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

Wolfgang, Angie and Rogers, Leslie A. and Ford, Eric B. (2016) Probabilistic Mass-Radius Relationship for Sub-Neptune-Sized Planets. Astrophysical Journal, 825 (1). Art. No. 19. ISSN 0004-637X. https://resolver.caltech.edu/CaltechAUTHORS:20160930-144349040

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Abstract

The Kepler Mission has discovered thousands of planets with radii <4 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-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 M/M_⨁ = 2.7(R/R_⨁)^(1.3), a scatter in mass of 1.9M_⨁, 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 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.3847/0004-637X/825/1/19DOIArticle
http://iopscience.iop.org/article/10.3847/0004-637X/825/1/19/metaPublisherArticle
https://arxiv.org/abs/1504.07557arXivDiscussion Paper
ORCID:
AuthorORCID
Rogers, Leslie A.0000-0003-0638-3455
Ford, Eric B.0000-0001-6545-639X
Additional Information:© 2016 American Astronomical Society. Received 2015 April 27; revised 2016 April 14; accepted 2016 April 28; published 2016 June 27. We thank Tom Loredo for lending his statistical expertise to the first version of this paper, which has facilitated increased clarity on some of the technical details of our modeling. We also thank the anonymous referee for suggesting additional points of discussion to provide crucial context to this work. This material was based upon work partially supported by the National Science Foundation under Grant DMS-1127914 to the Statistical and Applied Mathematical Sciences Institute, which organized a 3 week workshop on the Statistical Analysis of Kepler data during which the authors developed a preliminary hierarchical Bayesian model for this problem. This research was also supported in part by the NSF Grant No. PHY11-25915 to the UCSB Kavli Institute for Theoretical Physics, which brought together the authors for final work on this project during its Dynamics and Evolution of Earth-like Planets program. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. AW's financial support during this investigation was primarily provided by the National Science Foundation Graduate Research Fellowship under Grant No. 0809125, the UCSC Graduate Division's Eugene Cota-Robles Fellowship, with support during the referee process by the National Science Foundation under Award No. 1501440. LAR gratefully acknowledges support provided by NASA through Hubble Fellowship grant #HF-51313 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. EBF was supported in part by NASA Kepler Participating Scientist Program awards NNX12AF73G & NNX14AN76G, NASA Origins of Solar Systems awards NNX13AF61G & NNX14AI76G, and NASA Exoplanet Research Program award NNX15AE21G. 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: Kepler - The Kepler Mission.
Funders:
Funding AgencyGrant Number
NSFDMS-1127914
NSFPHY11-25915
NSF Graduate Research FellowshipDGE-0809125
University of California Santa CruzUNSPECIFIED
NSFAST-1501440
NASA Hubble FellowshipHF-51313
NASANAS 5-26555
NASANNX12AF73G
NASANNX14AN76G
NASANNX13AF61G
NASANNX14AI76G
NASANNX15AE21G
Pennsylvania State UniversityUNSPECIFIED
Pennsylvania Space Grant ConsortiumUNSPECIFIED
NASA/JPL/CaltechUNSPECIFIED
Subject Keywords:methods: statistical; planets and satellites: composition
Issue or Number:1
Record Number:CaltechAUTHORS:20160930-144349040
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160930-144349040
Official Citation:Angie Wolfgang et al 2016 ApJ 825 19
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:70714
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:03 Oct 2016 17:15
Last Modified:09 Mar 2020 13:18

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