Biases in the inferred mass-to-light ratio of globular clusters: no need for variations in the stellar mass function

From a study of the integrated light properties of 200 globular clusters (GCs) in M31, Strader et al. found that the mass-to-light ratios are lower than what is expected from simple stellar population models with a 'canonical' stellar initial mass function (IMF), with the discrepancy being larger at high metallicities. We use dynamical multimass models, that include a prescription for equipartition, to quantify the bias in the inferred dynamical mass as the result of the assumption that light follows mass. For a universal IMF and a metallicity-dependent present-day mass function, we find that the inferred mass from integrated light properties systematically underestimates the true mass, and that the bias is more important at high metallicities, as was found for the M31 GCs. We show that mass segregation and a flattening of the mass function have opposing effects of similar magnitude on the mass inferred from integrated properties. This makes the mass-to-light ratio as derived from integrated properties an inadequate probe of the low-mass end of the stellar mass function. There is, therefore, no need for variations in the IMF, nor the need to invoke depletion of low-mass stars, to explain the observations. Finally, we find that the retention fraction of stellar-mass black holes (BHs) is an equally important parameter in understanding the mass segregation bias. We speculatively put forward to idea that kinematical data of GCs can in fact be used to constrain the total mass in stellar-mass BHs in GCs.