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

We investigate the rates of production and thermalization of v_μ and v_τ 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 58, 013009 (1998)] and Burrows and Sawyer [Phys. Rev. C 58, 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 (ε v ≲ 10 MeV), but that nucleon scattering is always faster than or comparable to electron scattering above ε v ≃ 10 MeV. In addition, for ρ ≳ 10¹³ g cm^-3, T ≲ 14 MeV, and neutrino energies ≲60 MeV, nucleon-nucleon bremsstrahlung always dominates electron-positron annihilation as a production mechanism for v_μ and v_τ neutrinos.