Stars as Laboratories for Fundamental Physics - MPP Theory Group

Appendix C
Numerical Neutrino
Energy-Loss Rates
In normal stars with densities below nuclear there are four main reactions
that contribute to the energy loss by neutrino emission:
γ pl → νν Plasma process,
γ e − → e − νν Photoneutrino process,
e + e − → νν Pair annihilation,
e − (Z, A) → (Z, A) e − νν Bremsstrahlung.
(C.1)
Individual processes dominate in the regions of density and temperature
indicated in Fig. C.1. In the following, various analytic fit formulae for
these neutrino emission rates are reviewed.
C.1 Plasma Process
Widely used formulae for the plasma process are those of Beaudet, Petrosian,
and Salpeter (1967), Munakata, Kohyama, and Itoh (1985), and
Schinder et al. (1987), which all agree with each other to better than 1%
if the same effective coupling constants are used. All of these rates are
poor approximations for T ∼ < 10 8 K which is relevant for low-mass stars
because they were optimized for higher temperatures. Itoh et al. (1989)
have attempted to improve the accuracy at low temperatures, and Blinnikov
and Dunina-Barkovskaya (1994) gave rates which were optimized
for low-mass stars but fail for temperatures above about 10 8 K. At high
temperatures and densities, a poor approximation to the photon dispersion
relation was used in all of these works (Braaten 1991) whence
none of these rates are satisfactory. A new fit by Itoh et al. (1992) still
contains islands in the ρ-T -plane with errors of several 10%.
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