Statistical properties of SZ and X-ray cluster detections

Aims. We calibrate the number density, completeness, reliability, and the lower mass limit of galaxy-cluster detections through their thermal SZ signal and compare them to X-ray cluster detections. Methods. We simulate maps of the thermal SZ effect and the X-ray emission from light cones constructed in a large, hydrodynamical, cosmological simulation volume, including realistic noise contributions. The maps are convolved with linear, optimised, single- and multi-band filters to identify local peaks and their signal-to-noise ratios. The resulting peak catalogues are then compared to the halo population in the simulation volume to identify true and spurious detections. Results. Multi-band filtering improves the statistics of SZ cluster detections considerably compared to single- band filtering. Observations with the characteristics of ACT detect clusters with masses M >= 6-9 x 10(13) M circle dot/h, quite independent of redshift, reach 50% completeness at similar to 10(14) M circle dot/h and 100% completeness at similar to 2 x 10(14) M circle dot/h. Samples are contaminated by a few spurious detections, but they are only a small percentage of all detections. This is broadly comparable to X-ray cluster detections with XMM-Newton with 100 ks exposure time in the soft band, except that the mass limit for X-ray detections increases much more steeply with redshift than for SZ detections. A comparison of true and filtered signals in the SZ and X-ray maps confirms that the filters introduce at most a negligible bias.