The evolution of K* and the halo occupation distribution since z=1.5: observations versus simulations

We study the evolution of the K-band luminosity function (LF) and the halo occupation distribution (HOD) using Subaru observations of 15 X-ray clusters at z= 0.81.5 and compare the results with mock clusters (0 < z < 1.3) extracted from the Millennium Simulation and populated with galaxies by means of the semi-analytic model (SAM) of Bower et al., matched in mass to our observed sample. By fixing the faint-end slope (a=-0.9), we find that the characteristic luminosity K* defined by a Shechter LF is consistent with the predictions of the SAM, which are found, for the first time, to mimic well the evolution of K* in rich clusters at z= 1. However, we cannot distinguish between this model and a simple stellar population synthesis model invoking passive evolution with a formation redshift (zf? 5) consistent with the presence of an old red galaxy population ubiquitous in rich clusters at z= 1.5. We also see a small difference (?K*? 0.5) between our clusters and studies of the field population at similar redshifts, which suggests only a weak dependence of the luminous (L=L*) part of the LF on cluster environment. Turning to our study of the HOD, we find that within a radius corresponding to a density 500 times critical, high-z clusters tend to host smaller numbers of galaxies to a magnitude K*+ 2 compared to their low-z counterparts. This behaviour is also seen in the mock samples and is relatively insensitive to the average mass of the cluster haloes. In particular, we find significant correlations of the observed number of member cluster galaxies (N) with both z and cluster mass: . Finally, we examine the spatial distribution of galaxies and provide a new estimate of the concentration parameter for clusters at high redshift (). Our result is consistent with predictions from both our SAM mock clusters and predictions of dark matter haloes from the literature. The mock sample predictions rise slowly with decreasing redshift reaching at z= 0.