Momentum Space Resolution Dependence in Boltzmann Neutrino Radiation Hydrodynamics Simulations of Core-collapse Supernovae

Abstract

Finite momentum space resolution is a primary source of uncertainty in solving the Boltzmann equation with the discrete-ordinates method. In this paper, the momentum space resolution dependence of Boltzmann neutrino transport is studied by performing a series of two-dimensional core-collapse supernova (CCSN) simulations. The effects on the explosion dynamics are discussed by individually varying the resolutions of the zenith and azimuth angles in momentum space, and of the energy. It is found that a coarse zenith angle resolution artificially facilitates the explosion, even turning non-exploding models into exploding ones. This is because the coarse zenith angle grid cannot capture the forward-peaked distribution, thereby underestimating the flux factor and making neutrinos stay in the gain region for a longer time. The dependence on the azimuth angle resolution is found to have little effect for the present non-rotating models, which is understandable given the sphericity of the CCSN core. In contrast to the zenith angle resolution, a coarse energy resolution is found to artificially suppress the explosion. This is because the neutrino heating rate at intermediate energies ($\sim30$--$50\,\mathrm{MeV}$) is underestimated in the low-resolution case. Finally, the resolution dependence is studied for a one-dimensional black hole (BH) forming model. Unlike the explosion dynamics, BH formation does not exhibit a strong angular dependence. On the other hand, a coarse energy resolution is found to delay the BH formation time. This is because the momentum feedback is overestimated at low resolution, which allows a more massive neutron star to be supported.