, accretion disks

* Present adress: DARC, Observatoire de Paris-Meudon, 5, Place Jules Janssen, 92195 Meudon, France

Send offprint requests to: S. Bouquet

Correspondence to: (bouquet@bruyeres.cea.fr; christophe.ringeval@obspm.fr)

© European Southern Observatory (ESO) 2000

Online publication: March 9, 2000