Annu. Rev. Astron. Astrophys. 1992. 30: 499-542 Copyright © 1992 by Annual Reviews. All rights reserved

4.2 Age Concordance: Globular Clusters and Cosmic Nuclear Data

Perhaps the most compelling, plausibly achievable demonstration of a non-zero value of would be the identification of objects or material older than H₀^-1. Figure 4 shows that one would be forced to invoke models with significantly greater than zero if _M > 0.1. Such an argument would be strong because it is difficult to imagine escaping it through the usual sort of loopholes of ``astrophysical complications'' which prevent definite conclusions in so many cosmological considerations. In other words, the universe ought to be at least as old as the objects and material it contains. Of course astrophysical complications are still able to enter the picture when we get down to the quantitative question of how old the oldest objects actually are!

Galactic globular clusters are the stellar systems with the most reliably determined extreme ages. The calibration of stellar ages is a complex and highly developed subject with many thorough reviews (e.g. Rood 1990, VandenBerg & Smith 1988, VandenBerg 1990) and even whole volumes concerning it (Philip 1988). Here we only comment briefly on the most salient issues.

There are basically two techniques for using the models of stellar evolutionary theory to derive ages from observed globular cluster H-R diagrams. One may fit the theoretical isochrones directly to the observed main sequence color-magnitude track and turn-off in order to determine the mass of stars which have just exhausted their central hydrogen fuel. Alternately, one may use the magnitude difference between the main sequence and the horizontal branch (HB) to find the turn-off luminosity (taking the HB to have a fixed luminosity). The primary advantage of the former method is that it relies on the most secure regime of stellar evolution theory. Its worst disadvantage is that very small errors in matching theoretical to observed colors (which could be due to inaccurate reddening corrections, stellar atmosphere models, photometric calibration, and so on) lead to 5-7 times larger fractional errors in the derived ages. In other words, a 0.04 magnitude systematic shift in the color match corresponds to a 20-30% error in the age. The main advantage of the latter method is that it avoids color fitting (and hence these problems) altogether. Its primary difficulty is that the HB absolute magnitude is poorly known (based on RR Lyrae star studies) with the uncertainty being at least 0.2 magnitudes (Sandage 1990) corresponding to a 20% age uncertainty. Both techniques are discussed in detail and applied to the best available data for a large sample of globular clusters by Sandage & Cacciari (1990).

Despite these formidable difficulties, observational and theoretical, the consensus of expert opinion concerning the ages of the oldest globular clusters is impressive. All seem to agree that the best-fit ages are 15-18 Gyr or more, perhaps considerably more. (It turns out to be easier to extend the main sequence lifetime of low mass stars by introducing theoretical complications, which typically provide additional nuclear fuel or added support against gravity, than to lower the ages.) Of more interest in the present context, one wishes to know the lower limit on these oldest stellar ages; unfortunately, it is not a matter of formal errors but rather of informed judgments of how far various effects and uncertainties can be pushed. The range of expert opinion clusters around 12-14 Gyr whether based on considerations of many clusters (Sandage & Cacciari 1990, Rood 1990) or the few best studied cases such as 47 Tuc and M92 (VandenBerg 1990, Pagel 1990).

It may provide a useful perspective to note that determination of an age with some fractional accuracy corresponds to determining the distance twice as accurately. Thus, a 20% age uncertainty (the difference between 15 and 12 Gyr) corresponds to claiming a 10% uncertainty in the distance! This holds true whichever of the two techniques is employed.

