Example of the coupled evolution of a magma ocean and proto-atmosphere for an initial H₂+H₂O amount of 10N_TO and an initial magma ocean bottom pressure of 50 GPa, focusing on the behavior of volatiles and the boundary layer. The left and right columns show the results of Case 1 and Case 2, respectively. (a), (b) Atmospheric pressure of the total (black), H₂ (green), and H₂O (blue). (c), (d) Total amounts of H₂ (green) and H₂O (blue) normalized by the number of hydrogen molecules in the present-day terrestrial seawater (N_TO). (e), (f) H₂O distribution ratio in the atmosphere (blue), magma ocean (red), and mantle (orange). (g), (h) Surface temperature. (i), (j) H₂ diffusion rate into the magma ocean, normalized by N_TO. (k), (l) Overturn time of the boundary layer. (m), (n) Net outgoing radiation flux (black), outgoing longwave planetary radiation flux (red), and absorbed solar radiation flux (yellow).