μ and τ neutrino thermalization and production in supernovae: Processes and time scales

We investigate the rates of production and thermalization of [Formula Presented] and [Formula Presented] 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, Prakash, and Lattimer [Phys. Rev. D [Formula Presented] 013009 (1998)] and Burrows and Sawyer [Phys. Rev. C [Formula Presented] 554 (1998)] is employed. Furthermore, we derive formulas 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 [Formula Presented] but that nucleon scattering is always faster than or comparable to electron scattering above [Formula Presented] In addition, for [Formula Presented] and neutrino energies [Formula Presented] nucleon-nucleon bremsstrahlung always dominates electron-positron annihilation as a production mechanism for [Formula Presented] and [Formula Presented] neutrinos.