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Planets orbiting binary systems are relatively unexplored compared to those around single stars. Detections of circumbinary planets and planetary systems offer a first detailed view into our understanding of circumbinary planet formation and dynamical evolution. The BEBOP (Binaries Escorted by Orbiting Planets) radial velocity survey plays a special role in this adventure as it focuses on eclipsing single-lined binaries with an FGK dwarf primary and M dwarf secondary allowing for the highest-radial velocity precision using the HARPS and SOPHIE spectrographs. We obtained 4512 high-resolution spectra for the 179 targets in the BEBOP survey which we used to derive the stellar atmospheric parameters using both equivalent widths and spectral synthesis. We furthermore derive stellar masses, radii, and ages for all targets. With this work, we present the first homogeneous catalogue of precise stellar parameters for these eclipsing single-lined binaries., Comment: accepted for publication in MNRAS

The two-planet transiting system LHS 1140 has been extensively observed since its discovery in 2017, notably with $Spitzer$, HST, TESS, and ESPRESSO, placing strong constraints on the parameters of the M4.5 host star and its small temperate exoplanets, LHS 1140 b and c. Here, we reanalyse the ESPRESSO observations of LHS 1140 with the novel line-by-line framework designed to fully exploit the radial velocity content of a stellar spectrum while being resilient to outlier measurements. The improved radial velocities, combined with updated stellar parameters, consolidate our knowledge on the mass of LHS 1140 b (5.60$\pm$0.19 M$_{\oplus}$) and LHS 1140 c (1.91$\pm$0.06 M$_{\oplus}$) with unprecedented precision of 3%. Transits from $Spitzer$, HST, and TESS are jointly analysed for the first time, allowing us to refine the planetary radii of b (1.730$\pm$0.025 R$_{\oplus}$) and c (1.272$\pm$0.026 R$_{\oplus}$). Stellar abundance measurements of refractory elements (Fe, Mg and Si) obtained with NIRPS are used to constrain the internal structure of LHS 1140 b. This planet is unlikely to be a rocky super-Earth as previously reported, but rather a mini-Neptune with a $\sim$0.1% H/He envelope by mass or a water world with a water-mass fraction between 9 and 19% depending on the atmospheric composition and relative abundance of Fe and Mg. While the mini-Neptune case would not be habitable, a water-abundant LHS 1140 b potentially has habitable surface conditions according to 3D global climate models, suggesting liquid water at the substellar point for atmospheres with relatively low CO$_2$ concentration, from Earth-like to a few bars., Comment: 31 pages, 18 figures, accepted for publication in ApJL

Exoplanets can be detected with various observational techniques. Among them, radial velocity (RV) has the key advantages of revealing the architecture of planetary systems and measuring planetary mass and orbital eccentricities. RV observations are poised to play a key role in the detection and characterization of Earth twins. However, the detection of such small planets is not yet possible due to very complex, temporally correlated instrumental and astrophysical stochastic signals. Furthermore, exploring the large parameter space of RV models exhaustively and efficiently presents difficulties. In this review, we frame RV data analysis as a problem of detection and parameter estimation in unevenly sampled, multivariate time series. The objective of this review is two-fold: to introduce the motivation, methodological challenges, and numerical challenges of RV data analysis to nonspecialists, and to unify the existing advanced approaches in order to identify areas for improvement., Comment: Published in Annual Reviews of Statistics and Its Application, contains the main text and supplemental appendix

