Inhomogeneous magnetic coupling in exoplanets: the stop & go of WASP-18 b's atmospheric flows

TL;DR

This work tackles how magnetic coupling shapes the atmospheric dynamics of ultra-hot Jupiters with spatially varying ionization, using WASP-18 b as a case study. It develops an anisotropic magnetic drag parametrization that separately treats Pedersen and Hall currents and couples local ionization to momentum exchange and frictional heating, then implements this in the ExoRad 3D GCM. By comparing no-drag, uniform-drag, active-drag, and anisotropic-drag runs, the study shows that anisotropic drag weakens the dayside equatorial jet, induces terminator- and hotspot asymmetries, and alters heat redistribution, with observable consequences in phase curves and Doppler winds. The framework links microphysical ionization and conductivity to global climate features, providing a pathway to infer exoplanetary magnetic field strengths from atmospheric dynamics while outlining key limitations such as neglect of polarization fields and non-ideal MHD effects. Overall, the results demonstrate that magnetic drag physics, especially the Hall component, can drive qualitatively distinct circulation regimes and temperature patterns in UHJ atmospheres.

Abstract

Early studies of ionization in hot Jupiter atmospheres suggest that magnetic coupling can shape their dynamics. These effects may be most pronounced in ultra-hot Jupiters that sustain global magnetic fields. WASP-18 b hosts an ionized dayside atmosphere extending deep enough to be strongly influenced by magnetic forces. Phase curve observations suggest effective magnetic drag, yet its impact on the atmospheric circulation remains poorly constrained. This work explores how magnetic drag in an inhomogeneously ionized atmosphere shapes local and global dynamics to provide a pathway to constrain the planet's magnetic field strength. An analytical parameterization for anisotropic magnetic drag, including both Pedersen and Hall drag components, and associated frictional heating in the globally neutral atmosphere, is implemented in the 3D General Circulation Model ExoRad to study WASP-18 b's atmosphere. Climate characteristics are compared for different drag formulations to assess whether anisotropic physics is required to capture magnetic coupling effects. Anisotropic magnetic drag and frictional heating, both set by local ionization, strongly affect wind strength and direction in the upper atmosphere, modify the day-night circulation, and produce observable temperature asymmetries. They enhance the evening-morning terminator temperature difference near 0.1 bar and generate two off-equator hotspots with reduced eastward shift. The terminator regions are particularly sensitive to how magnetic drag is modeled. Anisotropic magnetic drag damps and redirects dayside-to-nightside winds, partially decoupling the equatorial flow at the morning terminator while maintaining the nightside jet. Locally varying drag forces and frictional heating create asymmetric temperature patterns manifesting as primary and secondary hotspot regions.

Figures (9)

• Figure 1: (a) Spatial variations in magnetic Reynolds number ($R_M$ (Eq. \ref{['eq:rm_calc']}), left) and (b) thermal ionization fraction ($x_e$, right) for WASP-18 b. Large areas of the dayside are in the intermediate and high-$R_M$ regimes, while ionization varies over many orders of magnitude, motivating an anisotropic drag treatment that accounts for local conductivity and magnetic geometry. The lines show gas temperature-pressure profiles averaged over all latitudes and over different regions in the atmosphere: dayside ($-90$°$<\phi\leq90$°), nightside ($|\phi|>90$°), morning ($-97.5$°$\leq\phi\leq-82.5$°) and evening terminator ($82.5$°$\geq\phi\geq97.5$°). Results of the simulation with anisotropic drag were used for the calculation of $R_M$, $x_e$, and the averaged temperature-pressure profiles shown here.
• Figure 2: Magnetization parameter (Eq. \ref{['eq:magnetization']}) profiles for ions ($k_i$) and electrons ($k_e$) averaged over all latitudes and over dayside atmosphere ($-90$°$<\phi\leq90$°). The blue dotted line ($\omega_{pe}/\nu_{en}$) shows the relation between the electron plasma frequency and the electron–neutral collision frequency averaged over the dayside atmosphere. The plasma coupling ratios are calculated from the ExoRad simulation for WASP-18 b with anisotropic drag. The dashed grey line shows where the plasma coupling ratio reaches unity.
• Figure 3: Hall ($K_{H,s}$) and Pedersen ($K_{P,s}$) drag coefficients for electrons ($s=e$) and ions ($s=i$) averaged over all latitudes and over dayside atmosphere ($-90$°$<\phi\leq90$°). $K_{H}=K_{H,i}-K_{H,e}$ and $K_{P}=K_{P,i}+K_{P,e}$ are the total Hall and Pedersen coefficients. The coefficients were calculated using the gas pressure-temperature profile from the ExoRad simulation run of WASP-18 b with anisotropic drag. The grey line shows $K_P$ obtained directly from ExoRad. It diverges from the calculated $K_P$ (blue line) in the upper atmosphere because the drag timescale in ExoRad is limited to $\tau_\mathrm{drag}\geq100$ s. The same applies for $K_H$ from ExoRad (not shown here).
• Figure 4: Maps of horizontal wind speed ($|\underline{v}_h|$) and streamlines (white lines) at two pressure levels ($p_\mathrm{gas}=$0.1 bar and $p_\mathrm{gas}=$0.001 bar) for the four different magnetic drag treatments (no drag, uniform drag, active drag, and anisotropic drag). The substellar point is centered at each map. The dashed black vertical lines mark the area at longitude $\pm 90^\circ$. The output of each velocity component is time-averaged over 100 days of simulation time to eliminate the small-scale fluctuations.
• Figure 5: Mean zonal wind for the four different magnetic drag treatments in different regions of the atmosphere: dayside atmosphere (first row), nightside atmosphere (second row), and total atmosphere (third row). The zonal wind velocity $u$ is averaged at a specific latitude, and pressure level across longitudes on the dayside ($-90$°$\leq\phi\leq 90$°), on the nightside ($|\phi|>90$°), and all longitudes. The black line shows the zero-wind contour, the boundary between superrotation and counterrotation. The output of the zonal wind velocity is time averaged over 100 days of simulation time to eliminate the small-scale fluctuations.