Random Models for Exploring Planet Compositions I: Uranus as an Example

TL;DR

This paper introduces a method to generate random interior models of planets, like Uranus, to explore possible compositions and structures without strict formation assumptions, aiding understanding of planetary formation clues.

Contribution

The authors present a novel code that generates random, monotonic density and temperature distributions consistent with planetary data, enabling exploration of interior structures without fixed formation constraints.

Findings

The code can produce diverse interior models fitting Uranus's observed parameters.

The rock-to-water ratio in Uranus is constrained to be less than about 2.

The approach helps identify necessary cosmogonic constraints for planetary modeling.

Abstract

Modeling the interior of a planet is difficult because the small number of measured parameters is insufficient to constrain the many variables involved in describing the interior structure and composition. One solution is to invoke additional constraints based on arguments about how the planet formed. However, a planet's actual structure and composition may hold clues to its formation which would be lost if this structure were not allowed by the initial assumptions. It is therefore interesting to explore the space of allowable compositions and structures in order to better understand which cosmogonic constraints are absolutely necessary. To this end, we describe a code for generating random, monotonic, density distributions, rho(r), that fit a given mass, radius, and moment of inertia. Integrating the equation of hydrostatic equilibrium gives the pressure, P(r), at each point in the body. We then provide three algorithms for generating a monotonic temperature distribution, T(r), and an associated composition that is consistent with the rho-P relation, and realistic equations of state. We apply this code to Uranus as a proof of concept, and show that the ratio of rock to water cannot be much larger than 2.