  Theoretical models of structure formation predict the presence of a hot
gaseous atmosphere around galaxies. While this hot circum-galactic medium (CGM)
has been observationally confirmed through UV absorption lines, the detection
of its direct X-ray emission remains scarce. 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 gas temperature,
hot gas fraction and stellar mass. We select a sample of galaxies from the
ultra-high resolution ($48\ \rm{cMpc\, h^{-1}}$) cosmological volume of the
Magneticum Pathfinder set of hydrodynamical cosmological simulations. We
classify them as star-forming (SF) or quiescent (QU) based on their specific
star-formation rate. For each galaxy we generate X-ray mock data using the
X-ray photon simulator PHOX, from which we obtain SB profiles out to the virial
radius for different X-ray emitting components, namely gas, active galactic
nuclei and X-ray binaries (XRBs). We fit a $\beta$-profile to each galaxy and
observe trends between its slope and global quantities of the simulated galaxy.
We find marginal differences between the average total SB profile of the CGM in
SF and QU galaxies, with the contribution from hot gas being the largest
($>50\%$) at radii $r>0.05\,R_{\rm{vir}}$. The contribution from X-ray binaries
(XRBs) equals the gas contribution for small radii and is non-zero for large
radii. The galaxy population shows positive correlations between global
properties and normalization of the SB profile. The slope of fitted
$\beta$-profiles correlates strongly with the total gas luminosity, which in
turn shows strong connections to the current accretion rate of the central
super-massive black hole (SMBH).
