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Register a new userUncovering the planets and stellar activity of CoRoT-7 using only radial velocities
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Stellar activity can induce signals in the radial velocities of stars, complicating the detection of orbiting low-mass planets. We present a method to determine the number of planetary signals present in radial-velocity datasets of active stars, using only radial-velocity observations. Instead of considering separate fits with different number of planets, we use a birth-death Markov chain Monte Carlo algorithm to infer the posterior distribution for the number of planets in a single run. In a natural way, the marginal distributions for the orbital parameters of all planets are also inferred. This method is applied to HARPS data of CoRoT-7. We confidently recover both CoRoT-7b and CoRoT-7c although the data show evidence for additional signals.
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Since the discovery of the transiting super-Earth CoRoT-7b, several investigations have yielded different results for the number and masses of planets present in the system, mainly owing to the stars high level of activity. We re-observed CoRoT-7 in January 2012 with both HARPS and CoRoT, so that we now have the benefit of simultaneous radial-velocity and photometric data. This allows us to use the off-transit variations in the stars light curve to estimate the radial-velocity variations induced by the suppression of convective blueshift and the flux blocked by starspots. To account for activity-related effects in the radial-velocities which do not have a photometric signature, we also include an additional activity term in the radial-velocity model, which we treat as a Gaussian process with the same covariance properties (and hence the same frequency structure) as the light curve. Our model was incorporated into a Monte Carlo Markov Chain in order to make a precise determination of the orbits of CoRoT-7b and CoRoT-7c. We measure the masses of planets b and c to be 4.73 +/- 0.95 Mearth and 13.56 +/- 1.08 Mearth, respectively. The density of CoRoT-7b is (6.61 +/- 1.72)(Rp/1.58 Rearth)^(-3) g.cm^(-3), which is compatible with a rocky composition. We search for evidence of an additional planet d, identified by previous authors with a period close to 9 days. We are not able to confirm the existence of a planet with this orbital period, which is close to the second harmonic of the stellar rotation at around 7.9 days. Using Bayesian model selection we find that a model with two planets plus activity-induced variations is most favoured.
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.
The CoRoT satellite has recently discovered the transits of a telluric planet across the disc of a late-type magnetically active star dubbed CoRoT-7, while a second planet has been detected after filtering out the radial velocity (hereafter RV) variations due to stellar activity. We investigate the magnetic activity of CoRoT-7 and use the results for a better understanding of its impact on stellar RV variations. We derive the longitudinal distribution of active regions on CoRoT-7 from a maximum entropy spot model of the CoRoT light curve. Assuming that each active region consists of dark spots and bright faculae in a fixed proportion, we synthesize the expected RV variations. Active regions are mainly located at three active longitudes which appear to migrate at different rates, probably as a consequence of surface differential rotation, for which a lower limit of Delta Omega / Omega = 0.058 pm 0.017 is found. The synthesized activity-induced RV variations reproduce the amplitude of the observed RV curve and are used to study the impact of stellar activity on planetary detection. In spite of the non-simultaneous CoRoT and HARPS observations, our study confirms the validity of the method previously adopted to filter out RV variations induced by stellar activity. We find a false-alarm probability < 0.01 percent that the RV oscillations attributed to CoRoT-7b and CoRoT-7c are spurious effects of noise and activity. Additionally, our model suggests that other periodicities found in the observed RV curve of CoRoT-7 could be explained by active regions whose visibility is modulated by a differential stellar rotation with periods ranging from 23.6 to 27.6 days.
Variations related to stellar activity and correlated noise can prevent the detections of low-amplitude signals in radial velocity data if not accounted for. This can be seen as the greatest obstacle in detecting Earth-like planets orbiting nearby stars with Doppler spectroscopy regardless of developments in instrumentation and rapidly accumulating amounts of data. We use a statistical model that is not sensitive to aperiodic and/or quasiperiodic variability of stellar origin. We demonstrate the performance of our model by re-analysing the radial velocities of the moderately active star CoRoT-7 ($log R_{rm HK} = -4.61$) with a transiting planet whose Doppler signal has proven rather difficult to detect. We find that the signal of the transiting planet can be robustly detected together with signals of two other planet candidates. Our results suggest that rotation periods of moderately active stars can be filtered out of the radial velocity noise, which enables the detections of low-mass planets orbiting such stars.
We investigated the discrepancy between planetary mass determination using the transit timing variations (TTVs) and radial velocities (RVs), by analysing the multi-planet system Kepler-9. Despite being the first system characterised with TTVs, there are several discrepant solutions in the literature, with those reporting lower planetary densities being apparently in disagreement with high-precision RV observations. To resolve this, we gathered HARPS-N RVs at epochs that maximised the difference between the predicted RV curves from discrepant solutions in the literature. We also re-analysed the full Kepler data-set and performed a dynamical fit, within a Bayesian framework, using the newly derived central and duration times of the transits. We compared these results with the RV data and found that our solution better describes the RV observations, despite the masses of the planets being nearly half that presented in the discovery paper. We therefore confirm that the TTV method can provide mass determinations that agree with those determined using high-precision RVs. The low densities of the planets place them in the scarcely populated region of the super-Neptunes / inflated sub-Saturns in the mass-radius diagram.
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