Neutrinospheres, resonant neutrino oscillations, and pulsar kicks
  Pulsars are rapidly rotating neutron stars and are the outcome of the collapse of the core of a massive star with a mass of the order of or larger than eight solar masses. This process releases a huge gravitational energy of about 10^{53} erg, mainly in the form of neutrinos. During the collapse the density increases, and so does the magnetic field due to the trapping of the flux lines of the progenitor star by the high conductivity plasma. When the density reaches a value of around 10^{12} g cm^{-3} neutrinos become trapped within the protoneutron star and a neutrinosphere, characterized inside by a diffusive transport of neutrinos and outside by a free streaming of neutrinos, is formed and lasts for a few seconds. Here we focus on the structure of the neutrinosphere, the resonant flavor conversion that can happen in its interior, and the neutrino flux anisotropies induced by this phenomena in the presence of a strong magnetic field. We present a detailed discussion in the context of the spherical Eddington model, which provides a simple but reasonable description of a static neutrino atmosphere, locally homogenous and isotropic. Energy and momentum are transported by neutrinos and antineutrinos flowing through an ideal gas of nonrelativistic, nondegenerate nucleons and relativistic, degenerate electrons and positrons. We examine the details of the asymmetric neutrino emission driven by active-sterile neutrino oscillations in the magnetized protoneutron star, and the possibility for this mechanism to explain the intrinsic large velocities of pulsars respect to nearby stars and associated supernova remnants. 
M. Barkovich, J. C. D'Olivo, and R. Montemayor