Red: profile of the intrinsic density of the hot coronal gas (from Eq. (6)) for a galaxy with M_vir = 10^13.3 M_⊙, r_vir = 526 kpc, T = T_vir = 6.5 × 10⁶ K (average of the galaxy halos in our sample), and normalization set as explained in Sect. 3.2. In blue, profile of the intrinsic average density expected for the cool circumgalactic medium if in pressure equilibrium with the corona, obtained through Eq. (8).