EFFICIENT FITTING OF MULTIPLANET KEPLERIAN MODELS TO RADIAL VELOCITY AND ASTROMETRY DATA

By Jason T. Wright, Andrew W. Howard. 2009

185 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Geophysics

View Paper: https://www.semanticscholar.org/paper/b8d8091ab152dc074e39d349e9c5c51734e6bca2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Timothy Morton
2. J. Johnson
3. Andrew W. Howard
4. G. Marcy
5. D. Charbonneau
6. B. Fulton
7. E. Petigura
8. M. Perryman

In Geophysics

1. B. Fulton
2. J. Wright
3. Jason Eastman
4. J. Johnson
5. Timothy Morton
6. E. Petigura
7. E. Sinukoff
8. J. Becker

Citations in the corpus

• Barycentric Corrections at 1 cm s-1 for Precise Doppler Velocities (2014, methodology): “They are now included as part of the EXOFAST package (Eastman et al. 2013)9 and can also be found at exoplanets.org10, along with the RVLIN (Wright & Howard 2009) and BOOTTRAN (Wang et al. 2012) orbit-fitting packages.”
• RETIRED A STARS AND THEIR COMPANIONS. III. COMPARING THE MASS–PERIOD DISTRIBUTIONS OF PLANETS AROUND A-TYPE STARS AND SUN-LIKE STARS (2009, methodology): “We derive Keplerian orbital solutions for the five previously-known planets in our sample using RVLIN, an efficient orbit-fitting routine written in IDL and based on a partial linearization of Kepler’s equations (Wright & Howard 2009).”
• ASTROMETRIC EXOPLANET DETECTION WITH GAIA (2014, background): “Combined observations therefore further constrain and improve the 3d orbit, as well as the individual component masses (e.g. Wright & Howard 2009).”
• Limits on Planetary Companions from Doppler Surveys of Nearby Stars (2016, methodology): “We fit models to the data using the Levenberg–Marquardt (L-M) χ2-minimization in the RV fitting package (RVLIN, Wright & Howard 2009).”
• RadVel: The Radial Velocity Modeling Toolkit (2018, methodology): “We employ modern Markov Chain Monte Carlo 1 a non-exhaustive list includes RVLIN (Wright & Howard 2009), Systemic (Meschiari et al. 2009; Meschiari & Laughlin 2010), EXOFAST (Eastman et al. 2013), rvfit (Iglesias-Marzoa et al. 2015), and ExoSOFT (Mede & Brandt 2017) (MCMC) sampling techniques and ro”
• CHARACTERIZING THE COOL KOIs. II. THE M DWARF KOI-254 AND ITS HOT JUPITER (2011, methodology): “For the RV data we fitted a Keplerian model using the partially linearized scheme of Wright & Howard (2009).”
• THE CALIFORNIA PLANET SURVEY. I. FOUR NEW GIANT EXOPLANETS (2010, methodology): “With the measured velocities for each star we performed a thorough search of the orbital parameter space for the best-fit, single-planet Keplerian orbital model using the partially-linearized, least-squares fitting procedure described in Wright & Howard (2009).”
• EXTRACTING RADIAL VELOCITIES OF A- AND B-TYPE STARS FROM ECHELLE SPECTROGRAPH CALIBRATION SPECTRA (2015, methodology): “We adopted the astrometrically derived period as a starting point for the fit, and fit the radial velocity time series to a Keplerian using the IDL program rvlin (Wright & Howard 2009, 2012).”