Core-collapse supernovae are among the most fascinating phenomena in astrophysics and provide a formidable challenge for theoretical investigation. They mark the spectacular end of the lives of massive stars and, in an explosive eruption, release as
much energy as the sun produces during its whole life. A better understanding of the astrophysical role of supernovae as birth sites of neutron stars, black holes, and heavy chemical elements, and more reliable predictions of the observable signals from stellar death events are tightly linked to the solution of the long-standing puzzle how collapsing stars achieve to explode. In this article our current knowledge of the processes that contribute to the success of the explosion mechanism are concisely reviewed. After a short overview of the sequence of stages of stellar core-collapse events, the general properties of the progenitor-dependent neutrino emission will be briefly described. Applying sophisticated neutrino transport in axisymmetric (2D) simulations with general relativity as well as in simulations with an approximate treatment of relativistic effects, we could find successful neutrino-driven explosions for a growing set of progenitor stars. First results of three-dimensional (3D) models have been obtained, and magnetohydrodynamic simulations demonstrate that strong initial magnetic fields in the pre-collapse core can foster the onset of neutrino-powered supernova explosions even in nonrotating stars. These results are discussed in the context of the present controversy about the value of 2D simulations for exploring the supernova mechanism in realistic 3D environments, and they are interpreted against the background of the current disagreement on the question whether the standing accretion shock instability (SASI) or neutrino-driven convection is the crucial agency that supports the onset of the explosion.
We perform hydrodynamic supernova simulations in spherical symmetry for over 100 single stars of solar metallicity to explore the progenitor-explosion and progenitor-remnant connections established by the neutrino-driven mechanism. We use an approxim
ative treatment of neutrino transport and replace the high-density interior of the neutron star (NS) by an inner boundary condition based on an analytic proto-NS core-cooling model, whose free parameters are chosen such that explosion energy, nickel production, and energy release by the compact remnant of progenitors around 20 solar masses are compatible with Supernova 1987A. Thus we are able to simulate the accretion phase, initiation of the explosion, subsequent neutrino-driven wind phase for 15-20 s, and the further evolution of the blast wave for hours to days until fallback is completed. Our results challenge long-standing paradigms. We find that remnant mass, launch time, and properties of the explosion depend strongly on the stellar structure and exhibit large variability even in narrow intervals of the progenitors zero-age-main-sequence mass. While all progenitors with masses below about 15 solar masses yield NSs, black hole (BH) as well as NS formation is possible for more massive stars, where partial loss of the hydrogen envelope leads to weak reverse shocks and weak fallback. Our NS baryonic masses of ~1.2-2.0 solar masses and BH masses >6 solar masses are compatible with a possible lack of low-mass BHs in the empirical distribution. Neutrino heating accounts for SN energies between some 10^{50} erg and about 2*10^{51} erg, but can hardly explain more energetic explosions and nickel masses higher than 0.1-0.2 solar masses. These seem to require an alternative SN mechanism.
