The build-up of the red sequence in the galaxy cluster MS1054−0321 at z= 0.831

Using one of the deepest data sets available, we determine that the red sequence of the massive cluster MS1054−0321 at z= 0.831 is well populated at all studied magnitudes, showing no deficit of faint (down to M*+ 3.5) red galaxies: the faint end of the colour-magnitude relation is neither empty nor underpopulated. The effect is quantified by the computation of the luminosity function (LF) of red galaxies. We found a flat slope, showing that the abundance of red galaxies is similar at faint and at intermediate magnitudes. Comparison with present-day and z∼ 0.4 LFs suggests that the slope of the LF is not changed, within the errors, between z= 0.831 and 0. Therefore, the analysis of the LF shows no evidence for a decreasing (with magnitude or redshift) number of faint red galaxies. The presence of faint red galaxies in high-redshift clusters disfavours scenarios where the evolution of red galaxies is mass-dependent, because the mass dependency should differentially depopulate the red sequence, while the MS1054−0321 colour-magnitude relation is populated as in nearby clusters and as in z∼ 0.4 clusters. The presence of abundant faint red galaxies in the high-redshift cluster MS1054−0321 restricts the room for allocating descendants of Butcher-Oemler galaxies, because they should change the faint end slope of the LF of red galaxies, while instead the same faint end slopes are observed in MS1054−0321, at z∼ 0 and at z∼ 0.4. In the rich MS1054−0321 cluster, the colour-magnitude relation seems to be fully in place at z= 0.831 and therefore red galaxies of all magnitudes were wholly assembled at higher redshift.