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 a pply it to the case of recovering an unknown star formation history, SFR(t) , from a colour-magnitude diagram. This method provides a non-parametric so lution with the advantage of requiring no initial assumptions on the SFR(t) . As a full maximum likelihood statistical model is used, one may exploit a ll the information available in the photometric data which can be explained by available isochrones. Extensive tests of the method show it to be relia ble under noise conditions comparable to those appropriate for real observa tions. Implications for future surveys, such as the GAIA mission are signif icant: accurate determination of the evolutionary history of the Milky Way is limited only by adequate spectroscopy and/or photometry to provide a det ermination of stellar metallicity and temperature for a sufficient sample o f stars of luminosities at and above an old main-sequence turnoff.