The Luminosity Function and Color-Magnitude Diagram of the Globular Cluster M12

In this paper we present the V and I luminosity functions and color-magnitude diagrams derived from wide-field (23 arcmin by 23 arcmin) BVI photometry of the intermediate metallicity ([Fe/H]=-1.3) Galactic globular cluster M12. Using observed values (and ranges of values) for the cluster metallicity, reddening, distance modulus, and age we compare these data to recent alpha-enhanced stellar evolution models for low mass metal-poor stars. We describe several methods of making comparisons between theoretical and observed luminosity functions in order to isolate the evolutionary timescale information the luminosity functions contain. We find no significant evidence of excesses of stars on the red giant branch, although the morphology of the subgiant branch in the observed luminosity function does not match theoretical predictions in a satisfactory way. Current uncertainties in Teff-color transformations (and possibly also in other physics inputs to the models) make more detailed conclusions about the subgiant branch morphology impossible. Given the recent constraints on cluster ages from the WMAP experiment (Spergel et al. 2003), we find that good fitting models that do not include He diffusion (both color-magnitude diagrams and luminosity functions) are too old (by approximately 1-2 Gyr) to adequately represent the cluster luminosity function. The inclusion of helium diffusion in the models provides an age reduction (compared to non-diffusive models) that is consistent with the age of the universe being 13.7+/-0.2 Gyr (Bennett et al. 2003).