The observable properties of galaxies depend on both internal processes and the external environment. In terms of the environmental role, we still do not have a clear picture of the processes driving the transformation of galaxies. The use of proxies for environment (e.g., host halo mass, distance to the N^th nearest neighbour, etc.), as opposed to the real physical conditions (e.g., hot gas density) may bear some responsibility for this. Here we propose a new method that directly links galaxies to their local environments, by using spatial cross-correlations of galaxy catalogues with maps from large-scale structure surveys (e.g., thermal Sunyaev-Zeldovich [tSZ] effect, diffuse X-ray emission, weak lensing of galaxies or the CMB). We focus here on the quenching of galaxies and its link to local hot gas properties. Maps of galaxy overdensity and quenched fraction excess are constructed from volume-limited SDSS catalogs, which are cross-correlated with tSZ effect and X-ray maps from Planck and ROSAT, respectively. Strong signals out to Mpc scales are detected for most cross-correlations and are compared to predictions from the EAGLE and BAHAMAS cosmological hydrodynamical simulations. The simulations successfully reproduce many, but not all, of the observed power spectra, with an indication that environmental quenching may be too efficient in the simulations. We demonstrate that the cross-correlations are sensitive to both the internal (e.g., AGN and stellar feedback) and external processes (e.g., ram pressure stripping, harassment, strangulation, etc.) responsible for quenching. The methods outlined in this paper can be adapted to other observables and, with upcoming surveys, will provide a stringent test of physical models for environmental transformation.
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