The interior of Uranus

Thermal profile, bulk composition, and the distribution of rock, water, and hydrogen and helium

Department of Astrophysics, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland

^★ Corresponding author; luca.morf@uzh.ch

Received: 13 May 2024
Accepted: 16 August 2024

Abstract

We present improved empirical density profiles of Uranus and interpret them in terms of their temperature and composition using a new random algorithm. The algorithm to determine the temperature and composition is agnostic with respect to the temperature gradient in non-isentropic regions and chooses amongst all possible gradients randomly that are stable against convection and correspond to an Equation of State (EoS) compatible composition. Our empirical models are based on an efficient implementation of the Theory of Figures (ToF) up to tenth order including a proper treatment of the atmosphere. The accuracy of tenth order ToF enables us to present accurate calculations of the gravitational moments of Uranus up to J₁₄: J₆ = (5.3078 ± 0.3312) 10⁻⁷, J₈ = (−1.1114 ± 0.1391) 10⁻⁸, J₁₀ = (2.8616 ± 0.5466) 10⁻¹⁰, J₁₂ = (−8.4684 ± 2.0889) 10⁻¹², and J₁₄ = (2.7508 ± 0.7944) 10⁻¹³. We consider two interior models of Uranus that differ with respect to the maximal number of materials allowed per layer of Uranus (three versus four composition components). The case with three materials does not allow Hydrogen and Helium (H-He) in deeper parts of Uranus and results in a higher water (H₂O) abundance which leads to lower central temperatures. On the other hand, the models with four materials allow H-He to be mixed into the deeper interior and lead to rock-dominated solutions. We find that these four composition components’ models are less reliable due to the underlying empirical models’ incompatibility with realistic Brunt frequencies. Most of our models are found to be either purely convective with the exception of boundary layers, or only convective in the outermost region above ~80% of the planets’ radius r_U. Almost all of our models possess a region ranging between ~(0.75–0.9) r_U that is convective and consists of ionic H₂O which could explain the generation of Uranus’ magnetic field.