The evolution of luminosity, colour and the mass-to-luminosity ratio of Galactic open clusters: comparison of discrete vs. continuous IMF models

(abridged) 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 NIR spectral range. (...) We construct a numerical SSP-model, with an underlying Salpeter IMF, valid within an upper $m_u$ and lower $m_l$ stellar mass range, and with total masses $M_c=10^2...10^4\,m_\odot$ 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 due to 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 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 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.
Comment: 15 pages, 13 figures, accepted for publication in Astronomy and Astrophysics