Parametrizing the exoplanet eccentricity distribution with the beta distribution.

By David Kipping. 2013

239 citations recorded by the source corpus.

It is suggested that the distribution of orbital eccentricities for extrasolar planets is well-described by the Beta distribution. Several properties of the Beta distribution make it a powerful tool for this purpose. For example, the Beta distribution can reproduce a diverse range of probability density functions (PDFs) using just two shape parameters (a and b). We argue that this makes it ideal for serving as a parametric model in Bayesian comparative population analysis. The Beta distribution is also uniquely defined over the interval zero to unity, meaning that it can serve as a proper prior for eccentricity when analysing the observations of bound extrasolar planets. Using nested sampling, we find that the distribution of eccentricities for 396 exoplanets detected through radial velocity with high signal-to-noise is well-described by a Beta distribution with parameters a = 0.867+/-0.044 and b = 3.03+/-0.17. The Beta distribution is shown to be 3.7 times more likely to represent the underlying distribution of exoplanet eccentricities than the next best model: a Rayleigh + exponential distribution. The same data are also used in an example population comparison utilizing the Beta distribution, where we find that the short- and long-period planets are described by distinct Beta distributions at a confidence of 11.6 sigma and display a signature consistent with the effects of tidal circularization.

Subfields: Astronomy and Astrophysics, Genetics, Statistics and Probability

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

In Genetics

In Statistics and Probability

Citations in the corpus

A SYSTEMATIC SEARCH FOR TRANSITING PLANETS IN THE K2 DATA (2015, methodology): “In this fit, we continue to model the trends in the data as a linear combination of the 150 ELCs but, at this point, we combine this with a realistic light curve model (Mandel & Agol 2002; Kipping 2013a).”
The California Legacy Survey. I. A Catalog of 178 Planets from Precision Radial Velocity Monitoring of 719 Nearby Stars over Three Decades (2021, methodology): “We drew the injected planet period and M isin from log-uniform distributions, and drew eccentricity from the beta distribution described in Kipping (2013), which was fit to a population of RV-observed planets.”
SOPHIE velocimetry of Kepler transit candidates XVII. The physical properties of giant exoplanets within 400 days of period (2015, methodology): “For the eccentricity, we used a Beta distribution as prior as recommended by Kipping (2013).”
The Occurrence and Architecture of Exoplanetary Systems (2014, background): “Hogg, Myers & Bovy (2010) and Kipping (2013) advocated the two-parameter beta distribution, dN de = Γ(a+ b) Γ(a)Γ(b) ea−1(1− e)b−1, (5) which has a number of desirable mathematical properties and provides a good fit for a = 0.867, b = 3.03 (the green curve in Fig.”
FRIENDS OF HOT JUPITERS. I. A RADIAL VELOCITY SEARCH FOR MASSIVE, LONG-PERIOD COMPANIONS TO CLOSE-IN GAS GIANT PLANETS (2013, methodology): “Here, we assume the long-period giant planet eccentricity distribution is well-replicated by the beta distribution (Kipping 2013): Pβ(e; a, b) = Γ(a+ b) Γ(a)Γ(b) ea−1(1− e)b−1 (2) where Pβ is the probability of a given eccentricity, Γ is a Gamma function, and a and b are constants that are fitted…”
Tidal Dissipation in Stars and Giant Planets (2014, background): “Orbits of shorter period are more likely to be of low eccentricity (e.g. Kipping 2013).”
ECCENTRICITY FROM TRANSIT PHOTOMETRY: SMALL PLANETS IN KEPLER MULTI-PLANET SYSTEMS HAVE LOW ECCENTRICITIES (2015, methodology): “Kipping (2013) suggests the use of a Beta distribution, which has the advantage of being convenient to use as a prior for transit fits.”
Binary Companions of Evolved Stars in APOGEE DR14: Search Method and Catalog of ∼5000 Companions (2018, methodology): “…a library of 536,870,912 prior samples generated under a prior similar to that defined in Price-Whelan et al. (2017): 1. uniform or isotropic in angle parameters, 2. uniform in log-period over the domain [1, 32768] day, 3. a beta distribution over eccentricity (using parameters from Kipping 2013).”
ASTROMETRIC EXOPLANET DETECTION WITH GAIA (2014, background): “…planets which Gaia would be sensitive to are less common; (5) eccentricities: we assumed that eccentricities of the 3d orbits follow a Beta distribution Pβ (e; a, b) ∝ ea−1 (1− e)b−1 , (11) with a = 0.867 and b = 3.03, as established from fits to radial velocity observations by Kipping (2013).”
PLANETS AROUND LOW-MASS STARS (PALMS). IV. THE OUTER ARCHITECTURE OF M DWARF PLANETARY SYSTEMS (2014, background): “The latter case is motivated by the distribution of RV-detected planets (Kipping 2013) and M dwarf binaries (Duchêne & Kraus 2013).”
THE OCCURRENCE OF POTENTIALLY HABITABLE PLANETS ORBITING M DWARFS ESTIMATED FROM THE FULL KEPLER DATASET AND AN EMPIRICAL MEASUREMENT OF THE DETECTION SENSITIVITY (2015, methodology): “We adopted a correction factor of 1.08 based on a beta distribution fit by Kipping (2013) to transiting planets with periods shorter than 382.3 days.”
The Orbital Eccentricity of Small Planet Systems (2018, methodology): “The use of a Beta distribution has also been advocated in the context of orbital eccentricities (e.g., Kipping 2013), which has the advantage of mathematically flexible properties.”