Measuring the Thermal Sunyaev-Zel'dovich Effect Through the Cross Correlation of Planck and WMAP Maps with ROSAT Galaxy Cluster Catalogs

Abstract: 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_M) and scales as \sigma_8^7.4 and \Omega_M^1.9 around the multipole (ell) ~ 1000. We constrain \sigma_8 and \Omega_M from the cross-power spectrum to be \sigma_8 (\Omega_M/0.30)^0.26 = 0.8 +/- 0.02. Since this cross spectrum produces a tight constraint in the \sigma_8 and \Omega_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_M to constrain dark energy or the sum of the neutrino masses.