On the efficiency of field star capture by star clusters

Context. 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 to become redder with increasing luminosity. Aims. In this paper, we evaluate to what extent field star capture over a Hubble time changes the photometric properties of star clusters. Given that field stars in early type giant galaxies are very metal-rich, their capture will make blue globular clusters redder and may in principle explain the blue tilt. Methods. We perform collisional N-body simulations to quantify the amount of field star capture occuring over a Hubble time to star clusters with 103 to 106 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 sigma ( 15 to 485 km s(-1)), we derive estimates on the mass fraction of captured field stars as a function of environment. Results. We find that integrated over a Hubble time, the ratio between captured field stars and total number of clusters stars is very low (less than or similar to 10(-4)), even for the smallest field star velocity dispersion sigma = 15 km s(-1). This holds for star clusters in the mass range of both open clusters and globular clusters. Furthermore we show that tidal friction has a negligible effect on the energy distribution of field stars after interaction with the cluster. We note that field star capture at the time of cluster formation, when the cluster potential increases with time, is more efficient. However, it cannot explain the trend that more massive star clusters are redder. Conclusions. Field star capture is not a probable mechanism for creating the colour-magnitude trend of metal-poor globular clusters.