Stars as Laboratories for Fundamental Physics - MPP Theory Group

72 Chapter 2
dance, which presumably is very close to the primordial value, has to
be 0.20 to achieve perfect agreement, or else the core mass at helium
ignition has to be 0.030 M ⊙ larger than given by the standard theory.
Alternatively, the zero-age HB models may represent the brightness
of RR Lyrae stars better than anticipated so that ∆ RR ≈ 0
in which case there is perfect agreement with the standard values
Y env ≈ Y primordial ≈ 0.23 and δM c = 0.
b) Ratio of HB/RGB Stars
Buzzoni et al. (1983) have determined the number of stars on the HB
(including RR Lyrae stars), 12 N HB , and on the RGB brighter than the
HB, N RGB , in 15 globular clusters. The resulting values for the number
ratio R = N HB /N RGB is shown in Fig. 2.21 as a function of metallicity.
The individual errors are found by assuming standard deviations of
N 1/2 for the number counts and adding the errors of N HB and N RGB
quadratically (Raffelt 1990b). The data are fit by a linear regression
log R = (0.162 ± 0.016) + (0.065 ± 0.032) Z 13 , (2.27)
also shown in Fig. 2.21.
Fig. 2.21. Number ratio of HB/RGB stars for 15 globular clusters according
to Buzzoni et al. (1983).
Comparing this result with the theoretical prediction of Eq. (2.24)
one finds that the metallicity dependence essentially agrees within the
12 Buzzoni et al. (1983) call this quantity N HB+RR .