Efficient fitting of multiplanet Keplerian models to radial velocity and astrometry data
- Creators
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Wright, J. T.
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Howard, A. W.
Abstract
We describe a technique for solving for the orbital elements of multiple planets from radial velocity (RV) and/or astrometric data taken with 1 m s^(–1) and μas precision, appropriate for efforts to detect Earth-massed planets in their stars' habitable zones, such as NASA's proposed Space Interferometry Mission. We include details of calculating analytic derivatives for use in the Levenberg-Marquardt (LM) algorithm for the problems of fitting RV and astrometric data separately and jointly. We also explicate the general method of separating the linear and nonlinear components of a model fit in the context of an LM fit, show how explicit derivatives can be calculated in such a model, and demonstrate the speed up and convergence improvements of such a scheme in the case of a five-planet fit to published RV data for 55 Cnc.
Additional Information
© 2009 The American Astronomical Society. Received 2008 October 14; accepted 2009 March 24; published 2009 April 30. Our membership on a SIM Planet-Finding Astrometry Analysis Team (P.I.: Matthew Muterspaugh) motivated Sections 3 and 4 of this work, and we are grateful to all of the teams involved for their efforts and insights into the problem. We thank Jeff Valenti and Nikolai Piskunov for encouraging us to calculate the explicit derivatives for a general linear least-squares problem. Nikolai Piskunov provided insight into the sources of instability in the LM search algorithm. Matthew Muterspaugh provided guidance with the problem of fitting astrometric orbits and understanding the small astrometric cross terms. We thank Martin Sirk, Sam Halverson, and John Asher Johnson for their work employing and debugging various versions of our code. J.T.W. received support from NSF grant AST-0504874, and A.W.H. received support from NASA contract NAS7-03001 (JPL#1336910).Attached Files
Published - Wright_2009_ApJS_182_205.pdf
Submitted - 0904.3725.pdf
Erratum - Wright_2013_ApJS_205_22.pdf
Files
Additional details
- Eprint ID
- 78418
- Resolver ID
- CaltechAUTHORS:20170621-123635345
- AST-0504874
- NSF
- NAS7-03001
- NASA
- 1336910
- JPL
- Created
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2017-06-21Created from EPrint's datestamp field
- Updated
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2023-06-01Created from EPrint's last_modified field