Nuclear chronometers also offer the possibility of obtaining a useful lower limit on the age of the universe. They give the age of the Solar System with great precision (Anders 1963), and a few chronometric pairs (notably ²³²Th-²³⁸U, ²³⁵U-²³⁸U, and ¹⁸⁷Re-¹⁸⁷Os) can, in principle, yield a mean heavy element age prior to the condensation of the Solar System (Schramm & Wasserburg 1970). Unfortunately, due to both observational uncertainties in their relative abundances and to the necessity of relying on highly speculative and poorly constrained models for the Galactic history of nucleosynthesis, the indicated age of the universe is extremely uncertain (Clayton 1988, Arnould & Takahashi 1990, Cowan et al 1991). Nevertheless, a conservative analysis (essentially assuming all of the heavy elements were synthesized promptly at the beginning of the universe) which allows for the abundance uncertainties indicates a somewhat interesting lower limit of 9.6 Gyr (Schramm 1990) for the age of the oldest heavy elements. Although this is less restrictive than the lower limits obtained from globular cluster studies discussed above, it may be more secure because the physics of nuclear decay is so much better understood than that of stellar evolution.

With these lower limits for the universe's age, we could obtain decisive information on from Figure 4 if only we had an accurately measured value of H₀. Figure 10 illustrates the situation. The shaded boxes show a reasonable range of observational determinations of the dynamical component of _M, and of H₀. Taking 0.1 as a lower limit of _M from dynamical studies (Trimble 1987), the open (k = - 1) models with = 0 require H₀ to be no larger than 64-76 km/s/Mpc, to be consistent with globular cluster ages. In the extreme case of _M = 1, = 0, the range is 48-57 km/s/Mpc. There would be an additional 25% increase to 71 or 95 km/s/Mpc (for the k = 0 and k = - 1 cases, respectively) if one more cautiously used the nucleochronometer limit quoted above. If the true value of H₀ were shown to be larger than these limits (pick your favorite!), then a non-zero would be required.

Figure 10. The age of the universe is shown as solid contours in the plane defined by H0 and M, (left) for open models with = 0, and (right) for flat models with tot = 1. Shaded boxes indicate likely observational ranges for these quantities. The contribution of baryons to M is bounded by nucleosynthesis to lie between the dotted curves. See text for discussion.

Clearly there is the possibility of a discovery here, but is there really any problem at the moment? Some optimistic commentators (Fukugita 1991, Peacock 1991, Fukugita & Hogan 1990) have been encouraged by the precision and consistency of several modern extragalactic distance indicators (Aaronson et al 1989, Jacoby et al 1990, Tonry 1991, Fukugita & Hogan 1991) to conclude that H₀ is quite likely to be within 10% of 80 km/s/Mpc. Such a value would require either invoking a non-zero cosmological constant or both abandoning a k = 0 cosmology and stretching the globular cluster ages to roughly the limit of their usually claimed uncertainties. This view has been a significant motivation for the recent renewed interest in non-zero . Moreover, even if the various extragalactic indicators (cited above) that indicate a large H₀ value are accurate indicators of relative distance, the resulting H₀ value is still dependent on the distances of the same few local calibrators, which are not established beyond reasonable doubt either (though see Madore & Freedman 1991, Freedman 1990). On the other hand, there is also some substantial evidence for small H₀ values (Arnett 1982, Arnett et al 1985, Branch 1987, Tammann 1987, Sandage 1988b, c, Eastman & Kirshner 1989, Roberts et al 1991, Press et al 1992, Narayan 1991) which we have no reason to disregard. In summary, a value of H₀ small enough to avoid any age concordance problems, even in an _M = 1, = 0 model, is not yet excluded.

As a matter of related interest, Figure 10 also shows as dotted lines the upper and lower bounds on _baryon H₀² that derive from cosmological light element abundances (Olive et al 1990, Walker et al 1991). At the lower-left corner of the shaded box in the left-hand figure, one notes that an open model consisting entirely of baryons with = 0 and _M = 0.1 is by no means strongly excluded. That such a model is currently so unfashionable testifies to the strength of theoretical prejudice for one or more of (a) inflation, (b) CDM theory (see below), or (c) exotic dark matter. The corresponding flat 0 model (right-hand figure) has an age that exceeds 30 Gyr, and is thus much less plausible: Not one observed stellar system even approaches such an age. One sees that a flat model thus effectively requires a nonbaryonic component of dynamical matter. The necessity of invoking two speculative elements should perhaps be counted as a strike against models.