Non-linear saturation of g-modes in proto-neutron stars: quieting the acoustic engine

According to Burrows et al.'s acoustic mechanism for core-collapse supernova explosions, the primary, l = 1, g-mode in the core of the proto-neutron star is excited to an energy of similar to 10(50) erg and damps by the emission of sound waves. Here we calculate the damping of the primary mode by the parametric instability, i.e. by non-linear, three-mode coupling between the low-order primary mode and pairs of high-order g-modes. We show that the primary mode is strongly coupled to highly resonant, neutrino damped pairs with n >similar to 10; such short wavelength interactions cannot be resolved in the simulations. We find that the parametric instability saturates the primary mode energy at similar to 10(48) erg, well below the energy needed to drive an explosion. We therefore conclude that acoustic power is unlikely to be energetically significant in core-collapse supernova explosions.