The dwarf galaxy population in Abell 2218
  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_{F606W}=-13.2 mag, mu_{0}=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\pm0.13 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. 
Michael B. Pracy, Roberto De Propris, Simon P. Driver, Warrick J.   Couch and Paul E.J. Nulsen