A HARDCORE model for constraining an exoplanet's core size

TL;DR

This paper introduces a method to constrain the core size of exoplanets using boundary conditions, enabling estimation of minimum and maximum core radius fractions despite degeneracies in interior structure models.

Contribution

The authors develop a boundary-condition-based approach to infer core size bounds of exoplanets from mass and radius data, even with light volatile envelopes.

Findings

CRFmin and CRFmax bounds are valid for differentiated planets.

Applying the method to Kepler-36b yields core radius fractions consistent with Earth's.

Uncertainty in core size estimates depends on measurement precision of planetary density.

Abstract

The interior structure of an exoplanet is hidden from direct view yet likely plays a crucial role in influencing the habitability of the Earth analogues. Inferences of the interior structure are impeded by a fundamental degeneracy that exists between any model comprising 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, CRFmin and CRFmax. 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 in-between. After validating on the Earth, we apply our method to Kepler-36b and measure CRFmin = (0.50 +/- 0.07), CRFmax = (0.78 +/- 0.02), and CRFmarg = (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 CRFmin and CRFmax have recovered uncertainties proportional to the relative error on the planetary density, but CRFmarg saturates to between 0.03 and 0.16 once delta rho/rho drops below 1-2 per cent. This implies that mass and radius alone cannot provide any better constraints on internal composition once bulk density constraints hit around a per cent, providing a clear target for observers.