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

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.

32 pages, 15 figures

References in corpus (5)

• Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core
• New models of Jupiter in the context of Juno and Galileo
• A new equation of state for dense hydrogen-helium mixtures
• Effect of Non-Adiabatic Thermal Profiles on the Inferred Compositions of Uranus and Neptune
• Empirical Models of Pressure and Density in Saturn's Interior: Implications for the Helium Concentration, its Depth Dependence, and Saturn's Precession Rate