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We show that a sterile neutrino with a mass in the 1--20 keV range and a small mixing with the electron neutrino can simultaneously explain the origin of the pulsar motions and the dark matter in the Universe. An asymmetric neutrino emission from a hot nascent neutron star can be the explanation of the observed pulsar velocities. In addition to the pulsar kick mechanism based on resonant neutrino transitions, we point out a new possibility: an asymmetric off-resonant emission of sterile neutrinos. The two cases correspond to different values of the masses and mixing angles. In both cases we identify the ranges of parameters consistent with the pulsar kick, as well as cosmological constraints.
Fuller et al. (Thu,) studied this question.