ON THE IMPACT OF THREE DIMENSIONS IN SIMULATIONS OF NEUTRINO-DRIVEN CORE-COLLAPSE SUPERNOVA EXPLOSIONS

We present one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) hydrodynamical simulations of core-collapse supernovae including a parameterized neutrino heating and cooling scheme in order to investigate the critical core neutrino luminosity (L-crit) required for explosion. In contrast to some previous works, we find that 3D simulations explode later than 2D simulations, and that L-crit at fixed mass accretion rate is somewhat higher in three dimensions than in two dimensions. We find, however, that in two dimensions L-crit increases as the numerical resolution of the simulation increases. In contrast to some previous works, we argue that the average entropy of the gain region is in fact not a good indicator of explosion but is rather a reflection of the greater mass in the gain region in two dimensions. We compare our simulations to semi-analytic explosion criteria and examine the nature of the convective motions in two dimensions and three dimensions. We discuss the balance between neutrino-driven buoyancy and drag forces. In particular, we show that the drag force will be proportional to a buoyant plume's surface area while the buoyant force is proportional to a plume's volume and, therefore, plumes with greater volume-to-surface-area ratios will rise more quickly. We show that buoyant plumes in two dimensions are inherently larger, with greater volume-to-surface-area ratios, than plumes in three dimensions. In the scenario that the supernova shock expansion is dominated by neutrino-driven buoyancy, this balance between buoyancy and drag forces may explain why 3D simulations explode later than 2D simulations and why L-crit increases with resolution. Finally, we provide a comparison of our results with other calculations in the literature.