Models for Old, Metal-Poor Stars with Enhanced α-Element Abundances. II. Their Implications for the Ages of the Galaxy's Globular Clusters and Field Halo Stars
The ages of globular clusters (GCs) and post-turnoff field stars in the Galactic halo are derived using new stellar evolutionary models that explicitly take into account the observed abundances of the α-elements. Whereas the distances of the field subgiants considered in this study are based on Hipparcos parallax measurements, theoretical zero-age horizontal-branch (ZAHB) loci have been used to set the GC distance scale. (As reported in Paper I, the latter imply RR Lyrae luminosities that are within 0.1-0.15 mag, on the high side, of those found for field variables from Baade-Wesselink, trignometic parallax, and statistical parallax studies.) Both the field and cluster observations indicate that the most metal-deficient stars are >~14 Gyr old while those with [Fe/H] <~-1.3 are 2-3 Gyr younger. Unless the O/Fe (or, more generally, the α/Fe) number abundance ratio rises quite steeply with decreasing [Fe/H], it seems unlikely that a significant age-metallicity relation can be avoided.Using what is effectively the ∆VHBTO method of determining relative cluster ages, we find that the dispersion in age at any [Fe/H] less than ~-1.0 is small (<~10%-15%). Even Arp 2 and IC 4499, which had been previously categorized as ``young GCs,'' probably have near-normal ages for their metallicities--though a more definitive conclusion must await improved photometry for these systems. Ruprecht 106 appears no more than 1-1.5 Gyr younger than M3, as opposed to the ~4 Gyr age difference that others have found. However, Palomar 12 and Terzan 7 are undoubtedly young, and they provide strong evidence that, at [Fe/H] >~-1.0, the ages of GCs differ by as much as 4 Gyr (or ~25%). (A much larger sample of metal-rich clusters must be studied to ascertain whether the distribution of ages at higher metallicities is broad or narrow: Pal 12 and Ter 7 could well be atypical and represent the tail of a distribution that is strongly peaked near 12 Gyr.) Importantly, for the best-observed systems, there is no obvious conflict between the relative age estimates based on the ∆VHBTO method, on the one hand, and the ∆(B-V)TO,RGB technique, on the other. However, there are some exceptions, like M68, M53, M13, and NGC 288 for which the two approaches give slightly different results, indicating that something in addition to, or besides, age must be playing a role. From isochrone/ZAHB fits to the C-M diagrams (CMDs) of the outer-halo GCs Pal 3, Pal 4, and Eridanus, we conclude that there is no more than a small dependence of age on Galactocentric distance. Pal 4 seems to have very close to the same age as NGC 362, NGC 1261, and NGC 1851, while Eridanus and Pal 3 appear to be <~1 Gyr younger than most inner-halo systems of the same metallicity. Unless our understanding of the HB phase of evolution is seriously in error, cluster-to-cluster age differences (at a given metallicity) are much too small for age to be the most important of the possible second parameters in determining the morphology of the horizontal branch (the first parameter being [Fe/H]). Finally, we suggest that the GC distance scale as inferred from studies of nearby RR Lyraes is not necessarily in conflict with that based on local subdwarfs. A reconciliation of the two approaches is possible simply by adopting a particular metallicity scale for the globular clusters--one that is much closer to the Zinn-West scale than to that recently proposed by Carretta & Gratton. Indeed, such a simple way of achieving consistency between subdwarf-based distances and those inferred from RR Lyraes seems compelling. If this suggestion is correct, then the ``long'' distance scale and low estimates of GC ages are not tenable. In fact, the adoption of the ``short'' distance scale, implying ages >~15 Gyr for the most metal-poor GCs (and <~18.30 for the true distance modulus of the Large Magellanic Cloud), leads to much improved agreement between synthetic and observed CMDs in the vicinity of the turnoff. It does cause a mismatch between predicted and observed HB luminosities, in the sense that the models are too bright by ~0.1-0.15 mag, but this may simply be an indication that current conductive opacities or the assumed chemical abundance parameters (Y, [O/Fe], and/or [α/Fe]) are not quite right.