Mu and Tau Neutrino Thermalization and Production in Supernovae: Processes and Timescales

Abstract

We investigate the rates of production and thermalization of $\nu_\mu$ and $\nu_\tau$ neutrinos at temperatures and densities relevant to core-collapse supernovae and protoneutron stars. Included are contributions from electron scattering, electron-positron annihilation, nucleon-nucleon bremsstrahlung, and nucleon scattering. For the scattering processes, in order to incorporate the full scattering kinematics at arbitrary degeneracy, the structure function formalism developed by Reddy et al. (1998) and Burrows and Sawyer (1998) is employed. Furthermore, we derive formulae for the total and differential rates of nucleon-nucleon bremsstrahlung for arbitrary nucleon degeneracy in asymmetric matter. We find that electron scattering dominates nucleon scattering as a thermalization process at low neutrino energies ($\epsilon_\nu\lesssim 10$ MeV), but that nucleon scattering is always faster than or comparable to electron scattering above $\epsilon_\nu\simeq10$ MeV. In addition, for $\rho\gtrsim 10^{13}$ g cm$^{-3}$, $T\lesssim14$ MeV, and neutrino energies $\lesssim60$ MeV, nucleon-nucleon bremsstrahlung always dominates electron-positron annihilation as a production mechanism for $\nu_\mu$ and $\nu_\tau$ neutrinos.