Growth of a Vortex Mode during Gravitational Collapse Resulting in Type II Supernova

Abstract

We investigate stability of a gravitationally collapsing iron core against non-spherical perturbation. The gravitationally collapsing iron core is approximated by a similarity solution for dynamically collapsing polytropic gas sphere. We find that the similarity solution is unstable against non-spherical perturbations. The perturbation grows in proportion to $(t-t_0{)}^{-\sigma }$ while the the central density increases in proportion to $(t-t_0{)}^{-2}$. The growth rate is $\sigma =1/3+\ell (\gamma -4/3)$, where $\gamma$ and $\ell$ denote the polytropic index and the parameter $\ell$ of the spherical harmonics, $Y_{\ell }^m(\theta ,\varphi )$, respectively. The growing perturbation is dominated by vortex motion. Thus it excites global convection during the collapse and may contribute to material mixing in a type II supernova.

AAS LaTeX, 14 pages including 6 figures, submitted to Astrophysical Journal in January

References in corpus (1)

• Stability of Dynamically Collapsing Gas Sphere

Cited by in corpus (3)

• Global Nonradial Instabilities of Dynamically Collapsing Gas Spheres
• The Boltzmann-radiation-hydrodynamics Simulations of Core-collapse Supernovae with Different Equations of State: the Role of Nuclear Composition and the Behavior of Neutrinos
• Critical Accretion Rate for Triggered Star Formation