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Register a new userXO-2b: a Prograde Planet with a Negligible Eccentricity, and an Additional Radial Velocity Variation
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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.
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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.
The star Kepler-1625 recently attracted considerable attention when an analysis of the stellar photometric time series from the Kepler mission was interpreted as showing evidence of a large exomoon around the transiting Jupiter-sized planet candidate Kepler-1625b. We aim to detect the radial velocity (RV) signal imposed by Kepler-1625b (and its putative moon) on the host star or, as the case may be, determine an upper limit on the mass of the transiting object. We took a total of 22 spectra of Kepler-1625 using CARMENES, 20 of which were useful. Observations were spread over a total of seven nights between October 2017 and October 2018, covering $125%$ of one full orbit of Kepler-1625b. We used the automatic Spectral Radial Velocity Analyser (SERVAL) pipeline to deduce the stellar RVs and uncertainties. Then we fitted the RV curve model of a single planet on a Keplerian orbit to the observed RVs using a $chi^2$ minimisation procedure. We derive upper limits on the mass of Kepler-1625b under the assumption of a single planet on a circular orbit. In this scenario, the $1,sigma$, $2,sigma$, and $3,sigma$ confidence upper limits for the mass of Kepler-1625b are $2.90,M_{rm J}$, $7.15,M_{rm J}$, and $11.60,M_{rm J}$, respectively. We present strong evidence for the planetary nature of Kepler-1625b, making it the 10th most long-period confirmed planet known today. Our data does not answer the question about a second, possibly more short-period planet that could be responsible for the observed transit timing variation of Kepler-1625b.
The Sun is the only star whose surface can be directly resolved at high resolution, and therefore constitutes an excellent test case to explore the physical origin of stellar radial-velocity (RV) variability. We present HARPS observations of sunlight scattered off the bright asteroid 4/Vesta, from which we deduced the Suns activity-driven RV variations. In parallel, the HMI instrument onboard the Solar Dynamics Observatory provided us with simultaneous high spatial resolution magnetograms, Dopplergrams, and continuum images of the Sun in the Fe I 6173A line. We determine the RV modulation arising from the suppression of granular blueshift in magnetised regions and the flux imbalance induced by dark spots and bright faculae. The rms velocity amplitudes of these contributions are 2.40 m/s and 0.41 m/s, respectively, which confirms that the inhibition of convection is the dominant source of activity-induced RV variations at play, in accordance with previous studies. We find the Doppler imbalances of spot and plage regions to be only weakly anticorrelated. Lightcurves can thus only give incomplete predictions of convective blueshift suppression. We must instead seek proxies that track the plage coverage on the visible stellar hemisphere directly. The chromospheric flux index R_HK derived from the HARPS spectra performs poorly in this respect, possibly because of the differences in limb brightening/darkening in the chromosphere and photosphere. We also find that the activity-driven RV variations of the Sun are strongly correlated with its full-disc magnetic flux density, which may become a useful proxy for activity-related RV noise.
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 determine the orbital eccentricities of individual small Kepler planets, through a combination of asteroseismology and transit light-curve analysis. We are able to constrain the eccentricities of 51 systems with a single transiting planet, which supplement our previous measurements of 66 planets in multi-planet systems. Through a Bayesian hierarchical analysis, we find evidence that systems with only one detected transiting planet have a different eccentricity distribution than systems with multiple detected transiting planets. The eccentricity distribution of the single-transiting systems is well described by the positive half of a zero-mean Gaussian distribution with a dispersion $sigma_e = 0.32 pm 0.06$, while the multiple-transit systems are consistent with $sigma_e = 0.083^{+0.015}_{-0.020}$. A mixture model suggests a fraction of $0.76^{+0.21}_{-0.12}$ of single-transiting systems have a moderate eccentricity, represented by a Rayleigh distribution that peaks at $0.26^{+0.04}_{-0.06}$. This finding may reflect differences in the formation pathways of systems with different numbers of transiting planets. We investigate the possibility that eccentricities are self-excited in closely packed planetary systems, as well as the influence of long-period giant companion planets. We find that both mechanisms can qualitatively explain the observations. We do not find any evidence for a correlation between eccentricity and stellar metallicity, as has been seen for giant planets. Neither do we find any evidence that orbital eccentricity is linked to the detection of a companion star. Along with this paper we make available all of the parameters and uncertainties in the eccentricity distributions, as well as the properties of individual systems, for use in future studies.
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