Probing Cosmology and Cluster Astrophysics with Multi-Wavelength Surveys I. Correlation Statistics

Upcoming multi-wavelength astronomical surveys will soon discover all massive galaxy clusters and provide unprecedented constraints on cosmology and cluster astrophysics. In this paper, we investigate the constraining power of the multi-band cluster surveys, through a joint analysis of three observables associated with clusters of galaxies, including thermal Sunyaev-Zel'dovich (tSZ) effect in cosmic microwave background (CMB), X-ray emission of ionized gas, and gravitational weak lensing effect of background galaxies by the cluster's gravitational potential. We develop a theoretical framework to predict and interpret two-point correlation statistics among the three observables using a semi-analytic model of intracluster medium (ICM) and halo-based approach. In this work, we show that the auto- and cross-angular power spectra in tSZ, X-ray and lensing statistics from upcoming missions (eROSITA, CMB-S4, and LSST) can help break the degeneracy between cosmology and ICM physics. These correlation statistics are less sensitive to selection biases, and are able to probe ICM physics in distant, faint and small clusters that are otherwise difficult to be detected individually. We show that the correlation statistics are able to provide cosmological constraints comparable to the conventional cluster abundance measurements, while constraining cluster astrophysics at the same time. Our results indicate that the correlation statistics can significantly enhance the scientific returns of upcoming multi-wavelength cluster surveys.