Resolution Dependence in Magnetohydrodynamic Simulations of Neutrino-Driven Core-Collapse Supernovae

We investigate the role of resolution and initial magnetic field strength on core-collapse supernovae in simulations of a non-rotating $13 \mathrm{M_\odot}$ progenitor. Specifically, we study the effect on shock revival, explosion dynamics, and the properties of the compact remnant. We run four models with different numerical grid resolutions with an initial central dipole field strength of $\mathord{\approx}10^{12}\, \mathrm{G}$. Two of those resolutions are also run with a weaker central magnetic field of $\mathord{\approx}10^{10}\, \mathrm{G}$ . The shock revival time for all models is largely independent of resolution and initial magnetic field strength, but we find higher explosion energies when the initial magnetism is stronger and at higher resolutions. We find that models with strong magnetic fields have lower neutrino luminosity and energies, due to a proto-neutron star (PNS) that is deformed by the strong magnetic fields. At higher resolutions, magnetic fields are amplified more efficiently in the gain region and in the PNS via the small-scale dynamo. Although the strong magnetic fields do not directly drive the explosion, they have a subsidiary impact on the explosion mechanism and compensate for the reduced neutrino heating. Stronger magnetic energies in the PNS also affect energy and angular momentum redistribution, leading to more extended and vigorous PNS convection zones at higher resolutions.