X-raying CAMELS: Constraining Baryonic Feedback in the Circum-Galactic Medium with the CAMELS simulations and eRASS X-ray Observations

The circumgalactic medium (CGM) around massive galaxies plays a crucial role in regulating star formation and feedback. Using the CAMELS simulation suite, we develop emulators for the X-ray surface brightness profile and the X-ray luminosity--stellar mass scaling relation to investigate how stellar and AGN feedback shape the X-ray properties of the hot CGM. Our analysis shows that at CGM scales ($10^{12} \lesssim M_{\rm halo}/M_\odot \lesssim 10^{13}$, $10\lesssim r/{\rm kpc} \lesssim 400$), stellar feedback more significantly impacts the X-ray properties than AGN feedback within the parameters studied. Comparing the emulators to recent eROSITA All-Sky Survey observations, it was found that stronger feedback than currently implemented in the IllustrisTNG, SIMBA, and Astrid simulations is required to match observed CGM properties. However, adopting these enhanced feedback parameters causes deviations in the stellar-mass-halo-mass relations from observational constraints below the group mass scale. This tension suggests possible unaccounted systematics in X-ray CGM observations or inadequacies in the feedback models of cosmological simulations.