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J. -B. Delisle

Publications and source records attributed to J. -B. Delisle.

At least 19 recordsLinked to original sources

Inferring planet occurrence rates from radial velocities

We introduce a new method to infer the posterior distribution for planet occurrence rates from radial-velocity (RV) observations. The approach combines posterior samples from the analysis of individual RV datasets of several stars, using importance sampling to reweight them appropriately. This eliminates the need for injection-recovery tests to compute detection limits and avoids the explicit definition of a detection threshold. We validate the method on simulated RV datasets and show that it yields unbiased estimates of the occurrence rate in different regions, with increasing precision as more stars are included in the analysis.

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TOI-7510: A solar-analog system of three transiting giant planets near a Laplace resonance chain

We report the confirmation and initial characterization of a compact and dynamically rich multiple giant planet system orbiting the solar analog TOI-7510. The system was recently identified as a candidate two-planet system in a machine-learning search of the TESS light curves. Using TESS data and photometric follow-up observations with ASTEP, CHEOPS, and EulerCam, we show that one transit was initially misattributed and that the system consists of three transiting giant planets with orbital periods of 11.5, 22.6, and 48.9 days. The planets have radii of 0.65, 0.96, and 0.94 R_J, making them the largest known trio of transiting planets. The system architecture lies near a 4:2:1 mean motion resonant chain, inducing large transit timing variations for all three planets. Photodynamical modeling gives mass estimates of 0.057, 0.41, and 0.60 M_J and favors low eccentricities and mutual inclinations. TOI-7510 is an interesting system for investigating the dynamical interactions and formation histories of compact systems of giant planets.

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Architecture of planetary systems with and without outer giant planets I. Inner planet detections around HD 23079, HD 196067, and HD 86226

Understanding the link between outer giant planets (OGPs) and inner light planets (ILPs) is key to understanding planetary system formation and architecture. The correlation between these two populations of planets is debated both theoretically -- different formation models predict either a correlation or an anticorrelation -- and observationally. Several recent attempts to constrain this correlation have yielded contradictory results, due to small-number statistics and heterogeneous samples. We present an ongoing long-term observational effort with CORALIE, HARPS, and ESPRESSO to probe the ILP occurrence in systems with and without OGP. In this first article of a series, we discuss how, from the design to the observations, we ensured the homogeneity of the samples, both in terms of stellar properties and observing strategy. We also present the first three detections of ILPs in our OGP host sample. We find a 8.3 mE planet at 5.75 d around HD 23079, a 10.4 mE planet at 4.6 d around HD 196067, and we confirm the 7.5 mE planet at 3.98 d around HD 86226. While a rigorous statistical analysis of our samples will be performed in subsequent studies, the relatively low number of detections in our sample seems to contradict previous studies that found a strong OGP-ILP correlation.

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The JADE code. II. Modeling the coupled orbital and atmospheric evolution of GJ 436 b to constrain its migration and companion

The observed architecture and modeled evolution of close-in exoplanets provide crucial insights into their formation pathways and survival mechanisms. To investigate these fundamental questions, we employed JADE, a comprehensive numerical code that models the coupled evolution of atmospheres and dynamics over secular timescales, rooted in present-day observations. JADE integrates photoevaporation with migration driven by von Zeipel-Lidov-Kozai (ZLK) cycles from an external perturber, allowing us to explore evolutionary scenarios where dynamical and atmospheric processes influence each other. Here, we specifically considered GJ 436 b, a warm Neptune with an eccentric orbit and polar spin-orbit angle that has survived within the "hot Neptune desert" despite ongoing atmospheric escape. Our extensive exploration included over 500 000 simulations in a framework that combines precomputed grids with Bayesian inference. This allowed us to constrain GJ 436 b's initial conditions and the properties of its putative companion within a ZLK hypothesis. Our results suggest that GJ 436 b formed at ~ 0.3 AU and, despite its current substantial atmospheric erosion, has experienced minimal cumulative mass loss throughout its history, thanks to a late inward migration triggered by a distant companion inducing ZLK oscillations. We find that initial mutual inclinations of 80° - 100° with this companion best reproduce the observed polar orbit. By combining our explored constraints with radial velocity detection limits, we identified the viable parameter space for the hypothetical GJ 436 c. We found that it strongly disfavors stellar and brown dwarf masses, which offers a useful guide for future observational searches. This work demonstrates how coupled modeling can shed light on the interplay shaping close-in exoplanets and explain the survival of volatile-rich worlds near the edges of the desert.

