Critical surface for explosions of rotational core-collapse supernovae

The effect of rotation on the explosion of core-collapse supernovae is investigated systematically in three-dimensional simulations. In order to obtain the critical conditions for explosion as a function of mass accretion rate, neutrino luminosity, and specific angular momentum, rigidly rotating matter was injected from the outer boundary with an angular momentum, which is increased every 500 ms. It is found that there is a critical value of the specific angular momentum, above which the standing shock wave revives, for a given combination of mass accretion rate and neutrino luminosity, i.e., an explosion can occur by rotation even if the neutrino luminosity is lower than the critical value for a given mass accretion rate in non-rotational models. The coupling of rotation and hydrodynamical instabilities plays an important role in characterizing the dynamics of shock revival for the range of specific angular momentum that are supposed to be realistic. Contrary to expectations from past studies, the most rapidly expanding direction of the shock wave is not aligned with the rotation axis. Being perpendicular to the rotation axis on average, it can be oriented in various directions. Its dispersion is small when the spiral mode of the standing accretion shock instability (SASI) governs the dynamics, while it is large when neutrino-driven convection is dominant. As a result of the comparison between two-dimensional and three-dimensional rotational models, it is found that m ≠ 0 modes of neutrino-driven convection or SASI are important for shock revival around the critical surface.