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Sensitivity Analyses of Exoplanet Occurrence Rates from Kepler and Gaia

Shabram, Megan I. and Batalha, Natalie and Thompson, Susan E. and Hsu, Danley C. and Ford, Eric B. and Christiansen, Jessie L. and Huber, Daniel and Berger, Travis and Catanzarite, Joseph and Nelson, Benjamin E. and Bryson, Steve and Belikov, Ruslan and Burke, Chris and Caldwell, Doug (2020) Sensitivity Analyses of Exoplanet Occurrence Rates from Kepler and Gaia. Astronomical Journal, 160 (1). Art. No. 16. ISSN 1538-3881.

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We infer the number of planets per star as a function of orbital period and planet size using Kepler archival data products with updated stellar properties from the Gaia Data Release 2. Using hierarchical Bayesian modeling and Hamiltonian Monte Carlo, we incorporate planet radius uncertainties into an inhomogeneous Poisson point process model. We demonstrate that this model captures the general features of the outcome of the planet formation and evolution around GK stars and provides an infrastructure to use the Kepler results to constrain analytic planet distribution models. We report an increased mean and variance in the marginal posterior distributions for the number of planets per GK star when including planet radius measurement uncertainties. We estimate the number of planets per GK star between 0.75 and 2.5 R⊕ and with orbital periods of 50–300 days to have a 68% credible interval of 0.49–0.77 and a posterior mean of 0.63. This posterior has a smaller mean and a larger variance than the occurrence rate calculated in this work and in Burke et al. for the same parameter space using the Q1−Q16 (previous Kepler planet candidate and stellar catalog). We attribute the smaller mean to many of the instrumental false positives at longer orbital periods being removed from the DR25 catalog. We find that the accuracy and precision of our hierarchical Bayesian model posterior distributions are less sensitive to the total number of planets in the sample, and more so for the characteristics of the catalog completeness and reliability and the span of the planet parameter space.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Shabram, Megan I.0000-0003-1179-3125
Batalha, Natalie0000-0002-7030-9519
Thompson, Susan E.0000-0001-7106-4683
Hsu, Danley C.0000-0003-3447-1890
Ford, Eric B.0000-0001-6545-639X
Christiansen, Jessie L.0000-0002-8035-4778
Huber, Daniel0000-0001-8832-4488
Berger, Travis0000-0002-2580-3614
Bryson, Steve0000-0003-0081-1797
Burke, Chris0000-0002-7754-9486
Caldwell, Doug0000-0003-1963-9616
Additional Information:© 2020 The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 2018 September 12; revised 2020 April 20; accepted 2020 May 5; published 2020 June 12. Shabram's research is supported by an appointment to the NASA Postdoctoral Program at the NASA Ames Research Center, administered by Universities Space Research Association under contract with NASA. This manuscript benefited from discussions at the Stanford Stan User's Group. This work benefited from Dan Foreman-Mackey's blog post regarding an experiment in open science for Kepler exoplanet occurrence rates. This work makes use of the Stan open-source Bayesian modeling language, Jupyter, and Python software including the SciPy ecosystem and Seaborn. E.B.F. and D.C.H. acknowledge the Penn State Center for Astrostatistics and Center for Exoplanets and Habitable Worlds, which is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. Computations for this research were performed on the Pennsylvania State University's Institute for CyberScience Advanced CyberInfrastructure (ICS-ACI). E.B.F. acknowledges support from NASA Exoplanets Research Program award No. NNX15AE21G. This work was partially supported by the NSF grant DMS 1127914 to the Statistical and Applied Mathematical Sciences Institute (SAMSI). The results reported herein benefitted from collaborations and/or information exchange within NASA's Nexus for Exoplanet System Science (NExSS) research coordination network sponsored by NASA's Science Mission Directorate. T.A.B. and D.H. acknowledge support by the National Science Foundation (AST-1717000) and the National Aeronautics and Space Administration under grants NNX14AB92G and NNX16AH45G. Software: Stan (Carpenter et al. 2017), SciPy (Jones et al. 2001), Seaborn (Waskom et al. 2017), Jupyter (Kluyver et al. 2016).
Group:Infrared Processing and Analysis Center (IPAC)
Funding AgencyGrant Number
NASA Postdoctoral ProgramUNSPECIFIED
Pennsylvania State UniversityUNSPECIFIED
Eberly College of ScienceUNSPECIFIED
Pennsylvania Space Grant ConsortiumUNSPECIFIED
Subject Keywords:Exoplanets; Exoplanet catalogs; Transit photometry; Bayesian statistics; Astrostatistics
Issue or Number:1
Classification Code:Exoplanets (498); Exoplanet catalogs (488); Transit photometry (1709); Bayesian statistics (1900); Astrostatistics (1882)
Record Number:CaltechAUTHORS:20200710-130949426
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Official Citation:Megan I. Shabram et al 2020 AJ 160 16
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104331
Deposited By: Tony Diaz
Deposited On:10 Jul 2020 22:40
Last Modified:10 Jul 2020 22:56

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