A hardcore model for constraining an exoplanet's core size

Abstract

The interior structure of an exoplanet is hidden from direct view yet likely plays a crucial role in influencing the habitability of Earth analogs. Inferences of the interior structure are impeded by a fundamental degeneracy that exists between any model comprising of more than two layers and observations constraining just two bulk parameters: mass and radius. In this work, we show that although the inverse problem is indeed degenerate, there exists two boundary conditions that enables one to infer the minimum and maximum core radius fraction, CRF min & CRF max . These hold true even for planets with light volatile envelopes, but require the planet to be fully differentiated and that layers denser than iron are forbidden. With both bounds in hand, a marginal CRF can also be inferred by sampling inbetween. After validating on the Earth, we apply our method to Kepler-36b and measure CRF min = (0.50 ± 0.07), CRF max = (0.78±0.02) and CRF marg = (0.64±0.11), broadly consistent with the Earth's true CRF value of 0.55. We apply our method to a suite of hypothetical measurements of synthetic planets to serve as a sensitivity analysis. We find that CRF min & CRF max have recovered uncertainties proportional to the relative error on the planetary density, but CRF marg saturates to between 0.03 to 0.16 once (∆ρ/ρ) drops below 1-2%. This implies that mass and radius alone cannot provide any better constraints on internal composition once bulk density constraints hit around a percent, providing a clear target for observers.

Precise mass and radius of a transiting super-Earth planet orbiting the M dwarf TOI-1235: a planet in the radius gap?

“…Based again on the mass and radius relationships from Zeng et al ( 2016), the best fit results in an iron core mass fraction of CRF = 0.10 +0.38 −0.10 , but the planet is also consistent with an Earthlike bulk composition (CRF ≈ 0.4-0.6). Furthermore, using Hardcore (Suissa et al 2018) and our R and M, the marginal core ratio fraction, CRF marg , is 0.53 ± 0.20, similar to the Earth's true CRF value of 0.55.…”

The GALAH Survey: using galactic archaeology to refine our knowledge of TESS target stars

“…A fundamental problem with inferring planetary compositions through mass-radius or ternary/quaternary diagrams (Rogers & Seager 2010;Brugger et al 2017) is that they cannot uniquely predict the interior composition of a given exoplanet. A variety of different interior compositions can lead to identical mass and radius values (Dorn et al 2015;Unterborn et al 2016;Suissa et al 2018;Unterborn & Panero 2019). This gives rise to an inherent density degeneracy problem.…”

“…Whilst the bulk density of a planet does provide clues to its potential bulk composition, it does not provide enough information for us to determine the geological structure of a potentially rocky planet, or to precisely determine its true composition. This is clearly illustrated by the work of Suissa, Chen & Kipping (2018), who demonstrate that a newly discovered 'Earth-like' planet (a planet observed to be both the same mass and the same size as the Earth; i.e. 1M ⊕ , 1R ⊕ ) could have a wide variety of internal compositions.…”

A fuzzy Multi-Criteria Decision Making approach for Exo-Planetary Habitability

“…However, water-rich rocky exoplanets need three basic components to explain their internal structure: iron in the core, silicates in the mantle, and water usually forming an outer layer of ice. In this case, for a given mass and radius, the theoretical models provide infinite internal structure solutions all compatible with those mass and radius values (Suissa et al, 2018;Zeng & Sasselov, 2013).…”

“…This would be the case for the inner planets of the solar system such as Mercury, Venus, Earth and Mars. When there are only two basic constituents, for a given planetary mass and radius, the theoretical models provide a unique solution for its internal structure (Suissa et al, 2018;Zeng & Sasselov, 2013).…”