Inflated hot Jupiters: Inferring average atmospheric velocity via Ohmic models coupled with internal dynamo evolution

Aims. The inflated radii observed in hundreds of hot Jupiters (HJ) represent a long-standing open issue. In this study, we quantitatively investigate this phenomenon within the framework of Ohmic dissipation arising from magnetic induction in the atmosphere, one of the most promising mechanisms for explaining the radius anomaly. Methods. Using MESA, we simulated the evolution of irradiated giant planets spanning the observed range of masses and equilibrium temperatures, incorporating an internal source of Ohmic dissipation that extends to deep layers of the envelope. We considered the heat-flux-dependent evolution of the deep-seated dynamo field on which the induced field depends. We adopted a state-of-the-art electrical conductivity, considering the thermal ionisation of alkali metals in the outer layers and the pressure-ionisation in the interior and the corresponding solutions for the induced currents across the planet. Results. We inferred that, in order to reproduce the range of observed radii, the atmospheric wind intensities averaged in the region p ≲ 10 bar have to be in the range O0.01-1 km/s and to decrease roughly linearly with planetary mass and much more steeply with equilibrium temperature. This is consistent with the expected effects of magnetic drag from the induced field, which is higher for more intense irradiation, via conductivity, and for larger masses, which have higher dynamo fields. Due to the evolution of the dynamo field and the proportionality of the induced currents on it, the Ohmic efficiency typically decreases by at least one order of magnitude from 0.1 to 10 Gyr, which is in contrast with the common assumption of a constant-in-time value. Notably, the extent of the main convective region and the associated heat flux supporting the dynamo is reduced in the presence of strong Ohmic dissipation, which in turn depends on the dynamo field strength, generating a non-trivial coupling of the latter with the atmospheric induction and potentially leading to the oscillatory behaviour of the field strength. These findings remain generally valid even when accounting for a long-term increase in the main-sequence host star luminosity, although this case can more readily lead to HJ re-inflation, consistent with previous studies.