We demonstrate a new Bayesian technique to invert color-magnitude diagrams of main sequence and white dwarf stars to reveal the underlying cluster properties of age , distance , metallicity , and line-of-sight absorption , as well as individual stellar masses .
The advantages our technique has over traditional analyses of color-magnitude diagrams are objectivity , precision , and explicit dependence on prior knowledge of cluster parameters .
Within the confines of a given set of often-used models of stellar evolution , the initial-final mass relation , and white dwarf cooling , and assuming photometric errors that one could reasonably achieve with the Hubble Space Telescope , our technique yields exceptional precision for even modest numbers of cluster stars .
For clusters with 50 to 400 members and one to a few dozen white dwarfs , we find typical internal errors of \sigma ( [ Fe/H ] ) \leq 0.03 dex , \sigma ( m - M _ { V } ) \leq 0.02 mag , and \sigma ( A _ { V } ) \leq 0.01 mag .
We derive cluster white dwarf ages with internal errors of typically only 10 % for clusters with only three white dwarfs and almost always \leq 5 % with ten white dwarfs .
These exceptional precisions will allow us to test white dwarf cooling models and standard stellar evolution models through observations of white dwarfs in open and globular clusters .