Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 65
A very important measure of the speed of evolution of a single star
along the RGB, HB, and AGB is the relative number of stars found on
these branches in a given cluster. Because for these advanced evolutionary
phases a single-star track is essentially an isochrone, these number
ratios R give us directly the relative amounts of time spent on these
branches (“R-method”). For example, a novel energy-loss mechanism
that operates mostly in the nondegenerate core of an HB star would
shorten the helium-burning lifetime. This possibility is constrained by
the relative number of stars found on the HB and RGB where the RGB
in this context refers to that part which is brighter than the HB.
When a star ascends the RGB, its hydrogen-burning shell encounters
at some point a discontinuity in the composition profile left behind
by a previous deep penetration of the envelope convection into the
region of varying hydrogen content caused by nuclear burning. The ascent
is briefly interrupted and the star stays at a fixed luminosity for a
brief period of time. Afterward, the hydrogen shell works itself through
a constant composition profile which was prepared by the convective
envelope. Therefore, at a brightness near the HB one expects to find
a “bump” in the number of stars on the RGB, i.e. in the distribution
∂N/∂M bol which essentially corresponds to dt/dM bol for a single-star
evolutionary track (Fig. 2.18). The bump was recently identified in a
number of clusters; for a particularly beautiful example see Fig. 2.19.
It has been suggested to use it as a standard candle to calibrate the
RR Lyrae brightness-metallicity relation (Fusi Pecci et al. 1990).
An important observable is the absolute brightness of RR Lyrae
stars which are not members of globular clusters. No reason is known
why these field stars for a given metallicity should be any different from
those found in a cluster and so brightness determinations of nearby
RR Lyrae stars provide important information about their luminosity
calibration.
2.4.2 Theoretical Relations
In order to test the standard stellar-evolution picture against the observables
introduced in Sect. 2.4.1 they need to be related to stellar
properties such as mass and chemical composition. In the past, extensive
grids of stellar evolutionary sequences have been calculated and
have been used to derive analytic approximations for the connection
between various stellar parameters; as a canonical standard I use the
evolutionary HB and RG sequences of Sweigart and Gross (1976, 1978).