Exoplanet Mass-Radius Relations Verified by the Solar System

Abstract

Understanding a planet's composition is necessary to understand its habitability. Inferring a planet's composition solely from observations of mass and radii requires the construction of planetary interior structure models. We present a new planetary interior structure model that includes significant physics excluded from previous models, such as the coexistence of many chemical species within the mantle, high pressure phase transitions of mantle materials, light elements within the planetary core and partitioning between the solid and liquid core, radiative transfer in the upper atmosphere, a prescription to calculate planetary transit radii rather than radii at a particular pressure, and more. We validate our resultant interior structure model by running forward models for the measured masses and compositions of Earth, Mars, the Moon, Venus, Mercury, and Europa. Our model produces radii and moment of inertia coefficients within 0.5% or 1 standard deviation of reality in all cases where the moment of inertia is well-constrained. In the case of a poorly-constrained moment of inertia, our model produces radii and moment of inertia coefficients within 1% or 3 standard deviations of reality. We present the resultant mass-radius curves between 0.01 and 100 Earth masses. We find that the radii of sub-Neptunes are consistent with planets made of either a few % H/He or 10s of % water, with surface temperature also playing a crucial factor. We find radii for pure Fe planets significantly systematically lower than much of the literature owing to our adoption of newer EOS. We fit power laws of the form M=R^X in a piecewise fashion with pieces being separated by changes in the state of the planetary interior: for a planet with Earth's composition, the solidification of the core at 2.25 Earth masses and onset of high pressure phases in the mantle at 3.41 Earth masses. At higher masses and core mass fractions, X becomes larger. The values of X for Earth-like and cold water worlds are within 1%. Previous values of X reported in the literature are only valid at masses below the solidification of the core.