Stars as Laboratories for Fundamental Physics - MPP Theory Group

50 Chapter 2
tribution of hot WDs derived by Fleming, Liebert, and Green (1986)—
see Tab. 2.2. They calculated cooling sequences for M = 0.6 M ⊙ and
0.8 M ⊙ with varying amounts of nonstandard cooling. The relative
number of WDs in the two hot temperature bins of Tab. 2.2 are shown
as a function of µ ν in Fig. 2.12.
These results seem to indicate that a significantly enhanced rate of
neutrino emission can be conservatively excluded. However, this view
may be challenged if one includes the possibility of residual hydrogen
burning near the WD surface which could mask neutrino cooling
because it would fill in some of the “neutrino dip” in the luminosity
function. Because it is not known how much hydrogen is retained by
a WD after the planetary nebula phase one has an adjustable parameter
to provide a desired amount of heating (Castellani, Degl’Innocenti,
and Romaniello 1994). However, preliminary investigations seem to indicate
that even when residual hydrogen burning is included the impact
of µ ν is masked only in one of the temperature bins used by Blinnikov
and Dunina-Barkovskaya (1994) so that a significant deformation of the
luminosity function appears to remain (Blinnikov and Degl’Innocenti
1995, private communication).
2.2.4 Cooling by Boson Emission
Standard or exotic neutrino emission from WDs (or neutron stars) has
the important property that it switches off quickly as the star cools
because of the steep temperature dependence of the emission rates.
Therefore, neutrinos cause a dip at the hot end of the luminosity function
while older WDs are left unaffected, even for significantly enhanced
neutrino cooling (Fig. 2.11). One may construct other cases, however,
where this is different. One example is when a putative low-mass boson
is emitted in place of a neutrino pair, say, in the bremsstrahlung
process e + (Z, A) → (Z, A) + e + νν. The reduced final-state phase
space then reduces the steepness of the temperature dependence of the
energy-loss rate. The possible existence of such particles is motivated
by theories involving spontaneously broken global symmetries. The
most widely discussed example is the axion which will be studied in
some detail in Chapter 14. For the present discussion all that matters
is the temperature variation of an assumed energy-loss rate.
The bremsstrahlung rate for pseudoscalar bosons will be calculated
in Chapter 3. For the highly degenerate limit the result is given in
Eq. (3.33) where α ′ = g 2 /4π is the relevant “fine-structure constant.”
Because this rate depends on the density only weakly through a factor