Comparison of the luminosity as a function of time as predicted by direct cooling calculations and the fit. The upper three thicker lines are for a 15 M_⊕ planet while the three thin lines below are for a 5 M_⊕ planet. Thegreen dashed line is the fit of Eq. (A.1). The other lines are direct simulations. The brown dashed-dotted and the red solid lines assume a rocky core, and a core consisting of 50% ice and 50% rocky material, respectively.