2009MNRAS.394.1529D

It has been recently shown that the dynamical V-band mass-to-light ratios of compact stellar systems with masses from 10⁶ to 10⁸M_☉ are not consistent with the predictions from simple stellar population models. Top-heavy stellar initial mass functions (IMFs) in these so-called ultra-compact dwarf galaxies (UCDs) offer an attractive explanation for this finding, the stellar remnants and retained stellar envelopes providing the unseen mass. We therefore construct a model which quantifies by how much the IMFs of UCDs would have to deviate in the intermediate- and high-mass range from the canonical IMF in order to account for the enhanced M/L_V ratio of the UCDs. The deduced high-mass IMF in the UCDs depends on the age of the UCDs and the number of faint products of stellar evolution retained by them. Assuming that the IMF in the UCDs is a three-part power law equal to the canonical IMF in the low-mass range and taking 20 per cent as a plausible choice for the fraction of the remnants of high-mass stars retained by UCDs, the model suggests the exponent of the high-mass IMF to be ~1.6 if the UCDs are 13Gyr old (i.e. almost as old as the Universe) or ~1.0 if the UCDs are 7Gyr old, in contrast to 2.3 for the Salpeter-Massey IMF. If the IMF was as top heavy as suggested here, the stability of the UCDs might have been threatened by heavy mass loss induced by the radiation and evolution of massive stars. The central densities of UCDs must have been in the range 10⁶ to 10⁷M_☉/pc3 when they formed with star formation rates of 10 to 100M_☉/yr.