Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBayesian analysis of radial velocity data of GJ667C with correlated noise: evidence for only 2 planets
132
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
GJ667C is the least massive component of a triple star system which lies at a distance of about 6.8 pc (22.1 light-years) from Earth. GJ667C has received much attention recently due to the claims that it hosts up to seven planets including three super-Earths inside the habitable zone. We present a Bayesian technique for the analysis of radial velocity (RV) data-sets in the presence of correlated noise component (red noise), with unknown parameters. We also introduce hyper-parameters in our model in order to deal statistically with under or over-estimated error bars on measured RVs as well as inconsistencies between different data-sets. By applying this method to the RV data-set of GJ667C, we show that this data-set contains a significant correlated (red) noise component with correlation timescale for HARPS data of order 9 days. Our analysis shows that the data only provides strong evidence for the presence of two planets: GJ667Cb and c with periods 7.19d and 28.13d respectively, with some hints towards the presence of a third signal with period 91d. The planetary nature of this third signal is not clear and additional RV observations are required for its confirmation. Previous claims of the detection of additional planets in this system are due the erroneous assumption of white noise. Using the standard white noise assumption, our method leads to the detection of up to five signals in this system. We also find that with the red noise model, the measurement uncertainties from HARPS for this system are under-estimated at the level of ~50 per cent.
rate research
Read More
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 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.
Stellar radial velocity (RV) measurements have proven to be a very successful method for detecting extrasolar planets. Analysing RV data to determine the parameters of the extrasolar planets is a significant statistical challenge owing to the presence of multiple planets and various degeneracies between orbital parameters. Determining the number of planets favoured by the observed data is an even more difficult task. Bayesian model selection provides a mathematically rigorous solution to this problem by calculating marginal posterior probabilities of models with different number of planets, but the use of this method in extrasolar planetary searches has been hampered by the computational cost of the evaluating Bayesian evidence. Nonetheless, Bayesian model selection has the potential to improve the interpretation of existing observational data and possibly detect yet undiscovered planets. We present a new and efficient Bayesian method for determining the number of extrasolar planets, as well as for inferring their orbital parameters, without having to calculate directly the Bayesian evidence for models containing a large number of planets. Instead, we work iteratively and at each iteration obtain a conservative lower limit on the odds ratio for the inclusion of an additional planet into the model. We apply this method to simulated data-sets containing one and two planets and successfully recover the correct number of planets and reliable constraints on the orbital parameters. We also apply our method to RV measurements of HD 37124, 47 Ursae Majoris and HD 10180. For HD 37124, we confirm that the current data strongly favour a three-planet system. We find strong evidence for the presence of a fourth planet in 47 Ursae Majoris, but its orbital period is suspiciously close to one year, casting doubt on its validity. For HD 10180 we find strong evidence for a six-planet system.
A number of giant planet pairs discovered by the radial velocity method with period ratios $lesssim 2$ may reside in mean motion resonances. Convergent orbital migration and resonant capture at the time of formation would naturally explain the present-day resonant orbital configurations of these systems. Planets that experience smooth migration and eccentricity damping forces due to a proto-planetary disk should not only capture into mean motion resonances but also end up in a specific dynamical configuration within the resonance, sometimes referred to as apsidal corotation resonance (ACR). Here we develop a method for testing the hypothesis that a planet pair resides in an ACR by directly fitting radial velocity data. The ACR hypothesis strongly restricts the number of free parameters describing the radial velocity signal and we compare fits using this highly restricted model to fits using a more conventional two-planet RV model by using nested sampling simulations. We apply our method to HD 45364 and HD 33844, two systems hosting giant planet pairs in 3:2 and 5:3 resonances, respectively. We demonstrate that the observations of both systems support an ACR configuration and we use the results of our ACR model fits to constrain possible migration histories of these systems.
We present a simple mathematical criterion for determining whether a given statistical model does not describe several independent sets of measurements, or data modes, adequately. We derive this criterion for two data sets and generalise it to several sets by using the Bayesian updating of the posterior probability density. To demonstrate the usage of the criterion, we apply it to observations of exoplanet host stars by re-analysing the radial velocities of HD 217107, Gliese 581, and u{psion} Andromedae and show that the currently used models are not necessarily adequate in describing the properties of these measurements. We show that while the two data sets of Gliese 581 can be modelled reasonably well, the noise model of HD 217107 needs to be revised. We also reveal some biases in the radial velocities of u{psion} Andromedae and report updated orbital parameters for the recently proposed 4-planet model. Because of the generality of our criterion, no assumptions are needed on the nature of the measurements, models, or model parameters. The method we propose can be applied to any astronomical problems, as well as outside the field of astronomy, because it is a simple consequence of the Bayes rule of conditional probabilities.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
