Top panels: Gas density profiles from the model presented in Sect. 5 with corrections described in Sects. 6.1.1 and 6.1.2 for M₅₀₀ = 2.5 × 10¹⁴ M_⊙ (left), M₅₀₀ = 5.0 × 10¹⁴ M_⊙ (center), and M₅₀₀ = 10¹⁵ M_⊙ (right) compared with observations from the REXCESS, XCOP, and HIGHMz samples respectively. For further details see the label of Fig. 18. Bottom panels: Same as top panels but for the entropy profiles.