Stars as Laboratories for Fundamental Physics - MPP Theory Group

74 Chapter 2
Most recently, the brightness of RR Lyrae stars in the Large Magellanic
Cloud was measured; it has a distance which is thought to be
well determined by other methods. Walker (1992) found
M RR = 0.48 + 0.15 Z 13 , (2.31)
if the same bolometric correction −0.06 is assumed.
In summary, a reasonably conservative estimate of the absolute
RR Lyrae bolometric brightness is
M RR = (0.60 ± 0.15) + 0.17 Z 13 . (2.32)
A comparison with Eq. (2.20) yields
3.5 Y 23 + ∆ RR + 7.3 δM c = 0.06 ± 0.15. (2.33)
This is in good agreement with the standard values Y env = 0.23, δM c =
0, and ∆ RR ≈ 0.1 mag.
2.4.4 Interpretation of the Observational Results
In order to interpret the observational results it is first assumed that
there is no anomalous core-mass increase. However, considering the
uncertainties entering the calculation of M c such as the precise value of
the relevant total stellar mass, uncertainties in the electron conductive
opacities, etc., it appears that a plausible range of uncertainty is δM c =
±0.010 M ⊙ even in the absence of any novel phenomena. Adopting this
uncertainty and adding it quadratically to the previous uncertainties,
the three observables from Eq. (2.26), (2.28), and (2.33) yield
Y env = (0.244 ± 0.012) − 0.23 ∆ RR
from ∆M tip
HB,
Y env = (0.251 ± 0.009) − 0.14 ∆ RR from R,
Y env = (0.247 ± 0.048) − 0.29 ∆ RR from M RR . (2.34)
The primordial helium abundance likely is in the range 22−24%; the
envelope abundance in globular clusters is probably slightly larger, depending
on details of gravitational settling on the MS and convective
dredge-up on the RGB. Therefore, with ∆ RR between 0 and 0.2 mag
these results are perfectly consistent.
In order to constrain Y env and δM c simultaneously it is assumed
that ∆ RR = 0.1 ± 0.1. Adding this error quadratically in Eq. (2.26),