The detection of terrestrial planets by radial velocity and photometry is hindered by the presence of stellar signals. Those are often modeled as stationary Gaussian processes, whose kernels are based on qualitative considerations, which do not fully leverage the existing physical understanding of stars. Our aim is to build a formalism which allows to transfer the knowledge of stellar activity into practical data analysis methods. In particular, we aim at obtaining kernels with physical parameters. This has two purposes: better modelling signals of stellar origin to find smaller exoplanets, and extracting information about the star from the statistical properties of the data. We consider several observational channels such as photometry, radial velocity, activity indicators, and build a model called FENRIR to represent their stochastic variations due to stellar surface inhomogeneities. We compute analytically the covariance of this multi-channel stochastic process, and implement it in the S+LEAF framework to reduce the cost of likelihood evaluations from $O(N^3)$ to $O(N)$. We also compute analytically higher order cumulants of our FENRIR model, which quantify its non-Gaussianity. We obtain a fast Gaussian process framework with physical parameters, which we apply to the HARPS-N and SORCE observations of the Sun, and constrain a solar inclination compatible with the viewing geometry. We then discuss the application of our formalism to granulation. We exhibit non-Gaussianity in solar HARPS radial velocities, and argue that information is lost when stellar activity signals are assumed to be Gaussian. We finally discuss the origin of phase shifts between RVs and indicators, and how to build relevant activity indicators. We provide an open-source implementation of the FENRIR Gaussian process model with a Python interface., Comment: Submitted to Astronomy \& Astrophysics

We report the detection of a gas-giant planet in orbit around both stars of an eclipsing binary star system that also contains the smaller, inner transiting planet TOI-1338b. The new planet, called TOI-1338/BEBOP-1c, was discovered using radial-velocity data collected with the HARPS and ESPRESSO spectrographs. Our analysis reveals it is a $65.2~\rm{M_{\oplus}}$ circumbinary planet with a period of $215.5~$days. This is the first detection of a circumbinary planet using radial-velocity observations alone, and makes TOI-1338/BEBOP-1 only the second confirmed multiplanet circumbinary system to date. We do not detect the smaller inner transiting planet with radial-velocity data, and can place an upper limit on the inner planet's mass at $21.8~\mathrm{M}_\oplus$ with $99\%$ confidence. The inner planet is the first circumbinary planet amenable for atmospheric characterisation, using the James Webb Space Telescope., Comment: The Version of Record of this article is published in Nature Astronomy, and is available online at https://doi.org/10.1038/s41550-023-01948-4 Main: 14-pages, 4-Figures, 1-table. Supporting material: 48-pages, 12-figures, 4-tables

When searching for exoplanets, one wants to count how many planets orbit a given star, and to determine what their orbital parameters are. If the estimated orbital elements are too far from those of a planet truly present, this should be considered as a false detection. This setting is a particular instance of a general one: aiming to retrieve which parametric components are in a dataset corrupted by nuisance signals, with a certain accuracy on their parameters. We exhibit a detection criterion minimizing false and missed detections, either as a function of their relative cost, or when the expected number of false detections is bounded. If the components can be separated in a technical sense discussed in detail, the optimal detection criterion is a posterior probability obtained as a by-product of Bayesian evidence calculations, and we discuss how it can be calibrated. We show on two simulations emulating exoplanet searches that it can significantly outperform other criteria. Finally, we show that our framework offers solutions for the identification of components of mixture models, and Bayesian false discovery rate control when hypotheses are not discrete., Comment: Accepted for publication in Annals of Applied Statistics

The radial velocity method is amongst the most robust and most established means of detecting exoplanets. Yet, it has so far failed to detect circumbinary planets despite their relatively high occurrence rates. Here, we report velocimetric measurements of Kepler-16A, obtained with the SOPHIE spectrograph, at the Observatoire de Haute-Provence's 193cm telescope, collected during the BEBOP survey for circumbinary planets. Our measurements mark the first radial velocity detection of a circumbinary planet, independently determining the mass of Kepler-16~(AB)~b to be $0.313 \pm 0.039\,{\rm M}_{\rm Jup}$, a value in agreement with eclipse timing variations. Our observations demonstrate the capability to achieve photon-noise precision and accuracy on single-lined binaries, with our final precision reaching $\rm 1.5~m\,s^{-1}$ on the binary and planetary signals. Our analysis paves the way for more circumbinary planet detections using radial velocities which will increase the relatively small sample of currently known systems to statistically relevant numbers, using a method that also provides weaker detection biases. Our data also contain a long-term radial velocity signal, which we associate with the magnetic cycle of the primary star., Comment: under review at MNRAS, 7 pages, 4 figures, all RV data in appendix

