Stars as Laboratories for Fundamental Physics - MPP Theory Group

70 Chapter 2
(at the RR Lyrae strip) and the RGB tip for which one finds with
Eqs. (2.19) and (2.20)
∆M tip
HB ≡ M RR − M tip
= 4.24 − 4.4 Y 23 + 0.35 Z 13 − ∆ RR + 4.5 δM c (2.22)
which is defined such that it is a positive number.
f) Ratio of HB/RGB Stars
The relative duration of the HB vs. RGB phase is given by the number
ratio of the stars on these branches where the RGB is defined as that
part which is brighter than the HB. The HB lifetime is found to be
(Buzzoni et al. 1983; Raffelt 1990b)
log(t HB /yr) = 8.01 + 0.37 Y 23 + 0.06 Z 13 − 2.9 δM c . (2.23)
The RGB lifetime cannot be expressed easily in terms of a simple linear
formula because of the RGB bump discussed earlier. A simple approximation
to the lifetime ratio R = t HB /t RGB is (Buzzoni et al. 1983;
Raffelt 1990b)
log R = 0.105 + 2.29 Y 23 + 0.029 Z 13 + 0.33 ∆ RR − 0.70 δM c .
(2.24)
This quantity is particularly sensitive to the helium content of the stars
and almost independent of the core mass at helium ignition.
2.4.3 Observational Results
a) Brightness at the RGB Tip
The brightness at the tip of the RGB can be estimated by the brightest
red giant in a given globular cluster. A homogeneous set of observations
of the brightest RGs in 33 globular clusters are those of Cohen, Frogel,
and Persson (1978), Da Costa, Frogel, and Cohen (1981), Cohen and
Frogel (1982) and Frogel, Persson, and Cohen (1981, 1983). According
to Frogel, Cohen, and Persson (1983) only in 26 of the 33 clusters
the brightest giant was likely observed; for those cases the bolometric
brightness difference between the brightest RGs and the HB are shown
as a function of metallicity in Fig. 2.20. Also shown is a linear fit
∆M tip
HB = 4.06 + 0.38 Z 13 . The observational errors are thought to be
less than about 0.05 mag.