Numerical modeling of core-collapse supernovae and compact objects

Massive stars (M ≥ 10M_⊙) end their lives with spectacular explosions due to gravitational collapse. The collapse turns the stars into compact objects such as neutron stars and black holes with the ejection of cosmic rays and heavy elements. Despite the importance of these astrophysical events, the mechanism of supernova explosions has been an unsolved issue in astrophysics. This is because clarification of the supernova dynamics requires the full knowledge of nuclear and neutrino physics at extreme conditions, and large-scale numerical simulations of neutrino radiation hydrodynamics in multi-dimensions. This article is a brief overview of the understanding (with difficulty) of the supernova mechanism through the recent advance of numerical modeling at supercomputing facilities. Numerical studies with the progress of nuclear physics are applied to follow the evolution of compact objects with neutrino emissions in order to reveal the birth of pulsars/black holes from the massive stars.