Galaxy Clusters in the Line of Sight to Background Quasars: II.
  Environmental effects on the sizes of baryonic halo sizes
  Based on recent results on the frequency of MgII absorption line systems in
the "QSO behind RCS clusters" survey (QbC), we analyse the effects of the
cluster environment on the sizes of baryonic haloes around galaxies. We use two
independent models, i) an empirical halo occupation model which fits current
measurements of the clustering and luminosity function of galaxies at low and
high redshifts, and ii) the GALFORM semi-analytic model of galaxy formation,
which follows the evolution of the galaxy population from first principles,
adjusted to match the statistics of low and high redshift galaxies. In both
models we constrain the MgII halo sizes of field and cluster galaxies using
observational results on the observed MgII statistics. Our results for the
field are in good agreement with previous works, indicating a typical \mgii\
halo size of $r_MgII ~ 50h_71^-1kpc in the semi-analytic model, and slightly
lower in the halo occupation number approach. For the cluster environment, we
find that both models require a median MgII halo size of r_MgII< 10h_71^-1kpc
in order to reproduce the observed statistics on absorption line systems in
clusters of galaxies. Based on the Chen & Tinker (2008) result that stronger
systems occur closer to the MgII halo centre, we find that strong absorption
systems in clusters of galaxies occur at roughly a fixed fraction of the
cold-warm halo size out to 1h_71^-1Mpc from the cluster centres. In contrast,
weaker absorption systems appear to occur at progressively shorter relative
fractions of this halo as the distance to the cluster centre decreases.
