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

1. INTRODUCTION

As fossil relics dating from the formation of the Galaxy and as the oldest objects in the Universe for which reliable ages can be derived, the Galaxy's globular star clusters have been the subject of intensive investigation for more than four decades. Their age distribution and the trends that they define of age with metallicity, position in the Galaxy, and kinematic properties are direct tracers of the chronology of the first epoch of star formation in the Galactic halo. Whether the globular cluster (GC) system encompasses an age range of several billion years or whether the majority of the GCs are nearly coeval is still the subject of lively debate. In a companion review, Stetson, VandenBerg & Bolte (1996) summarize the many advances that have been made in the determination of relative GC ages and assess their implications for Galactic formation scenarios. Absolute cluster ages - which are the focus of the present study - provide a vital constraint on the age of the Universe and thereby on the cosmological models that are used to describe it. Globular clusters may well have been the first stellar systems to form in the Universe (Peebles & Dicke 1968), probably within approximately 10⁹ yr after the Big Bang (see Sandage 1993c).

The current widespread interest in securing accurate globular cluster ages results from the dilemma that these ages pose for the presently preferred model in cosmology - a matter-dominated, Einstein-de Sitter universe. This model is characterized by the choice of _Total = 1 (as required by most formulations of inflation theory), with the cosmological-constant term, , taken to be zero, implying _Matter = 1. In this case, the expansion age of the Universe is given by t₀ = (2/3)H₀^-1, which works out to 8.3 Gyr if the Hubble constant H₀ is taken to be 80 km s^-1Mpc^-1. Support for this particular value of H₀, or one within ± 10-15% of it, has been boosted by the detection and analysis of Cepheid variables in Virgo cluster galaxies using both the Canada-France-Hawaii Telescope (Pierce et al 1994) and the Hubble Space Telescope (Freedman et al 1994;, Kennicutt, Freedman & Mould 1995). Moreover, very similar estimates have been favored in most recent reviews of H₀ determinations (e.g. Jacoby et al 1992, Huchra 1992;, van den Bergh 1992, 1994).

These results notwithstanding, significant support persists for H₀ < 65 km s^-1 Mpc^-1 (e.g. Saha et al 1994, 1995; Birkinshaw & Hughes 1994; Hamuy et al 1995; Sandage et al 1996); consequently, such lower values cannot yet be ruled out. But, even if H₀ were as low as 55 km s^-1Mpc^-1, the implied age for the Universe from the standard cosmological model is only 12.2 Gyr, which is also inconsistent with the GC-based estimate of ~ 16 Gyr. ² Thus the standard model would appear to fail the "age concordance" test, which is simply that the age of all things in the Universe must be smaller than the elapsed time since the Big Bang. Although there is increasing observational evidence for _Matter 0.3 (Vogeley et al 1992, Carlberg et al 1996, Squires et al 1996), even for a low-density, = 0 Universe (for which t₀ H₀^-1), it may not be possible to achieve compatibility with the GC age constraint if H₀ is as high as many people believe. This has lead to increasing speculation that the cosmological constant is nonzero (e.g. Efstathiou 1995); however, before stellar age estimates can be used to rule out any cosmologies, a reappraisal of the errors associated with GC age determinations is worthwhile. It is our intent to do just that.

In Section 2 we review the uncertainties in the stellar evolution models due to possible errors in the relevant input physics: nuclear reaction rates, opacities, nonideal gas law effects in the equation of state, and the treatment of convection. In this section we also discuss the effects of input physics that are not normally a component of standard models: rotation, diffusion, and main-sequence mass loss. The observed chemical abundance trends among GC giants are highlighted therein because they provide perhaps the strongest indication of inadequacies in the stellar models for very metal-poor stars. We then briefly consider the possible role of unconventional physics, describe some pertinent observational tests of stellar evolution theory, and briefly recall the very first estimates of GC ages.

As has been recognized for a number of years, the dominant error in the derivation of ages from the luminosity of main-sequence turnoff stars in GCs [which we designate as L^TO, M_bol(TO), or M_V(TO)] is the uncertainty in the Population II distance scale (cf Renzini 1991). In Section 3 we discuss the issue of globular cluster distances. There appears to be a dichotomy developing, with a "long" distance scale based on nearby subdwarfs, the calibration of the horizontal branch (HB) in the LMC, and analyses of the pulsational properties of cluster RR Lyrae variables and a "short" distance scale based on Baade-Wesselink and statistical parallax studies of field RR Lyraes. The disagreement in the implied luminosity of the HB from the two calibrations is 0.25 mag. We express some preference for the long distance scale, in which case the implied age for the metal-poor cluster M92 is ~ 15 Gyr: For the short distance scale its age is increased to 18 Gyr. A brief summary of the ramifications of such ages for cosmology is given in Section 4.

² Since the 1970s there has been general agreement that the oldest of the Galaxy's GCs has an age somewhere between 14 and 19 Gyr, with 16 ± 3 Gyr being perhaps the most frequently mentioned estimate: See, for instance, Demarque & McClure (1977), Carney (1980), Sandage, Katem & Sandage (1981), VandenBerg (1983), Gratton (1985), Peterson (1987), Buonanno, Corsi & Fusi Pecci (1989), Lee, Demarque & Zinn (1990), Rood (1990), Iben (1991), Renzini (1991), Salaris, Chieffi & Straniero (1993), Sandage (1993c), Chaboyer (1995), Bolte & Hogan (1995), Mazzitelli, D'Antona & Caloi (1995). These represent a small fraction of the published reviews and original investigations over this period that have reached basically the same conclusion. Back.