Exploring deep and hot adiabats as a potential solution to the radius inflation problem in brown dwarfs

Aims. The anomalously large radii of highly irradiated gaseous exoplanets has remained a mystery for some time. One mechanism that has been suggested as a solution for hot Jupiters is the heating of the deep atmosphere via the vertical advection of potential temperature, resulting in increased internal entropy. In this work, we intend to explore whether this mechanism can also explain the observed brown dwarf radii trend: a general increase in the observed radius with irradiation, with an exception, however, for highly irradiated brown dwarfs orbiting white dwarfs. Methods. We used a 3D global circulation model (GCM) known as DYNAMICO to run a series of long-timescale models of the deep atmospheres of Kepler-13Ab, KELT-1b, and SDSS1411B. These models allowed us to explore not only whether a stable advective adiabat can develop in this context, but also to consider the associated dynamics. Results. We find that our brown dwarf models fall into two distinct regimes. First, Kepler-13Ab and KELT-1b both show signs of significant deep heating and, hence, are able to maintain adiabats that are hotter than 1D models predict. On the other hand, SDSS1411B exhibits a much weaker downward heating profile that not only struggles to heat the interior under ideal conditions, but is highly sensitive to the presence of deep radiative dynamics. Conclusions. We conclude that the vertical advection of potential temperature by large-scale atmospheric circulations constitutes a robust mechanism to explain the trend of increasing inflation with irradiation. This includes an exception for highly irradiated brown dwarfs orbiting white dwarfs, which can be understood as occurring due to the role that increasing rotational influence plays in the context of 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 radius inflation in our brown dwarf sample. Finally, in order to confirm the validity of this explanation, we suggest that this work should be followed by future studies of brown dwarfs atmospheres using next-generation, fully radiative GCMs