We present results from a deep photometric study of the rich galaxy cluster Abell 2218 ( z = 0.18 ) based on archival HST WFPC2 F606W images .
These have been used to derive the luminosity function to extremely faint limits ( M _ { F 606 W } \approx - 13.2 mag , \mu _ { 0 } \approx 24.7 mag arcsec ^ { -2 } ) over a wide field of view ( 1.3 h ^ { -2 } Mpc ^ { 2 } ) .
We find the faint-end slope of the luminosity function to vary with environment within the cluster , going from \alpha = -1.23 \pm 0.13 within the projected central core of the cluster ( 100 < r < 300 h ^ { -1 } kpc ) to \alpha = -1.49 \pm 0.06 outside this radius ( 300 < r < 750 h ^ { -1 } kpc ) .
We infer that the core is ’ dwarf depleted ’ , and further quantify this by studying the ratio of ‘ dwarf ’ to ‘ giant ’ galaxies and its dependency as a function of cluster-centric radius and local galaxy density .
We find that this ratio varies strongly with both quantities , and that the dwarf galaxy population in A2218 has a more extended distribution than the giant galaxy population .