Stars as Laboratories for Fundamental Physics - MPP Theory Group

66 Chapter 2
a) Composition Parameters
The chemical composition is characterized by the helium content and
the metallicity. The convective envelope on the RGB at some point
reaches down into the region of a variable composition profile caused
by nuclear burning, causing a certain amount of processed material
(helium) to be dredged up. Therefore, the helium mass fraction Y env
of the envelope is slightly larger than the value Y at formation. The
amount of dredge-up is approximately given by (Sweigart, Renzini, and
Tornambé 1987)
∆Y s ≡ Y env − Y ≈ 0.0136 + 0.0055 Z 13 , (2.14)
where the metallicity parameter Z 13 is defined in Eq. (2.16) below.
However, because the exact amount of convective dredge-up is somewhat
model dependent, and because measurements of 12 C/ 13 C ratios
in metal-poor field red giants seem to indicate that the dredge-up of
processed material is more efficient than predicted by standard calculations
(Sneden, Pilachewski, and VandenBerg 1986) it is best to use Y env
rather than Y as an independent parameter to characterize red giants
and HB stars. 10
Gravitational settling of helium throughout the MS evolution has
the opposite effect of reducing the envelope abundance relative to the
initial homogeneous value. In recent evolutionary sequences which were
calculated to estimate the effect of helium diffusion on the inferred
globular-cluster ages a decrease between ∆Y s = −0.009 and −0.015 was
found (Proffitt and Michaud 1991; Chaboyer et al. 1992). Therefore,
the effect of MS gravitational settling and that of RG convective dredgeup
appear to cancel each other more or less so that Y env appears to be
much closer to the initial value Y than had been thought previously.
The metallicity is usually characterized by the mass fraction Z of
elements heavier than helium. Because iron is most important for the
opacities one often uses the abundance of iron relative to hydrogen
as a metallicity measure. It is characterized by the quantity [Fe/H]
which is the logarithmic abundance of iron over hydrogen relative to
the solar value. If the solar metallicity is taken to be Z ⊙ = 0.02 so that
10 In their calculation of RG sequences, Sweigart and Gross (1978) used the symbol
Y to denote the MS helium abundance; the envelope abundance near the helium
flash can be inferred from their tabulation of ∆Y s values for each sequence. In
their 1976 study of HB sequences, they used the symbol Y to denote the envelope
abundance which is here consistently called Y env .