Why simple stellar population models do not reproduce the colours of Galactic open clusters

Context. For Galactic open clusters, fundamental parameters such as age or reddening are usually determined independently of their integrated colours. For extragalactic clusters, on the other hand, they are derived by comparing their integrated colours with predictions of simple stellar population (SSP) models. Aims. We search for an explanation of the disagreement between the observed integrated colours of 650 local Galactic clusters and the theoretical colours of present-day SSP models. Methods. We check the hypothesis that the systematic offsets between observed and theoretical colours, which are (B - V) approximate to 0.3 and (J - K(s)) approximate to 0.8, are caused by neglecting the discrete nature of the underlying mass function. Using Monte Carlo simulations, we construct artificial clusters of coeval stars taken from a mass distribution defined by an Salpeter initial mass function (IMF) and compare them with corresponding continuous-IMF SSP models. Results. If the discreteness of the IMF is taken into account, the model fits the observations perfectly and is able to explain naturally a number of red outliers observed in the empirical colour-age relation. We find that the systematic offset between the continuous- and discrete-IMF colours reaches its maximum of about 0.5 in (B - V) for a cluster mass M(c) = 10(2) M(circle dot) at ages log t approximate to 7, and diminishes substantially but not completely to about one hundredth of a magnitude at log t > 7.9 at cluster masses M(c) > 10(5) M(circle dot). At younger ages, it is still present even in massive clusters, and for M(c) <= 10(4) M(circle dot) it is larger than 0.1 mag in (B - V). Only for very massive clusters (M(c) > 10(6) M(circle dot)) with ages log t < 7.5 is the offset small (of the order of 0.04 mag) and smaller than the typical observational error of colours of extragalactic clusters.