Scaling the Earth: A Sensitivity Analysis of Terrestrial Exoplanetary Interior Models

Abstract

An exoplanet's structure and composition are first-order controls of the planet's habitability. We explore which aspects of bulk terrestrial planet composition and interior structure affect the chief observables of an exoplanet: its mass and radius. We apply these perturbations to the Earth, the planet we know best. Using the mineral physics toolkit BurnMan to self-consistently calculate mass-radius models, we find that core radius, presence of light elements in the core and an upper-mantle consisting of low-pressure silicates have the largest effect on the final calculated mass at a given radius, none of which are included in current mass-radius models. We expand these results provide a self-consistent grid of compositionally as well as structurally constrained terrestrial mass-radius models for quantifying the likelihood of exoplanets being "Earth-like." We further apply this grid to Kepler-36b, finding that it is only ∼20% likely to be structurally similar to the Earth with Si/Fe = 0.9 compared to Earth's Si/Fe = 1 and Sun's Si/Fe = 1.19.

The Pressure and Temperature Limits of Likely Rocky Exoplanets

“…Rocky planets that reflect their refractory stellar abundances and lack a significant volatile‐rich envelope with R ≤ 1.5 R ⊕ are limited in mass to 5 Earth masses for Fe/Mg < 1.5 and Si/Mg ∼ 1. Changing Si/Mg relative to Fe/Mg and variable mantle potential temperature will both have minimal impact on the mantle density within observational uncertainties, typically 20% in mass and 4% in radius (Dorn et al, ; Unterborn et al, ). We calculate that for planets smaller than 1.5 Earth radii, the CMB pressure is, to first order, a function planetary radius (equation ), reaching a maximum pressure of 630 GPa at 1.5 R ⊕ .…”

“…Our rocky exoplanetary modeling approach assuming pure solid iron cores leads to an upper bound in CMB pressure at a given Fe/Mg and Si/Mg. Those cores composed of liquid iron and/or containing light elements will have a lower density relative to ϵ ‐Fe used in our models (Schaefer et al, ; Unterborn et al, ). In the case of a liquid iron core without light elements, the CRF of a planet is negligibly larger compared to our models adopting a solid ϵ ‐Fe core (Unterborn et al, ).…”

“…Those cores composed of liquid iron and/or containing light elements will have a lower density relative to ϵ ‐Fe used in our models (Schaefer et al, ; Unterborn et al, ). In the case of a liquid iron core without light elements, the CRF of a planet is negligibly larger compared to our models adopting a solid ϵ ‐Fe core (Unterborn et al, ). However, in a planet with a core containing light elements, but with constant CMF, there will be an overall reduction in planet mass.…”

The structure of terrestrial bodies: Impact heating, corotation limits, and synestias

“…The composition of super‐Earths appears to span cool rocky bodies to partially gaseous bodies, with a possible composition transition around 1.5 R Earth [ Weiss and Marcy , ; Rogers , ]. However, the rocky portions of such planets have been assumed to have a high bulk density, based on the mass‐radius relationships for cold bodies [e.g., Zharkov and Trubitsyn , ; Valencia et al , ; Swift et al , ; Hubbard , ; Zeng and Sasselov , ; Zeng et al , ; Unterborn et al , ]. The equilibrium surface temperatures of exoplanets are generally higher than the terrestrial bodies in our solar system, and a few known cases are even hot enough to consider a surface with partially vaporized silicates (e.g., Kepler‐78b [ Sanchis‐Ojeda et al , ] and 55 Cancri e [ Demory et al , ]).…”

A Catalog of Stellar Unified Properties (CATSUP) for 951 FGK-Stars within 30 pc

“…To meaningfully constrain exoplanet compositions, one needs to distinguish a bulk density of 2 g cm −3 (like the densities of Ganymede and Titan, made of rock and ice per Showman & Malhotra 1999) from one of 5 g cm −3 (like the densities of Mercury, Venus, and Earth, with metal cores and rocky mantles per Wanke 1981). To measure density at this precision requires constraining planetary mass and radius, and therefore stellar mass and radius, to within about 10% (Unterborn et al 2016). In order to move beyond simple questions of whether a planet is rock with ice or rock with a large metal core, inclusion of elemental ratios, inferred from the host star, must be included.…”