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A second low-mass planet orbiting the nearby M-dwarf GJ 536

GJ 536 is a low-mass star, located 10 pc away from the Sun, that hosts a low-mass planet orbiting with a period of 8.71 days. Based on an analysis of the radial velocity (RV) time series obtained from the available data of the spectrographs HARPS, HARPS-N, CARMENES and HIRES, we announce the discovery of a second low-mass planet orbiting the star. We performed a RV global analysis on RV, spectroscopic activity indicators, and ASAS photometry, within the multidimensional Gaussian process framework, updated the parameters of GJ 536 b, and found significant evidence of the presence of a second planet. GJ 536 c is a low-mass planet ($m_{p} \sin i$ = 5.89 $\pm$ 0.70 M$_{\oplus}$), orbiting with a period of 32.761 $\pm$ 0.015 days, at a distance of 0.1617 $\pm$ 0.0028 au from its parent star. It induces an RV semi-amplitude of 1.80 $\pm$ 0.20 m$\cdot$s$^{-1}$. Given its distance to the star, it receives a flux of 1.692 $\pm$ 0.069 F$_{\oplus}$, for an equilibrium temperature of 290.5 $\pm$ 9.5 K. We update the mass of the planet GJ 536 b to $m_{p} \sin i$ = 6.37 $\pm$ 0.38 M$_{\oplus}$. The orbits of both planets are consistent with circular. We explored the use of statistical Doppler imaging on the photometric and RV data, and find a tentative projected obliquity of the stellar rotation axis of 58$^{+16}_{-19}$ deg. Current evidence does not support the presence of additional planets with masses > 5 M$_{\oplus}$for orbital periods up to 100 days, or > 10 M$_{\oplus}$ for periods up to 1000 days.

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Mapping the exo-Neptunian landscape. A ridge between the desert and savanna

Atmospheric and dynamical processes are thought to play a major role in shaping the distribution of close-in exoplanets. A striking feature of such distribution is the Neptunian desert, a dearth of Neptunes on the shortest-period orbits. We aimed to define the boundaries of the Neptunian desert and study its transition into the savanna, a moderately populated region at larger orbital distances. We built a sample of planets and candidates based on the Kepler DR25 catalogue and weighed it according to the transit and detection probabilities. We delimited the Neptunian desert as the close-in region of the period-radius space with no planets at a 3$σ$ level, and provide the community with simple, ready-to-use approximate boundaries. We identified an overdensity of planets separating the Neptunian desert from the savanna (3.2 days $ \lessapprox P_{\rm orb}$ $\lessapprox$ 5.7 days) that stands out at a 4.7$σ$ level above the desert and at a 3.5$σ$ level above the savanna, which we propose to call the Neptunian ridge. The period range of the ridge matches that of the hot Jupiter pileup ($\simeq$3-5 days), which suggests that similar evolutionary processes might act on both populations. We find that the occurrence fraction between the pileup and warm Jupiters is about twice that between the Neptunian ridge and savanna. Our revised landscape supports a previous hypothesis that a fraction of Neptunes were brought to the edge of the desert (i.e. the newly identified ridge) through high-eccentricity tidal migration (HEM) late in their life, surviving the evaporation that eroded Neptunes having arrived earlier in the desert. The ridge thus appears as a true physical feature illustrating the interplay between photoevaporation and HEM, providing further evidence of their role in shaping the distribution of close-in Neptunes.

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The ANTARESS workflow I. Optimal extraction of spatially resolved stellar spectra with high-resolution transit spectroscopy

