Cerviño, M.; Pérez, E.; **Sánchez, N.**; Román-Zúñiga, C.; Valls-Gabaud, D.

UP2010: Have Observations Revealed a Variable Upper End of the Initial Mass Function? ASP Conference Proceedings, Vol. 440. Proceedings of a Conference held at Sedona, Arizona, USA 20-25 June 2010 Edited by Marie Treyer, Ted K.Wyder, James D. Neill, Mark Seibert, Janice C. Lee. San Francisco: Astronomical Society of the Pacific, 2011., p.133

06/2011

We present the underlying relations between color-magnitude diagrams (CMDs) and synthesis models through the use of stellar luminosity distribution functions. CMD studies make direct use of the stellar luminosity distribution function while, in general, synthesis models only use its mean value, even though high-order moments can also be obtained. We show that the mean high-order moments and integrated luminosity distribution functions of stellar ensembles are related to the stellar luminosity distribution function within the formalism of probabilistic synthesis models. More details have been yet presented in Cerviño & Luridiana (2006) and references therein. As a direct application of this formalism, we discuss two key issues. First, we discuss inferences on the upper mass limit of the IMF as a function of the total mass of clusters. Second, we apply extreme value theory to show that the cluster mass obtained from normalising the IMF between m_{max} and m_{up} does not provide the cluster mass in the case where only one star in this mass range is present, as assumed in the IGIMF theory. It provides, instead, the cluster mass with a 60% probability to have a star with mass larger than m_{max}. We argue that, in light of this result, the basic formulation of the IGIMF theory must be revised.