Dark matter sterile neutrinos in stellar collapse: alteration of   energy/lepton number transport and a mechanism for supernova explosion   enhancement
  We investigate matter-enhanced Mikheyev-Smirnov-Wolfenstein (MSW) active-sterile neutrino conversion in the $\nu_e \rightleftharpoons \nu_s$ channel in the collapse of the iron core of a pre-supernova star. For values of sterile neutrino rest mass $m_s$ and vacuum mixing angle $\theta$ (specifically, $0.5 {\rm keV}< m_s<10 {\rm keV}$ and $\sin^22\theta> 5\times{10}^{-12}$) which include those required for viable sterile neutrino dark matter, our one-zone in-fall phase collapse calculations show a significant reduction in core lepton fraction. This would result in a smaller homologous core and therefore a smaller initial shock energy, disfavoring successful shock re-heating and the prospects for an explosion. However, these calculations also suggest that the MSW resonance energy can exhibit a minimum located between the center and surface of the core. In turn, this suggests a post-core-bounce mechanism to enhance neutrino transport and neutrino luminosities at the core surface and thereby augment shock re-heating: (1) scattering-induced or coherent MSW $\nu_e\to\nu_s$ conversion occurs deep in the core, at the first MSW resonance, where $\nu_e$ energies are large ($\sim 150$ MeV); (2) the high energy $\nu_s$ stream outward at near light speed; (3) they deposit their energy when they encounter the second MSW resonance $\nu_s\to\nu_e$ just below the proto-neutron star surface. 
Jun Hidaka and George M. Fuller