Stars as Laboratories for Fundamental Physics - MPP Theory Group

586 Appendix C
Fig. C.1. Regions of density and temperature where the indicated neutrino
emission processes contribute more than 90% of the total. µ e is the electron
“mean molecular weight,” i.e. roughly the number of baryons per electron.
The bremsstrahlung contribution depends on the chemical composition. The
solid lines are for helium, the dotted ones for iron which yields a larger
bremsstrahlung rate.
A detailed comparison of these formulae with the exact rates was
performed by Haft, Raffelt, and Weiss (1994). They provided a new
fitting formula which approximates the analytic emission rate to within
5% in the entire regime where the plasma process dominates.
C.2 Photoneutrino and Pair-Annihilation
Process
Beaudet, Petrosian, and Salpeter (1967) provided analytic approximations
for the photoneutrino and pair-annihilation processes. Dicus
(1972) gave global correction factors to these rates to include neutralcurrent
effects. Schinder et al. (1987) numerically recalculated the emission
rates in the standard model and found good agreement with the
BPS formulae together with the Dicus correction factors. They supplemented
the BPS rates for the temperature range 10 10 −10 11 K.
An alternate set of approximation formulae was provided by Itoh
et al. (1989) who improved on their previous work (Munakata, Kohyama,
and Itoh 1985). In Fig. C.2 I show the relative deviation between
the Itoh et al. (1989) with the Schinder et al. (1987) rates. The total