TY - JOUR
T1 - Predicting Exoplanet Masses and Radii
T2 - A Nonparametric Approach
AU - Ning, Bo
AU - Wolfgang, Angie
AU - Ghosh, Sujit
N1 - Funding Information:
The authors thank the Statistical and Applied Mathematical Sciences Institute (SAMSI) for bringing the authors together and providing space and funding for continued collaborations. The authors also thank Tom Loredo and Eric Ford for their valuable suggestions on this work while it was in development at SAMSI, Eric Ford for providing detailed revisions on the first version of the manuscript, Shubham Kanodia and Gudmundur Stefansson for their work in translating the R code into Python, and Matthias Yang He and Eric Ford for their work in testing the number of effective nonzero weights while translating the code into Julia. Furthermore, the authors thank the two referees who provided valuable suggestions to improve the paper. This material was based on work partially supported by the National Science Foundation under Grant DMS-1127914 to the Statistical and Applied Mathematical Sciences Institute. A.W. acknowledges support from the National Science Foundation Astronomy & Astrophysics Postdoctoral Fellowship program under Award No. 1501440. The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. Facility: NASA Exoplanet Archive. Software: R and python.
Publisher Copyright:
© 2018. The American Astronomical Society. All rights reserved.
PY - 2018/12/10
Y1 - 2018/12/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85058468084&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85058468084&partnerID=8YFLogxK
U2 - 10.3847/1538-4357/aaeb31
DO - 10.3847/1538-4357/aaeb31
M3 - Article
AN - SCOPUS:85058468084
VL - 869
JO - Astrophysical Journal
JF - Astrophysical Journal
SN - 0004-637X
IS - 1
M1 - 5
ER -