Transport and thermochemical kinetics of alkali species in hot Jupiter atmospheres: implications for magnetic models

Interactions between the planetary magnetic field of a hot Jupiter and the winds within its atmosphere are moderated by the electron and ion abundances. For a solar metallicity atmosphere at pressures between 10 and $10^{-4}$ bar, the primary sources for these charged species are expected to be the potassium and sodium atoms, and models of magnetic effects in hot Jupiter atmospheres have typically assumed that charged species exist within the atmosphere in their equilibrium abundances. In this work, we investigate the thermochemical kinetics of alkali species within a hot Jupiter atmosphere, thus allowing for the thermal ionization fraction to depart from equilibrium, and demonstrate that quenching of ions occurs between 1 and 10 mbar. This increase in ionization fraction on the nightside and at mid-latitudes results in stronger magnetic interaction, here modelled using the magnetic drag approximation, further slowing the jet and altering the global circulation. We additionally show that while quenching occurs, large magnetic resistivities resulting from low electron abundances continue to exist on the nightside between 10 and 100 mbar, in tension with magnetohydrodynamic models that assume horizontally uniform magnetic resistivities to simplify the explicit integration of the induction equation. At lower pressures ($\sim$ 0.1 mbar) where the electrons have become horizontally homogenized, the magnetic Reynolds number approaches or exceeds unity, signalling the breakdown of the magnetic drag approximation. We thus stress that chemical kinetics represents a dynamically important component of modelling hot Jupiter atmospheres while at the same time further complicating the treatment of magnetic effects.