A finite strain approach to thermal expansivity’s pressure dependence

George Helffrich

doi:10.2138/am-2017-6007

Abstract

The pressure dependence of thermal expansivity affects mineral density at pressure and is an extrapolator for calculating self-compression adiabats of a self-gravitating body. I review different models for the pressure dependence of expansivity and how to decide which performs best. A finite strain model, proposed here, performs better when used to calculate adiabatic temperature lapses in both the solid silicate and liquid metal parts of a planet than either an ad-hoc exponential dependence on pressure or a commonly used mineral physics model. Choosing a particular thermal expansivity pressure dependence leads to significantly different temperatures in planetary interiors, and to inferred subsolidus properties related to homologous melting temperature. In particular, thermal expansivity in liquid metal in planetary cores at pressures comparable to Earth’s core is significantly affected. The universality of the parameterization provides a simple way to model rocky planet interiors in our solar system and exoplanet interiors.

Highlights

Planetary accretion is the process by which a planet grows from a nucleation site in the nebular dust and gas disk surrounding a young star into a self-gravitating body in orbit around the star
The simplest formulas do not decrease fast enough through the mantle and core range of f to reproduce the tabulated decreases compiled from geophysical sources (Stacey 1992)
The a models explored here focused on three aspects of the resulting adiabatic profiles: (1) their convexity; (2) their temperature lapse; and (3) their approximation to the known density profile of the Earth

Summary

Introduction

Planetary accretion is the process by which a planet grows from a nucleation site in the nebular dust and gas disk surrounding a young star into a self-gravitating body in orbit around the star. After planets grow sufficiently large to differentiate, solid-state convection in the silicate mantle and liquid state convection in the metallic cores govern the thermal structure (Breuer et al 2010). These are essentially adiabatic temperature profiles set by the conditions at the convective boundary layers (the surface or the core-mantle boundary).

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