Probabilistic Mass–radius Relationship for Sub-Neptune-Sized Planets

Abstract

The Kepler Mission has discovered thousands of planets with radii <4 Å R , 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-toNeptune size range where there are no Solar System analogs. Previous works have derived deterministic, one-toone 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 Å M 1.9 , 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 (R pl < 4 Å R ). More broadly, this work provides a framework for further analyses of the M-R relation and its probable dependencies on period and stellar properties.

Probabilistic Constraints on the Mass and Composition of Proxima b

“…Bottom: mass-radius relationships for the rocky (blue) and sub-Neptune (red) populations. The plotted relationships are from Wolfgang et al (2016;solid) and Weiss & Marcy (2014;dashed). sample of 65 transiting exoplanets, in which they find evidence for the two populations discussed in Section 2.3. Through leastsquares regression, they find the densities of the rocky planets to increase linearly with planet radius:…”

“…Wolfgang et al (2016) suggest a spread of ±1.9 M ⊕ for the sub-Neptune planets, which we adopt for our simulations. For rocky planets, the spread is noticeably smaller.…”

“…Since mass-radius relationships typically find a strong dependence of mass on radius (M∝R 3-4 ; e.g., Weiss & Marcy 2014;Wolfgang et al 2016), we assume a priori that Proximab (M1.3 M ⊕ ) is larger than 0.7 R ⊕ . Therefore, for this Letter we adopt the regression curve fitted to the binned data, but set the occurrence rates to be flat for R<1 R ⊕ .…”

“…4 E P P 0.63 Wolfgang et al (2016) use an expanded version of this data set to fit power-law M-R relationships using a more statistically robust Bayesian method. For the rocky planets, they find…”

Dynamical rearrangement of super-Earths during disk dispersal

“…The observed systems are selected from the NASA Exoplanet Archive (http://exoplanetarchive.ipac.caltech.edu/), their planet masses are obtained from Wolfgang et al (2016)'s mass-radius relationship (their Eq (1)):…”