Cosmological constraints from the observed angular cross-power spectrum
  between Sunyaev-Zel'dovich and X-ray surveys
  We present the first detection of the cross-correlation angular power
spectrum between the thermal Sunyaev-Zel'dovich (tSZ) effect and the X-ray
emission over the full sky. The tSZ effect and X-rays are produced by the same
hot gas within groups and clusters of galaxies, which creates a naturally
strong correlation between them that can be used to boost the joint signal and
derive cosmological parameters. We computed the correlation between the ROSAT
All Sky Survey in the 0.5-2 keV energy band and the tSZ effect reconstructed
from six Planck all-sky frequency maps between 70 and 545 GHz. We detect a
significant correlation over a wide range of angular scales. In the range
$50<\ell < 2000$, the cross-correlation of X-rays to tSZ is detected at an
overall significance of 28 $\sigma$. As part of our systematic study, we
performed a multi-frequency modelling of the AGN contamination and the
correlation between cosmic infra-red background and X-rays. Taking advantage of
the strong dependence of the cross-correlation signal on the amplitude of the
power spectrum, we constrained $\sigma_8 = 0.804 \pm 0.037$, where modelling
uncertainties dominate statistical and systematic uncertainties. We also
derived constraints on the mass indices of scaling relations between the halo
mass and X-ray luminosity, L$_{500}$-M$_{500}$, and SZ signal,
Y$_{500}$-M$_{500}$, $a_{\rm sz} + a_{\rm x} = 3.37 \pm 0.09$, and on the
indices of the extra-redshift evolution, $\beta_{\rm sz} + \beta_{\rm x} =
0.4^{+0.4}_{-0.5}$.
