The Luminosity Distribution in Galaxy Clusters: A Dwarf Population -   Density Relation?
  Recent work suggests that rich clusters of galaxies commonly have large populations of dwarf (i.e. low luminosity) members, that is their luminosity function (LF) turns up to a steep slope at the faint end. This population, or more particularly the relative numbers of dwarfs to giants, appears to be very similar for clusters of similar morphology, but may vary between cluster types. We have previously suggested that dwarfs may be more common in less compact, spiral rich clusters. Similarly we have found evidence for population gradients across clusters, in that the dwarf population appears more spatially extended. In the present paper we summarise the current evidence and propose, in analogy to the well-known morphology - density relation, that what we are seeing is a dwarf population - density relation; dwarfs are more common in lower density environments. Finally we discuss recent semi-analytic models of galaxy formation in the hierarchical clustering picture, which may give clues as to the origin of our proposed relation. 
S. Phillipps (Univ. Bristol), S.P. Driver (U.N.S.W., Sydney) W.J.   Couch (U.N.S.W., Sydney), R.M. Smith (Univ. Wales, Cardiff)