High-resolution spectrographs open a detailed window onto the atmospheres of stars and planets. As the number of systems observed with different instruments grows, it is crucial to develop a standard in analyzing spectral time series of exoplanet transits and occultations, for the benefit of reproducibility. Here, we introduce the ANTARESS workflow, a set of methods aimed at processing high-resolution spectroscopy datasets in a robust way and extracting accurate exoplanetary and stellar spectra. While a fast preliminary analysis can be run on order-merged 1D spectra and cross-correlation functions (CCFs), the workflow was optimally designed for extracted 2D echelle spectra to remain close to the original detector counts, limit the spectral resampling, and propagate the correlated noise. Input data from multiple instruments and epochs were corrected for relevant environmental and instrumental effects, processed homogeneously, and analyzed independently or jointly. In this first paper, we show how planet-occulted stellar spectra extracted along the transit chord and cleaned from planetary contamination provide a direct comparison with theoretical stellar models and enable a spectral and spatial mapping of the photosphere. We illustrate this application of the workflow to archival ESPRESSO data, using the Rossiter-McLaughlin effect Revolutions (RMR) technique to confirm the spin-orbit alignment of HD\,209458b and unveil biases in WASP-76b's published orbital architecture. Because the workflow is modular and its concepts are general, it can support new methods and be extended to additional spectrographs to find a range of applications beyond the proposed scope. In a companion paper, we will present how planet-occulted spectra can be processed further to extract and analyze planetary spectra decontaminated from the star, providing clean and direct measurements of atmospheric properties.

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Photo-dynamical characterisation of the TOI-178 resonant chain

The TOI-178 system consists of a nearby late K-dwarf transited by six planets in the super-Earth to mini-Neptune regime, with radii ranging from 1.2 to 2.9 earth radius and orbital periods between 1.9 and 20.7 days. All planets but the innermost one form a chain of Laplace resonances. The fine-tuning and fragility of such orbital configurations ensure that no significant scattering or collision event has taken place since the formation and migration of the planets in the protoplanetary disc, hence providing important anchors for planet formation models. We aim to improve the characterisation of the architecture of this key system, and in particular the masses and radii of its planets. In addition, since this system is one of the few resonant chains that can be characterised by both photometry and radial velocities, we aim to use it as a test bench for the robustness of the planetary mass determination with each technique. We perform a global analysis of all available photometry and radial velocity. We also try different sets of priors on the masses and eccentricity, as well as different stellar activity models, to study their effects on the masses estimated by each method. We show how stellar activity is preventing us from obtaining a robust mass estimation for the three outer planets using radial velocity data alone. We also show that our joint photo-dynamical and radial velocity analysis resulted in a robust mass determination for planets c to g, with precision of 12% for the mass of planet c, and better than 10% for planets d to g. The new precisions on the radii range from 2 to 3%. The understanding of this synergy between photometric and radial velocity measurements will be valuable during the PLATO mission. We also show that TOI-178 is indeed currently locked in the resonant configuration, librating around an equilibrium of the chain.

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A resonant sextuplet of sub-Neptunes transiting the bright star HD 110067

Planets with radii between that of the Earth and Neptune (hereafter referred to as sub-Neptunes) are found in close-in orbits around more than half of all Sun-like stars. Yet, their composition, formation, and evolution remain poorly understood. The study of multi-planetary systems offers an opportunity to investigate the outcomes of planet formation and evolution while controlling for initial conditions and environment. Those in resonance (with their orbital periods related by a ratio of small integers) are particularly valuable because they imply a system architecture practically unchanged since its birth. Here, we present the observations of six transiting planets around the bright nearby star HD 110067. We find that the planets follow a chain of resonant orbits. A dynamical study of the innermost planet triplet allowed the prediction and later confirmation of the orbits of the rest of the planets in the system. The six planets are found to be sub-Neptunes with radii ranging from 1.94 to 2.85 Re. Three of the planets have measured masses, yielding low bulk densities that suggest the presence of large hydrogen-dominated atmospheres.

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Exploring the Brown Dwarf Desert with Precision Radial Velocities and Gaia DR3 Astrometric Orbits

Context. The observed scarcity of brown dwarfs in close orbits (within 10 au) around solar-type stars poses significant questions about the origins of these substellar companions. These questions impact our broader understanding of planetary formation processes. However, to resolve these formation mechanisms, accurate observational constraints are essential. Most of the brown dwarfs have been discovered by radial velocity surveys, but this method introduces uncertainties due to its inability to determine the orbital inclination, leaving the true mass-and thus their true nature-unresolved. This highlights the crucial role of astrometric data, helping us distinguish between genuine brown dwarfs and stars. Aims. We aim to refine the mass estimates of massive companions to solar-type stars, mostly discovered through radial velocity measurements and subsequently validated using Gaia DR3 astrometry, to gain a clearer understanding of their true mass and occurrence rates. Methods. We selected a sample of 31 sources with substellar companion candidates validated by Gaia DR3 and with available radial velocities. Using the Gaia DR3 solutions as prior information, we performed an MCMC fit with the available radial velocity measurements to integrate these two sources of data and thus obtain an estimate of their true mass. Results. Combining radial velocity measurements with Gaia DR3 data led to more precise mass estimations, leading us to reclassify several systems initially labeled as brown dwarfs as low-mass stars. Out of the 32 analyzed companions, 13 are determined to be stars, 17 are sub-stellar, and 2 have inconclusive results with the current data. Importantly, using these updated masses, we reevaluated the occurrence rate of brown dwarf companions (13-80 M$_{jup}$ ) on close orbits (<10 au) in the CORALIE sample, determining a tentative occurrence rate of $0.8^{+0.3}_{-0.2}\%$

