The role of Ohmic dissipation of internal currents on Hot Jupiter radii

The inflated radii observed in hundreds of Hot Jupiters represent a long-standing open issue. The observed correlation between radii and irradiation strength, and the occasional extreme cases, nearly double the size of Jupiter, remain without a comprehensive quantitative explanation. In this investigation, we delve into this issue within the framework of Ohmic dissipation, one of the most promising mechanisms for explaining the radius anomaly. Using the evolutionary code MESA, we simulate the evolution of irradiated giant planets, spanning the range 1 to 8 Jupiter masses, incorporating an internal source of Ohmic dissipation located beneath the radiative-convective boundary. Our modeling is based on physical parameters, and accounts for the approximated conductivity and the evolution of the magnetic fields, utilizing widely-used scaling laws. We compute the radius evolution across a spectrum of masses and equilibrium temperatures, considering varying amounts of Ohmic dissipation, calculated with the internal conductivity profile and an effective parametrization of the currents, based on the typical radius of curvature of the field lines. Our analysis reveals that this internal Ohmic dissipation can broadly reproduce the range of observed radii using values of radius of curvature up to about one order of magnitude lower than what we estimate from the Juno measurements of the Jovian magnetosphere and from MHD dynamo simulations presented herein. The observed trend with equilibrium temperature can be explained if the highly-irradiated planets have more intense and more small-scale magnetic fields. This suggests the possibility of an interplay between atmospherically induced currents and the interior, via turbulence, in agreement with recent box simulations of turbulent MHD in atmospheric columns.