Predicting Exoplanet Masses and Radii: A Nonparametric Approach

Abstract

A fundamental endeavor in exoplanetary research is to characterize the bulk compositions of planets via measurements of their masses and radii. With future sample sizes of hundreds of planets to come from TESS and PLATO, we develop a statistical method that can flexibly yet robustly characterize these compositions empirically, via the exoplanet M–R relation. Although the M–R relation has been explored in many prior works, they mostly use a power-law model, with assumptions that are not flexible enough to capture important features in current and future M–R diagrams. To address these shortcomings, a nonparametric approach is developed using a sequence of Bernstein polynomials. We demonstrate the benefit of taking the nonparametric approach by benchmarking our findings with previous work and showing that a power law can only reasonably describe the M–R relation of the smallest planets and that the intrinsic scatter can change non-monotonically with different values of a radius. We then apply this method to a larger data set, consisting of all the Kepler observations in the NASA Exoplanet Archive. Our nonparametric approach provides a tool to estimate the M–R relation by incorporating heteroskedastic measurement errors into the model. As more observations will be obtained in the near future, this approach can be used with the provided R code to analyze a larger data set for a better understanding of the M–R relation.

A Joint Mass–Radius–Period Distribution of Exoplanets

“…This low value for the low mass break is below most planets in the sample, perhaps indicating weak support for including this break based on the CKS sample. This is supported by the nonparametric mass-radius relation fit by Ning et al (2018), which found no evidence for a low mass break in the mass-radius relation with the current mass-radius sample. The scatter parameters σ 0 , σ 1 , σ 2 that we retrieve are higher across the board (0.07 +0.02 −0.01 vs 0.04 +0.01 −0.01 , 0.27 +0.03 −0.03 vs 0.15 +0.02 −0.01 , and 0.11 +0.03 −0.02 vs 0.07 +0.01 −0.01 , respectively).…”

Four Newborn Planets Transiting the Young Solar Analog V1298 Tau

“…Assuming that the V1298 Tau planets will follow the mature exoplanet mass-radius relation of Chen & Kipping (2017) in the future, we calculated the expected final radii to estimate that the planets might contract by 40-90% (68% confidence interval) over the subsequent evolution of the system. These results are not changed significantly when adopting the nonparametric mass-radius relation of Ning et al (2018).…”

No Evidence for Lunar Transit in New Analysis of Hubble Space Telescope Observations of the Kepler-1625 System

“…The planet transit time was uniform over the timespan of the observations, and inclination was uniform from 0 − 90 • . The planet mass was log-normally distributed, M p ∼ 10 2.5±0.5 M ⊕ , based on the expectation for Jupiter-radius objects from Ning et al (2018). For the moon model, we allowed the transit time to vary uniformly over the entire visit.…”