Assuming that the neutrino luminosity from the neutron star core is sufficiently high to drive supernova explosions by the neutrino-heating mechanism, we show that low-mode (l = 1, 2) convection can develop from random seed perturbations behind the shock. A slow onset of the explosion is crucial, requiring the core luminosity to vary slowly with time, in contrast to the burst-like exponential decay assumed in previous work. Gravitational and hydrodynamic forces by the globally asymmetric supernova ejecta were found to accelerate the remnant neutron star on a timescale of more than a second to velocities above 500 km/s, in agreement with observed pulsar proper motions.
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