Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 45
Fig. 2.10. Observed WD luminosity function as in Tab. 2.1. The dotted
line represents Mestel’s cooling law with a constant WD birthrate of
B = 10 −3 pc −3 Gyr −1 . The dashed line is from the numerical cooling curve
of a 0.6 M ⊙ WD (Koester and Schönberner 1986), including neutrino losses
and assuming the same constant birthrate.
2.2.2 Cooling Theory
A WD has no nuclear energy sources and so it shines on its residual thermal
energy: the evolution of a WD must be viewed as a cooling process
(Mestel 1952). Because electron conduction is an efficient mechanism
of energy transfer the interior can be viewed, to a first approximation,
as an isothermal heat bath with a total amount of thermal energy U.
Because the nondegenerate surface layers have a large “thermal resistance,”
they insulate the hot interior from the cold surrounding space,
throttling the energy loss L γ by photon radiation. Of course, WDs can
also lose energy by neutrino volume emission L ν , and by novel particle
emission L x . Hence, WD cooling is governed by the equation
dU/dt = −(L γ + L ν + L x ). (2.4)
This simple picture ignores the possibility of residual hydrogen burning
near the surface, a possibly important luminosity source for young
WDs (e.g. Castellani, Degl’Innocenti, and Romaniello 1994; Iben and
Tutukov 1984). I will get back to this problem below.