Probabilistic MassRadius Relationship for SubNeptuneSized Planets
Abstract
The Kepler Mission has discovered thousands of planets with radii <4 {R}_{\oplus }, paving the way for the first statistical studies of the dynamics, formation, and evolution of these subNeptunes and superEarths. 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 EarthtoNeptune size range where there are no Solar System analogs. Previous works have derived deterministic, onetoone 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 massradius relationship (MR relation) evaluated within a Bayesian framework, which both quantifies this intrinsic dispersion and the uncertainties on the MR 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 MR relation can be described as a power law with a dispersion that is constant and normally distributed, we find that M/{M}_{\oplus }=2.7{(R/{R}_{\oplus })}^{1.3}, a scatter in mass of 1.9{M}_{\oplus }, and a mass constraint to physically plausible densities, is the “bestfit” probabilistic MR relation for the sample of RVmeasured transiting subNeptunes (R _{pl} < 4 {R}_{\oplus }). More broadly, this work provides a framework for further analyses of the MR relation and its probable dependencies on period and stellar properties.
 Publication:

The Astrophysical Journal
 Pub Date:
 July 2016
 DOI:
 10.3847/0004637X/825/1/19
 arXiv:
 arXiv:1504.07557
 Bibcode:
 2016ApJ...825...19W
 Keywords:

 methods: statistical;
 planets and satellites: composition;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 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