Atmospheric profiles for a generic hot-Neptune planet at different metallicities. The left column shows a set of models with a fixed mass-loss rate. The right column shows another set of models with a fixed density at the planet radius, leading to different mass-loss rates at different metallicities. For every model, the value of T₀ is chosen such that it is consistent with the mean of the nonisothermal temperature profile of panel d or i between 1 R_p and 2 R_p. Those values for T₀ can be found in the text in Sects. 3.2.1 and 3.2.4. In panels e and j, solid lines show the radiative heating rates and dashed lines show the radiative cooling rates.