Validation of selection function, sample contamination and mass calibration in galaxy cluster samples

We construct and validate the selection function of the MARD-Y3 galaxy cluster sample. This sample was selected through optical follow-up of the 2nd ROSAT faint source catalogue with Dark Energy Survey year 3 data. The selection function is modelled by combining an empirically constructed X-ray selection function with an incompleteness model for the optical follow-up. We validate the joint selection function by testing the consistency of the constraints on the X-ray flux-mass and richness-mass scaling relation parameters derived from different sources of mass information: (1) cross-calibration using South Pole Telescope Sunyaev-Zel'dovich (SPT-SZ) clusters, (2) calibration using number counts in X-ray, in optical and in both X-ray and optical while marginalizing over cosmological parameters, and (3) other published analyses. We find that the constraints on the scaling relation from the number counts and SPT-SZ cross-calibration agree, indicating that our modelling of the selection function is adequate. Furthermore, we apply a largely cosmology independent method to validate selection functions via the computation of the probability of finding each cluster in the SPT-SZ sample in the MARD-Y3 sample and vice versa. This test reveals no clear evidence for MARD-Y3 contamination, SPT-SZ incompleteness or outlier fraction. Finally, we discuss the prospects of the techniques presented here to limit systematic selection effects in future cluster cosmological studies.