Ohmic Dissipation in Mini-Neptunes

In the presence of a magnetic field and weakly ionizing winds, ohmic dissipation is expected to take place in the envelopes of Jovian and lower-mass planets alike. While the process has been investigated on the former, there have been no studies done on mini-Neptunes so far. From structure and thermal evolution models, we determine that the required energy deposition for halting the contraction of mini-Neptunes increases with planetary mass and envelope fraction. Scaled to the insolation power, the ohmic heating needed is small $\sim10^{-5}$ -- orders of magnitude lower than for exo-Jupiters $\sim 10^{-2}$. Conversely, from solving the magnetic induction equation, we find that ohmic energy is dissipated more readily for lower-mass planets and those with larger envelope fractions. Combining these two trends, we find that ohmic dissipation in hot mini-Neptunes is strong enough to inflate their radii ($\sim 10^{15}$ W for $T_{eq}=1400K$). The implication is that the radii of hot mini-Neptunes may be attributed in part to ohmic heating. Thus, there is a trade-off between ohmic dissipation and H/He content for hot mini-Neptunes, adding a new degeneracy for the interpretation of the composition of such planets. In addition, ohmic dissipation would make mini-Neptunes more vulnerable to atmospheric evaporation.