Synthesis models in a probabilistic framework: Metrics of fitting

Abstract

Stellar population synthesis codes provide the description of the total luminosity resulting from the combination of an ensemble of sources as a function of given physical parameters. Their final aim is to enable users to make inferences about the physical parameters (star formation history, mass transformed into stars, etc.) from the light observed in stellar clusters or galaxies. However, synthesis codes results cannot be interpreted in an one-to-one relation between an observed total luminosity and a theoretical model result since (a) we have not access to the intimate composition of the ensemble of stars and (b) the very theoretical method implicit in populations synthesis makes use of (probabilistic) distributions and there is not an unique model result that describes the integrated luminosity of an ensemble. In general, synthesis models provide the mean value of the distribution of possible integrated luminosities, this distribution (and not only its mean value) being the actual description of the integrated luminosity. Therefore, to obtain the closest model to an observation only provides confidence about the precision of such a fit, but not information about the accuracy of the result. In this contribution we show how to overcome this drawback and we propose the use of the theoretical mean-averaged dispersion that can be produced by synthesis models as a metric of fitting to infer accurate physical parameters of observed systems.