On the efficiency of field star capture by star clusters

Abstract

An exciting recent finding regarding scaling relations among globular clusters is the so-called 'blue tilt': clusters of the blue sub-population follow a trend of redder colour with increasing luminosity. In this paper we evaluate to which extent field star capture over a Hubble time may explain the 'blue tilt'. We perform collisional N-body simulations to quantify the amount of field star capture occuring over a Hubble time to star clusters with 10^3 to 10^6 stars. In the simulations we follow the orbits of field stars passing through a star cluster and calculate the energy change that the field stars experience due to gravitational interaction with cluster stars during one passage through the cluster. The capture condition is that their total energy after the passage is smaller than the gravitational potential at the cluster's tidal radius. By folding this with the fly-by rates of field stars with an assumed space density as in the solar neighbourhood and a range of velocity dispersions, we derive estimates on the mass fraction of captured field stars as a function of environment. We find that integrated over a Hubble time, the ratio between captured field stars and total number of clusters stars is very low (<~ 10^(-4)), even for the smallest considered field star velocity dispersion sigma=15 km/s. This holds for star clusters in the mass range of both open clusters and globular clusters. We furthermore show that tidal friction has a negligible effect on the energy distribution of field stars after interaction with the cluster. We conclude that field star capture is not a probable mechanism for creating the colour-magnitude trend of metal-poor globular clusters.