THE INTERPRETATION OF COLOR-MAGNITUDE DIAGRAMS THROUGH NUMERICAL-SIMULATION AND BAYESIAN-INFERENCE

We present a new method designed to aid in the interpretation of the c olor-magnitude diagrams (CMDs) of resolved stars in nearby galaxies. A CMD is a two-dimensional distribution of data points with well unders tood Gaussian measurement errors created from two independent observat ions. The most rigorous way to interpret a CMD is to create a model CM D through Monte Carlo simulation using theoretical stellar evolution t racks to see what combination of initial conditions provides the best match with the observed data. In this paper we describe how best to qu antitatively compare these types of model and data. A good model CMD m ust contain a spatial distribution of points that matches the data and also has the same relative numbers of red stars, blue stars, and any other features seen in the data. This kind of detailed information can be obtained by using the assumptions of Bayesian inference to calcula te the likelihood of a model CMD being a good match to the data CMD. T o illustrate the effectiveness of this approach, we have created sever al test scenarios using simplified data sets. We have derived a method that allows us to determine whether a model is distributed as the dat a over the entire CMD, and whether the relative numbers of points in p arts of the diagram are different. We can also determine whether a goo d match can be made to part of the data, which will be useful when att empting to model complex star formation histories. Our examples show t hat the results are very sensitive to the size of the measurement erro rs in the data, and so it is only the accuracy of these errors that re stricts our ability to distinguish the good from the bad models. Our m ethod is sufficiently robust and automated that we can search through large areas of parameter space without having to inspect the models vi sually.