Closing the Loop: A Self-Consistent Model of Optical, X-ray, and SZ Scaling Relations for Clusters of Galaxies

We demonstrate that optical data from SDSS, X-ray data from ROSAT and Chandra, and SZ data from Planck, can be modeled 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 clusters 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 fit YSZ-M relation is in good agreement with the observed amplitude of the thermal SZ power spectrum for a WMAP7 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 \leq 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.

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