Fast Bayesian Inference for Exoplanet Discovery in Radial Velocity Data

Abstract

Inferring the number of planets $N$ in an exoplanetary system from radial velocity (RV) data is a challenging task. Recently, it has become clear that RV data can contain periodic signals due to stellar activity, which can be difficult to distinguish from planetary signals. However, even doing the inference under a given set of simplifying assumptions (e.g. no stellar activity) can be difficult. It is common for the posterior distribution for the planet parameters, such as orbital periods, to be multimodal and to have other awkward features. In addition, when $N$ is unknown, the marginal likelihood (or evidence) as a function of $N$ is required. Rather than doing separate runs with different trial values of $N$, we propose an alternative approach using a trans-dimensional Markov Chain Monte Carlo method within Nested Sampling. The posterior distribution for $N$ can be obtained with a single run. We apply the method to $\nu$ Oph and Gliese 581, finding moderate evidence for additional signals in $\nu$ Oph with periods of 36.11 $\pm$ 0.034 days, 75.58 $\pm$ 0.80 days, and 1709 $\pm$ 183 days; the posterior probability that at least one of these exists is 85%. The results also suggest Gliese 581 hosts many (7-15) "planets" (or other causes of other periodic signals), but only 4-6 have well determined periods. The analysis of both of these datasets shows phase transitions exist which are difficult to negotiate without Nested Sampling.

Accepted for publication in MNRAS. 9 pages, 12 figures. Code at http://www.github.com/eggplantbren/Exoplanet

References in corpus (8)

• The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms
• Stellar Activity Masquerading as Planets in the Habitable Zone of the M dwarf Gliese 581
• The HARPS search for southern extra-solar planets. X. A m sin i = 11 Mearth planet around the nearby spotted M dwarf GJ 674
• Exploring Exoplanet Populations with NASA's Kepler Mission
• Gaussian Process Modelling of Asteroseismic Data
• Bayesian Inference from Observations of Solar-Like Oscillations
• MOA-2013-BLG-220Lb: Massive Planetary Companion to Galactic-Disk Host
• Vertical-likelihood Monte Carlo

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• Statistical methods for exoplanet detection with radial velocities
• BEBOP III. Observations and an independent mass measurement of Kepler-16 (AB) b -- the first circumbinary planet detected with radial velocities
• DMPP-4: Candidate sub-Neptune mass planets orbiting a naked-eye star
• Computing Entropies With Nested Sampling
• PCAT-DE: Reconstructing point-like and diffuse signals in astronomical images using spatial and spectral information
• BEBOP II: Sensitivity to sub-Saturn circumbinary planets using radial-velocities