The Colour-Magnitude Relation as a Constraint on the Formation of Rich Cluster Galaxies

In this paper, we examine the role that the colour-magnitude relation (CMR) can play in constraining the formation history of rich cluster galaxies. Firstly, we consider the colour evolution of galaxies after star formation ceases. We show that the scatter of the CMR places a strong constraint on the spread in age of the bulk of the stellar population. However, although the bulk of stars must be formed in a short period, continuing formation of stars in a fraction of the galaxies is not so strongly constrained. We examine a model in which star formation occurs over an extended period of time in most galaxies. An extension of this type of star formation history allows us to reconcile the small present-day scatter of the CMR with the observed blue galaxy fractions of intermediate redshift galaxy clusters. Secondly, the CMR can also be used to constrain the degree of merging between pre-existing stellar systems. This test relies on the slope of the CMR. We show that random mergers between galaxies very rapidly remove any well-defined CMR. However, we prefer to examine the merger process using a self-consistent merger tree. In such a model there are two effects: massive galaxies preferentially merge with systems of similar mass; and the rate of mass growth is considerably smaller than for the random merger case. As a result of both of these effects, the CMR persists through a larger number of merger steps. The passive evolution of galaxy colours and their averaging in dissipationless mergers provide opposing constraints on the formation of cluster galaxies in a hierarchical model; but at the level of current constraints, a compromise solution appears possible.