Inverting Color‐Magnitude Diagrams to Access Precise Star Cluster Parameters: A Bayesian Approach

We demonstrate a new Bayesian technique to invert color-magnitude diagrams ofmain sequence and white dwarf stars to reveal the underlying cluster propertiesof age, distance, metallicity, and line-of-sight absorption, as well asindividual stellar masses. The advantages our technique has over traditionalanalyses of color-magnitude diagrams are objectivity, precision, and explicitdependence on prior knowledge of cluster parameters. Within the confines of agiven set of often-used models of stellar evolution, the initial-final massrelation, and white dwarf cooling, and assuming photometric errors that onecould reasonably achieve with the Hubble Space Telescope, our technique yieldsexceptional precision for even modest numbers of cluster stars. For clusterswith 50 to 400 members and one to a few dozen white dwarfs, we find typicalinternal errors of sigma([Fe/H]) <= 0.03 dex, sigma(m-M) <= 0.02 mag, andsigma(Av) <= 0.01 mag. We derive cluster white dwarf ages with internal errorsof typically only 10% for clusters with only three white dwarfs and almostalways <= 5% with ten white dwarfs. These exceptional precisions will allow usto test white dwarf cooling models and standard stellar evolution modelsthrough observations of white dwarfs in open and globular clusters.Comment: 36 pages, including 17 figures, accepted to ApJ. Higher res versions of fig 15 & 16 available upon request to first autho