Dynamical stability for the gravitational evolution of a homogeneous polytrope

Details Dynamical stability for the gravitational evolution of a homogeneous polytrope Dynamical stability for the gravitational evolution of a homogeneous polytrope

Mar 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000a%26a...355..564r&link_type=abstract

Astronomy and Astrophysics, v.355, p.564-572 (2000)

Astronomy and Astrophysics

Astrophysics

1

Stars: Formation, Hydrodynamics, Instabilities, Accretion, Accretion Disks

Scientific paper

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 !=q 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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