On the Impact of Three Dimensions in Simulations of Neutrino-Driven Core-Collapse Supernova Explosions
Abstract
We present 1D, 2D, and 3D hydrodynamical simulations of core-collapse supernovae including a parameterized neutrino heating and cooling scheme in order to investigate the critical core neutrino luminosity (Lcrit) required for explosion. In contrast to some previous works, we find that 3D simulations explode later than 2D simulations, and that Lcrit at fixed mass accretion rate is somewhat higher in 3D than in 2D. We find, however, that in 2D Lcrit 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 2D. We compare our simulations to semi-analytic explosion criteria and examine the nature of the convective motions in 2D and 3D. 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 2D are inherently larger, with greater volume-to-surface area ratios, than plumes in 3D. 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 Lcrit increases with resolution. Finally, we provide a comparison of our results with other calculations in the literature.