Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 43
asymptotic giant evolution which can amount to an ejection of the entire
envelope and thus to the formation of a planetary nebula (Fig. 2.7).
A theoretical evolutionary track for a 3 M ⊙ star from the MS to the
WD stage was calculated, e.g. by Mazzitelli and D’Antona (1986). The
central stars of planetary nebulae are identified with nascent WDs. The
rate of WD formation inferred from the luminosity function discussed
below agrees within a factor of about 2 with the observed formation
rate of planetary nebulae, which means that both quantities agree to
within their statistical and systematic uncertainties.
The hottest and brightest WDs have luminosities of L ≈ 0.5 L ⊙
while the faintest ones are observed at L ≈ 0.5×10 −4 L ⊙ . Thus, because
of their small surface area WDs are intrinsically faint (see the
Hertzsprung-Russell diagram Fig. 2.9). This implies that they can be
observed only in the solar neighborhood, for bright WDs out to about
100 pc (300 lyr). Because their vertical scale height in the galactic disk
is about 250 pc (Fleming, Liebert, and Green 1986) the observed WDs
homogeneously fill a spherical volume around the Sun. One may then
express the observed number of WDs in terms of a volume density; it
is of order 10 −2 pc −3 .
The observed luminosity function (the space density of WDs per
brightness interval) is shown in Fig. 2.10 and listed in Tab. 2.1 according
to Fleming, Liebert, and Green (1986) and Liebert, Dahn, and Monet
(1988). The operation of a novel cooling mechanism can be constrained
by three important features which characterize the luminosity function:
its slope, which signifies the form of the cooling law, its amplitude,
which characterizes the cooling time and WD birthrate, and its sudden
break at log(L/L ⊙ ) ≈ −4.7, which characterizes the beginning of WD
formation. Even the oldest WDs have not had time to cool to lower
luminosities. From this break one can infer an age for the galactic
disk of 8−10.5 Gyr (Winget et al. 1987; Liebert, Dahn, and Monet
1988; Iben and Laughlin 1989; Wood 1992) while Hernanz et al. (1994)
find 9.5−12 Gyr on the basis of their cooling calculations which include
crystallization effects.
Because of the WD mass-radius relationship the surface temperature
and luminosity are uniquely related for a given WD mass. Therefore,
instead of the luminosity function one may consider the temperature
distribution which, in principle, is independent of uncertain WD
distance determinations. Fleming, Liebert, and Green (1986) gave the
distribution of their sample of hot WDs in several temperature bins
(Tab. 2.2). Numerical cooling calculations of Blinnikov and Dunina-
Barkovskaya (1994) found good agreement with this distribution, as-