  We show that a sterile neutrino with 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.
