The determination of globular cluster ages continues to be an active field of research. There are two widely applied methods used to estimate cluster ages - isochrone fitting and differential measures through careful comparisons of the location of the principal stellar sequences on the CMD.
For the isochrone fitting we used the isochrones computed by by Proffitt & Vanden Berg (1991) using a [O/Fe] ratio of between 0.75 and 0.40, which include the effect of He diffusion and the isochrones by Bergbusch & Vanden Berg (1992), which adopted a [O/Fe] ratio between 0.75 and 0.23. We also compared the Bell & Vanden Berg (1987) theoretical isochrones with the CMD morphology of the turnoff region in g, r system.
The 
parameter of Flannery & Johnson (1982)
was used as a fitting statistics and we calculated this parameter for
E(g-r) between (0.01-0.1), 16.5 
, 
and age between 
.
Figure 6: Comparison of the Proffitt & Vanden Berg (1991) theoretical
isochrones (solid curves) with fiducial line of Palomar 13 (crosses) for
[Fe/H] = -2.26, -1.66 and -1.26 for an age of 12 Gyr. Palomar 13 data have been
corrected for a distance modulus of 17.23 mag and reddening 0.05
The best statistics was reached for a cluster age of 12 Gyr,
with metallicity 
at the isochrones by
Proffitt & Vanden Berg (1991).
The implied distance modulus derived from the
comparison with the isochrones is 17.23 with E(B-V)=0.05.
The best fit isochrones are shown in Fig. 6 (click here).
There is a large disagreement between the theoretically calculated isochrones
and the red giant branch.
Figure 7: Comparison of the Bergbusch & Vanden Berg (1992) theoretical
isochrones (solid curves) with fiducial line of Palomar 13 (crosses) for
, -1.66 and -1.48 for an age of 12 Gyr. Palomar 13 data have
been corrected for a distance modulus of 17.19 mag and reddening 0.05
Figure 7 (click here) shows a comparison between the theoretical isochrones of
Bergbusch & Vanden Berg (1992).
The best statistics was reached for a cluster age of 12 Gyr,
with metallicity 
, 
.
The implied distance modulus derived from the
comparison with the isochrones is 17.19 with E(B-V)=0.05.
When was made a comparison between the different sets of isochrones it was found that the diffusive isochrones did not fit the observations as well as the nondiffusive ones.
Figure 8: Comparison of the Vanden Berg & Bell (1987) theoretical
isochrones (solid curves) with the color-magnitude diagram of Palomar 13 (crosses) for
metal abundance [Fe/H] of -2.27, -1.77 and -1.27 for age of 12 Gyr. Palomar 13 data have been
corrected for a distance modulus of 17.20 mag and reddening 0.07
The similar result 
, 
, (M-m) = 17.20
and E(g - r)=0.07
was found by using isochrones of Bell & Vanden Berg (1987)
calculated in g, r system (Fig. 8 (click here)).
Due to some uncertainties in the locations of the fiducial points, E(B-V) and [Fe/H] the total external uncertainty at this method is 3 Gyr (Bolte 1990).
Figure 9: Fiducial sequences for Palomar 13 (crosses)
and Palomar 5. The clusters were shifted to a common reddening and distance
A second approach to determine an age of Palomar 13 was made using calibration
of Chaboyer et al. (1992) (see their formula 1).
Assuming 
and 
we have calculated
.
Table 5: 
consistency test for Palomar 13
According to resent work of Buonanno et al. (1993), Buonanno et al. (1995a,
b) we used the ``vertical" method, based on the
magnitude difference between the horizontal branch and the main sequence
turnoff and the ``horizontal" method based on the color difference between
the base of RGB and the main sequence turnoff. We will consider the same
reference clusters as Buonanno et al. (1995) for Arp 2. The necessary data
for all objects are listed in Table 5. The TO-to-RGB color difference for
Palomar 13 is 
The error was computed using the procedure
suggested by Vanden Berg et al. (1990) in which parabolic
arcs are fit to stars in appropriate boxes in the color - magnitude
diagram. The comparison with M 3, NGC 6752, Rup 106, Arp 2 and MPC -
the metal-poor clusters in the table produces inconsistent age
differences. Consistent differential ages are obtained in comparison
with Pal5 (Smith et al. 1986) (Fig. 9 (click here)). The
estimated error is approximately 2 Gyr.