Hydrodynamical simulations of type-II supernovae in one and two dimensions are performed for the revival phase of the delayed shock by neutrino energy deposition. Starting with a post-collapse model of the 1.31 M
ʘ iron core of a 15 M
ʘ star immediately after the stagnation of the prompt shock about 10 ms after core bounce, the models are followed for several hundred milliseconds with varied neutrino fluxes from the neutrino sphere. The variation of the neutrino luminosities is motivated by the considerable increase of the neutrino emission due to convective processes inside and close to the neutrino sphere (see Janka 1993), which are driven by negative gradients of entropy and electron concentration left behind by the prompt shock (Burrows & Fryxell 1992, Janka & Müller 1992). The size of this luminosity increase remains to be quantitatively analyzed yet and may require multi-dimensional neutrino transport. However, in the presented simulations the region below the neutrino sphere is cut out and replaced by an inner boundary condition, so that the convective zone is only partially included and the neutrino flows are treated as a freely changeable energy source.
For small neutrino luminosities the energy transfer to the matter is insufficient to revive the stalled shock. However, there is a sharp transition to successful explosions, when the neutrino luminosities lie above some ‘threshold value’. Once the shock is driven out and the density and temperature of the matter between neutrino sphere and shock start to decrease during the expansion, suitable conditions for further neutrino energy deposition are maintained, and an explosion results. With the neutrino energy deposition the entropy per nucleon in the region between neutrino sphere and shock grows, and convective overturn will set in. Multi-dimensional simulations show that due to the large pressure scale height a large-scale pattern of up-flows and down-flows with velocities close to the local speed of sound develops. Consequently, cold, postshock material is advected down into the neutrino heating layer close to the neutrino sphere and hot material is transported outwards, thus reducing energy losses by re-emission of neutrinos and increasing the pressure behind the shock. Therefore these convective processes are found to be a very important aid to the delayed supernova explosion. In fact, two-dimensional models explode even in cases where spherically symmetrical computations fail.