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' × 23') 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 with recent α-enhanced stellar evolution models for low-mass metal-poor stars. We describe several methods of making comparisons between theoretical and observed luminosity functions to isolate the evolutionary timescale information that 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 T_eff-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, we find that good-fitting models that do not include He diffusion (both color-magnitude diagrams and luminosity functions) are too old (by ~1-2 Gyr) to adequately represent the cluster luminosity function. The inclusion of helium diffusion in the models provides an age reduction (compared with nondiffusive models) that is consistent with the age of the universe being 13.7 ± 0.2 Gyr.