Exploring deep and hot adiabats as a potential solution to the radius inflation problem in brown dwarfs: Long-timescale models of the deep atmospheres of KELT-1b, Kepler-13Ab, and SDSS1411B

The anomalously large radii of highly-irradiated gaseous exoplanets has long been a mystery. One mechanism suggested as a solution for hot Jupiters is the heating of the deep atmosphere via the vertical advection of potential temperature resulting in an increased internal entropy. Here we intend to explore if this mechanism can also explain the observed brown dwarf radii trend: a general increase in radius with irradiation, with an exception for highly-irradiated brown dwarfs orbiting white dwarfs. We use a 3D GCM, DYNAMICO, to run a series of long-timescale models of the atmospheres of Kepler-13Ab, KELT-1b, and SDSS1411B. These models allow us to explore not only if a stable advective adiabat can develop, but also the associated dynamics. We find that our models fall into two distinct regimes: Kepler-13Ab and KELT-1b both show signs of significant deep heating and hence maintain adiabats that are hotter than 1D models predict. On the other hand, SDSS1411B exhibits a much weaker downward heating profile which not only struggles to heat the interior under ideal conditions, but is highly sensitive to the presence of deep radiative dynamics. We find that the vertical advection of potential temperature by large-scale atmospheric circulations represents a robust mechanism to explain the trend of increasing inflation with irradiation, including the exception for highly irradiated brown dwarfs orbiting white dwarfs. This can be understood as occurring due to the role that increasing rotational influence plays on mid- to-high latitude advective dynamics. Furthermore, when paired with a suitable parametrisation of the outer atmosphere irradiation profile, this mechanism alone could potentially provide a complete explanation for the observed levels of inflation in our brown dwarfs.