The Intrinsic Temperature and Radiative-Convective Boundary Depth in the Atmospheres of Hot Jupiters

Abstract

In giant planet atmosphere modelling, the intrinsic temperature $T_{\mathrm{int}}$ and radiative-convective boundary (RCB) are important lower boundary conditions. Often in one-dimensional radiative-convective models and in three-dimensional general circulation models it is assumed that $T_{\mathrm{int}}$ is similar to that of Jupiter itself, around 100 K, which yields a RCB around 1 kbar for hot Jupiters. In this work, we show that the inflated radii, and hence high specific entropy interiors, of hot Jupiters suggest much higher $T_{\mathrm{int}}$ values. Assuming the effect is primarily due to current heating (rather than delayed cooling), we derive an equilibrium relation between $T_{\mathrm{eq}}$ and $T_{\mathrm{int}}$, showing that the latter can take values as high as 700 K. In response, the RCB moves upward in the atmosphere. Using one-dimensional radiative-convective atmosphere models, we find RCBs of only a few bars, rather than the kilobar typically supposed. This much shallower RCB has important implications for the atmospheric structure, vertical and horizontal circulation, interpretations of phase curves, and the effect of deep cold traps on cloud formation.

6 pages, 4 figures, accepted to ApJ Letters. This version corrects the constants in equation 3; our calculations used the form in equation 2, so none of our other results are changed. An corresponding erratum has been submitted to ApJ Letters