Stars as Laboratories for Fundamental Physics - MPP Theory Group

76 Chapter 2
may be substantial and thus would shorten the helium-burning lifetime
as the nuclear fuel would be consumed faster.
The HB/RGB number ratio R indicates that the acceleration of the
HB evolution must not be too extreme. From Eq. (2.24) together with
the observational result Eq. (2.27) one finds
δ log R = 0.01 ± 0.06, (2.37)
if one adopts Y env = 0.24 ± 0.02, ∆ RR = 0.1 ± 0.1, and δM c =
±0.010 M ⊙ . Therefore, R cannot be smaller by much more than about
10% of its standard value. Put another way, the helium-burning lifetime
of low-mass stars is determined within about 10% from the ratio
of HB/RGB stars in globular clusters.
With lesser statistical significance this result is corroborated by
number counts of clump giants in open clusters which consist of more
recently formed stars in the galactic disk (Population I). Clump giants
in open clusters correspond to HB stars in globular clusters; instead
of forming a horizontal branch they are concentrated in a clump near
the base of the RGB. Cannon (1970) compared the number of clump
giants in the open cluster M67 with the number of stars per luminosity
interval near the MS turnoff and found t He ≈ 1.5×10 8 yr, with a
large statistical uncertainty, however, because there were only 5 clump
giants. (Open clusters tend to be much less populous than globular
ones.) Tinsley and Gunn (1976) derived t He = (1.27 ± 0.29) × 10 8 yr
from low-mass giants of the old galactic disk population. These results
are in full agreement with Eq. (2.23).
2.4.5 An Alternate Analysis
The above discussion of the globular-cluster limits is a somewhat updated
version of my own previous work (Raffelt 1990b). Very recently,
Catelan, de Freitas Pacheco, and Horvath (1995) have provided an independent
new and extended analysis. While they closely follow the
line of reasoning of Raffelt (1990b) they have changed numerous details.
Of the 26 globular clusters which enter the ∆M tip
HB argument,
and of the 15 clusters which enter the R-method, they have discarded
several with an extreme HB morphology. For the absolute brightness
of RR Lyrae stars they have employed Walker’s (1992) values which
depend on a precise knowledge of the LMC distance. For the brightness
difference between zero-age HB stars and RR Lyrae stars they use
∆ RR = 0.31 + 0.10 [Fe/H] = 0.18 + 0.10 Z 13 .