Conditions for Shock Revival by Neutrino Heating in Core-Collapse Supernovae
Abstract
Energy deposition by neutrinos can rejuvenate the stalled bounce shock and can provide the energy for the supernova explosion of a massive star. This neutrino-heating mechanism, however, is not finally accepted or proven as the trigger of the explosion. Part of the problem is that different groups have obtained seemingly discrepant results, and the complexity of the hydrodynamic models often hampers a clear and simple interpretation of the results. This demands a deeper theoretical understanding of the requirements of a successful shock revival. An approach is described here which allows one to discuss the neutrino heating phase analytically by a time-dependent treatment. A criterion is derived which formulates the minimum requirements for shock revival. It shows that the success of the supernova shock does not only depend on the neutrino heating in the gain region and the mass infall to the shock. It is also sensitive to the energy loss by neutrino emission in the cooling layer outside the neutrinosphere, which governs the accretion of matter into the nascent neutron star. The analysis shows that neutrino-driven shock expansion and acceleration are neither likely to occur at very early times after core bounce, when the mass infall rate is still very high, nor at late times when the accretion rate has become too low. However, there is a window of conditions, realized at intermediate post-bounce times, where the mass accretion by the shock and the neutrinospheric luminosity define favorable conditions for shock revival. This space of advantageous conditions widens with a larger value of the shock stagnation radius. The importance of convective energy transport in the neutrino-heating region is confirmed.Keywords
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