Quantifying the Uncertainty in the Orbits of Extrasolar Planets

By Eric B. Ford. 2003

250 citations recorded by the source corpus.

Precise radial velocity measurements have led to the discovery of ∼100 extrasolar planetary systems. We investigate the uncertainty in the orbital solutions that have been fitted to these observations. Understanding these uncertainties will become more and more important as the discovery space for extrasolar planets shifts to longer and longer periods. While detections of short-period planets can be rapidly refined, planets with long orbital periods will require observations spanning decades to constrain the orbital parameters precisely. Already in some cases, multiple distinct orbital solutions provide similarly good fits, particularly in multiple-planet systems. We present a method for quantifying the uncertainties in orbital fits and addressing specific questions directly from the observational data rather than relying on best-fit orbital solutions. This Markov chain Monte Carlo (MCMC) technique has the advantage that it is well suited to the high-dimensional parameter spaces necessary for the multiple-planet systems. We apply the MCMC technique to several extrasolar planetary systems, assessing the uncertainties in orbital elements for several systems. Our MCMC simulations demonstrate that for some systems there are strong correlations between orbital parameters and/or significant non-Gaussianities in parameter distributions, even though the measurement errors are nearly Gaussian. Once these effects are considered, the actual uncertainties in orbital elements can be significantly larger or smaller than the published uncertainties. We also present simple applications of our methods, such as predicting the times of possible transits for GJ 876.

Subfields: Astronomy and Astrophysics, Instrumentation, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ff57974ec84a8bbc914fb8c79e03c1d0bd6a2107

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Citations in the corpus

Hot nights on extrasolar planets: mid‐infrared phase variations of hot Jupiters (2007, methodology): “We use a 105-step Markov chain Monte Carlo with Metropolis– Hastings algorithm (Ford 2005) to determine the best-fitting sinusoid, which is shown as the curve in the top panel of Figs 2–4.”
RETIRED A STARS AND THEIR COMPANIONS. III. COMPARING THE MASS–PERIOD DISTRIBUTIONS OF PLANETS AROUND A-TYPE STARS AND SUN-LIKE STARS (2009, methodology): “This method of error analysis has been shown to be more efficient and accurate than bootstrap Monte Carlo resampling techniques (Ford 2005).”
EFFICIENT FITTING OF MULTIPLANET KEPLERIAN MODELS TO RADIAL VELOCITY AND ASTROMETRY DATA (2009, methodology): “One Bayesean method of exploring complex or highdimensional spaces is the Markov chain Monte Carlo method (MCMC; Metropolis et al. 1953; Hastings 1970), which has been productively employed in the context of orbital fitting (e.g. Ford 2004; Driscoll & Fischer 2005; Balan & Lahav 2008).”
PASTIS: Bayesian extrasolar planet validation. I. General framework, models, and performance (2014, methodology): “The details and many of the caveats of the application of MCMC algorithms to astrophysical problems, and to extrasolar planet research in particular, have already been presented in the literature (e.g. Tegmark et al. 2004; Ford 2005, 2006) and will not be repeated here.”
LOW FALSE POSITIVE RATE OF KEPLER CANDIDATES ESTIMATED FROM A COMBINATION OF SPITZER AND FOLLOW-UP OBSERVATIONS (2015, methodology): “Our MCMC implementation uses the Metropolis-Hasting algorithm with Gibbs sampling (Tegmark et al. 2004; Ford 2005).”
The CARMENES Search for Exoplanets around M Dwarfs: A Low-mass Planet in the Temperate Zone of the Nearby K2-18 (2018, methodology): “We followed Ford (2005) and fit for √ e cosω and √ e sinω instead of the eccentricity e and argument of periastron ω to increase the rate of convergence.”
EXPLORING SHORT GAMMA-RAY BURSTS AS GRAVITATIONAL-WAVE STANDARD SIRENS (2009, methodology): “MCMC methods are widely used in diverse astrophysical applications, ranging from high precision cosmology (e.g. Dunkley et al. 2009, Sievers et al. 2009) to extrasolar planet studies (e.g. Ford 2005, Winn et al. 2007).”
Origins of Eccentric Extrasolar Planets: Testing the Planet-Planet Scattering Model (2007, methodology): “Previous work has shown that the bootstrap-style estimates of parameter uncertainties employed by Butler et al. (2006) can differ significantly from uncertainty estimates based on the posterior probability distribution for model parameters (Ford 2005; Gregory 2005, 2006).”
A ~7.5 M⊕ Planet Orbiting the Nearby Star, GJ 876 (2005, methodology): “Newtonian models yield far better fits to the data than do Keplerian models because there is a clear signal of periapse regression in the data (Ford 2005).”
Improving the Efficiency of Markov Chain Monte Carlo for Analyzing the Orbits of Extrasolar Planets (2005, background): “Radial velocity observations taken at the times when the predictive distribution has an unusually large width would be particularly valuable (Loredo 2004; Ford 2005b).”
STRUCTURE AND EVOLUTION OF PRE-MAIN-SEQUENCE CIRCUMSTELLAR DISKS (2009, methodology): “To characterize the posteriori distribution we adopt a Markov Chain Monte Carlo (MCMC) method (see, e.g., Ford 2005, Fitzgerald et al. 2007).”
Orbital and atmospheric characterization of the planet within the gap of the PDS 70 transition disk (2018, methodology): “To explore the possible orbital solutions of PDS 70 b, we applied the Markov-Chain Monte-Carlo (MCMC) Bayesian analysis technique (Ford 2005, 2006) developed for β Pictoris (Chauvin et al. 2012), and which is well suited for observations covering a small part of the whole orbit (for large orbital…”
DISCOVERY AND VALIDATION OF Kepler-452b: A 1.6 R⨁ SUPER EARTH EXOPLANET IN THE HABITABLE ZONE OF A G2 STAR (2015, methodology): “To estimate the posterior distribution on each fitted parameter in our transit model, we used an MCMC approach similar to the procedure outlined in Ford (2005) and implemented in Rowe et al. (2014).”
INFRARED TRANSMISSION SPECTROSCOPY OF THE EXOPLANETS HD 209458b AND XO-1b USING THE WIDE FIELD CAMERA-3 ON THE HUBBLE SPACE TELESCOPE (2013, methodology): “We fit their photometry for all 10 bands simultaneously, using a Markov Chain Monte Carlo (MCMC) method with Gibbs sampling (Ford 2005), to determine the band-averaged value of Rp/Rs, as well as a/Rs and i.”
PLANETARY CANDIDATES OBSERVED BY KEPLER. VI. PLANET SAMPLE FROM Q1–Q16 (47 MONTHS) (2015, methodology): “The uncertainties in our best fit parameters are somewhat correlated, so we use a Markov Chain Monte Carlo (MCMC) approach to improve our error bars, similar to that outlined in Ford (2005).”
Analytic Approximations for Transit Light-Curve Observables, Uncertainties, and Covariances (2008, methodology): “More details on the MCMC algorithm are given by Tegmark et al. (2004) and Ford (2005).”