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

Abstract

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. We simulate the evolution of irradiated giant planets with MESA, 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 infer average atmospheric wind intensities, averaged in the region $p < 10$ bar, in the range 0.01-1 km/s in order to reproduce the range of observed radii, decreasing 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, at 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, potentially leading to an 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.