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

4. SUMMARY

The quest to determine accurate globular cluster ages and to ascertain when the first of these objects formed in the Galaxy (and how long that formation epoch lasted - see the companion review by Stetson et al 1996) is, without a doubt, one of the grand adventures in astronomy. It involves nearly all aspects of stellar astronomy and has profound importance for some of the biggest questions our species has ever asked: How did our Galaxy form? How old is the Universe? Is the Universe infinite, and will it exist forever? It has taken the effort of many researchers in many countries around the world to get to where we are now. Despite the enormous progress that has been made, the answers to such age-related questions remain elusive. Although the globular clusters are simple in many respects, being composed of low-mass stars of essentially the same age and initial chemical composition, our understanding of stellar evolution has not yet progressed far enough to be able to explain, in a fully self-consistent way and with sufficient precision, the entire wealth of information that we have garnered through the use of sophisticated observational techniques. This is particularly true for the later stages of evolution: Models for upper main-sequence and turnoff stars appear to meet the challenge of the observational tests so far devised.

As many others have found previously, our best estimate of the ages of the most metal-poor GCs, which are presumably the oldest, is 15^-3₊₅ Gyr (allowing for the full impact of helium diffusion, which was not treated in the models that were fitted to the M92 CMD). This figure could easily be off by 1-2 Gyr in either direction, but it would be very difficult (in our opinion) to reduce it to below 12 Gyr, or to increase it much above 20 Gyr. (These can probably be regarded as 2 limits, though it is difficult to assign confidence intervals in this way because the errors in the models and in the various procedures used to obtain an age estimate are likely not Gaussian in sum total.) We favor an imbalance in the attached error bar for two reasons. First, the effects of He diffusion were allowed for in this estimate: Ignoring them would imply about a 7% increase in age. Second, we have opted for the distance scale defined by the local subdwarfs, which is within 0.1-0.2 mag of that implied by the calibration of RR Lyraes in the LMC (using the Cepheid-based distance to this system) and studies of the pulsational properties of cluster variable stars. The use of the distance scale based on B-W and statistical parallax measures of field RR Lyraes would also imply higher ages for the GCs. This estimate, which has remained essentially unchanged for (at least) the past 25 years despite steady refinements in both theory and observations during this period, should be regarded as quite a robust result by the cosmology community.

Although it is a common practice to simply add 1 Gyr to the best estimate of globular cluster ages to account for the formation time of these objects, there is potentially a fairly large range in the number that must be added to derive the age of the Universe. As shown in Figure 10 (for a more detailed analysis see Tayler 1986), the actual correction depends sensitively on the values of H₀, _Matter, and the formation redshift of the GCs. The redshift at which galaxies like the Milky Way formed remains one of the most important open questions in observational cosmology. However, based on chemical-abundance measurements in absorption-line systems along the line of sight to distant quasars, it appears that gas in the Universe underwent significant enrichment between redshifts z of 3.5 to 2 (e.g. Lanzetta, Wolfe & Turnshek 1995, Wolfe et al 1995), and it therefore seems likely that the formation epoch of GCs was earlier than z = 3.5 (also see Sandage 1993c). Although there are theoretical reasons for believing that globular clusters formed before galaxies (Peebles & Dicke 1968), perhaps at redshifts as large as 10, the existence of field halo stars in the halo of the Milky Way that are significantly more metal-poor than GC stars may argue against this hypothesis. Still, with these limits on z, the age of the Universe is very likely 10⁹ yr (see Figure 10) older than the Galactic GC system.

Figure 10. The time from the Big Bang to a given redshift as a function of various combinations of H0 and Total = Matter (i.e. the cosmological constant is assumed to be zero). Friedmann cosmological models are assumed.

The solid curves in Figure 11 indicate loci of constant expansion age on the _Matter versus H₀ plane for Friedmann models with = 0. Because we believe that a firm lower limit to GC ages is 12 Gyr (equal to our best estimate minus a generous error bar of 3 Gyr), the 12 Gyr curve should be shifted to somewhat lower H₀ values (at fixed _Matter) to allow for the elapsed time between the Big Bang and GC formation (see Figure 10). But even as it stands, _Matter = 1, = 0 Einstein-de Sitter universes are rejected at the 95% confidence level for H₀ = 65 ± 10% km s^-1 Mpc^-1. Furthermore, if H₀ ~ 80 ± 8 km s^-1 Mpc^-1 [see van den Bergh's (1995) summary of the HST H₀ Key Project results], then our age-based upper limit to H₀ is inconsistent at the ~ 3 level.

Figure 11. Expansion-age isochrones (for ages from 8 to 18 Gyr, as indicated) as a function of H0 and Matter, assuming Friedman cosmological models. Given that globular clusters set a firm lower limit of 12 Gyr for the age of the Universe (see text), those combinations of H0 and Matter outside of the hatched area are precluded, unless the cosmological constant is nonzero. Our best estimate of GC ages is represented by the thick 15 Gyr locus.

The two most widely discussed alternatives to the standard model to bring expansion ages into concordance with those derived for GCs are low-_Matter, = 0, spatially open universes or low-_Matter, spatially flat universes that have a nonzero value of . For the first case, if we assume a large value for the formation redshift, then there is no 1 overlap between H₀ = 80 ± 8 km s^-1 Mpc^-1 and our GC-age constraint on the Hubble constant: For H₀ < 70, the 1 error bars do overlap. For the second case (see the excellent review on nonzero models by Carroll, Press & Turner 1992), a positive value of provides a term [ = / (3H₀²)] that can be added to _Matter to give a spatially flat Universe (and preserve inflation). For instance, for = 0.8, and assuming _Matter = 0.2, the expansion age is 13.5 Gyr if H₀ = 80 km s^-1 Mpc^-1. Although possibilities clearly exist for this alternative, there are already volume-z tests (e.g. the fraction of gravitationally lensed quasars; see Ostriker & Steinhardt 1995) that may exclude values for as high as this. Also, because the effects of nonzero change with time, a whole new set of fine-tuning problems may be introduced into cosmology. The implications of stellar ages ~ 15 Gyr may, indeed, become profound in the next few years as the efforts to determine H₀ reduce the total (internal plus external) distance scale errors to 10%.

Acknowledgments

We thank Márcio Catelan, Brian Chaboyer, Francesca D'Antona, Flavio Fusi Pecci, Bob Kraft, Charles Proffitt, Harvey Richer, Bob Rood, and Matt Shetrone for helpful information We are especially grateful to Allan Sandage for his careful reading of the manuscript and for offering a number of helpful suggestions that have served to improve this paper. The tremendous support and encouragement from Jim Hesser and David Hartwick are also much appreciated. DAV acknowledges, with gratitude, the award of a Killam Research Fellowship from The Canada Council and the support of an operating grant from the Natural Sciences and Engineering Council of Canada.