Satellite Content and Halo Mass of Galaxy Clusters: Comparison between Red-Sequence and Halo-based Optical Cluster Finders

Cluster cosmology depends critically on how the optical clusters are selected from imaging surveys. We compare the conditional luminosity function (CLF) and weak lensing halo masses between two different cluster samples at fixed richness, detected within the same volume ($0.1{<}z{<}0.34$) using the red-sequence and halo-based methods. After calibrating our CLF deprojection method against mock galaxy samples, we measure the 3D CLFs by cross-correlating clusters with SDSS photometric galaxies. As expected, the CLFs of the red-sequence and halo-based finders exhibit redder and bluer populations, respectively. We also find significant shape discrepancies between the two CLFs at the faint end, where the red-sequence clusters show a strong deficit of faint galaxies but a bump at $M_r{\sim}-20.5$, while the halo-based clusters host an increasing number of blue satellites. By comparing the subsamples of clusters that have a match between the two catalogues to those without matches, we discover that the CLF shape depends sensitively on the cluster centroiding. However, the average weak lensing halo mass between the matched and non-matched clusters are roughly consistent with each other in either cluster sample. Since the colour preferences of the two cluster finders are almost orthogonal, such a consistency indicates that the scatter in the mass-richness relation of either cluster sample is close to random. Therefore, while the choice of how optical clusters are identified impacts the satellite content, our result suggests that it should not introduce strong systematics biases in cluster cosmology.