Exoplanets transiting bright nearby stars are key objects for advancing our knowledge of planetary formation and evolution. The wealth of photons from the host star gives detailed access to the atmospheric, interior, and orbital properties of the planetary companions. $\nu^2$ Lupi (HD 136352) is a naked-eye ($V = 5.78$) Sun-like star that was discovered to host three low-mass planets with orbital periods of 11.6, 27.6, and 107.6 days via radial velocity monitoring (Udry et al. 2019). The two inner planets (b and c) were recently found to transit (Kane et al. 2020), prompting a photometric follow-up by the brand-new $CHaracterising\:ExOPlanets\:Satellite\:(CHEOPS)$. Here, we report that the outer planet d is also transiting, and measure its radius and mass to be $2.56\pm0.09$ $R_{\oplus}$ and $8.82\pm0.94$ $M_{\oplus}$, respectively. With its bright Sun-like star, long period, and mild irradiation ($\sim$5.7 times the irradiation of Earth), $\nu^2$ Lupi d unlocks a completely new region in the parameter space of exoplanets amenable to detailed characterization. We refine the properties of all three planets: planet b likely has a rocky mostly dry composition, while planets c and d seem to have retained small hydrogen-helium envelopes and a possibly large water fraction. This diversity of planetary compositions makes the $\nu^2$ Lupi system an excellent laboratory for testing formation and evolution models of low-mass planets., Comment: Published in Nature Astronomy. 60 pages, 18 Figures, 6 Tables. This is the authors' version of the manuscript. The final authenticated version is available online at https://www.nature.com/articles/s41550-021-01381-5

Searches for periodicity in time series are often done with models of periodic signals, whose statistical significance is assessed via false alarm probabilities or Bayes factors. However, a statistically significant periodic model might not originate from a strictly periodic source. In astronomy in particular, one expects transient signals that show periodicity for a certain amount of time before vanishing. This situation is encountered for instance in the search for planets in radial velocity data. While planetary signals are expected to have a stable phase, amplitude and frequency - except when strong planet-planet interactions are present - signals induced by stellar activity will typically not exhibit the same stability. In the present article, we explore the use of periodic functions multiplied by time windows to diagnose whether an apparently periodic signal is truly so. We suggest diagnostics to check whether a signal is consistently present in the time series, and has a stable phase, amplitude and period. The tests are expressed both in a periodogram and Bayesian framework. Our methods are applied to the Solar HARPS-N data as well as HD 215152, HD 69830 and HD 13808. We find that (i) the HARPS-N Solar data exhibits signals at the Solar rotation period and its first harmonic ($\sim$ 13.4 days). The frequency and phase of the 13.4 days signal appear constant within the estimation uncertainties, but its amplitude presents significant variations which can be mapped to activity levels. (ii) as previously reported, we find four, three and two planets orbiting HD 215152, HD 69830 and HD 13808., Comment: Accepted for publication in Astronomy & Astrophysics

Context. In exoplanet searches with radial velocity data, the most common statistical significance metrics are the Bayes factor and the false alarm probability (FAP). Both have proved useful, but do not directly address whether an exoplanet detection should be claimed. Furthermore, it is unclear which detection threshold should be taken and how robust the detections are to model misspecification. Aims. The present work aims at defining a detection criterion which conveys as precisely as possible the information needed to claim an exoplanet detection. We compare this new criterion to existing ones in terms of sensitivity and robustness. Methods. We define a significance metric called the false inclusion probability (FIP) based on the posterior probability of presence of a planet. Posterior distributions are computed with the nested sampling package Polychord. We show that for FIP and Bayes factor calculations, defining priors on linear parameters as Gaussian mixture models allows to significantly speed up computations. The performances of the FAP, Bayes factor and FIP are studied with simulations as well as analytical arguments. We compare the methods assuming the model is correct, then evaluate their sensitivity to the prior and likelihood choices. Results. Among other properties, the FIP offers ways to test the reliability of the significance levels, it is particularly efficient to account for aliasing and allows to exclude the presence of planets with a certain confidence. We find that, in our simulations, the FIP outperforms existing detection metrics. We show that planet detections are sensitive to priors on period and semi-amplitude and that letting free the noise parameters offers better performances than fixing a noise model based on a fit to ancillary indicators., Comment: Accepted for publication in Astronomy & Astrophysics

