  Neutrino oscillations in a core-collapse supernova may be responsible for the
observed rapid motions of pulsars. Three-dimensional numerical calculations
show that, in the absence of neutrino oscillations, the recoil velocities of
neutron stars should not exceed 200 km/s, while there exists a substantial
population of pulsars that move faster than 1000 km/s. A small asymmetry in the
neutrino emission may be the solution of this long-standing puzzle. Such an
asymmetry could arise from neutrino oscillations, but, given the present bounds
on the neutrino masses, the pulsar kicks require a sterile neutrino with a 1-20
keV mass and a small mixing with active neutrinos. The same particle can be the
cosmological dark matter. Its existence can be confirmed by X-ray telescopes if
they detect X-ray photons from the decays of the relic sterile neutrinos. One
can also verify the neutrino kick mechanism by observing gravity waves from a
nearby supernova.
