A Method for Determining the Star Formation History of a Mixed Stellar Population

Abstract

We present a method to determine the star formation history of a mixed stellar population from its photometry. We perform a χ 2 minimization between the observed photometric distribution and a model photometric distribution, based on theoretical isochrones. The initial mass function, distance modulus, interstellar reddening, binary fraction, and photometric errors are incorporated into the model, making it directly comparable to the data. The model is a linear combination of individual synthetic color-magnitude diagrams (CMDs), each of which represents the predicted photometric distribution of a stellar population of a given age and metallicity. While the method is similar to existing synthetic CMD algorithms, we describe several key improvements in our implementation. In particular, we focus on the derivation of accurate error estimates on the star formation history to enable comparisons between such histories, either from different objects or from different regions of a single object. We present extensive tests of the algorithm, using both simulated and actual photometric data. From a preliminary application of the algorithm to a subregion of the Large Magellanic Cloud (LMC), we find that the that the lull in star formation observed among the LMC's cluster population between 3 and 8 Gyr ago is also present in the field population. The method was designed with flexibility and generality in mind, and we make the code available for use by the astronomical community.