Theoretical models of structure formation predict the presence of a hot gaseous atmosphere around galaxies. While this hot circumgalactic medium (CGM) has been observationally confirmed through UV absorption lines, the detection of its direct X-ray emission remains scarce. Recent results from the eROSITA collaboration have claimed the detection of the CGM out to the virial radius for a stacked sample of Milky Way-mass galaxies. We investigate theoretical predictions of the intrinsic CGM X-ray surface brightness (SB) using simulated galaxies and connect them to their global properties, such as the gas temperature, hot gas fraction, and stellar mass. We selected a sample of central galaxies from the ultra-high-resolution cosmological volume ($48 cMpc $) of the Magneticum Pathfinder set of hydrodynamical cosmological simulations. We classified them as star-forming (SF) or quiescent (QU) based on their specific star formation rate (SFR). For each galaxy, we generated X-ray mock data using the X-ray photon simulator from which we obtained SB profiles out to the virial radius for different X-ray emitting components; namely, gas, active galactic nuclei (AGNs), and X-ray binaries (XRBs). We fit a β-profile to the gas component of each galaxy and observed trends between its slope and global quantities of the simulated galaxy. We found marginal differences among the average total SB profile in SF and QU galaxies beyond r>0.05 The relative contribution from hot gas exceeds $70%$ and is non-zero (lesssim 10%) for XRBs in both galaxy types. At small radii (r<0.05 XRBs dominate the SB profile over the hot gas for QU galaxies. We found positive correlations between the galaxies' global properties and the normalization of their SB profiles. The fitted β-profile slope is correlated with the total gas luminosity, which, in turn, shows strong connections to the current accretion rate of the central supermassive black hole (SMBH). We found the halo scaling relations to be consistent with the literature.
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