arXiv subjects

T. Moulin

Publications and source records attributed to T. Moulin.

At least 19 recordsLinked to original sources

arXiv2026

The SPHERE infrared survey for exoplanets (SHINE) V. Full sample characterization

Unbiased surveys of large stellar samples are the prime means through which the prevalence of exoplanets can be derived, and crucial constraints to planet formation models can be set. Direct imaging (DI) is ideally positioned to probe the outer regions (5-300au) of planetary systems, providing complementary information to techniques such as transits and radial velocities. We present the full sample of the SpHere INfrared survey for Exoplanets (SHINE), the second largest DI campaign to date. SHINE observed 460 stars between 2015 and 2023 thanks to the guaranteed time observations (GTO) allocated by ESO to the SPHERE consortium at VLT. The goal of this paper is to homogeneously derive the stellar properties of the targets and to define a subsample of young single hosts to be used as a starting point for the final statistical analysis of the survey. Stellar ages were determined based on kinematic indicators (such as the membership to young moving groups), age diagnostics (lithium abundance, rotation, activity), and isochrone fitting. A thorough vetting for binarity was undertaken combining astrometric, spectroscopic, and imaging data. A subsample of 333 stars, covering a large extent of stellar ages and masses, was constructed. Selection criteria, global features, as well as the properties of individual stars are reported and discussed.

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arXiv2025

First Light for the GRAVITY+ Adaptive Optics: Extreme Adaptive Optics for the Very Large Telescope Interferometer

GRAVITY+ improves by orders of magnitude the sensitivity, sky-coverage and contrast of the Very Large Telescope Interferometer (VLTI). A central part of this project is the development of Gravity Plus Adaptive Optics (GPAO), a dedicated high-order and laser-guide star Adaptive Optics (AO) system for VLTI. GPAO consists of four state-of-the-art AO systems equipping all 8m-class Unit Telescopes (UTs) for the wavefront correction of the VLTI instruments. It offers both visible and infrared Natural Guide Star (NGS) and Laser Guide Star (LGS) operations. The paper presents the design, operations and performances of GPAO. We illustrate the improvement brought by GPAO with interferometric observations obtained during the commissioning of the NGS mode end-2024. These science results include the first optical interferometry observations of a redshift $z\sim4$ quasar, the spectroscopy of a cool brown-dwarf with magnitude $K\sim 21.0$, the first observations of a Class I young star with GRAVITY, and the first sub-micro arcsecond differential astrometry in the optical. Together with the entire GRAVITY+ project, the implementation of GPAO is a true paradigm shift for observing the optical Universe at very high angular resolution.

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arXiv2025

The SPHERE infrared survey for exoplanets (SHINE). V. Complete observations, data reduction and analysis, detection performances, and final results

During the past decade, state-of-the-art planet-finder instruments like SPHERE@VLT, coupling coronagraphic devices and extreme adaptive optics systems, unveiled, thanks to large surveys, around 20 planetary mass companions at semi-major axis greater than 10 astronomical units. Direct imaging being the only detection technique to be able to probe this outer region of planetary systems, the SPHERE infrared survey for exoplanets (SHINE) was designed and conducted from 2015 to 2021 to study the demographics of such young gas giant planets around 400 young nearby solar-type stars. In this paper, we present the observing strategy, the data quality, and the point sources analysis of the full SHINE statistical sample as well as snapSHINE. Both surveys used the SPHERE@VLT instrument with the IRDIS dual band imager in conjunction with the integral field spectrograph IFS and the angular differential imaging observing technique. All SHINE data (650 datasets), corresponding to 400 stars, including the targets of the F150 survey, are processed in a uniform manner with an advanced post-processing algorithm called PACO ASDI. An emphasis is put on the classification and identification of the most promising candidate companions. Compared to the previous early analysis SHINE F150, the use of advanced post-processing techniques significantly improved by one or 2 magnitudes (x3-x6) the contrast detection limits, which will allow us to put even tighter constraints on the radial distribution of young gas giants. This increased sensitivity directly places SHINE as the largest and deepest direct imaging survey ever conducted. We detected and classified more than 3500 physical sources. One additional substellar companion has been confirmed during the second phase of the survey (HIP 74865 B), and several new promising candidate companions are awaiting second epoch confirmations.

