Why Simple Stellar Population models do not reproduce the colours of Galactic open clusters

(...) 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. We check the hypothesis that the systematic offsets between observed and theoretical colours, which are $(B$$-$$V)\approx 0.3$ and $(J$$-$$K_s)\approx 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. 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 \textit{systematic} offset between the continuous- and discrete-IMF colours reaches its maximum of about 0.5 in $(B$$-$$V)$ for a cluster mass $M_c=10^2 m_\odot$ at ages $\log t\approx 7$, and diminishes substantially but not completely to about one hundredth of a magnitude at $\log t >7.9$ at cluster masses $M_c> 10^5 m_\odot$. At younger ages, it is still present even in massive clusters, and for $M_c \leqslant 10^4 m_\odot$ it is larger than 0.1 mag in $(B$$-$$V)$. Only for very massive clusters ($M_c>10^6 m_\odot$) 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.