Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 53
White dwarfs have residual atmospheres which may be hydrogen
rich (DA white dwarfs) or helium rich (DB); the DA stars are about
four times more frequent. The surface layers of DA white dwarfs are
not fundamentally different from those of main-sequence or giant stars
and so for appropriate conditions one expects Cepheid-type pulsations.
Indeed, where the faint continuation of the Cepheid instability strip
intersects with the locus of WDs in the Hertzsprung-Russell diagram
(Fig. 2.9) one finds the DA variables (DAV), also known as ZZ Ceti
stars after their prototype example. They have pulsation periods of a
few minutes.
The oscillation period depends on the temperature of the layer
which exhibits the κ instability (Sect. 2.1.9) and thus excites the pulsations,
and also on the radius of the star. Therefore, the slowing
down of the period P is a direct measure of the temperature decrease
and thus of the WD cooling speed. Standard pulsation theory yields
P ˙ /P ≈ −a T ˙ /T + b Ṙ/R where the dimensionless constants a and b
are of order unity (Winget, Hansen, and van Horn 1983). Because
a WD has an almost fixed radius, the second term may be ignored.
The time scale of cooling and of the period change are then related by
T/ T ˙ = −a P/ P ˙ . ZZ Ceti stars have surface temperatures in the neighborhood
of 13,000 K where the cooling time scale is of order 1 Gyr.
For a period of a few minutes one is talking of a period decrease
P ˙ = O(10 −14 s s −1 ), not an easy quantity to measure.
After upper limits on P ˙ had been established over the years for a
number of cases, Kepler et al. (1991) succeeded at a measurement for
the DAV star G117–B15A (Tab. 2.3) using the Whole Earth Telescope
which allows for nearly 24 h a day coverage of a given object.
A variety of model calculations give P ˙ = 2−5 × 10 −15 s s −1 , somewhat
smaller than the measured value, i.e. the star appears to cool
Table 2.3. Properties of the DAV star G117–B15A.
Surface temperature T eff 13,200 K
Luminosity log(L/L ⊙ ) −2.3
Bolometric brightness M bol 10.49 mag
Mass M (0.49 ± 0.03) M ⊙
Pulsation period P (215.197,387 ± 0.000,001) s
Period change P ˙ (12 ± 4) × 10 −15 s s −1
P/ P ˙ (0.57 ± 0.17) Gyr