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 , \mathrm { CRF } _ { \mathrm { min } } & \mathrm { CRF } _ { \mathrm { 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 \mathrm { CRF } _ { \mathrm { min } } = ( 0.50 \pm 0.07 ) , \mathrm { CRF } _ { \mathrm { max } } = ( 0.78 \pm 0.02 ) and \mathrm { CRF } _ { \mathrm { marg } } = ( 0.64 \pm 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 \mathrm { CRF } _ { \mathrm { min } } & \mathrm { CRF } _ { \mathrm { max } } have recovered uncertainties proportional to the relative error on the planetary density , but \mathrm { CRF } _ { \mathrm { marg } } saturates to between 0.03 to 0.16 once ( \Delta \rho / \rho ) drops below 1-2 % .
This implies that mass and radius alone can not provide any better constraints on internal composition once bulk density constraints hit around a percent , providing a clear target for observers .