The photometric evolution of dissolving star clusters I. First predictions

The broad-band photometric evolution of unresolved star clusters is calculated in a simplified way, including the preferential loss of low-mass stars due to mass segregation. The stellar mass function of a cluster evolves due to three effects: ( a) the evolution of the massive stars reduces their number; (b) tidal effects before cluster-wide mass segregation reduce the mass function homogeneously, i.e. independently of the stellar mass; (c) after mass segregation has finished, tidal effects preferentially remove the lowest-mass stars from the cluster. These effects result in a narrowing of the stellar mass range. These effects are described quantitatively, following the results of N-body simulations, and are taken into account in the calculation of the photometric history, based on the (GALEV) cluster evolution models for solar metallicity and a Salpeter mass function. We find the following results: (1) During the first similar to 40% of the lifetime of a cluster its colour evolution is adequately described by the standard (GALEV) models (without mass segregation) but the cluster becomes fainter due to the loss of stars by tidal effects. (2) Between similar to 40 and similar to 80% of its lifetime (independent of the total lifetime), the cluster becomes bluer due to the loss of low-mass stars. This will result in an underestimate of the age of clusters if standard cluster evolution models are used. (3) After similar to 80% of the total lifetime of a cluster it will rapidly become redder. This will result in an overestimate of the age of clusters if standard cluster evolution models are used. (4) Clusters with mass segregation and the preferential loss of low-mass stars evolve along almost the same tracks in colour-colour diagrams as clusters without mass segregation. Only if the total lifetime of clusters can be estimated can the colours be used to give reliable age estimates. (5) The changes in the colour evolution of unresolved clusters due to the preferential loss of low-mass stars will affect the determination of the star formation histories of galaxies if they are derived from clusters that have a total lifetime of less than about 30 Gyr. (6) The preferential loss of low-mass stars might explain the presence of old (similar to 13 Gyr) clusters in NGC 4365 which are photometrically disguised as intermediate-age clusters (2-5 Gyr), if the expected total lifetime of these clusters is between 16 and 32 Gyr.