Stars as Laboratories for Fundamental Physics - MPP Theory Group

Numerical Neutrino Energy-Loss Rates 587
Fig. C.2. Deviation between the Schinder et al. (1987) and the Itoh et al.
(1989) rates for the photoneutrino and pair-annihilation processes. Compared
are the total emission rates where the plasma rate of Haft, Raffelt and
Weiss (1994) and the bremsstrahlung rate (helium) of Itoh and Kohyama
(1983) were used. The contours indicate were the individual processes dominate
(Fig. C.1).
energy-loss rates for the photo and pair process was calculated according
to these authors, while in each case the plasma rate of Haft, Raffelt,
and Weiss (1994) and the bremsstrahlung rate for helium of Itoh and
Kohyama (1983) were taken. Therefore, deviations occur only in the
range of temperatures and densities where the photo or pair process
dominates. The largest deviations in the lower left corner of Fig. C.2
are around 25%. However, there the absolute magnitude of neutrino
emission is very small (see below) so that the difference between the
rates in this regime does not appear to be of much practical significance.
Another analytic approximation formula for the pair process was
derived by Blinnikov and Rudzskiĭ (1989).