2.3.7. Age of the globular clusters

The RR Lyr calibration is also crucial in the estimation of the age of globular clusters, since the stellar age is proportional to the inverse of luminosity, i.e., inverse square of the distance. The modern evolution tracks of the main sequence agree reasonably well among authors. There are some disagreements in colours around the turn-off point, largely depending on the treatment of convection, but the luminosity is little affected (e.g., Renzini 1991; Vandenberg et al. 1996, especially their Fig. 1). Absolute magnitude at the turn-off point M_V^TO of the main sequence is hence a good indicator of the age, as (Renzini 1991),

(6)

in units of Gyr, or

(7)

if (3) is included. The difference of the magnitudes between the turn-off point and RR Lyr (M_V^TO - M_V^RR) varies little among clusters and is measured to be 3.5 ± 0.1 mag (Buonanno et al. 1989; see Chaboyer et al. 1996 for a compilation). The metallicity dependence of the cluster age disappears if a = 0.35, i.e., the globular cluster formation is coeval (Sandage 1993b). Both (4) and (5), however, give a 0.2, ⁽²⁾ which indicates that metal-poor clusters appear older.

The dichotomous calibrations of RR Lyr obviously affect the age of globular clusters. Another large uncertainty is whether the age-metallicity correlation is real, indicating metal-poor clusters formed earlier, or is merely due to a systematic error, with the formation of globular cluster being coeval. The possibilities are four-fold:

In addition there are ± 10% errors from various sources (Renzini 1991; Bolte & Hogan 1995; VandenBerg et al. 1996; Chaboyer et al. 1996). Figure 3 shows the age of various clusters from Gratton et al. (1997) and Chaboyer et al. (1998) both using the calibration close to (5). The [Fe/H] dependence is apparent.

The claims of Gratton et al. (1997), Reid (1997) and Chaboyer et al. (1998) for young universe (11-12 Gyr) assume a coeval-formation interpretation together with the long RR Lyr calibration and take a mean of globular cluster ages. Three other possibilities, however, are not excluded.

Figure 3. Age of globular clusters as a function of [Fe/H]. The solid points are from Gratton et al. (1997) for three different stellar evolution models. The open points are from Chaboyer et al. (1998). The solid line shows (7) but offset by -0.06. The dashed line is 11.8 Gyr of Gratton et al.

² A remark is made on a recent analysis of Kovács & Jurcsik (1996), who obtained a < 0.19 from a model-independent approach using the Fourier coefficients of the light curves that correlate with the metal abundance. Back.