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Article Dans Une Revue Astronomy and Astrophysics - A&A Année : 2000

Dynamical stability for the gravitational evolution of a homogeneous polytrope

C. Ringeval
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S. Bouquet
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Résumé

The dynamic stability of the spherical gravitational evolution (collapse or expansion) for a homogeneous polytropic gas with any exponent $\gamma ,$ is studied using the lagrangian formalism. We obtain the analytical expression for density perturbations at the first order. In the case $\gamma =~4/3,$ 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 $\gamma \not = 4/3$ 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 $\gamma <4/3,$ and for a collapsing one, for $\gamma >5/3.$
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Dates et versions

hal-00103211 , version 1 (03-10-2006)

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  • HAL Id : hal-00103211 , version 1

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C. Ringeval, S. Bouquet. Dynamical stability for the gravitational evolution of a homogeneous polytrope. Astronomy and Astrophysics - A&A, 2000, 355, pp.564-572. ⟨hal-00103211⟩
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