Ultra-hot giant exoplanets receive thousands of times Earth's insolation. Their high-temperature atmospheres (>2,000 K) are ideal laboratories for studying extreme planetary climates and chemistry. Daysides are predicted to be cloud-free, dominated by atomic species and substantially hotter than nightsides. Atoms are expected to recombine into molecules over the nightside, resulting in different day-night chemistry. While metallic elements and a large temperature contrast have been observed, no chemical gradient has been measured across the surface of such an exoplanet. Different atmospheric chemistry between the day-to-night ("evening") and night-to-day ("morning") terminators could, however, be revealed as an asymmetric absorption signature during transit. Here, we report the detection of an asymmetric atmospheric signature in the ultra-hot exoplanet WASP-76b. We spectrally and temporally resolve this signature thanks to the combination of high-dispersion spectroscopy with a large photon-collecting area. The absorption signal, attributed to neutral iron, is blueshifted by -11+/-0.7 km s-1 on the trailing limb, which can be explained by a combination of planetary rotation and wind blowing from the hot dayside. In contrast, no signal arises from the nightside close to the morning terminator, showing that atomic iron is not absorbing starlight there. Iron must thus condense during its journey across the nightside., Comment: Published in Nature (Accepted on 24 January 2020.) 33 pages, 11 figures, 3 tables

Mass-radius relationships for water-rich rocky planets are usually calculated assuming most water is present in condensed (either liquid or solid) form. Planet density estimates are then compared to these mass-radius relationships, even when these planets are more irradiated than the runaway greenhouse irradiation limit (around 1.1~times the insolation at Earth for planets orbiting a Sun-like star), for which water has been shown to be unstable in condensed form and would instead form a thick H2O-dominated atmosphere. Here we use the LMD Generic numerical climate model to derive new mass-radius relationships appropriate for water-rich rocky planets that are more irradiated than the runaway greenhouse irradiation limit, meaning planets endowed with a steam, water-dominated atmosphere. For a given water-to-rock mass ratio, these new mass-radius relationships lead to planet bulk densities much lower than calculated when water is assumed to be in condensed form. In other words, using traditional mass-radius relationships for planets that are more irradiated than the runaway greenhouse irradiation limit tends to dramatically overestimate -- possibly by several orders of magnitude -- their bulk water content. In particular, this result applies to TRAPPIST-1 b, c, and d, which can accommodate a water mass fraction of at most 2, 0.3 and 0.08 %, respectively, assuming planetary core with a terrestrial composition. In addition, we show that significant changes of mass-radius relationships (between planets less and more irradiated than the runaway greenhouse limit) can be used to remove bulk composition degeneracies in multiplanetary systems such as TRAPPIST-1. Finally, we provide an empirical formula for the H2O steam atmosphere thickness which can be used to construct mass-radius relationships for any water-rich, rocky planet more irradiated than the runaway greenhouse irradiation threshold., Comment: Final version published in A&A. (small typos in Tables 1 and 2 have been corrected)

Despite the existence of co-orbital bodies in the solar system, and the prediction of the formation of co-orbital planets by planetary system formation models, no co-orbital exoplanets (also called trojans) have been detected thus far. Here we study the signature of co-orbital exoplanets in transit surveys when two planet candidates in the system orbit the star with similar periods. Such pair of candidates could be discarded as false positives because they are not Hill-stable. However, horseshoe or long libration period tadpole co-orbital configurations can explain such period similarity. This degeneracy can be solved by considering the Transit Timing Variations (TTVs) of each planet. We then focus on the three planet candidates system TOI-178: the two outer candidates of that system have similar orbital period and had an angular separation near $\pi/3$ during the TESS observation of sector 2. Based on the announced orbits, the long-term stability of the system requires the two close-period planets to be co-orbitals. Our independent detrending and transit search recover and slightly favour the three orbits close to a 3:2:2 resonant chain found by the TESS pipeline, although we cannot exclude an alias that would put the system close to a 4:3:2 configuration. We then analyse in more detail the co-orbital scenario. We show that despite the influence of an inner planet just outside the 2:3 mean-motion resonance, this potential co-orbital system can be stable on the Giga-year time-scale for a variety of planetary masses, either on a trojan or a horseshoe orbit. We predict that large TTVs should arise in such configuration with a period of several hundred days. We then show how the mass of each planet can be retrieved from these TTVs.

