Left: map of the average Compton cooling to the warm corona heating (q_h) ratio in the χ–τ_cor plane, with χ being defined by Eq. (12). The color scale on the right ranges from 20 (black) to 100% (white). The other parameters are fixed to T_bb = 10⁵ K, ξ₀ = 10³ erg s⁻¹ cm, and n_H = 10¹² cm⁻³. The solid green line refers to χ = 1, that is, the case of radiative equilibrium between a corona and a nondissipative disk that it covers entirely; it divides the χ–τ_cor into two regions that can be characterized by different radiative equilibrium properties (see Sect. 2). The region above the green line, that is, χ >  1, agrees with a nondissipative disk covered by a patchy corona. The dashed lines correspond to different values of the corona covering factor from 0.95 to 0.40 (see Eq. (A.9)). The region below the green line, that is, χ <  1, agrees with a slab corona above a disk which is now dissipative (F_disk >  0). The blue contours correspond to different values of the logarithm of the warm corona heating q_h (in unit of erg s⁻¹ cm³). Right: cooling and heating process fractions with respect to the warm corona heating q_h across the corona for τ_cor = 20 but for two different values of χ, 0.753 (bottom) and 1.35 (top). This corresponds to the simulations indicated in the left panel with either a “+” or an “x”, respectively.