paper

Probabilistic Mass-Radius Relationship for Sub-Neptune-Sized Planets

arXiv:1504.07557 · doi:10.3847/0004-637X/825/1/19

Abstract

The Kepler Mission has discovered thousands of planets with radii , paving the way for the first statistical studies of the dynamics, formation, and evolution of these sub-Neptunes and super-Earths. Planetary masses are an important physical property for these studies, and yet the vast majority of Kepler planet candidates do not have theirs measured. A key concern is therefore how to map the measured radii to mass estimates in this Earth-to-Neptune size range where there are no Solar System analogs. Previous works have derived deterministic, one-to-one relationships between radius and mass. However, if these planets span a range of compositions as expected, then an intrinsic scatter about this relationship must exist in the population. Here we present the first probabilistic mass-radius relationship (M-R relation) evaluated within a Bayesian framework, which both quantifies this intrinsic dispersion and the uncertainties on the M-R relation parameters. We analyze how the results depend on the radius range of the sample, and on how the masses were measured. Assuming that the M-R relation can be described as a power law with a dispersion that is constant and normally distributed, we find that , a scatter in mass of , and a mass constraint to physically plausible densities, is the "best-fit" probabilistic M-R relation for the sample of RV-measured transiting sub-Neptunes (). More broadly, this work provides a framework for further analyses of the M-R relation and its probable dependencies on period and stellar properties.

14 pages, 5 figures, 2 tables. Accepted to the Astrophysical Journal on April 28, 2016. Select posterior samples and code to use them to compute the posterior predictive mass distribution are available at https://github.com/dawolfgang/MRrelation

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