Stars as Laboratories for Fundamental Physics - MPP Theory Group

48 Chapter 2
process γ → ν e ν e which is studied in detail in Chapter 6; numerical
emission rates are discussed in Appendix C. The neutrino energy-loss
rate as a function of temperature is shown in Fig. C.6; for a WD the
short-dashed curve (2ρ/µ e = 10 6 g cm −3 ) is most appropriate.
Neutrino cooling causes a depression of the WD luminosity function
at the bright end. The dashed line in Fig. 2.10 represents a numerical
cooling calculation for a 0.6 M ⊙ WD which included neutrinos
(Koester and Schönberner 1986); the “neutrino dip” is clearly visible.
The photon decay γ → νν is a neutrino process made possible by
the medium-induced photon dispersion relation and by the mediuminduced
effective photon-neutrino coupling (Chapter 6). As such this
process is not observable in the laboratory, although there is no doubt
about its reality. Still, it is encouraging to see it so plainly in the WD
luminosity function.
If neutrino emission were much stronger than standard, the neutrino
dip would be correspondingly deeper. Stothers (1970) used the
observation of several bright WDs in the Hyades cluster to constrain the
efficiency of neutrino cooling; at that time the existence and magnitude
of a direct neutrino-electron interaction had not yet been experimentally
established. Stothers found that an emission rate 300 times larger
than standard could be conservatively excluded.
Recently, Blinnikov and Dunina-Barkovskaya (1994) have studied
this subject in detail. Their motivation was the possible existence of
a neutrino magnetic dipole moment which would enhance the effective
neutrino-photon coupling and thus the efficiency of the plasma
process. For the present general discussion it is enough to think of
their study as an arbitrary variation of the neutrino emissivity, even
though the magnetic-moment induced plasma emission rate has a different
density dependence—see Eq. (6.94) for details. For the pertinent
conditions the energy-loss rate induced by the assumed dipole
moment µ ν is roughly 0.06 µ 2 12 times the standard one where µ 12 ≡
µ ν /10 −12 µ B (Bohr magneton µ B ). Blinnikov and Dunina-Barkovskaya
(1994) calculated the luminosity function for 0.6 M ⊙ WDs for the standard
case (µ 12 = 0, dashed line in Fig. 2.11) and for a roughly 25-fold
increased rate of neutrino cooling (µ 12 = 20, dotted line in Fig. 2.11).
The birthrate of WDs was assumed constant and adjusted to optimize
the agreement with the observations. For µ 12 = 0 they needed
B = 0.62×10 −3 pc −3 Gyr −1 while for µ 12 = 20 the best fit was achieved
for 0.67 in these units.
Blinnikov and Dunina-Barkovskaya (1994) pointed out that a particularly
sensitive observable for the neutrino dip is the temperature dis-