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A review of planetary systems around HD 99492, HD 147379 and HD 190007 with HARPS-N

The Rocky Planet Search (RPS) program is dedicated to a blind radial velocity (RV) search of planets around bright stars in the Northern hemisphere, using the high-resolution echelle spectrograph HARPS-N installed on the Telescopio Nazionale Galileo (TNG). The goal of this work is to revise and update the properties of three planetary systems by analysing the HARPS-N data with state-of-the-art stellar activity mitigation tools. The stars considered are HD 99492 (83Leo B), HD 147379 (Gl617 A) and HD 190007. We employ a systematic process of data modelling, that we selected from the comparison of different approaches. We use YARARA to remove instrumental systematics from the RV, and then use SPLEAF to further mitigate the stellar noise with a multidimensional correlated noise model. We also search for transit features in the Transiting Exoplanets Survey Satellite (TESS) data of these stars. We report on the discovery of a new planet around HD 99492, namely HD 99492 c, with an orbital period of 95.2 days and a minimum mass of msin i = 17.9 M_Earth, and refine the parameters of HD 99492 b. We also update and refine the Keplerian solutions for the planets around HD 147379 and HD 190007, but do not detect additional planetary signals. We discard the transiting geometry for the planets, but stress that TESS did not exhaustively cover all the orbital phases. The addition of the HARPS-N data, and the use of advanced data analysis tools, has allowed us to present a more precise view of these three planetary systems. It demonstrates once again the importance of long observational efforts such as the RPS program. Added to the RV exoplanet sample, these planets populate two apparently distinct populations revealed by a bimodality in the planets minimum mass distribution. The separation is located between 30 and 50 M_Earth.

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DREAM II. The spin-orbit angle distribution of close-in exoplanets under the lens of tides

The spin-orbit angle, or obliquity, is a powerful observational marker that allows us to access the dynamical history of exoplanetary systems. Here, we have examined the distribution of spin-orbit angles for close-in exoplanets and put it in a statistical context of tidal interactions between planets and their stars. We confirm the observed trends between the obliquity and physical quantities directly connected to tides, namely the stellar effective temperature, the planet-to-star mass ratio, and the scaled orbital distance. We further devised a tidal efficiency factor combining critical parameters that control the strength of tidal effects and used it to corroborate the strong link between the spin-orbit angle distribution and tidal interactions. In particular, we developed a readily usable formula to estimate the probability that a system is misaligned, which will prove useful in global population studies. By building a robust statistical framework, we reconstructed the distribution of the three-dimensional spin-orbit angles, allowing for a sample of nearly 200 true obliquities to be analyzed for the first time. This realistic distribution maintains the sky-projected trends, and additionally hints toward a striking pileup of truly aligned systems. The comparison between the full population and a pristine subsample unaffected by tidal interactions suggests that perpendicular architectures are resilient toward tidal realignment, providing evidence that orbital misalignments are sculpted by disruptive dynamical processes that preferentially lead to polar orbits. On the other hand, star-planet interactions seem to efficiently realign or quench the formation of any tilted configuration other than for polar orbits, and in particular for antialigned orbits.

