  The thermal Sunyaev-Zel'dovich (SZ) effect and soft X-ray emission are
routinely observed around massive galaxies and in galaxy groups and clusters.
We study these observational diagnostics of galaxy haloes for a suite of
cosmological `zoom-in' simulations from the `Feedback In Realistic
Environments' project, which spans a large range in halo mass 10^10-10^13
Msun). We explore the effect of stellar feedback on the hot gas observables.
The properties of our simulated groups, such as baryon fractions, SZ flux, and
X-ray luminosities (L_X), are broadly consistent with existing observations,
even though feedback from active galactic nuclei is not included. We make
predictions for future observations of lower-mass objects for both SZ and
diffuse X-ray measurements, finding that they are not just scaled-down versions
of massive galaxies, but more strongly affected by galactic winds driven by
star formation. Low-mass haloes (<~10^11 Msun) retain a low fraction of their
baryons, which results in a strong suppression of the SZ signal. Our
simulations therefore predict a scaling with halo mass that is steeper than
self-similar for haloes less massive than 10^13 Msun. For halo masses <~10^12
Msun, L_X is time-variable and correlated primarily with the star formation
rate (SFR). For these objects, the diffuse X-ray emission is powered mostly by
galactic winds and the gas dominating the X-ray emission is flowing out with
radial velocities close to the halo's circular velocity. For halo masses
>~10^13 Msun, on the other hand, L_X is much less variable and not correlated
with the SFR, because the emission originates from the quasi-hydrostatic,
virialized halo gas.
