De-leptonization and Non-Axisymmetric Instabilities in Core Collapse   Supernovae
  The timescale of de-leptonization by neutrino loss and associated contraction of a proto-neutron star is short compared to the time to progagate a shock through the helium core of a massive star, and so the de-leptonization phase does not occur in the vacuum of space, but within the supernova ambiance whether or not there has been a successful explosion. Dynamical non-axisymmetric instabilities (NAXI) are predicted for sufficiently strongly differentially rotating proto-neutron stars. Some modes are unstable for small values of the ratio of rotational kinetic energy to binding energy, T/|W| > 0.01. The NAXI are likely to drive magnetoacoustic waves into the surrounding time-dependent density structure. These waves represent a mechanism of the dissipation of the free energy of differential rotation of the proto-neutron star, and the outward deposition of this energy may play a role in the supernova explosion process. We estimate the power produced by this process and the associated timescale and discuss the possible systematics of the de-leptonization phase in this context. A likely possibility is that the proto-neutron star will spin down through these effects before de-leptonization and produce substantial but not excessive energy input. 
J. Craig Wheeler and Shizuka Akiyama