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A HARPS-N mass for the elusive Kepler-37d: a case study in disentangling stellar activity and planetary signals

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 Added by Vinesh Rajpaul
 Publication date 2021
  fields Physics
and research's language is English




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To date, only 18 exoplanets with radial velocity (RV) semi-amplitudes $<2$ m/s have had their masses directly constrained. The biggest obstacle to RV detection of such exoplanets is variability intrinsic to stars themselves, e.g. nuisance signals arising from surface magnetic activity such as rotating spots and plages, which can drown out or even mimic planetary RV signals. We use Kepler-37 - known to host three transiting planets, one of which, Kepler-37d, should be on the cusp of RV detectability with modern spectrographs - as a case study in disentangling planetary and stellar activity signals. We show how two different statistical techniques - one seeking to identify activity signals in stellar spectra, and another to model activity signals in extracted RVs and activity indicators - can enable detection of the hitherto elusive Kepler-37d. Moreover, we show that these two approaches can be complementary, and in combination, facilitate a definitive detection and precise characterisation of Kepler-37d. Its RV semi-amplitude of $1.22pm0.31$ m/s (mass $5.4pm1.4$ $M_oplus$) is formally consistent with TOI-178bs $1.05^{+0.25}_{-0.30}$ m/s, the latter being the smallest detected RV signal of any transiting planet to date, though dynamical simulations suggest Kepler-37ds mass may be on the lower end of our $1sigma$ credible interval. Its consequent density is consistent with either a water-world or that of a gaseous envelope ($sim0.4%$ by mass) surrounding a rocky core. Based on RV modelling and a re-analysis of Kepler-37 TTVs, we also argue that the putative (non-transiting) planet Kepler-37e should probably be stripped of its confirmed status.



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We present a comprehensive analysis of 10 years of HARPS radial velocities of the K2V dwarf star HD 13808, which has previously been reported to host two unconfirmed planet candidates. We use the state-of-the-art nested sampling algorithm PolyChord to compare a wide variety of stellar activity models, including simple models exploiting linear correlations between RVs and stellar activity indicators, harmonic models for the activity signals, and a more sophisticated Gaussian process regression model. We show that the use of overly-simplistic stellar activity models that are not well-motivated physically can lead to spurious `detections of planetary signals that are almost certainly not real. We also reveal some difficulties inherent in parameter and model inference in cases where multiple planetary signals may be present. Our study thus underlines the importance both of exploring a variety of competing models and of understanding the limitations and precision settings of ones sampling algorithm. We also show that at least in the case of HD 13808, we always arrive at consistent conclusions about two particular signals present in the RV, regardless of the stellar activity model we adopt; these two signals correspond to the previously-reported though unconfirmed planet candidate signals. Given the robustness and precision with which we can characterize these two signals, we deem them secure planet detections. In particular, we find two planets orbiting HD 13808 at distances of 0.11, 0.26 AU with periods of 14.2, 53.8 d, and minimum masses of 11, 10 Earth masses.
Radial velocity perturbations induced by stellar surface inhomogeneities including spots, plages and granules currently limit the detection of Earth-twins using Doppler spectroscopy. Such stellar noise is poorly understood for stars other than the Sun because their surface is unresolved. In particular, the effects of stellar surface inhomogeneities on observed stellar radial velocities are extremely difficult to characterize, and thus developing optimal correction techniques to extract true stellar radial velocities is extremely challenging. In this paper, we present preliminary results of a solar telescope built to feed full-disk sunlight into the HARPS-N spectrograph, which is in turn calibrated with an astro-comb. This setup enables long-term observation of the Sun as a star with state-of-the-art sensitivity to radial velocity changes. Over seven days of observing in 2014, we show an average 50cms radial velocity rms over a few hours of observation. After correcting observed radial velocities for spot and plage perturbations using full-disk photometry of the Sun, we lower by a factor of two the weekly radial velocity rms to 60cms. The solar telescope is now entering routine operation, and will observe the Sun every clear day for several hours. We will use these radial velocities combined with data from solar satellites to improve our understanding of stellar noise and develop optimal correction methods. If successful, these new methods should enable the detection of Venus over the next two to three years, thus demonstrating the possibility of detecting Earth-twins around other solar-like stars using the radial velocity technique.
We present high-precision linear polarization observations of four bright hot Jupiter systems ($tau$ Boo, HD 179949, HD 189733 and 51 Peg) and use the data to search for polarized reflected light from the planets. The data for 51 Peg are consistent with a reflected light polarization signal at about the level expected with 2.8$sigma$ significance and a false alarm probability of 1.9 per cent. More data will be needed to confirm a detection of reflected light in this system. HD 189733 shows highly variable polarization that appears to be most likely the result of magnetic activity of the host star. This masks any polarization due to reflected light, but a polarization signal at the expected level of $sim$20 ppm cannot be ruled out. $tau$ Boo and HD 179949 show no evidence for polarization due to reflected light. The results are consistent with the idea that many hot Jupiters have low geometric albedos. Conclusive detection of polarized reflected light from hot Jupiters is likely to require further improvements in instrument sensitivity.
[Abridged] Context. Stellar activity is an important source of systematic errors and uncertainties in the characterization of exoplanets. Most of the techniques used to correct for this activity focus on an ad hoc data reduction. Aims. We have developed a software for the combined fit of transits and stellar activity features in high-precision long-duration photometry. Our aim is to take advantage of the modelling to derive correct stellar and planetary parameters, even in the case of strong stellar activity. Methods. We use an analytic approach to model the light curve. The code KSint, modified by adding the evolution of active regions, is implemented into our Bayesian modelling package PASTIS. The code is then applied to the light curve of CoRoT-2. The light curve is divided in segments to reduce the number of free parameters needed by the fit. We perform a Markov chain Monte Carlo analysis in two ways. In the first, we perform a global and independent modelling of each segment of the light curve, transits are not normalized and are fitted together with the activity features, and occulted features are taken into account during the transit fit. In the second, we normalize the transits with a model of the non-occulted activity features, and then we apply a standard transit fit, which does not take the occulted features into account. Results. Our model recovers the activity features coverage of the stellar surface and different rotation periods for different features. We find variations in the transit parameters of different segments and show that they are likely due to the division applied to the light curve. Neglecting stellar activity or even only bright spots while normalizing the transits yields a $sim 1.2sigma$ larger and $2.3sigma$ smaller transit depth, respectively. The stellar density also presents up to $2.5sigma$ differences depending on the normalization technique...
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