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

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 − t0) −σ while the the central density increases in proportion to (t − t0) −2. The growth rate is σ = 1/3 + l (γ − 4/3), where γ and l denote the polytropic index and the parameter l of the spherical harmonics, Y m l (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. Subject headings: gravitation — hydrodynamics — instabilities — stars: supernovae