On the mass of dense star clusters in starburst galaxies from spectrophotometry

The mass of unresolved young star clusters derived from spectrophotometric data may well be off by a factor of 2 or more once the migration of massive stars driven by mass segregation is accounted for. We quantify this effect for a large set of cluster parameters, including variations in the stellar initial mass function (IMF), the intrinsic cluster mass, and mean mass density. Gas-dynamical models coupled with the Cambridge stellar evolution tracks allow us to derive a scheme to recover the real cluster mass given measured half-light radius, one-dimensional velocity dispersion and age. We monitor the evolution with time of the ratio of real to apparent mass through the parameter η. When we compute η for rich star clusters, we find non-monotonic evolution in time when the IMF stretches beyond a critical cut-off mass of 25.5-M⊙. We also monitor the rise of colour gradients between the inner and outer volume of clusters: we find trends in time of the stellar IMF power indices overlapping well with those derived for the Large Magellanic Cloud cluster NGC 1818 at an age of 30-Myr. We argue that the core region of massive Antennae clusters should have suffered from much segregation despite their low ages. We apply these results to a cluster mass function, and find that the peak of the mass distribution would appear to observers shifted to lower masses by as much as 0.2-dex. The star formation rate derived for the cluster population is then underestimated by from 20 to 50 per cent.