  We simulate stacked observations of nearby hot X-ray coronae associated with
galaxies in the EAGLE and Illustris-TNG hydrodynamic simulations. A forward
modeling pipeline is developed to predict 4-year eROSITA observations and
stacked image analysis, including the effects of instrumental and astrophysical
backgrounds. We propose an experiment to stack z~0.01 galaxies separated by
specific star-formation rate (sSFR) to examine how the hot (T>=10^6 K)
circumgalactic medium (CGM) differs for high- and low-sSFR galaxies. The
simulations indicate that the hot CGM of low-mass (M_*~10^{10.5} Msol),
high-sSFR (defined as the top one-third ranked by sSFR) central galaxies will
be detectable to a galactocentric radius r~30-50 kpc. Both simulations predict
lower luminosities at fixed stellar mass for the low-sSFR galaxies (the lower
third of sSFR) with Illustris-TNG predicting 3x brighter coronae around
high-sSFR galaxies than EAGLE. Both simulations predict detectable emission out
to r~150-200 kpc for stacks centered on high-mass (M_*~10^{11.0} Msol)
galaxies, with EAGLE predicting brighter X-ray halos. The extended soft X-ray
luminosity correlates strongly and positively with the mass of circumgalactic
gas within the virial radius (f_{CGM}). Prior analyses of both simulations have
established that f_{CGM} is reduced by expulsive feedback driven mainly by
black hole growth, which quenches galaxy growth by inhibiting replenishment of
the ISM. Both simulations predict that eROSITA stacks should not only
conclusively detect and resolve the hot CGM around L^* galaxies for the first
time, but provide a powerful probe of how the baryon cycle operates, for which
there remains an absence of consensus between state-of-the-art simulations.
