Neutrino transport with Monte Carlo method: I. Towards fully consistent implementation of nucleon recoils in core-collapse supernova simulations

The small energy exchange via nucleon recoils in neutrino-nucleon scattering is now supposed to be one of the important factors for successful explosion of core-collapse supernovae (CCSNe) as they can change neutrino spectra through accumulation of a large number of scatterings. In finite-difference methods employed for neutrino transport in CCSN simulations, we normally can not afford to deploy a large enough number of energy bins needed to resolve this small energy exchange and sub-grid techniques are employed one way or another. In this paper we study quantitatively with the Monte Carlo (MC) method how well such a treatment performs. We first investigate the effects of nucleon recoils on the neutrino spectra and confirm that the average energy is reduced by $\sim$15% for heavy-lepton neutrinos and by much smaller quantities for other types of neutrinos in a typical post-bounce situation. It is also observed that the nucleon scattering dominates the electron scattering in the thermalization of neutrino spectra in all flavors. We then study possible artifacts that the coarse energy grid may produce in the finite-difference methods. In order to mimic the latter calculation, we re-distribute MC particles in each energy bin after a certain interval in a couple of ways and study how the results are affected and depend on the energy-resolution. We also discuss possible implications of our results for the finite-difference methods.
Comment: 22 pages, 11 figures, submitted to ApJS