Stars as Laboratories for Fundamental Physics - MPP Theory Group

44 Chapter 2
Table 2.1. Observed WD luminosity function according to Fleming, Liebert,
and Green (1986) and Liebert, Dahn, and Monet (1988). For the hot and
bright degenerates (upper part of the table) a large fraction of their spectrum
lies in the ultraviolet, causing a large discrepancy between the absolute visual
magnitude M V and the absolute bolometric magnitude M bol . For the hot
dwarfs the bins orginally had been chosen on the M V scale with a width
of 0.5 mag, centered on the half-magnitudes; the listed M bol is the mean in
these intervals.
Mean Mean dN/dM bol
M V M bol log(L/L ⊙ ) [pc −3 mag −1 ] log(dN/dM bol )
9.5 5.50 −0.31 1.22×10 −6 −5.91 (+0.18,−0.31)
10.0 6.88 −0.86 1.01×10 −5 −5.00 (+0.14,−0.21)
10.5 7.84 −1.25 2.16×10 −5 −4.67 (+0.13,−0.18)
11.0 8.92 −1.68 9.56×10 −5 −4.02 (+0.12,−0.16)
11.5 10.12 −2.16 1.21×10 −4 −3.92 (+0.11,−0.15)
12.0 11.24 −2.61 1.51×10 −4 −3.82 (+0.11,−0.16)
12.5 11.98 −2.90 2.92×10 −4 −3.54 (+0.11,−0.16)
13.0 12.55 −3.13 6.07×10 −4 −3.22 (+0.20,−0.39)
13.50 −3.51 0.89×10 −3 −3.05 (+0.14,−0.21)
14.50 −3.91 1.34×10 −3 −2.87 (+0.14,−0.20)
15.50 −4.31 0.24×10 −3 −3.62 (+0.18,−0.31)
Table 2.2. Temperature distribution of hot WDs according to Fleming,
Liebert, and Green (1986).
T eff [10 3 K]
Fraction of WDs
40−80 (7.06 ± 1.27) × 10 −3
20−40 0.235 ± 0.026
12−20 0.759 ± 0.083
suming that the WD mass function was peaked around 0.7 M ⊙ which
is somewhat larger than the canonical value of 0.6 M ⊙ . For the present
purpose, however, the smallness of this difference is taken as a confirmation
of the standard WD cooling theory.