  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.
