Annu. Rev. Astron. Astrophys. 1996. 34: 461-510 Copyright © 1996 by Annual Reviews. All rights reserved

2.4. Uncertainty in L^TO Due to the Assumed Chemistry of Stars

It has long been known that the predicted age of a star of a given mass depends on its initial helium and heavy-element abundances (e.g. Demarque 1967, Iben & Rood 1970). Even the special importance of the CNO elements for stellar ages was appreciated early on (e.g. Simoda & Iben 1968). This has driven a huge, ongoing effort by many observers to define the detailed run of chemical abundances in field and halo stars as accurately as possible. Thanks to that effort, we now know (for instance) that [C/Fe] and [N/Fe] ~ 0 over 0.3 [Fe/H] -2 and that the elements synthesized by -capture processes (e.g. O, Ne, Mg, Si, etc) are enhanced, relative to iron, in metal-poor stars by a factor of 2-3 (see the comprehensive review by Wheeler, Sneden & Truran 1989). (In the standard notation, this corresponds to [/Fe] 0.3-0.5, where represents O or Ne or Mg, etc.) It is not yet definite that all of the so-called -elements scale together as there is considerable scatter in the field star observations (some of it real): Thus, the precise shapes of the mean relations between the various [element/Fe] ratios as a function of [Fe/H] still have some degree of uncertainty. Also, whether or not field and GC dwarfs of the same iron content are chemically indistinguishable remains a matter of some concern. But the chemistry of stars appears to be largely under control.

High-resolution spectroscopy (e.g. Cohen 1979, Sneden et al 1991) and the tightness of observed CMDs (e.g. Stetson 1993;, Folgheraiter, Penny & Griffiths 1993) have established that the dispersion in Fe abundances is very small in nearly all GCs ( Cen and possibly M22 being exceptions). Moreover, the spectroscopic data now yield [Fe/H] values that are accurate to within ± 0.2 dex, if not better. According to the upper panel of Figure 4 - which shows plots of the turnoff luminosity versus age relations that VandenBerg et al (1996) have computed for various choices of [Fe/H], [/Fe], and Y - this implies an uncertainty in the age at a given M _bol(TO) of about ± 1 Gyr ( ± 7%). Furthermore, since the -element contents of stars in the extremely metal-deficient clusters like M92 appear to be within ± 0.15 dex of [/Fe] = 0.4 (e.g. Sneden et al 1991;, McWilliam, Geisler & Rich 1992), the corresponding age uncertainty is expected to be about ± 4% (judging from Figure 4). This makes a total uncertainty of ± 11% in the turnoff ages due to current errors in heavy-element abundance determinations. ⁴

Figure 4. Turnoff luminosity vs age relations for various chemical composition parameters.

Helium-abundance uncertainties could potentially affect age estimates at the few percent level (see the upper panel of Figure 4), but Y appears to be rather well determined, in spite of the fact that the methods used are indirect. [Spectral features due to helium can be detected in hot HB stars, but gravitational settling is known to be important in them (e.g. Heber et al 1986).] Foremost among these techniques is the so-called R-method (Iben 1968b), which compares the ratio of the predicted HB and RGB lifetimes, t_HB / t_RGB, as a function of Y, with the observed number ratio of stars in these phases. Using mainly the calibration of Buzzoni et al (1983) (also see Caputo, Martinez Roger & Paez 1987), nearly all applications of the R-method (e.g. Buonanno, Corsi & Fusi Pecci 1985;, Ferraro et al 1992, 1993) have yielded Y = 0.23 ± 0.02. Discrepant results have been obtained for a few globulars, such as M68 (Walker 1994), for which the R-method implies Y ~ 0.17; however, in that particular case, the analogous ratio of the numbers of asymptotic-giant branch to RGB stars gives an estimate of the helium abundance that is within 1 of Y = 0.23. (Why M68 has such an anomalous R value is presently unknown.)

Fits to the morphologies of observed HB populations (e.g. Dorman, VandenBerg & Laskarides 1989;, Dorman, Lee & VandenBerg 1991) and to the red edges of the RR Lyrae instability strips in clusters (Bono et al 1995) reinforce the R-method results. Pulsation models have traditionally favored Y 0.30, but due to the advent of the OPAL (Rogers & Iglesias 1992) and OP (Seaton et al 1994) opacities, lower values of Y can now be accommodated (Kovács et al 1992, Cox 1995). The adoption of Y 0.23 in models for GC stars is further supported by the fact that this value is very close to that predicted by standard and inhomogeneous Big Bang nucleosynthesis calculations (see, e.g. Krauss & Romanelli 1990, Mathews, Schramm & Meyer 1993, respectively), as well as empirical determinations of the pregalactic helium abundance (Pagel et al 1992;, Izotov, Thuan & Lipovetsky 1994;, Olive & Steigman 1995).

We conclude this section by emphasizing the importance of oxygen to stellar age determinations. Plotted in the lower panel of Figure 4 are the age versus turnoff luminosity relations that Salaris et al (1993) have derived for [Fe/H] = -2.3 and various assumptions about the element mix. This plot shows that most of the reduction in age at a given L^TO that results from an enhancement in the -elements is due to oxygen. Getting the oxygen abundance right is, therefore, a much bigger concern than having precise abundances for most of the other heavy elements. This result is not unexpected given the large abundance of oxygen and its role as a catalyst in the CNO-cycle and as a major contributor to bound-free opacities in stellar interiors (see, e.g. VandenBerg 1992).

⁴ At first sight, Figure 4 would appear to contradict the claim by Chieffi, Straniero & Salaris (1991) that enhancements in the -elements do not lead to younger ages for the GCs (also see Bencivenni et al 1991). But, in fact, the reason why they obtained similar ages using either -enhanced or scaled-solar abundance isochrones is that they set the distances to the globulars using theoretical horizontal-branch calculations, which predict that the HB luminosity should decrease as [ / Fe] increases. Only by an appropriate adjustment of the GC distance scale is it possible to reach the conclusion that ages are insensitive to [ / Fe]: The turnoff age-luminosity relations computed by Salaris, Chieffi & Straniero (1993) both for [ / Fe] = 0.0 and for [ / Fe] > 0.0 are very similar to those derived by VandenBerg et al (1996). Back.