CRITERIA FOR CORE-COLLAPSE SUPERNOVA EXPLOSIONS BY THE NEUTRINO MECHANISM

We investigate the criteria for successful core-collapse supernova explosions by the neutrino mechanism. We find that a critical-luminosity/mass accretion rate condition distinguishes nonexploding from exploding models in hydrodynamic one-dimensional (1D) and two-dimensional (2D) simulations. We present 95 such simulations that parametrically explore the dependence on neutrino luminosity, mass accretion rate, resolution, and dimensionality. While radial oscillations mediate the transition between 1D accretion (nonexploding) and exploding simulations, the nonradial standing accretion shock instability characterizes 2D simulations. We find that it is useful to compare the average dwell time of matter in the gain region with the corresponding heating timescale, but that tracking the residence time distribution function of tracer particles better describes the complex flows in multidimensional simulations. Integral quantities such as the net heating rate, heating efficiency, and mass in the gain region decrease with time in nonexploding models but, for 2D exploding models, increase before, during, and after explosion. At the onset of explosion in 2D, the heating efficiency is similar to 2%-similar to 5% and the mass in the gain region is similar to 0.005 to similar to 0.01 M-circle dot. Importantly, we find that the critical luminosity for explosions in 2D is similar to 70% of the critical luminosity required in 1D. This result is not sensitive to resolution or whether the 2D computational domain is a quadrant or the full 180 degrees. We suggest that the relaxation of the explosion condition in going from 1D to 2D (and to, perhaps, 3D) is of a general character and is not limited by the parametric nature of this study.