3.1. Quality color-magnitude diagrams
We have seen in the last few years remarkable advances in the quality of CMD's for globular clusters. The first advance was the development of CCD panoramic detectors; the second was the high quality data from the fixed HST, which permit the construction of high quality CMD's down to faint main sequence magnitudes. The reduction in crowding, even in the cluster core make high precision photometry possible, with a high degree of completeness. Figure 4 illustrates the main sequence turnoff of NGC 6752 from the work of Rubenstein and Bailyn (1997), obtained with HST. Note the well-delineated lower main sequence and the clear distribution of binaries along the sequence. We are still learning how best to exploit fully data of this quality for age determinations. New fitting techniques which make use of the complete sequence in the CMD are being devised to constrain theoretical isochrones in a more effective way than was possible until now. And for the first time, it has now become possible to construct high precision luminosity functions right into the center of globular clusters (see Section 2.3).
Figure 4. CMD for NGC 6752 by Rubenstein & Bailyn (1997), based on HST observations.
3.2. Distances of globular clusters
Uncertainties in the distances of globular clusters have long been recognized as the primary uncertainty in globular cluster age determinations (see e.g. Renzini 1991). There are three ways currently available to measure the distance of a globular cluster: (1) the use of RR Lyrae variables as standard candles; (2) main sequence fitting; and (3) fitting to the white dwarf sequence. The first two ways are the traditional ways, which have alternately been emphasized over the years; the third way has only recently become possible with the HST.
3.2.1. RR Lyrae variables
This method was favored early on, when it was believed that all RR Lyrae variables have the same magnitude, near Mv(RR) = 0. More recent work has shown that the RR Lyrae variables are fainter and that Mv(RR) depends on metallicity (Sandage 1990). It is convenient to write:
where the slope is the primary concern for studies of the relative ages of globular clusters (Zinn 1985; Sarajedini and King 1989; Carney et al. 1992). Both and must be known for absolute ages determinations. Chaboyer et al. (1996a) recently explored the consequences for globular cluster ages of the choice of and , and on the basis of the data available at the time, selected = 0.20 and = 0.98 as "best" values. The derived value of Mv(RR) for each [Fe/H] was then combined with theoretical turnoff luminosities to calibrate the V method.
3.2.2. Main sequence fitting
In principle, one could determine the position of the main sequence for a given [Fe/H] with the help of nearby halo stars with known parallaxes. The argument is based on the assumption that high velocity field dwarfs, which are metal-poor and share the halo kinematics of globular clusters, must be identical to globular cluster main sequence stars. This straightforward approach cannot be used at this time in the absence of a sufficient sample of well determined parallaxes for halo field stars. The release of the Hipparcos parallax catalogue in 1997 should remedy this deficiency and may revive main sequence fitting as a viable way to determine globular cluster distances.
3.2.3. White dwarf sequence
The detection of the white dwarf cooling sequence in some globular clusters is now possible with HST (Richer et al. 1995). Figure 5 shows the recent observations of white dwarfs in NGC 6752 by Renzini et al. (1996). The derived distance modulus of 13.05 is in excellent agreement with the distance modulus of 12.96 assigned to NGC 6752 by Chaboyer et al. (1996a) from their Mv(RR) calibration.
Figure 5. White dwarf sequence in NGC 6752 (denoted by black dots), superimposed in the instrumental HST CMD on the sequence of calibrating white dwarfs with known statistical parallaxes, denoted by asterisks and squares (Renzini et al. 1996). A distance modulus of 13.05 has been derived for the cluster.
Spectroscopic observations must also provide the cluster metallicity [Fe/H] and [ / Fe], the degree of -capture element enhancement in the cluster. Both of these quantities enter in the microscopic physics of the stellar model in a sensitive way and are major sources of age uncertainty (see Section 5). The initial helium abundance cannot be measured spectroscopically in the main sequence stars and is taken to be the near-primordial value observed in very metal-poor gaseous nebulae, i.e. Y = 0.23 to 0.24.