The neutrino-heating mechanism remains a viable possibility for the cause of the explosion in a wide mass range of supernova progenitors. This is demonstrated by recent two-dimensional hydrodynamic simulations with detailed, energy-dependent neutrino transport. Neutrino-driven explosions were not only found for stars in the range of 8-10 solar masses with ONeMg cores and in case of the iron core collapse of a progenitor with 11 solar masses, but also for a ``typical progenitor model of 15 solar masses. For such more massive stars, however, the explosion occurs significantly later than so far thought, and is crucially supported by large-amplitude bipolar oscillations due to the nonradial standing accretion shock instability (SASI), whose low (dipole and quadrupole) modes can develop large growth rates in conditions where convective instability is damped or even suppressed. The dominance of low-mode deformation at the time of shock revival has been recognized as a possible explanation of large pulsar kicks and of large-scale mixing phenomena observed in supernovae like SN 1987A.
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