2011A&A...525A.122P

We found in previous studies that standard simple stellar population (SSP) models are unable to describe or explain the colours of Galactic open clusters both in the visible and in the near-infrared (NIR) spectral range. The reason for this disagreement is the continuous nature of the stellar initial mass function (IMF) in clusters, which is the underlying assumption in the SSP models. In reality, the Galactic open clusters are sparsely populated with the brightest stars responsible for integrated fluxes. In this study, we aim at constructing discrete SSP-models that are able to adequately describe the observed magnitude-, colour-, and mass-to-luminosity-ratio-age relations of open clusters by including a number of seldom considered effects. We construct a numerical SSP-model with an underlying Salpeter IMF, which is valid within an upper m_u and lower m_l stellar mass range, and with the total masses M_c=10² ... 10⁴m_☉ typical of open clusters. We assume that the mass loss from a cluster is provided by mass loss from evolved stars and by the dynamical evaporation of low-mass members because of two-body relaxation. The data for the latter process were scaled to the models from high-resolution N-body calculations. We also investigate how a change of the m_l-limit influences the magnitudes and colours of clusters of a given mass and derive a necessary condition for a luminosity and colour flash. The discreteness of the IMF leads to bursts in the magnitude and colour of model clusters at moments when red supergiants or giants appear and then die. The amplitude of the burst depends on the cluster mass and on the spectral range; it is strongly increased in the NIR compared to optical passbands. In the discrete case variations of the parameter m_l are able to substantially change the magnitude-age and M/L-age relations. For the colours, the lowering of m_l considerably amplifies the discreteness effect. The influence of dynamical mass loss on colour and magnitude is weak, although it provides a change of the slopes of the considered relations, improving their agreement with observations. For the Galactic open clusters we determined luminosity and tidal mass independent of each other. The derived mass-to-luminosity ratio shows, on average, an increase with cluster age in the optical, but gradually declines with age in the NIR. The observed flash statistics can be used to constrain m_l in open clusters.