Based on recent results on the frequency of Mg ii  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 Mg ii  halo sizes of field and cluster galaxies using observational results on the observed Mg ii  statistics .
Our results for the field are in good agreement with previous works , indicating a typical Mg ii  halo size of r _ { Mg { \sc II } } \simeq 50 h _ { 71 } ^ { -1 } kpc 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 Mg ii  halo size of r _ { Mg { \sc II } } < 10 h _ { 71 } ^ { -1 } kpc 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 Mg ii  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 1 h _ { 71 } ^ { -1 } Mpc 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 .
These results reinforce our conclusions from Paper I and provide additional independent support for the stripping scenario of the cold gas of galaxies in massive clusters by the hot intracluster gas , e.g. , as seen from X-ray data .