Thermalization and Production of Neutrinos in Dense Nuclear Matter
Todd A. Thompson
Todd A. Thompson, Adam Burrows, and Jorge E. Horvath,
Mu and Tau Neutrino Thermalization and Production in Supernovae: Processes and Timescales, Physical Review C, 62, 035802 (2000).
Supernova theorists have long recognized the importance of neutrino-electron scattering
as an energy exchange mechanism in supernovae. Much effort has been exerted to include
the full collision integral in the solution to the neutrino Boltzmann equation.
Neutrino-nucleon scattering has been included in simulations as well, but never as an
energy exchange mechanism. It has always been included as an important source of opacity,
but the energy exchange has been assumed negligible. In fact, although the average energy
transfer per scattering is relatively small in these interactions, the cross section
for scattering is much larger than that for neutrino-electron scattering. It seems plausible,
then, that each process may play an important role in supernovae -- each with a different regime
of importance as an energy exchange mechanism.
To test this, we have developed an algorithm for solving the full collision term of the
neutrino Boltzmann equation in an isotropic homogeneous thermal bath of scatterers. We set
the temperature, density, and composition of the bath to reflect representative points
at snapshots in time within a core-collapse supernova.
To the right we include a movie showing equilibration via both scattering processes
and a figure, which summarizes the thermalization rate.
Nucleon-nucleon bremsstrahlung has recently been recognized as an important
neutrino production mechanism in supernovae. Other neutrino production
processes include the charged-current reactions, which produce electron
and anti-electron neutrinos, plasmon decay, and electron-positron annihilation.
The latter two processes, like bremsstrahlung, produce neutrinos of all species.
Bremsstrahlung has been ignored as a production mechanism in fully dynamical
supernova calculations to date as it has been assumed sub-dominant in comparison with
In order to test the validity of this approximation, we study production of mu and tau neutrinos
in a isotropic thermal bath. Given zero initial phase-space occupancy at all energies, we solve
the Boltzmann equation for the time evolution of the neutrino phase-space distribution function using
the full production integral. We follow both neutrinos and anti-neutrinos. The final equilibrium
phase-space distribution should be Fermi-Dirac with zero chemical potential.
To the right we include a movie showing production of the equilibrium Fermi sea of neutrinos
via both bremsstrahlung and electron/positron annihilation. We also include a figure
summarizing the relevant rates at two different points in a representative stellar profile.
In conducting the production study above, we employed the one-pion exchange approximation
and made some simplifying assumptions concerning the resulting matrix element. We calculated the
Boltzmann equation production term and the spectrum in the non-degenerate limit and
at arbitrary degeneracy. Note that we include the contributions from neutron-neutron,
proton-proton, and neutron-proton bremsstrahlung in computing the final rates.
To the right are two figures that illustrate the difference between the non-degenerate limit,
which generally over-predicts the rate, and the case of arbitrary degeneracy.