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 (CM) relation is linear without evidence for significant bending down to absolute magnitudes that are seldom probed in the literature (M-R = -12.5 mag). The CM relation is thin (+/- 0.04 mag) and its thickness is quite independent of the magnitude. The luminosity function (LF) 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 dependence 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 a homogeneous population over four decades in stellar mass, providing a second piece of evidence against faint red galaxies being a recent cluster population.