Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 71
Fig. 2.20. Bolometric brightness difference between the horizontal branch
and the brightest red giant in 26 globular clusters from the observations
referenced in the text.
However, because there are relatively few stars near the tip on the
RGB (on average about 10 mag −1 in the observed clusters), the brightest
RG is on average about 0.1 mag below the actual RGB tip. Raffelt
(1990b) estimated the richness of the RGB near the tip for each cluster
on the basis of the first few brightest stars provided by the observations
and thus estimated the expected brightness difference between
the brightest RG and the tip. This yields a linear regression
∆M tip
HB = (4.19 ± 0.03) + (0.41 ± 0.06) Z 13 , (2.25)
about 0.13 mag brighter than the fit shown in Fig. 2.20. The slope of
Eq. (2.25) agrees very well with the theoretical expectation Eq. (2.22),
provided that ∆ RR does not introduce a large modification.
More recent observations are those of Da Costa and Armandroff
(1990) who also found excellent agreement between the theoretical slope
of the brightness of the RGB tip luminosity as a function of metallicity.
Because the coefficient of the metallicity dependence agrees well
with the predicted value one may restrict a further comparison between
theory and observation to ∆M tip
HB at a given metallicity for which
it is best to use the average value [Fe/H] = −1.48 or Z 13 = −0.18
of the globular clusters used in Fig. 2.20. Inserting these values into
Eqs. (2.22) and (2.25) and adding the errors quadratically one finds
4.4 Y 23 + ∆ RR − 4.5 δM c = 0.06 ± 0.03. (2.26)
If ∆ RR = 0.2 mag this result implies that the envelope helium abun-