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arXiv2024

The SPHERE view of the Taurus star-forming region

The sample of planet-forming disks observed by high-contrast imaging campaigns over the last decade is mature enough to enable the demographical analysis of individual star-forming regions. We present the full census of Taurus sources with VLT/SPHERE polarimetric images available. The whole sample sums up to 43 targets (of which 31 have not been previously published) corresponding to one-fifth of the Class II population in Taurus and about half of such objects that are observable. A large fraction of the sample is apparently made up of isolated faint disks (equally divided between small and large self-shadowed disks). Ambient signal is visible in about one-third of the sample. This probes the interaction with the environment and with companions or the outflow activity of the system. The central portion of the Taurus region almost exclusively hosts faint disks, while the periphery also hosts bright disks interacting with their surroundings. The few bright disks are found around apparently older stars. The overall picture is that the Taurus region is in an early evolutionary stage of planet formation. Yet, some objects are discussed individually, as in an intermediate or exceptional stage of the disk evolution. This census provides a first benchmark for the comparison of the disk populations in different star forming regions.

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arXiv2021

A SPHERE survey of self-shadowed planet-forming disks

To date, nearly two hundred planet-forming disks have been imaged with high resolution. Our propensity to study bright and extended objects is however biasing our view of the disk demography. In this work, we contribute to alleviate this bias by analyzing fifteen disks targeted with VLT/SPHERE that look faint in scattered light. Sources were selected based on a low far-IR excess from the spectral energy distribution. The comparison with the ALMA images available for a few sources shows that the scattered light surveyed by these datasets is only detected from a small portion of the disk extent. The mild anti-correlation between the disk brightness and the near-IR excess demonstrates that these disks are self-shadowed: the inner disk rim intercepts much starlight and leaves the outer disk in penumbra. Based on the uniform distribution of the disk brightness in scattered light across all spectral types, self-shadowing would act similarly for inner rims at a different distance from the star. We discuss how the illumination pattern of the outer disk may evolve with time. Some objects in the sample are proposed to be at an intermediate stage toward bright disks from the literature with either no shadow or with sign of azimuthally confined shadows.

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arXiv2021

TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrA

We present the confirmation of a new sub-Neptune close to the transition between super-Earths and sub-Neptunes transiting the M2 dwarf TOI- 269 (TIC 220479565, V = 14.4 mag, J = 10.9 mag, Rstar = 0.40 Rsun, Mstar = 0.39 Msun, d = 57 pc). The exoplanet candidate has been identified in multiple TESS sectors, and validated with high-precision spectroscopy from HARPS and ground-based photometric follow-up from ExTrA and LCO-CTIO. We determined mass, radius, and bulk density of the exoplanet by jointly modeling both photometry and radial velocities with juliet. The transiting exoplanet has an orbital period of P = 3.6977104 +- 0.0000037 days, a radius of 2.77 +- 0.12 Rearth, and a mass of 8.8 +- 1.4 Mearth. Since TOI-269 b lies among the best targets of its category for atmospheric characterization, it would be interesting to probe the atmosphere of this exoplanet with transmission spectroscopy in order to compare it to other sub-Neptunes. With an eccentricity e = 0.425+0.082-0.086, TOI-269 b has one of the highest eccentricities of the exoplanets with periods less than 10 days. The star being likely a few Gyr old, this system does not appear to be dynamically young. We surmise TOI-269 b may have acquired its high eccentricity as it migrated inward through planet-planet interactions.

