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

Abstract

We investigate the stability of a gravitationally collapsing iron core against nonspherical perturbation. The gravitationally collapsing iron core is approximated by a similarity solution for a dynamically collapsing polytropic gas sphere. We find that the similarity solution is unstable against nonspherical perturbations. The perturbation grows in proportion to (t - t0)-σ while the central density increases in proportion to (t - t0)-2. The growth rate is σ = + ℓ(γ - 4/3), where γ and ℓ denote the polytropic index and the parameter ℓ of the spherical harmonics, Y(θ,φ), 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.