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.
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