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arXiv2021

The SPHERE infrared survey for exoplanets (SHINE)- I Sample definition and target characterization

Large surveys with new-generation high-contrast imaging instruments are needed to derive the frequency and properties of exoplanet populations with separations from $\sim$5 to 300 AU. A careful assessment of the stellar properties is crucial for a proper understanding of when, where, and how frequently planets form, and how they evolve. The sensitivity of detection limits to stellar age makes this a key parameter for direct imaging surveys. We describe the SpHere INfrared survey for Exoplanets (SHINE), the largest direct imaging planet-search campaign initiated at the VLT in 2015 in the context of the SPHERE Guaranteed Time Observations of the SPHERE consortium. In this first paper we present the selection and the properties of the complete sample of stars surveyed with SHINE, focusing on the targets observed during the first phase of the survey (from February 2015 to February 2017). This early sample composed of 150 stars is used to perform a preliminary statistical analysis of the SHINE data, deferred to two companion papers presenting the survey performance, main discoveries, and the preliminary statistical constraints set by SHINE. Based on a large database collecting the stellar properties of all young nearby stars in the solar vicinity (including kinematics, membership to moving groups, isochrones, lithium abundance, rotation, and activity), we selected the original sample of 800 stars that were ranked in order of priority according to their sensitivity for planet detection in direct imaging with SPHERE. The properties of the stars that are part of the early statistical sample were revisited, including for instance measurements from the GAIA Data Release 2.

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arXiv2021

The SPHERE infrared survey for exoplanets (SHINE) -- II. Observations, Data reduction and analysis Detection performances and early-results

Over the past decades, direct imaging has confirmed the existence of substellar companions (exoplanets or brown dwarfs) on wide orbits (>10 au) from their host stars. To understand their formation and evolution mechanisms, we have initiated in 2015 the SPHERE infrared survey for exoplanets (SHINE), a systematic direct imaging survey of young, nearby stars to explore their demographics.} {We aim to detect and characterize the population of giant planets and brown dwarfs beyond the snow line around young, nearby stars. Combined with the survey completeness, our observations offer the opportunity to constrain the statistical properties (occurrence, mass and orbital distributions, dependency on the stellar mass) of these young giant planets.} {In this study, we present the observing and data analysis strategy, the ranking process of the detected candidates, and the survey performances for a subsample of 150 stars, which are representative of the full SHINE sample. The observations were conducted in an homogeneous way from February 2015 to February 2017 with the dedicated ground-based VLT/SPHERE instrument equipped with the IFS integral field spectrograph and the IRDIS dual-band imager covering a spectral range between 0.9 and 2.3 $μ$m. We used coronographic, angular and spectral differential imaging techniques to reach the best detection performances for this study down to the planetary mass regime.}

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arXiv2020

Investigating three Sirius-like systems with SPHERE

Sirius-like systems are wide binaries composed of a white dwarf (WD) and a companion of a spectral type earlier than M0. The WD progenitor evolves in isolation, but its wind during the AGB phase pollutes the companion surface and transfers some angular momentum. Within SHINE survey that uses SPHERE at the VLT, we acquired images of HD2133, HD114174, and CD-567708 and combined this data with high resolution spectra of the primaries, TESS, and literature data. We performed accurate abundance analyses for the MS. We found brighter J and K magnitudes for HD114174B than obtained previously and extended the photometry down to 0.95 micron. Our new data indicate a higher temperature and then shorter cooling age (5.57+/-0.02 Gyr) and larger mass (0.75+/-0.03 Mo) for this WD than previously assumed. This solved the discrepancy previously found with the age of the MS star. The two other WDs are less massive, indicating progenitors of ~1.3 Mo and 1.5-1.8 Mo for HD2133B and CD-56 7708B, respectively. We were able to derive constraints on the orbit for HD114174 and CD-56 7708. The composition of the MS stars agrees fairly well with expectations from pollution by the AGB progenitors of the WDs: HD2133A has a small enrichment of n-capture elements, which is as expected for pollution by an AGB star with a mass <1.5 Mo; CD-56 7708A is a previously unrecognized mild Ba-star, which is expected due to pollution by an AGB star with a mass in the range of 1.5-3.0 Mo; and HD114174 has a very moderate excess of n-capture elements, which is in agreement with the expectation for a massive AGB star to have a mass >3.0 Mo. On the other hand, none of these stars show the excesses of C that are expected to go along with those of n-capture elements. This might be related to the fact that these stars are at the edges of the mass range where we expect nucleosynthesis related to thermal pulses.

