On the magnetodynamics of zonal band formation in substellar atmospheres

The formation of zonal bands is widespread in planetary, brown dwarf, and exoplanetary atmospheres, yet the role of magnetic fields in shaping these flows remains poorly constrained. While hydrodynamic models link jet formation to the Rhines effect, substellar atmospheres possess strong magnetic fields and significant degrees of ionisation, suggesting that the Lorentz force may play a key role in atmospheric circulation and zonal band formation. Building on earlier work on zonal band suppression, we develop a tangent‑plane magnetohydrodynamical model to determine when magnetic effects enhance or disrupt zonal band formation. Our analysis shows that even modest fields can significantly modify jet structure and its latitudinal extent. In a fully ionised atmosphere, the zonal band latitude shifts by approximately $27\degree$ per decade increase in the mean equatorial magnetic field strength, over the range $10^{-3}-0.1$\,T. For degrees of ionisation $10^{-2}-1$, and at constant mean equatorial magnetic field strength, the zonal band latitude shifts equatorward by approximately $29\degree$ per decade increase in the degree of ionisation. We derive a simple diagnostic for identifying magnetically influenced circulation that can also infer the magnitude of the background magnetic field and the atmospheric degree of ionisation. This framework offers a pathway to interpreting banded variability and atmospheric dynamics in brown dwarfs and exoplanets.