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Dynamical stability for the gravitational evolution of a homogeneous polytrope
C. Ringeval * and
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 , is studied using the lagrangian formalism. We obtain the analytical expression for density perturbations at the first order.
In the case , 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 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 , and for a collapsing one, for .
Key words: stars: formation hydrodynamics instabilities accretion, accretion disks
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Online publication: March 9, 2000