Red-sequence cluster finding in the Millennium Simulation

We investigate halo mass selection properties of red-sequence cluster finders using galaxy populations of the Millennium Simulation (MS). A clear red sequence exists for MS galaxies in massive haloes at redshifts z < 1, and we use this knowledge to inform a cluster-finding algorithm applied to 500 h -1 Mpc projections of the simulated volume. At low redshift (z = 0.4), we find that 90 per cent of the clusters found have galaxy membership dominated by a single, real-space halo, and that 10 per cent are blended systems for which no single halo contributes a majority of a cluster's membership. At z = 1, the fraction of blends increases to 22 per cent, as weaker redshift evolution in observed colour extends the comoving length probed by a fixed range of colour. Other factors contributing to the increased blending at high z include broadening of the red sequence and confusion from a larger number of intermediatemass haloes hosting bright red galaxies of magnitude similar to those in higher mass haloes. Our method produces catalogues of cluster candidates whose halo mass selection function, p(M|N gal , z), is characterized by a bimodal lognormal model with a dominant component that reproduces well the real-space distribution, and a redshift-dependent tail that is broader and displaced by a factor of ∼2 lower in mass. We discuss implications for X-ray properties of optically selected clusters and offer ideas for improving both mock catalogues and cluster finding in future surveys.