We measure a significant correlation between the thermal Sunyaev-Zel ’ dovich effect in the Planck and WMAP maps and an X-ray cluster map based on ROSAT .
We use the 100 , 143 and 343 GHz Planck maps and the WMAP 94 GHz map to obtain this cluster cross spectrum .
We check our measurements for contamination from dusty galaxies using the cross correlations with the 220 , 545 and 843 GHz maps from Planck .
Our measurement yields a direct characterization of the cluster power spectrum over a wide range of angular scales that is consistent with large cosmological simulations .
The amplitude of this signal depends on cosmological parameters that determine the growth of structure ( \sigma _ { 8 } and \Omega _ { \mathrm { M } } ) and scales as \sigma _ { 8 } ^ { 7.4 } and \Omega _ { \mathrm { M } } ^ { 1.9 } around the multipole ( \ell ) \sim 1000 .
We constrain \sigma _ { 8 } and \Omega _ { \mathrm { M } } from the cross-power spectrum to be \sigma _ { 8 } ( \Omega _ { \mathrm { M } } / 0.30 ) ^ { 0.26 } = 0.8 \pm 0.02 .
Since this cross spectrum produces a tight constraint in the \sigma _ { 8 } and \Omega _ { \mathrm { M } } plane the errors on a \sigma _ { 8 } constraint will be mostly limited by the uncertainties from external constraints .
Future cluster catalogs , like those from eRosita and LSST , and pointed multi-wavelength observations of clusters will improve the constraining power of this cross spectrum measurement .
In principle this analysis can be extended beyond \sigma _ { 8 } and \Omega _ { \mathrm { M } } to constrain dark energy or the sum of the neutrino masses .