Objective Determination of Star Formation Histories

Objective determination of a star formation history from a colour-magnitude diagram, independently of assumed parametric descriptions, is necessary to determine the evolutionary history of a galaxy. We introduce a new method for solving maximum likelihood problems through variational calculus, and apply it to the case of recovering an unknown star formation history, SFR(t), from a colour-magnitude diagram. This method provides a non-parametric solution with the advantage of requiring no initial assumptions on the SFR(t). As a full maximum likelihood statistical model is used, one may exploit all the information available in the photometric data which can be explained by available isochrones. Extensive tests of the method show it to be reliable under noise conditions comparable to those appropriate for real observations. Implications for future surveys, such as the GAIA mission are significant: accurate determination of the evolutionary history of the Milky Way is limited only by adequate spectroscopy and/or photometry to provide a determination of stellar metallicity and temperature for a sufficient sample of stars of luminosities at and above an old main-sequence turnoff.