The Influence of Atmospheric Scattering and Absorption on Ohmic Dissipation in Hot Jupiters

Abstract

Using semi-analytical, one-dimensional models, we elucidate the influence of scattering and absorption on the degree of Ohmic dissipation in hot Jovian atmospheres. With the assumption of Saha equilibrium, the variation in temperature is the main driver of the variations in the electrical conductivity, induced current and Ohmic power dissipated. Atmospheres possessing temperature inversions tend to dissipate most of the Ohmic power superficially, at high altitudes, whereas those without temperature inversions are capable of greater dissipation deeper down. Scattering in the optical range of wavelengths tends to cool the lower atmosphere, thus reducing the degree of dissipation at depth. Purely absorbing cloud decks (in the infrared), of a finite extent in height, allow for localized reductions in dissipation and may reverse a temperature inversion if they are dense and thick enough, thus greatly enhancing the dissipation at depth. If Ohmic dissipation is the mechanism for inflating hot Jupiters, then variations in the atmospheric opacity (which may be interpreted as arising from variations in metallicity and cloud/haze properties) and magnetic field strength naturally produce a scatter in the measured radii at a given strength of irradiation. Future work will determine if these effects are dominant over evolutionary effects, which also contribute a scatter to the measured radii.