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Improving Orbit Estimates for Incomplete Orbits with a New Approach to Priors: with Applications from Black Holes to Planets

O’Neil, K. Kosmo and Martinez, G. D. and Hees, A. and Ghez, A. M. and Do, T. and Witzel, G. and Konopacky, Q. and Becklin, E. E. and Chu, D. S. and Lu, J. R. and Matthews, K. and Sakai, S. (2019) Improving Orbit Estimates for Incomplete Orbits with a New Approach to Priors: with Applications from Black Holes to Planets. Astronomical Journal, 158 (1). Art. No. 4. ISSN 1538-3881.

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We propose a new approach to Bayesian prior probability distributions (priors) that can improve orbital solutions for low-phase-coverage orbits, where data cover less than ~40% of an orbit. In instances of low phase coverage—such as with stellar orbits in the Galactic center or with directly imaged exoplanets—data have low constraining power and thus priors can bias parameter estimates and produce underestimated confidence intervals. Uniform priors, which are commonly assumed in orbit fitting, are notorious for this. We propose a new observable-based prior paradigm that is based on uniformity in observables. We compare performance of this observable-based prior and of commonly assumed uniform priors using Galactic center and directly imaged exoplanet (HR 8799) data. The observable-based prior can reduce biases in model parameters by a factor of two and helps avoid underestimation of confidence intervals for simulations with less than ~40% phase coverage. Above this threshold, orbital solutions for objects with sufficient phase coverage—such as S0-2, a short-period star at the Galactic center with full phase coverage—are consistent with previously published results. Below this threshold, the observable-based prior limits prior influence in regions of prior dominance and increases data influence. Using the observable-based prior, HR 8799 orbital analyses favor low-eccentricity orbits and provide stronger evidence that the four planets have a consistent inclination of ~30° to within 1σ. This analysis also allows for the possibility of coplanarity. We present metrics to quantify improvements in orbital estimates with different priors so that observable-based prior frameworks can be tested and implemented for other low-phase-coverage orbits.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
O’Neil, K. Kosmo0000-0003-2400-7322
Martinez, G. D.0000-0002-7476-2521
Hees, A.0000-0002-2186-644X
Ghez, A. M.0000-0003-3230-5055
Do, T.0000-0001-9554-6062
Witzel, G.0000-0003-2618-797X
Konopacky, Q.0000-0002-9936-6285
Chu, D. S.0000-0003-3765-8001
Lu, J. R.0000-0001-9611-0009
Sakai, S.0000-0001-5972-663X
Additional Information:© 2019 The American Astronomical Society. Received 2018 September 14; revised 2019 March 22; accepted 2019 April 14; published 2019 June 7. We thank the staff of the Keck Observatory, especially Randy Campbell, Jason Chin, Scott Dahm, Heather Hershey, Carolyn Jordan, Marc Kassis, Jim Lyke, Gary Puniwai, Julie Renaud-Kim, Luca Rizzi, Terry Stickel, Hien Tran, Peter Wizinowich, and former director Taft Armandroff for all their help in obtaining observations. We also thank Dimitrios Psaltis, Eric B. Ford, and David W. Hogg for their feedback and contributions. Support for this work at UCLA was provided by the W. M. Keck Foundation, NSF grant AST-1412615, and the Preston Graduate Fellowship. The W. M. Keck Observatory is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.
Funding AgencyGrant Number
W. M. Keck FoundationUNSPECIFIED
Preston Graduate FellowshipUNSPECIFIED
Subject Keywords:Galaxy: center – Galaxy: fundamental parameters – methods: statistical – planets and satellites: fundamental parameters
Issue or Number:1
Record Number:CaltechAUTHORS:20190607-132725628
Persistent URL:
Official Citation:K. Kosmo O'Neil et al 2019 AJ 158 4
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96206
Deposited By: Tony Diaz
Deposited On:07 Jun 2019 21:20
Last Modified:14 Oct 2019 22:17

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