MP08 comparison case. Left panel: atmospheric gas density (solid line) and temperature (dashed) as a function of height (distance from the planet’s center) in the protoplanet’s atmosphere (outer radiative zone). Right panel: opacity as a function of height in the numerical model of MP08 (dashed line: grain opacity only) and in the analytical model of this work (thick solid line: combined grain and gas opacity). The thin blue solid (dashed) line is the gas (grain) opacity alone.