Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 73
stated uncertainty; it is very shallow anyway. Therefore, one compares
at the average metallicity of the 15 clusters, [Fe/H] = −1.54 or Z 13 =
−0.24, adds the errors quadratically, and finds
Y 23 + 0.14 ∆ RR − 0.31 δM c = 0.021 ± 0.008. (2.28)
With ∆ RR ≈ 0.2 mag and δM c ≈ 0 this confirms a primordial helium
abundance of around 23%.
c) RR Lyrae Absolute Brightness
The RR Lyrae absolute brightness as well as the precise variation of
M RR with metallicity is the single most discussed issue about globularcluster
color-magnitude diagrams because the distance and thus the
age determination depends critically on this quantity. For example,
when using ∆VHB
TO measurements like the ones shown in Fig. 2.17, the
inferred relative ages of globular clusters depend crucially on the slope
a of M RR = a [Fe/H] + b.
One possibility to determine a is the use of the pulsation frequencies
of these variable stars. The result is about 0.35, almost twice as large
as that obtained by theoretical zero-age HB models or by synthetic
HBs, an issue known as the Sandage period shift effect (Sandage 1990
and references therein; Iben and Renzini 1984; Renzini and Fusi Pecci
1988). While this issue is crucial for a relative age determination of
globular clusters, it is of relatively minor importance for the present
discussion where the zero point b for an intermediate metallicity is the
most crucial quantity.
Probably the most direct determination of M RR is to use nearby
field RR Lyrae stars for which, in principle, a distance determination by
parallax measurements is possible. Barnes and Hawley (1986) applied
the method of statistical parallaxes to a sample of 142 stars and found
a mean absolute visual brightness of (0.68 ± 0.14) mag. Assuming a
bolometric correction for RR Lyrae stars of −0.06 mag this leads to
⟨M RR ⟩ = (0.62 ± 0.14) mag. (2.29)
The average metallicity of this sample is probably [Fe/H] ≈ −1.4.
The Baade-Wesselink method applied to a total of 25 field RR Lyrae
stars, and using a bolometric correction of −0.06, leads to
M RR = 0.72 + 0.19 Z 13 (2.30)
(Sandage and Cacciari 1990, and references therein).