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Neutrino oscillations in a core-collapse supernova may be responsible for theobserved rapid motions of pulsars. Three-dimensional numerical calculationsshow that, in the absence of neutrino oscillations, the recoil velocities ofneutron stars should not exceed 200 km/s, while there exists a substantialpopulation of pulsars that move faster than 1000 km/s. A small asymmetry in theneutrino emission may be the solution of this long-standing puzzle. Such anasymmetry could arise from neutrino oscillations, but, given the present boundson the neutrino masses, the pulsar kicks require a sterile neutrino with a 1-20keV mass and a small mixing with active neutrinos. The same particle can be thecosmological dark matter. Its existence can be confirmed by X-ray telescopes ifthey detect X-ray photons from the decays of the relic sterile neutrinos. Onecan also verify the neutrino kick mechanism by observing gravity waves from anearby supernova.Comment: Invited talk at the 5th Workshop on "Neutrino Oscillations and their  Origin" (NOON-2004), Tokyo, Japan, February 11-15, 2004; 10 pages, 2 figure

NEUTRINO OSCILLATIONS, AND THE ORIGIN OF PULSAR VELOCITIES AND DARK MATTER