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>6-9e13 M_o/h, quite independent of redshift, reach 50% completeness at ~1e14 M_o/h and 100% completeness at ~2e14 M_o/h. Samples are contaminated by only a few per cent spurious 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.
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