  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.
