  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, such
that the radiative-convective boundary (RCB) is defined by a single
temperature, pressure, and opacity. In reality the spatially inhomogenous
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.
