Collisional and Fast Neutrino Flavor Instabilities in Two-dimensional Core-collapse Supernova Simulation with Boltzmann Neutrino Transport

We present a comprehensive study on the occurrences of the collisional flavor instability (CFI) and the fast flavor instability (FFI) of neutrinos based on a two-dimensional (2D) core-collapse supernova (CCSN) simulation performed with a Boltzmann radiation hydrodynamics code. We find that CFI occurs in a region with the baryon-mass density of $10^{10}\lesssim \rho \lesssim 10^{12}\,\mathrm{g}\,\mathrm{cm}^{-3}$, which is similar to the previous results in one-dimensional (1D) CCSN models. In contrast to 1D, however, the CFI region varies with time vigorously in the 2D model, whereas it had a quiescent structure in 1D. This is attributed to the fact that the turbulent flows advected from a gain region account for the temporal variations. Another noticeable difference from the 1D models is the appearance of resonance-like CFI where number densities of $\nu_e$, $\bar\nu_e$ nearly coincide each other. The CFI growth rate there is enhanced and can reach $\sim10^{-3}\,\mathrm{cm}^{-1}$. As for FFI, on the other hand, it appears in three different regions; (1) the region overlapped with the resonance-like CFI, (2) neutrino decoupling regions where $\bar{\nu}_e$'s are strongly emitted, and (3) optically thin regions where neutral-current scatterings dominate over charged-current reactions. Although overall properties for FFI are consistent with previous studies, we find that the number of electron-neutrinos lepton number crossing (ELN crossing) temporary becomes multiple, which can be assessed accurately only by multi-angle treatments in neutrino transport. We find that the growth rate of FFI is always higher than CFI if both of them occur, which suggests that the former is dominant for the linear evolution.