Self-Consistent Model Atmospheres and the Cooling of the Solar System's Giant Planets

Abstract

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 T eff of the planet with a model that also matches the planet's current gravity field constraints. This is predominantly due to advances in the high-pressure 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. The atmosphere grids are published here as tables, so that they may be used by the wider community.

Bayesian Evolution Models for Jupiter With Helium Rain and Double-Diffusive Convection

“…As demonstrated by Guillot et al (2004), the inclusion of alkali metals enhances the opacity enough to ensure convection at all depths within a present-day Jupiter. Our models, which include modern opacities and self-consistently allow for radiative transport wherever ∇ rad < ∇ ad , confirm this result: the intermediate radiative window is only mildly subadiabatic (∇ − ∇ ad ∼ −10 −1 ) and vanishes before t ∼ 2 × 10 8 yr (see also Fortney et al 2011), and has an insignificant effect on the overall cooling time. Thus for the homogeneous phases of the evolution, our models may be directly compared to models constructed assuming ∇ = ∇ ad always.…”

“…We apply the self-consistent model atmospheres of Fortney et al (2011) as fit analytically by Leconte & Chabrier (2013), which provide the temperature at the 10 bar level T 10 as a function of surface gravity g and intrinsic temperature T int . The planet's effective temperature T eff in a given timestep is given by…”

A new vision of giant planet interiors: Impact of double diffusive convection

“…Conventional models based on fully adiabatic thermal profiles notably lead to cooling times about 15% longer than the age of the solar system for Jupiter (Fortney et al 2011). In principle, the hotter non-adiabatic internal structures suggested in the present paper will prolong the cooling and thus worsen the problem.…”

Giant Impact: An Efficient Mechanism for the Devolatilization of Super-Earths

“…Despite their similar masses, radii, and compositions, thermal evolution models of Uranus and Neptune suggest that right after their formation, Neptune may have been relatively luminous but Uranus relatively faint (e.g. Hubbard & Macfarlane 1980;Fortney et al 2011). Stevenson (1986) suggested that this dichotomy may be accounted for if a violent head-on collision yielded a hot and homogeneous interior of Neptune, whereas an oblique collision caused a tilted Uranus with a stably-stratified interior.…”