Bayesian priors for transiting planets

Bayesian priors for transiting planets

Authors:

Kipping et al

Abstract:

As astronomers push towards discovering ever-smaller transiting planets, it is increasingly common to deal with low signal-to-noise ratio (SNR) events, where the choice of priors plays an influential role in Bayesian inference. In the analysis of exoplanet data, the selection of priors is often treated as a nuisance, with observers typically defaulting to uninformative distributions. Such treatments miss a key strength of the Bayesian framework, especially in the low SNR regime, where even weak a priori information is valuable. When estimating the parameters of a low-SNR transit, two key pieces of information are known: (i) the planet has the correct geometric alignment to transit and (ii) the transit event exhibits sufficient signal-to-noise to have been detected. These represent two forms of observational bias. Accordingly, when fitting transits, the model parameter priors should not follow the intrinsic distributions of said terms, but rather those of both the intrinsic distributions and the observational biases. In this work, we derive the shape of these priors for trapezoidal transits and occultations, including the case of grazing events. These results naturally explain why the observed population shows a bias towards equatorial transits and why the observational bias of ratio-of-radii is super-quadratic, scaling as (RP/R⋆)5/2. We may account for these observational biases by adding on log likelihood penalty terms, for which we provide Python code to generate, ExoPriors.

Bayesian Exoplanet Validation

PASTIS: Bayesian extrasolar planet validation II. Constraining exoplanet blend scenarios using spectroscopic diagnoses

Authors:

Santerne et al

Abstract:

The statistical validation of transiting exoplanets proved to be an efficient technique to secure the nature of small exoplanet signals which cannot be established by purely spectroscopic means. However, the spectroscopic diagnoses are providing us with useful constraints on the presence of blended stellar contaminants. In this paper, we present how a contaminating star affects the measurements of the various spectroscopic diagnoses as function of the parameters of the target and contaminating stars using the model implemented into the PASTIS planet-validation software. We find particular cases for which a blend might produce a large radial velocity signal but no bisector variation. It might also produce a bisector variation anti-correlated with the radial velocity one, as in the case of stellar spots. In those cases, the full width half maximum variation provides complementary constraints. These results can be used to constrain blend scenarios for transiting planet candidates or radial velocity planets. We review all the spectroscopic diagnoses reported in the literature so far, especially the ones to monitor the line asymmetry. We estimate their uncertainty and compare their sensitivity to blends. Based on that, we recommend the use of BiGauss which is the most sensitive diagnosis to monitor line-profile asymmetry. In this paper, we also investigate the sensitivity of the radial velocities to constrain blend scenarios and develop a formalism to estimate the level of dilution of a blended signal. Finally, we apply our blend model to re-analyse the spectroscopic diagnoses of HD16702, an unresolved face-on binary which exhibits bisector variations.

Bayesian Analysis of Hot Jupiter Kepler-2b

A Bayesian Analysis of Kepler-2b Using the EXONEST Algorithm

Authors:

Placek et al

Abstract:

The study of exoplanets (planets orbiting other stars) is revolutionizing the way we view our universe. High-precision photometric data provided by the Kepler Space Telescope (Kepler) enables not only the detection of such planets, but also their characterization. This presents a unique opportunity to apply Bayesian methods to better characterize the multitude of previously confirmed exoplanets. This paper focuses on applying the EXONEST algorithm to characterize the transiting short-period-hot-Jupiter, Kepler-2b. EXONEST evaluates a suite of exoplanet photometric models by applying Bayesian Model Selection, which is implemented with the MultiNest algorithm. These models take into account planetary effects, such as reflected light and thermal emissions, as well as the effect of the planetary motion on the host star, such as Doppler beaming, or boosting, of light from the reflex motion of the host star, and photometric variations due to the planet-induced ellipsoidal shape of the host star. By calculating model evidences, one can determine which model best describes the observed data, thus identifying which effects dominate the planetary system. Presented are parameter estimates and model evidences for Kepler-2b.

Sinistra, Gliese 581 Systems Modeled: SInistra has 2 Exoplanets/Brown Dwarfs, Gliese 581 Five or Six Exoplanets

The Probabilities of Orbital-Companion Models for Stellar Radial Velocity Data

Authors:

Hou et al

Abstract:

The fully marginalized likelihood, or Bayesian evidence, is of great importance in probabilistic data analysis, because it is involved in calculating the posterior probability of a model or re-weighting a mixture of models conditioned on data. It is, however, extremely challenging to compute. This paper presents a geometric-path Monte Carlo method, inspired by multi-canonical Monte Carlo to evaluate the fully marginalized likelihood. We show that the algorithm is very fast and easy to implement and produces a justified uncertainty estimate on the fully marginalized likelihood. The algorithm performs efficiently on a trial problem and multi-companion model fitting for radial velocity data. For the trial problem, the algorithm returns the correct fully marginalized likelihood, and the estimated uncertainty is also consistent with the standard deviation of results from multiple runs. We apply the algorithm to the problem of fitting radial velocity data from HIP 88048 (ν Oph) and Gliese 581. We evaluate the fully marginalized likelihood of 1, 2, 3, and 4-companion models given data from HIP 88048 and various choices of prior distributions. We consider prior distributions with three different minimum radial velocity amplitude Kmin. Under all three priors, the 2-companion model has the largest marginalized likelihood, but the detailed values depend strongly on Kmin. We also evaluate the fully marginalized likelihood of 3, 4, 5, and 6-planet model given data from Gliese 581 and find that the fully marginalized likelihood of the 5-planet model is too close to that of the 6-planet model for us to confidently decide between them.