MHD Models of Hot Jupiter atmospheres

The unique properties of Hot Jupiters (HJs) have motivated extensive research efforts focusing on their detection, characterization, and theoretical modeling. However, observations and models must develop hand in hand to unravel the complex interplay of physical processes such as atmospheric winds, radiative transfer, and chemistry. Those shape and constrain observable properties including radius inflation, hotspot offsets, day–night brightness contrasts, Doppler-shifted spectral lines, and potentially radio emission associated with magnetic fields.

Magnetic effects are expected to become increasingly important with rising equilibrium temperature, as electrical conductivity increases steeply due to alkali metal ionization. Under these conditions, magnetic coupling between atmospheric flows and the planetary magnetic field becomes unavoidable. However, most existing models of magnetized Hot Jupiter atmospheres are either tailored to individual benchmark planets or rely on simplified magnetic prescriptions, such as linear drag or kinematic induction, despite the inherently nonlinear nature of magnetic field generation and saturation. While such approaches may be adequate for weakly conducting atmospheres, they cannot capture magnetic field amplification, Lorentz-force feedback, or the transition to magnetically dominated regimes.

To test these expectations in a self-consistent framework, we exploit a fully nonlinear magnetohydrodynamic (MHD) model that treats Hot Jupiter atmospheres as an anelastic fluid with homogeneous electrical conductivity in a stably stratified spherical shell. The system is subject to rotation, permanent dayside irradiation, and an imposed deep-interior dipolar magnetic field. We systematically explore models spanning equilibrium temperatures from 1000 to 3000 K by increasing the electrical conductivity accordingly.

Our simulations confirm that for temperatures up to about 1400 K, electromagnetic effects are negligible and atmospheric dynamics are dominated by a strong, axisymmetric prograde equatorial jet with peak velocities of several km/s. In this hydrodynamic regime, the longitudinal position of the brightness maximum may lie either east or west of the substellar point. For temperatures between roughly 1400 and 1900 K -nearly half of the known Hot Jupiter population- magnetic induction becomes significant. Bending and stretching of the internal field generate a predominantly azimuthal atmospheric magnetic field that can exceed the internal field strength by up to an order of magnitude, leading to a substantial reduction of flow amplitudes, particularly in the zonal direction. At even higher temperatures, corresponding to the Ultra-Hot Jupiter regime, magnetic induction in the atmosphere becomes sufficiently efficient to even drive a self-sustained stratospheric dynamo. Under these conditions, the flow and magnetic field are small-scale and time-dependent. Moreover, the magnetic field becomes independent of both the internal magnetic field and the electrical conductivity.

By systematically exploring a wide range of temperatures and thus electrical conductivities, our results can be related to observable quantities, such as day-to-night side brightness difference, hot spot advection for IR photometry or Doppler shift and line broadening for transmission spectroscopy and might provide a physically sound basis for interpreting current and future observations.