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, $\beta_{\rm sz} + \beta_{\rm x} = 0.4^{+0.4}_{-0.5}$.