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Two temperate Earth-mass planets orbiting the nearby star GJ1002

We report the discovery and characterisation of two Earth-mass planets orbiting in the habitable zone of the nearby M-dwarf GJ~1002 based on the analysis of the radial-velocity (RV) time series from the ESPRESSO and CARMENES spectrographs. The host star is the quiet M5.5~V star GJ~1002 (relatively faint in the optical, $V \sim 13.8$ mag, but brighter in the infrared, $J \sim 8.3$ mag), located at 4.84 pc from the Sun. We analyse 139 spectroscopic observations taken between 2017 and 2021. We performed a joint analysis of the time series of the RV and full-width half maximum (FWHM) of the cross-correlation function (CCF) to model the planetary and stellar signals present in the data, applying Gaussian process regression to deal with the stellar activity. We detect the signal of two planets orbiting GJ~1002. GJ~1002~b is a planet with a minimum mass $m_p \sin i $ of 1.08 $\pm$ 0.13 M$_{\oplus}$ with an orbital period of 10.3465 $\pm$ 0.0027 days at a distance of 0.0457 $\pm$ 0.0013 au from its parent star, receiving an estimated stellar flux of 0.67 $F_{\oplus}$. GJ~1002 c is a planet with a minimum mass $m_p \sin i $ of 1.36 $\pm$ 0.17 M$_{\oplus}$ with an orbital period of 21.202 $\pm$ 0.013 days at a distance of 0.0738 $\pm$ 0.0021 au from its parent star, receiving an estimated stellar flux of 0.257 $F_{\oplus}$. We also detect the rotation signature of the star, with a period of 126 $\pm$ 15 days. GJ~1002 is one of the few known nearby systems with planets that could potentially host habitable environments. The closeness of the host star to the Sun makes the angular sizes of the orbits of both planets ($\sim$ 9.7 mas and $\sim$ 15.7 mas, respectively) large enough for their atmosphere to be studied via high-contrast high-resolution spectroscopy with instruments such as the future spectrograph ANDES for the ELT or the LIFE mission.

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Analytical determination of orbital elements using Fourier analysis. II. Gaia astrometry and its combination with radial velocities

The ESA global astrometry space mission Gaia has been monitoring the position of a billion stars since 2014. The analysis of such a massive dataset is challenging in terms of the data processing involved. In particular, the blind detection and characterization of single or multiple companions to stars (planets, brown dwarfs, or stars) using Gaia astrometry requires highly efficient algorithms. In this article, we present a set of analytical methods to detect and characterize companions in scanning space astrometric time series as well as via a combination of astrometric and radial velocity time series. We propose a general linear periodogram framework and we derive analytical formulas for the false alarm probability (FAP) of periodogram peaks. Once a significant peak has been identified, we provide analytical estimates of all the orbital elements of the companion based on the Fourier decomposition of the signal. The periodogram, FAP, and orbital elements estimates can be computed for the astrometric and radial velocity time series separately or in tandem. These methods are complementary with more accurate and more computationally intensive numerical algorithms (e.g., least-squares minimization, Markov chain Monte Carlo, genetic algorithms). In particular, our analytical approximations can be used as an initial condition to accelerate the convergence of numerical algorithms. Our formalism has been partially implemented in the Gaia exoplanet pipeline for the third Gaia data release. Since the Gaia astrometric time series are not yet publicly available, we illustrate our methods on the basis of Hipparcos data, together with on-ground CORALIE radial velocities, for three targets known to host a companion: HD 223636 (HIP 117622), HD 17289 (HIP 12726), and HD 3277 (HIP 2790).

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A CHEOPS-enhanced view of the HD3167 system

Much remains to be understood about the nature of exoplanets smaller than Neptune, most of which have been discovered in compact multi-planet systems. With its inner ultra-short period planet b aligned with the star and two larger outer planets d-c on polar orbits, the multi-planet system HD 3167 features a peculiar architecture and offers the possibility to investigate both dynamical and atmospheric evolution processes. To this purpose we combined multiple datasets of transit photometry and radial velocimetry (RV) to revise the properties of the system and inform models of its planets. This effort was spearheaded by CHEOPS observations of HD 3167b, which appear inconsistent with a purely rocky composition despite its extreme irradiation. Overall the precision on the planetary orbital periods are improved by an order of magnitude, and the uncertainties on the densities of the transiting planets b and c are decreased by a factor of 3. Internal structure and atmospheric simulations draw a contrasting picture between HD 3167d, likely a rocky super-Earth that lost its atmosphere through photo-evaporation, and HD 3167c, a mini-Neptune that kept a substantial primordial gaseous envelope. We detect a fourth, more massive planet on a larger orbit, likely coplanar with HD 3167d-c. Dynamical simulations indeed show that the outer planetary system d-c-e was tilted, as a whole, early in the system history, when HD 3167b was still dominated by the star influence and maintained its aligned orbit. RV data and direct imaging rule out that the companion that could be responsible for the present-day architecture is still bound to the HD\,3167 system. Similar global studies of multi-planet systems will tell how many share the peculiar properties of the HD3167 system, which remains a target of choice for follow-up observations and simulations.

