Abstract details

Synthesis models predict the integrated properties of stellar populations. Several problems exis in this field, mostly related to the fact that integrated properties are distributed. To date, this aspect ha been either ignored (as in standard synthesis models, which are inherently deterministic) o interpreted phenomenologically (as in Monte Carlo simulations, which describe distributed propertie rather than explain them). We approach population synthesis as a problem in probability theory, i which stellar luminosities are random variables extracted from the stellar luminosity distributio function (sLDF). With standard distribution theory, we derive the population LDF (pLDF) for clusters o any size from the sLDF, obtaining the scale relations that link the sLDF to the pLDF. We recover th predictions of standard synthesis models, which are shown to compute the mean of the luminosit function. We provide diagnostic diagrams and a simplified recipe for testing the statistical richness o observed clusters, thereby assessing whether standard synthesis models can be safely used or statistical treatment is mandatory. We also recover the predictions of Monte Carlo simulations, with th additional bonus of being able to interpret them in mathematical and physical terms. We give example of problems that can be addressed through our probabilistic formalism: calibrating the SBF method determining the luminosity function of globular clusters, comparing different isochrone sets, tracing th sLDF by means of resolved data, including fuzzy stellar properties in population synthesis, amon others. Additionally, the algorithmic nature of our method makes it suitable for developing analysi tools for the Virtual Observatory