Solar calibration and the ages of the old disk clusters M67, NGC 188, and NGC 6791

Theoretical isochrones have been constructed to derive the ages of the old disk star clusters M67, NGC 188, and NGC 6791. Ages were derived using Cox-Stewart opacities, and the LAOL opacities for the Ross-Aller and Grevesse mixtures. In each case, the models were calibrated using a standard solar model calibration in which the helium abundance Y is adjusted to match the solar luminosity at the solar age, and the mixing length parameter α is chosen to reproduce the solar radius [Guenther et al., ApJ, 345, 1022 (1989)]. Such a calibration is independent of the uncertainties in the color of the Sun. The color transformation of Green [Calibration of Stellar Ages (Davis, Schenectady, 1988)] was adopted. We find that provided the proper solar calibration is applied, the derived ages depend little on the choice of opacity tables and surface boundary conditions. For M67 and NGC 188, we derive the ages: 4.0^+1.0_-0.5 Gyr and 6.5^+1.5_-0.5 Gyr, respectively, where the main uncertainty resides in the estimate of interstellar reddening. These ages are close to the recent independent age estimates by Hobbs & Thornburn [AJ, in press (1991)] and Hobbs et al. [AJ, 100, 710 (1990)], for M67 and NGC 188, respectively, and by Caputo et al. [AJ, 99, 261 (1990)] for NGC 188. The age of NGC 6791 is about 1.0 Gyr larger than that of NGC 188, if the two clusters have the same metallicity. If NGC 6791 is more metal rich, its age is more uncertain, and could be as low as 6.5 Gyr.