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 intermediate-mass 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|Ngal, 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.