Ohmic heating in the upper atmosphere of hot exoplanets

The influence of a time-varying magnetic field

Département d’Astrophysique/AIM CEA/IRFU, CNRS/INSU, Univ. Paris-Saclay & Univ. de Paris 91191 Gif-sur-Yvette, France

^★ Corresponding author; antoine.strugarek@cea.fr

Received: 17 October 2024
Accepted: 18 December 2024

Abstract

Context. Exoplanets on close-in orbits are subject to intense X-ray and ultraviolet (XUV) irradiation from their star. Their atmosphere heats up, sometimes to the point where it will thermally escape from the gravitational potential of the planet. Nonetheless, XUV is not the only source of heating in such atmospheres. Indeed, close-in exoplanets are embedded in a medium (the stellar wind) with strong magnetic fields that can significantly vary along the orbit. Variations in this magnetic field can induce currents in the upper atmosphere, which dissipate and locally heat it up through Ohmic heating.

Aims. The aim of this work is to quantify Ohmic heating in the upper atmosphere of hot exoplanets, due to an external time-varying magnetic field, and to compare it to the XUV heating.

Methods. Ohmic heating depends strongly on the conductivity properties of the upper atmosphere. We developed a 1D formalism to assess the level and the localization of Ohmic heating depending on the conductivity profile. The formalism is applied to the specific cases of Trappist-1 b and π Men c.

Results. Ohmic heating can reach values up to 10⁻³ erg s⁻¹ cm⁻³ in the upper atmospheres of hot exoplanets. It is expected to be stronger the closer the planet and the lower its central star mass, as these conditions maximize the strength of the ambient magnetic field around the planet. The location of maximal heating depends on the conductivity profile (but does not necessarily occurs at the peak of conductivity) and, in particular, on the existence and strength of a steady planetary field. Such extra heating can play a role in the thermal budget of the escaping atmosphere when the planetary atmospheric magnetic fields is between 0.01 and 1 G.

Conclusions. We confirm that Ohmic heating can play an important role in setting the thermal budget of the upper atmosphere of hot exoplanets and can even surpass the XUV heating in the most favorable cases. When it is strong, a corollary is that the upper atmosphere screens efficiently time-varying external magnetic fields, preventing them from penetrating deeper in the atmosphere or even within the planet itself. We find that both Trappist-1b and π Men c are likely being subjected to intense Ohmic heating.