# Modeling the cross power spectrum of Sunyaev-Zel'dovich and X-ray surveys

## TL;DR

This paper models the cross power spectrum of Sunyaev-Zel'dovich and X-ray surveys, showing its potential to improve constraints on cosmological parameters and cluster scaling laws with upcoming data.

## Contribution

It provides a comprehensive model of the tSZ-X cross correlation, analyzing its dependence on cosmology and cluster physics, and evaluates its observational prospects.

## Key findings

- Uncertainty of 47% in the cross spectrum normalization due to current knowledge.
- Signal-to-noise ratio of 31.5 achievable with realistic surveys.
- Potential to constrain the cross correlation amplitude to 3.2%, improving current limits.

## Abstract

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.