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Register a new userBias and robustness of eccentricity estimates from radial velocity data
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Eccentricity is a parameter of particular interest as it is an informative indicator of the past of planetary systems. It is however not always clear whether the eccentricity fitted on radial velocity data is real or if it is an artefact of an inappropriate modelling. In this work, we address this question in two steps: we first assume that the model used for inference is correct and present interesting features of classical estimators. Secondly, we study whether the eccentricity estimates are to be trusted when the data contain incorrectly modelled signals, such as missed planetary companions, non Gaussian noises, correlated noises with unknown covariance, etc. Our main conclusion is that data analysis via posterior distributions, with a model including a free error term gives reliable results provided two conditions. First, convergence of the numerical methods needs to be ascertained. Secondly, the noise power spectrum should not have a particularly strong peak at the semi period of the planet of interest. As a consequence, it is difficult to determine if the signal of an apparently eccentric planet might be due to another inner companion in 2:1 mean motion resonance. We study the use of Bayes factors to disentangle these cases. Finally, we suggest methods to check if there are hints of an incorrect model in the residuals. We show on simulated data the performance of our methods and comment on the eccentricities of Proxima b and 55 Cnc f.
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Motivated by recent discussions, both in private and in the literature, we use a Monte Carlo simulation of planetary systems to investigate sources of bias in determining the mass-radius distribution of exoplanets for the two primary techniques used to measure planetary masses---Radial Velocities (RVs) and Transit Timing Variations (TTVs). We assert that mass measurements derived from these two methods are comparably reliable---as the physics underlying their respective signals is well understood. Nevertheless, their sensitivity to planet mass varies with the properties of the planets themselves. We find that for a given planet size, the RV method tends to find planets with higher mass while the sensitivity of TTVs is more uniform. This ``sensitivity bias implies that a complete census of TTV systems is likely to yield a more robust estimate of the mass-radius distribution provided there are not important physical differences between planets near and far from mean-motion resonance. We discuss differences in the sensitivity of the two methods with orbital period and system architecture, which may compound the discrepancies between them (e.g., short period planets detectable by RVs may be more dense due to atmospheric loss). We advocate for continued mass measurements using both approaches as a means both to measure the masses of more planets and to identify potential differences in planet structure that may result from their dynamical and environmental histories.
We present results from a data challenge posed to the radial velocity (RV) community: namely, to quantify the Bayesian evidence for n={0,1,2,3} planets in a set of synthetically generated RV datasets containing a range of planet signals. Participating teams were provided the same likelihood function and set of priors to use in their analysis. They applied a variety of methods to estimate Z, the marginal likelihood for each n-planet model, including cross-validation, the Laplace approximation, importance sampling, and nested sampling. We found the dispersion in Z across different methods grew with increasing n-planet models: ~3 for 0-planets, ~10 for 1-planet, ~100-1000 for 2-planets, and >10,000 for 3-planets. Most internal estimates of uncertainty in Z for individual methods significantly underestimated the observed dispersion across all methods. Methods that adopted a Monte Carlo approach by comparing estimates from multiple runs yielded plausible uncertainties. Finally, two classes of numerical algorithms (those based on importance and nested samplers) arrived at similar conclusions regarding the ratio of Zs for n and (n+1)-planet models. One analytic method (the Laplace approximation) demonstrated comparable performance. We express both optimism and caution: we demonstrate that it is practical to perform rigorous Bayesian model comparison for <=3-planet models, yet robust planet discoveries require researchers to better understand the uncertainty in Z and its connections to model selection.
We present precise radial velocities of XO-2 taken with the Subaru HDS, covering two transits of XO-2b with an interval of nearly two years. The data suggest that the orbital eccentricity of XO-2b is consistent with zero within 2$sigma$ ($e=0.045pm0.024$) and the orbit of XO-2b is prograde (the sky-projected spin-orbit alignment angle $lambda=10^{circ}pm72^{circ}$). The poor constraint of $lambda$ is due to a small impact parameter (the orbital inclination of XO-2b is almost 90$^{circ}$). The data also provide an improved estimate of the mass of XO-2b as $0.62pm0.02$ $M_{rm Jup}$. We also find a long-term radial velocity variation in this system. Further radial velocity measurements are necessary to specify the cause of this additional variation.
We present observations with the planet finder SPHERE of a selected sample of the most promising radial velocity (RV) companions for high-contrast imaging. Using a Monte Carlo simulation to explore all the possible inclinations of the orbit of wide RV companions, we identified the systems with companions that could potentially be detected with SPHERE. We found the most favorable RV systems to observe are : HD,142, GJ,676, HD,39091, HIP,70849, and HD,30177 and carried out observations of these systems during SPHERE Guaranteed Time Observing (GTO). To reduce the intensity of the starlight and reveal faint companions, we used Principle Component Analysis (PCA) algorithms alongside angular and spectral differential imaging. We injected synthetic planets with known flux to evaluate the self-subtraction caused by our data reduction and to determine the 5$sigma$ contrast in the J band $vs$ separation for our reduced images. We estimated the upper limit on detectable companion mass around the selected stars from the contrast plot obtained from our data reduction. Although our observations enabled contrasts larger than 15 mag at a few tenths of arcsec from the host stars, we detected no planets. However, we were able to set upper mass limits around the stars using AMES-COND evolutionary models. We can exclude the presence of companions more massive than 25-28 MJup around these stars, confirming the substellar nature of these RV companions.
The hunt for Earth analogue planets orbiting Sun-like stars has forced the introduction of novel methods to detect signals at, or below, the level of the intrinsic noise of the observations. We present a new global periodogram method that returns more information than the classic Lomb-Scargle periodogram method for radial velocity signal detection. Our method uses the Minimum Mean Squared Error as a framework to determine the optimal number of genuine signals present in a radial velocity timeseries using a global search algorithm, meaning we can discard noise spikes from the data before follow-up analysis. This method also allows us to determine the phase and amplitude of the signals we detect, meaning we can track these quantities as a function of time to test if the signals are stationary or non-stationary. We apply our method to the radial velocity data for GJ876 as a test system to highlight how the phase information can be used to select against non-stationary sources of detected signals in radial velocity data, such as rotational modulation of star spots. Analysis of this system yields two new statistically significant signals in the combined Keck and HARPS velocities with periods of 10 and 15 days. Although a planet with a period of 15 days would relate to a Laplace resonant chain configuration with three of the other planets (8:4:2:1), we stress that follow-up dynamical analyses are needed to test the reliability of such a six planet system.
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