Three‐Dimensional Simulations of Standing Accretion Shock Instability in Core‐Collapse Supernovae

Abstract

We have studied non-axisymmetric standing accretion shock instability, or\nSASI, by 3D hydrodynamical simulations. This is an extention of our previous\nstudy on axisymmetric SASI. We have prepared a spherically symmetric and steady\naccretion flow through a standing shock wave onto a proto-neutron star, taking\ninto account a realistic equation of state and neutrino heating and cooling.\nThis unperturbed model is supposed to represent approximately the typical\npost-bounce phase of core-collapse supernovae. We then have added a small\nperturbation (~1%) to the radial velocity and computed the ensuing evolutions.\nNot only axisymmetric but non-axisymmetric perturbations have been also\nimposed. We have applied mode analysis to the non-spherical deformation of the\nshock surface, using the spherical harmonics. We have found that (1) the growth\nrates of SASI are degenerate with respect to the azimuthal index m of the\nspherical harmonics Y_l^m, just as expected for a spherically symmetric\nbackground, (2) nonlinear mode couplings produce only m=0 modes for the\naxisymmetric perturbations, whereas m=!0 modes are also generated in the\nnon-axisymmetric cases according to the selection rule for the quadratic\ncouplings, (3) the nonlinear saturation level of each mode is lower in general\nfor 3D than for 2D because a larger number of modes are contributing to\nturbulence in 3D, (4) low l modes are dominant in the nonlinear phase, (5) the\nequi-partition is nearly established among different m modes in the nonlinear\nphase, (6) the spectra with respect to l obey power laws with a slope slightly\nsteeper for 3D, and (7) although these features are common to the models with\nand without a shock revival at the end of simulation, the dominance of low l\nmodes is more remarkable in the models with a shock revival.\n