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Global dynamics and architecture of the Kepler-444 system

S-type planets, which orbit one component of multiple-star systems, place strong constraints on the planet formation and evolution models. A notable case study is Kepler-444, a triple-star system whose primary is orbited by five planets smaller than Venus in a compact configuration, and for which the stellar binary companion revolves around the primary on a highly eccentric orbit. Having access to the most precise up-to-date masses and orbital parameters is highly valuable to understand formation and evolution processes. We provide the first full dynamical exploration of this system, with the goal to refine those parameters. The planetary system does not appear in any of low-order two or three-planet mean-motion resonances (MMR). We provide the most precise up-to-date dynamical parameters for the planets and the stellar binary companion, using an approach that makes use of the Numerical Analysis of Fundamental Frequencies (NAFF) fast chaos indicator. The orbit of the latter is constrained by new observations from HIRES and Gaia, and also by the stability analysis. This update further challenges the planets formation processes. We also test the dynamical plausibility of a sixth planet in the system, following hints observed in the Hubble Space Telescope (HST) data. We find that this putative planet could exist over a broad range of masses, and with an orbital period roughly comprised between 12 and 20 days. We note an overall good agreement of the system with short-term orbital stability. This suggests that a diverse range of planetary system architectures could be found in multiple-star systems, potentially further challenging the planet formation models.

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Unbiasing the density of TTV-characterised sub-Neptunes: Update of the mass-radius relationship of 34 Kepler planets

Transit Timing Variations (TTVs) can provide useful information on compact multi-planetary systems observed by transits, by putting constraints on the masses and eccentricities of the observed planets. This is especially helpful when the host star is not bright enough for radial velocity follow-up. However, in the past decades, numerous works have shown that TTV-characterised planets tend to have a lower densities than RV-characterised planets. Re-analysing 34 Kepler planets in the super-Earth to sub-Neptunes range using the RIVERS approach, we show that at least part of these discrepancies was due to the way transit timings were extracted from the light curve, which had a tendency to under-estimate the TTV amplitudes. We recover robust mass estimates (i.e. low prior dependency) for 23 of the planets. We compare these planets the RV-characterised population. A large fraction of these previously had a surprisingly low density now occupy a place of the mass-radius diagram much closer to the bulk of the known planets, although a slight shift toward lower densities remains, which could indicate that the compact multi-planetary systems characterised by TTVs are indeed composed of planets which are different from the bulk of the RV-characterised population. These results are especially important for obtaining an unbiased view of the compact multi-planetary systems detected by Kepler, TESS, and the upcoming PLATO mission.

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A general stability-driven approach for the refinement of multi-planet systems

Over the past years, the amount of detected multi-planet systems significantly grew, an important sub-class of which being the compact configurations. A precise knowledge of them is crucial to understand the conditions with which planetary systems form and evolve. However, observations often leave these systems with large uncertainties, notably on the orbital eccentricities. This is especially prominent for systems with low-mass planets detected with Radial Velocities (RV), the amount of which is more and more important in the exoplanet population. It is becoming a common approach to refine these parameters with the help of orbital stability arguments. Such dynamical techniques can be computationally expensive. In this work we use an alternative procedure faster by orders of magnitude than classical N-body integration approaches. We couple a reliable exploration of the parameter space with the precision of the Numerical Analysis of Fundamental Frequencies (NAFF, Laskar 1990) fast chaos indicator. We also propose a general procedure to calibrate the NAFF indicator on any multi-planet system without additional computational cost. This calibration strategy is illustrated on HD 45364, in addition to yet-unpublished measurements obtained with the HARPS and CORALIE high-resolution spectrographs. We validate the calibration approach on HD 202696. We test the performances of this stability-driven approach on two systems with different architectures. First we study HD 37124, a 3-planet system composed of planets in the Jovian regime. Then, we analyse HD 215152, a compact system of four low-mass planets. We demonstrate the potential of the NAFF stability-driven approach to refine the orbital parameters and planetary masses. We stress the importance of undertaking systematic global dynamical analyses on every new multi-planet system discovered.

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