Self-Consistent Model Atmospheres and the Cooling of the Solar System's   Giant Planets
  We compute grids of radiative-convective model atmospheres for Jupiter, Saturn, Uranus, and Neptune over a range of intrinsic fluxes and surface gravities. The atmosphere grids serve as an upper boundary condition for models of the thermal evolution of the planets. Unlike previous work, we customize these grids for the specific properties of each planet, including the appropriate chemical abundances and incident fluxes as a function of solar system age. Using these grids, we compute new models of the thermal evolution of the major planets in an attempt to match their measured luminosities at their known ages. Compared to previous work, we find longer cooling times, predominantly due to higher atmospheric opacity at young ages. For all planets, we employ simple "standard" cooling models that feature adiabatic temperature gradients in the interior H/He and water layers, and an initially hot starting point for the calculation of subsequent cooling. For Jupiter we find a model cooling age 10% longer than previous work, a modest quantitative difference. This may indicate that the hydrogen equation of state used here overestimates the temperatures in the deep interior of the planet. For Saturn we find a model cooling age 20% longer than previous work. However, an additional energy source, such as that due to helium phase separation, is still clearly needed. For Neptune, unlike in work from the 1980s and 1990s, we match the measured Teff of the planet with a model that also matches the planet's current gravity field. This is predominantly due to advances in the equation of state of water. This may indicate that the planet possesses no barriers to efficient convection in its deep interior. However, for Uranus, our models exacerbate the well-known problem that Uranus is far cooler than calculations predict, which could imply strong barriers to interior convective cooling. 
J. J. Fortney, M. Ikoma, N. Nettelmann, T. Guillot, M. S. Marley
astro-ph.EP