Closing the loop: a self-consistent model of optical, X-ray and Sunyaev–Zel'dovich scaling relations for clusters of Galaxies

We demonstrate that optical data from Sloan Digital Sky Survey, X-ray data from ROSAT and Chandra, and Sunyaev–Zel'dovich (SZ) data from Planck can be modelled in a fully self-consistent manner. After accounting for systematic errors and allowing for property covariance, we find that scaling relations derived from optical and X-ray selected cluster samples are consistent with one another. Moreover, these cluster scaling relations satisfy several non-trivial spatial abundance constraints and closure relations. Given the good agreement between optical and X-ray samples, we combine the two and derive a joint set of LX-M and YSZ-M relations. Our best-fitting YSZ-M relation is in good agreement with the observed amplitude of the thermal SZ power spectrum for a Wilkinson Microwave Anisotropy Probe 7 cosmology, and is consistent with the masses for the two CLASH galaxy clusters published thus far. We predict the halo masses of the remaining z ≤ 0.4 CLASH clusters, and use our scaling relations to compare our results with a variety of X-ray and weak lensing cluster masses from the literature.