New evidence for a linear colour-magnitude relation and a single Schechter function for red galaxies in a nearby cluster of galaxies down to M*+8

The colour and luminosity distributions of red galaxies in the cluster Abell 1185 (z=0.0325) were studied down to M*+8 in the B, V and R bands. The colour-magnitude (hereafter CM) relation is linear without evidence for a significant bending down to absolute magnitudes which are seldom probed in literature (M_R=-12.5 mag). The CM relation is thin (+/-0.04 mag) and its thickness is quite independent from the magnitude. The luminosity function of red galaxies in Abell 1185 is adequately described by a Schechter function, with a characteristic magnitude and a faint end slope that also well describe the LF of red galaxies in other clusters. There is no passband dependency of the LF shape other than an obvious M* shift due to the colour of the considered population. Finally, we conclude that, based on colours and luminosity, red galaxies form an homogeneous population over four decades in stellar mass, providing a second evidence against faint red galaxies being a recent cluster population.