Modeling the cross power spectrum of Sunyaev-Zel'dovich and X-ray
  surveys
  Thermal Sunyaev-Zel'dovich (tSZ) effect and X-ray emission from galaxy
clusters have been extensively used to constrain cosmological parameters. These
constraints are highly sensitive to the relations between cluster masses and
observables (tSZ and X-ray fluxes). The cross-correlation of tSZ and X-ray data
is thus a powerful tool, in addition of tSZ and X-ray based analysis, to test
our modeling of both tSZ and X-ray emission from galaxy clusters. We chose to
explore this cross correlation as both emissions trace the hot gas in galaxy
clusters and thus constitute one the easiest correlation that can be studied.
We present a complete modeling of the cross correlation between tSZ effect and
X-ray emission from galaxy clusters, and focuses on the dependencies with
clusters scaling laws and cosmological parameters. We show that the present
knowledge of cosmological parameters and scaling laws parameters leads to an
uncertainties of 47\% on the overall normalization of the tSZ-X cross
correlation power spectrum. We present the expected signal-to-noise ratio for
the tSZ-X cross-correlation angular power spectrum considering the sensitivity
of actual tSZ and X-ray surveys from {\it Planck}-like data and ROSAT. We
demonstrate that this signal-to-noise can reach 31.5 in realistic situation,
leading to a constraint on the amplitude of tSZ-X cross correlation up to
3.2\%, fifteen times better than actual modeling limitations. Consequently,
used in addition to other probes of cosmological parameters and scaling
relations, we show that the tSZ-X is a powerful probe to constrain scaling
relations and cosmological parameters.
