Journal Article

Adiabatic perturbations in homologous conventional polytropic core collapses of a spherical star

Yi Cao and Yu-Qing Lou

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 403, issue 1, pages 491-495
Published in print March 2010 | ISSN: 0035-8711
Published online March 2010 | e-ISSN: 1365-2966 | DOI:
Adiabatic perturbations in homologous conventional polytropic core collapses of a spherical star

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We perform a non-radial adiabatic perturbation analysis on homologous conventional polytropic stellar core collapses. The core collapse features a polytropic exponent Γ= 4/3 relativistic gas under self-gravity of spherical symmetry while three-dimensional perturbations involve an adiabatic exponent γ with γ≠Γ such that the Brunt–Väisälä buoyancy frequency does not vanish. With proper boundary conditions, we derive eigenvalues and eigenfunctions for different modes of oscillations. In reference to stellar oscillations and earlier results, we examine behaviours of different modes and the criterion for instabilities. The acoustic p modes and surface f modes remain stable. For γ < Γ, convective instabilities appear as unstable internal gravity g modes. For γ > Γ, sufficiently low-order internal gravity g+ modes are stable, whereas sufficiently high-order g+ modes, which would have been stable in a static star, become unstable during self-similar core collapses. For supernova explosions, physical consequences of such inevitable g mode instabilities are speculated.

Keywords: hydrodynamics; instabilities; waves; stars: neutron; stars: oscillations; supernovae: general

Journal Article.  3386 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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