N-body modelling of globular clusters: masses, mass-to-light ratios and intermediate-mass black holes

Abstract

We have determined the masses and mass-to-light ratios of 50 Galactic globular clusters by comparing their velocity dispersion and surface brightness profiles against a large grid of 900 N-body simulations of star clusters of varying initial concentration, size and central black hole mass fraction. Our models follow the evolution of the clusters under the combined effects of stellar evolution and two-body relaxation allowing us to take the effects of mass segregation and energy equipartition between stars self-consistently into account. For a subset of 16 well observed clusters we also derive their kinematic distances. We find an average mass-to-light ratio of Galactic globular clusters of $<M/L_V>=1.98 \pm 0.03$, which agrees very well with the expected M/L ratio if the initial mass function of the clusters was a standard Kroupa or Chabrier mass function. We do not find evidence for a decrease of the average mass-to-light ratio with metallicity. The surface brightness and velocity dispersion profiles of most globular clusters are incompatible with the presence of intermediate-mass black holes (IMBHs) with more than a few thousand $M_\odot$ in them. The only clear exception is $\omega$ Cen, where the velocity dispersion profile provides strong evidence for the presence of a $\sim$40,000 $M_\odot$ IMBH in the centre of the cluster.