Deep-atmosphere forcing (equilibrium) temperature and the ratio of timescales explored, illustrating convergence. Left: relationship between the deep-atmosphere forcing (equilibrium) temperature and the resulting deep-atmosphere temperature. The dotted curve represents the initial adiabatic conditions. The solid curve illustrates the deviation from this due to the convective motion. The final profile shows a departure from the adiabatic branch towards the diabatic branch. The dashed curve highlights a transient early stage when the perturbation towards the diabatic branch is most pronounced. Right: ratio of the forcing timescales τ_chem ∕τ_rad for T₀ = 2522 K with τ_chem = 1, 10, 100, and 1000 s; τ_rad = 100 s for all values. Convergence is reached once τ_chem∕τ_rad < 1.