Top panels: global properties (empty black dots) and after correction for the E_z factor (solid red dots) recovered from their thermodynamic profiles for the following input values for (M₅₀₀, z): (8 × 10¹⁴ M_⊙, 0.05), (5 × 10¹⁴ M_⊙, 0.05), (2 × 10¹⁴ M_⊙, 0.05), (8 × 10¹⁴ M_⊙, 0.5), (5 × 10¹⁴ M_⊙, 0.5), (2 × 10¹⁴ M_⊙, 1). The dashed magenta lines identify the best-fit relations of Eq. (7). A core-excised bolometric luminosity is considered. Bottom panels: red dots are the quantities (from left to right: f_g, f_T, b) estimated in our model for the following input values for (M₅₀₀, z): (8 × 10¹⁴ M_⊙, 0.05), (5 × 10¹⁴ M_⊙, 0.05), (2 × 10¹⁴ M_⊙, 0.05), (8 × 10¹⁴ M_⊙, 0.5), (5 × 10¹⁴ M_⊙, 0.5), and (2 × 10¹⁴ M_⊙, 1); the blue dotted line indicates Ω_b/Ω_m = 0.157 (Planck Collaboration XXVII 2016); the dashed magenta lines show the predictions following the relations: f_g = 0.124 𝒯^0.23, f_T = 0.687 𝒯^0.07 and 1 − b = h₀ = 1, where f_g and f_T are the absolute values, i.e. multiplied by the assumed normalisations of 0.1 and , respectively.