Mass Segregation in Globular Clusters

We present the results of a new study of mass segregation in two-component star clusters, based on a large number of numerical N-body simulations using our recently developed dynamical Monte Carlo code. Specifically, we follow the dynamical evolution of clusters containing stars with individual masses m₁ as well as a tracer population of objects with individual masses m₂. We consider both light tracers (μ ≡ m₂/m₁ < 1) and heavy tracers (μ > 1) and a variety of King model initial conditions. In all of our simulations we use a realistically large number of stars for globular clusters, N = 10⁵, but we ignore the effects of binaries and stellar evolution. For heavy tracers, which could represent stellar remnants such as neutron stars or black holes in a globular cluster, we characterize in a variety of ways the tendency for these objects to concentrate in or near the cluster core. In agreement with simple theoretical arguments, we find that the characteristic time for this mass segregation process varies as 1/μ. For models with very light tracers (μ ≲ 10^-2), which could represent free-floating planets or brown dwarfs, we find the expected depletion of light objects in the cluster core but also sometimes a significant enhancement in the halo. That is, for some initial conditions, the number density of light objects in the cluster halo increases over time, in spite of the higher overall evaporation rate of lighter objects through the tidal boundary. Using these results along with a simplified initial mass function, we estimate the optical depth to gravitational microlensing by planetary mass objects or brown dwarfs in typical globular clusters. For some initial conditions, the optical depth in the halo owing to very low mass objects could be much greater than that of luminous stars. If we apply our results to M22, using the recent null detection of Sahu, Anderson, & King, we find an upper limit of ~25% at the 63% confidence level for the current mass fraction of M22 in the form of very low mass objects.