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The circumgalactic medium (CGM) around massive galaxies plays a crucial role in regulating star formation and feedback. Using the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) 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 active galactic nucleus (AGN) feedback shape the X-ray properties of the hot CGM. Our analysis shows that at CGM scales (1012 Mhalo/Me  1013, 10 r kpc−1  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 (eRASS) observations, it is found that stronger feedback than is currently implemented in the IllustrisTNG, SIMBA, and Astrid simulations is required to match the 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 for systematics in X-ray CGM observations or inadequacies in the feedback models of cosmological simulations. 

Most diffuse baryons, including the circumgalactic medium (CGM) surrounding galaxies and the intergalactic medium (IGM) in the cosmic web, remain unmeasured and unconstrained. Fast radio bursts (FRBs) offer an unparalleled method to measure the electron dispersion measures (DMs) of ionized baryons. Their distribution can resolve the missing baryon problem and constrain the history of feedback theorized to impart significant energy to the CGM and IGM. We analyze the Cosmology and Astrophysics with Machine Learning Simulations using three suites, IllustrisTNG, SIMBA, and Astrid, each varying six parameters (two cosmological and four astrophysical feedback), for a total of 183 distinct simulation models. We find significantly different predictions between the fiducial models of the suites owing to their different implementations of feedback. SIMBA exhibits the strongest feedback, leading to the smoothest distribution of baryons and reducing the sight-line-to-sight-line variance in DMs between z = 0 and 1. Astrid has the weakest feedback and the largest variance. We calculate FRB CGM measurements as a function of galaxy impact parameter, with SIMBA showing the weakest DMs due to aggressive active galactic nucleus (AGN) feedback and Astrid the strongest. Within each suite, the largest differences are due to varying AGN feedback. IllustrisTNG shows the most sensitivity to supernova feedback, but this is due to the change in the AGN feedback strengths, demonstrating that black holes, not stars, are most capable of redistributing baryons in the IGM and CGM. We compare our statistics directly to recent observations, paving the way for the use of FRBs to constrain the physics of galaxy formation and evolution.