The galaxy cluster Y-SZ-L-X and Y-SZ-M relations from the WMAP 5-yr data

We use multifrequency matched filters to estimate, in the WMAP 5-year data, the Sunyaev-Zel'dovich (SZ) fluxes of 893 ROSAT NORAS/REFLEX clusters spanning the luminosity range L-X,L-[0.1-2.4] (keV) = 2x10(41)-3.5x10(45) erg s(-1). The filters are spatially optimised by using the universal pressure profile recently obtained from combining XMM-Newton observations of the REXCESSsample and numerical simulations. Although the clusters are individually only marginally detected, we are able to firmly measure the SZ signal (>10 sigma) when averaging the data in luminosity/mass bins. The comparison between the bin-averaged SZ signal versus luminosity and X-ray model predictions shows excellent agreement, implying that there is no deficit in SZ signal strength relative to expectations from the X-ray properties of clusters. Using the individual cluster SZ flux measurements, we directly constrain the Y-500-L-X and Y-500-M-500 relations, where Y-500 is the Compton y-parameter integrated over a sphere of radius r(500). The Y-500-M-500 relation, derived for the first time in such a wide mass range, has a normalisation Y*(500) = [1.60 +/- 0.19] x 10(-3) arcmin(2) at M-500 = 3 x 1014 h(-1) M-circle dot, in excellent agreement with the X-ray prediction of 1.54 x 10(-3) arcmin(2), and a mass exponent of alpha = 1.79 +/- 0.17, consistent with the self-similar expectation of 5/3. Constraints on the redshift exponent are weak due to the limited redshift range of the sample, although they are compatible with self-similar evolution.