Excitation of g-modes in a proto-neutron star by the standing accretion shock instability

The acoustic-revival mechanism in core-collapse supernovae, proposed recently by the Arizona group led by A. Burrows, is an interesting new scenario. With an aim to understanding the elementary processes involved in this mechanism, we have calculated the eigenfrequencies and eigenfunctions for the g-mode oscillations of a nonrotating proto-neutron star. The possible excitation of these modes by the standing accretion shock instability, or SASI, is discussed. We have formulated the forced oscillations of g-modes due to external pressure perturbations exerted on the proto-neutron star's surface. The driving pressure fluctuations have been adopted from our previous computations of axisymmetric SASI in the nonlinear regime. We pay particular attention to low-l modes, since these are the modes that are dominant in SASI and what Burrows et al. claim to have played an important role in their acousticrevival scenario. Here l is the index of the spherical harmonic functions, Y_l ^m. Although the frequency spectrum of nonlinear SASI is broadened substantially by nonlinear couplings, the typical frequency is still much smaller than those of the ,ç-modes, leading to a severe impedance mismatch. As a result, the excitations of various g-modes are rather inefficient, and the energy of the saturated g-modes is ∼10⁵⁰ ergs or less, with the g₂ mode being the largest in our model. Here the g₂ mode has two radial nodes and is confined to the interior of the convective region. The energy transfer rate from the g-modes to outgoing sound waves is estimated from the growth of the g-modes to be ∼10 ⁵¹ ergs s^-1 in the models studied in this paper.