  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-Zel'dovich [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.
