The influence of differential irradiation and circulation on the thermal evolution of gas giant planets. I. Upper limits from radiative equilibrium

As a planet ages, it cools and its radius shrinks at a rate set by the efficiency with which heat is transported from the interior out to space. The bottleneck for this transport is at the boundary between the convective interior and the radiative atmosphere; the opacity there sets the global cooling rate. Models of planetary evolution are often one dimensional (1D), such that the radiative-convective boundary (RCB) is defined by a single temperature, pressure, and opacity. In reality the spatially inhomogeneous stellar heating pattern and circulation in the atmosphere could deform the RCB, allowing heat from the interior to escape more efficiently through regions with lower opacity. We present an analysis of the degree to which the RCB could be deformed and the resultant change in the evolutionary cooling rate. In this initial work we calculate the upper limit for this effect by comparing an atmospheric structure in local radiative equilibrium to its 1D equivalent. We find that the cooling through an uneven RCB could be enhanced over cooling through a uniform RCB by as much as 10%-50%. We also show that the deformation of the RCB (and the enhancement of the cooling rate) increases with a greater incident stellar flux or a lower inner entropy. Our results indicate that this mechanism could significantly change a planet's thermal evolution, causing it to cool and shrink more quickly than would otherwise be expected. This may exacerbate the well-known difficulty in explaining the very large radii observed for some hot Jupiters.