Mass segregation in young star clusters - can it be detected from the integrated photometric properties?

We consider the effect of mass segregation on the observable integrated properties of star clusters. The measurable properties depend on a combination of the dynamical age of the cluster and the physical age of the stars in the cluster. To investigate all possible combinations of these two quantities, we propose an analytical model for the mass function of segregated star clusters that agree with the results of N-body simulations, in which any combination can be specified. For a realistic degree of mass segregation and a fixed density profile, we find with increasing age an increase in the measured core radii and a central surface brightness which decreases in all filters more rapidly than what is expected from stellar evolution alone. Within a gigayear, the measured core radius increases by a factor of 2 and the central surface density in all filters of a segregated cluster will be overestimated by a similar factor if mass segregation is not taken into account during the conversion from light to mass. We find that the V - I colour of mass-segregated clusters decreases with radius by about 0.1-0.2 mag, which could be observable. From recent observations of partially resolved extragalactic clusters, a decreasing half-light radius with increasing wavelength was observed, which was attributed to mass segregation. These observations cannot be reproduced by our models. In addition, we provide physical arguments based on the evolution of individual stars that one should not expect strong dependence of core radius as a function of the wavelength. We find that the differences between measured radii in different filters are always smaller than 5 per cent.