Towards an Understanding of the Resolution Dependence of Core-Collapse Supernova Simulations

Using our new state-of-the-art core-collapse supernova (CCSN) code Fornax, we explore the dependence upon spatial resolution of the outcome and character of three-dimensional (3D) supernova simulations. For the same 19-M$_{\odot}$ progenitor star, energy and radial binning, neutrino microphysics, and nuclear equation of state, changing only the number of angular bins in the $\theta$ and $\phi$ directions, we witness that our lowest resolution 3D simulation does not explode. However, when jumping progressively up in resolution by factors of two in each angular direction on our spherical-polar grid, models then explode, and explode slightly more vigorously with increasing resolution. This suggests that there can be a qualitative dependence of the outcome of 3D CCSN simulations upon spatial resolution. The critical aspect of higher spatial resolution is the adequate capturing of the physics of neutrino-driven turbulence, in particular its Reynolds stress. The greater numerical viscosity of lower-resolution simulations results in greater drag on the turbulent eddies that embody turbulent stress, and, hence, in a diminution of their vigor. Turbulent stress not only pushes the temporarily stalled shock further out, but bootstraps a concomitant increase in the deposited neutrino power. Both effects together lie at the core of the resolution dependence we observe.