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