Best-fit slope β of each galaxy’s gas SB profile labeled as a Sβ profile (Eq. (9)) against various halo properties within R_vir: (a) gas luminosity L_X, gas; (b) stellar mass M_* obtained from stellar resolution elements bound to the parent halo; (c) gas fraction f_gas derived from gas resolution elements bound to the parent halo excluding star-forming and low-temperature (< 10⁵ K) gas. In panel (c) the dotted magenta line indicates the cosmic baryon fraction in the simulation; (d) emissivity weighted hot gas temperature T_gas. The exact retrieval of these quantities is outlined in Section 4. The thick solid line in each panel indicates the median value of β. For comparison, we include the sample of massive elliptical galaxies from O’Sullivan et al. (2003) (O’sul+03) and massive star-forming galaxies of Li et al. (2017). Additionally, we compare to β models of the MW from Miller & Bregman (2015) (M&B15) and Nicastro et al. (2016) (model A) in (b) and (c).