  Neutrino oscillations in a core-collapse supernova may be responsible for the
observed rapid motions of pulsars. Given the present bounds on the neutrino
masses, the pulsar kicks require a sterile neutrino with mass 2-20 keV and a
small mixing with active neutrinos. The same particle can be the cosmological
dark matter. Its existence can be confirmed the by the X-ray telescopes if they
detect a 1-10 keV photon line from the decays of the relic sterile neutrinos.
In addition, one may be able to detect gravity waves from a pulsar being
accelerated by neutrinos in the event of a nearby supernova.
