The photometric evolution of star clusters and the preferential loss of low-mass bodies - with an application to globular clusters

Context. To obtain an accurate description of broad-band photometric star cluster evolution, certain effects should be accounted for. Energy equipartition leads to mass segregation and the preferential loss of low-mass stars, while stellar remnants severely influence cluster mass-to-light ratios. Moreover, the stellar initial mass function and cluster metallicity affect photometry as well. Due to the continuous production of stellar remnants, their impact on cluster photometry is strongest for old systems like globular clusters. This, in combination with their low metallicities, evidence for mass segregation, and a possibly deviating stellar initial mass function, makes globular clusters interesting test cases for cluster models. Aims. In this paper we describe cluster models that include the effects of the preferential loss of low-mass stars, stellar remnants, choice of initial mass function and metallicity. The photometric evolution of clusters is predicted, and the results are applied to Galactic globular clusters. Methods. The cluster models presented in this paper represent an analytical description of the evolution of the underlying stellar mass function due to stellar evolution and dynamical cluster dissolution. Stellar remnants are included by using initial-remnant mass relations, while cluster photometry is computed from the Padova 1999 isochrones. Results. Our study shows that the preferential loss of low-mass stars strongly affects cluster magnitude, colour and mass-to-light ratio evolution, as it increases cluster magnitudes and strongly decreases mass-to-light ratios. The effects of stellar remnants are prominent in the evolution of cluster mass, magnitude and mass-to-light ratio, while variations of the initial mass function induce similar, but smaller changes. Metallicity plays an important role for cluster magnitude, colour and mass-to-light ratio evolution. The different effects can be clearly separated with our models. We apply the models to the Galactic globular cluster population. Its properties like the magnitude, colour and mass-to-light ratio ranges are well reproduced with our models, provided that the preferential loss of low-mass stars and stellar remnants are included. We also show that the mass-to-light ratios of clusters with similar ages and metallicities cannot be assumed to be constant for all cluster luminosities due to the mass-dependence of the half-mass relaxation time. Instead, mass-to-light ratio increases with cluster luminosity and mass. Conclusions. These models underline the importance of more detailed cluster models when considering cluster photometry. By including the preferential loss of low-mass stars and the presence of stellar remnants, the magnitude, colour and mass-to-light ratio ranges of modelled globular clusters are significantly altered. With the analytic framework provided in this paper, observed cluster properties can be interpreted in a more complete perspective.