Cyclic sedimentation has varied at several timescales and this variability has been geologically well documented at Milankovitch timescales, controlled in part by climatically (insolation) driven sea-level changes. At the longer (tens of Myr) timescales connection between astronomical parameters and sedimentation via cyclic solar-system motions within the Milky Way has also been proposed, but this hypothesis remains controversial because of the lack of long geological records. The absence of a physical mechanism that could explain the connection between climate and astronomy at these longer timescales led to the explanation of plate motions as the main driver of climate on Earth. Here we statistically show a prominent and persistent ~36 Myr sedimentary cyclicity superimposed on two megacycles (~250 Myr) in a relatively well-constrained sea-level (SL) record of the past 542 Myr (Phanerozoic eon). Given the possible link between amplitudes of the ~36 and ~250 Myr cyclicities in SL record and the potential that these periodicities fall into the frequency band of solar system motions, we suggest an astronomical origin, and model these periodicities as originating from the path of the solar system in the Milky Way as vertical and radial periods that modulate the flux of cosmic rays on Earth. Our finding of the ~36 Myr SL cyclicity lends credibility to the existing hypothesis about the imprint of solar-system vertical period on the geological record. The ~250 Myr megacycles are tentatively attributed to a radial period. However, the tectonic drivers also remain potentially plausible. The potential existence of a correlation between the modeled astronomical signal and the geological record may offer an indirect proxy to understand the structure and history of the Milky Way by providing a 542 Myr long record of the path of the Sun in our Galaxy., Comment: 47 pages, 19 figures, Accepted for publication in Global and Planetary Change

In the context of the ESA M5 (medium mission) call we proposed a new satellite mission, Theia, based on relative astrometry and extreme precision to study the motion of very faint objects in the Universe. Theia is primarily designed to study the local dark matter properties, the existence of Earth-like exoplanets in our nearest star systems and the physics of compact objects. Furthermore, about 15 $\%$ of the mission time was dedicated to an open observatory for the wider community to propose complementary science cases. With its unique metrology system and "point and stare" strategy, Theia's precision would have reached the sub micro-arcsecond level. This is about 1000 times better than ESA/Gaia's accuracy for the brightest objects and represents a factor 10-30 improvement for the faintest stars (depending on the exact observational program). In the version submitted to ESA, we proposed an optical (350-1000nm) on-axis TMA telescope. Due to ESA Technology readiness level, the camera's focal plane would have been made of CCD detectors but we anticipated an upgrade with CMOS detectors. Photometric measurements would have been performed during slew time and stabilisation phases needed for reaching the required astrometric precision., Comment: http://theia.phyip3.dur.ac.uk

We present a novel approach for analysing radial velocity data that combines two features: all the planets are searched at once and the algorithm is fast. This is achieved by utilizing compressed sensing techniques, which are modified to be compatible with the Gaussian processes framework. The resulting tool can be used like a Lomb-Scargle periodogram and has the same aspect but with much fewer peaks due to aliasing. The method is applied to five systems with published radial velocity data sets: HD 69830, HD 10180, 55 Cnc, GJ 876 and a simulated very active star. The results are fully compatible with previous analysis, though obtained more straightforwardly. We further show that 55 Cnc e and f could have been respectively detected and suspected in early measurements from the Lick observatory and Hobby-Eberly Telescope available in 2004, and that frequencies due to dynamical interactions in GJ 876 can be seen., Comment: Accepted for publication in MNRAS