Stability of the Accretion Flows with Stalled Shocks in Core-Collapse Supernovae

Bearing in mind the application to the theory of core-collapse supernovae, we performed a global linear analysis on the stability of spherically symmetric accretion flows through a standing shock wave onto a proto neutron star. As unperturbed flows, we adopted the spherically symmetric steady solutions obtained with realistic equation of state and formulae for neutrino reaction rates taken into account. These solutions are characterized by the mass accretion rate and neutrino luminosity. Then we solved the equations for linear perturbations numerically, and obtained the eigen frequencies and eigen functions. We found (1) the flows are stable for all modes if the neutrino luminosity is lower than a certain value, e.g. ∼ 1× 10 ergs/s for Ṁ = 1.0M⊙/s. (2) For larger luminosities, the non-radial instabilities are induced, probably via the advection-acoustic cycles. Interestingly, the modes with l = 2 and 3 become unstable at first for relatively low neutrino luminosities, e.g. ∼ 2 − 3 × 10 ergs/s for the same accretion rate, whereas the l = 1 mode is the most unstable for higher luminosities, ∼ 3 − 7 × 10 ergs/s. These are all oscillatory modes. (3) For still larger luminosities, & 7× 10 ergs/s for Ṁ = 1.0M⊙/s, non-oscillatory modes, both radial and non-radial, become unstable. These non-radial modes were identified as convection. The growth rates of the convective modes have a peak at l = 5 − 11, depending on the luminosity. We confirmed the results obtained by numerical simulations that the instabilities induced by the advection-acoustic cycles are more important than the convection for lower neutrino luminosities. Yukawa Institute for Theoretical Physics, Kyoto University, Oiwake-cho, Sakyo, Kyoto 606-8502, Japan; [email protected] Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan; [email protected] Advanced Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan