Constraining the Depth of the Winds on Uranus and Neptune via Ohmic Dissipation

TL;DR

This paper constrains the maximum depth of atmospheric winds on Uranus and Neptune by analyzing Ohmic dissipation, linking electrical conductivity profiles to interior structure models, and providing upper bounds on wind penetration depths.

Contribution

It introduces a method to calculate electrical conductivity profiles using ab initio simulations and applies it to ice giant models to estimate wind depth limits.

Findings

Maximum wind penetration depth on Uranus above 0.93R_U

Maximum wind penetration depth on Neptune above 0.95R_N

Higher water abundance leads to shallower wind limits

Abstract

Determining the depth of atmospheric winds in the outer planets of the Solar System is a key topic in planetary science. We provide constraints on these depths in Uranus and Neptune via the total induced Ohmic dissipation, due to the interaction of the zonal flows and the planetary magnetic fields. An upper bound can be placed on the induced dissipation via energy and entropy flux throughout the interior. The induced Ohmic dissipation is directly linked to the electrical conductivity profile of the materials involved in the flow. We present a method for calculating electrical conductivity profiles of ionically conducting hydrogen-helium-water mixtures under planetary conditions, using results from ab initio simulations. We apply this prescription on several ice giant interior structure models available in the literature, where all the heavy elements are represented by water. According to the energy (entropy) flux budget, the maximum penetration depth for Uranus lies above $0.93R_{\mathrm{\scriptscriptstyle{U}}}$ ($0.90R_{\mathrm{\scriptscriptstyle{U}}}$) and for Neptune above $0.95R_{\mathrm{\scriptscriptstyle{N}}}$ ($0.92R_{\mathrm{\scriptscriptstyle{N}}}$). These results for the penetration depths are upper bounds, and are consistent with previous estimates based on the contribution of the zonal winds to the gravity field. As expected, interior structure models with higher water abundance in the outer regions have also a higher electrical conductivity and therefore reach the Ohmic limit at shallower regions. Thus, our study shows that the likelihood of deep-seated winds on Uranus and Neptune drops significantly with the presence of water in the outer layers.