Core entropy vs. age for a planet mass ﹩M/ M_{\mathrm{J}\,}=0.32﹩ (dotted red), 1.0 (solid black), and 3.2 (dashed). For each mass, surface isotherms ﹩T_{\mathrm{deep}\,}( \mathrm{K}\,) =1000﹩, 2000, and 3000 are shown from bottom to top. Luminosity is independent of ﹩T_{\mathrm{deep}\,}﹩ for ﹩T_{\mathrm{deep}\,}=1000{\mbox{--}} 2000﹩ K; hence, the curves nearly overlie each other (see Fig. 4).