Annu. Rev. Astron. Astrophys. 1992. 30:
499-542
Copyright © 1992 by . 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 *H*_{0}^{-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 ^{232}Th-^{238}U,
^{235}U-^{238}U, and ^{187}Re-^{187}Os) 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 *H*_{0}.
Figure 10 illustrates the situation. The shaded
boxes show a reasonable range of observational determinations of the
dynamical component of
_{M}, and of
*H*_{0}. Taking 0.1 as a lower limit of
_{M} from dynamical
studies
(Trimble 1987),
the open (*k* = - 1) models
with _{} = 0 require
*H*_{0} 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 *H*_{0} were shown to be
larger than these limits (pick your favorite!), then a non-zero
_{} would be required.

A more extreme version of this argument is to take best-fit globular
cluster ages of 15-20 Gyr and note that this places upper limits of
33-43 km/s/Mpc if one insists on a model with
_{M} = 1,
_{} = 0.

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 *H*_{0} 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 *H*_{0} value are accurate
indicators of
relative distance, the resulting *H*_{0} 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 *H*_{0} 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 *H*_{0} 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}
*H*_{0}^{2} 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.