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arXiv2020

The SPHERE infrared survey for exoplanets (SHINE). III. The demographics of young giant exoplanets below 300 au with SPHERE

The SHINE project is a 500-star survey performed with SPHERE on the VLT for the purpose of directly detecting new substellar companions and understanding their formation and early evolution. Here we present an initial statistical analysis for a subsample of 150 stars that are representative of the full SHINE sample. Our goal is to constrain the frequency of substellar companions with masses between 1 and 75 MJup and semimajor axes between 5 and 300 au. We adopt detection limits as a function of angular separation from the survey data for all stars converted into mass and projected orbital separation using the BEX-COND-hot evolutionary tracks and known distance to each system. Based on the results obtained for each star and on the 13 detections in the sample, we use a MCMC tool to compare our observations to two different types of models. The first is a parametric model based on observational constraints, and the second type are numerical models that combine advanced core accretion and gravitational instability planet population synthesis. Using the parametric model, we show that the frequencies of systems with at least one substellar companion are $23.0_{-9.7}^{+13.5}\%$, $5.8_{-2.8}^{+4.7}\%$, and $12.6_{-7.1}^{+12.9}\%$ for BA, FGK, and M stars, respectively. We also demonstrate that a planet-like formation pathway probably dominates the mass range from 1-75 MJup for companions around BA stars, while for M dwarfs, brown dwarf binaries dominate detections. In contrast, a combination of binary star-like and planet-like formation is required to best fit the observations for FGK stars. Using our population model and restricting our sample to FGK stars, we derive a frequency of $5.7_{-2.8}^{+3.8}\%$, consistent with predictions from the parametric model. More generally, the frequency values that we derive are in excellent agreement with values obtained in previous studies.

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arXiv2020

A family portrait of disk inner rims around Herbig Ae/Be stars: Hunting for warps, rings, self shadowing, and misalignments in the inner astronomical units

The innermost astronomical unit in protoplanetary disks is a key region for stellar and planet formation, as exoplanet searches have shown a large occurrence of close-in planets that are located within the first au around their host star. We aim to reveal the morphology of the disk inner rim using near-infrared interferometric observations with milli-arcsecond resolution provided by infrared interferometry. We provide reconstructed images of 15 objects selected from the Herbig AeBe survey carried out with PIONIER at the VLTI, using SPARCO. We find that 40% of the systems are centrosymmetric at the angular resolution of the observations. For the rest of the objects, we find evidence for asymmetric emission due to moderate-to-strong inclination of a disk-like structure for 30% of the objects and noncentrosymmetric morphology due to a nonaxisymmetric and possibly variable environment (30%). Among the systems with a disk-like structure, 20% show a resolved dust-free cavity. The image reconstruction process is a powerful tool to reveal complex disk inner rim morphologies. At the angular resolution reached by near-infrared interferometric observations, most of the images are compatible with a centrally peaked emission (no cavity). For the most resolved targets, image reconstruction reveals morphologies that cannot be reproduced by generic parametric models. Moreover, the nonaxisymmetric disks show that the spatial resolution probed by optical interferometers makes the observations of the near-infrared emission sensitive to temporal evolution with a time-scale down to a few weeks. The evidence of nonaxisymmetric emission that cannot be explained by simple inclination and radiative transfer effects requires alternative explanations, such as a warping of the inner disks. Interferometric observations can, therefore, be used to follow the evolution of the asymmetry of those disks at a sub-au scale.

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arXiv2020

Spirals inside the millimeter cavity of transition disk SR 21

Hydrodynamical simulations of planet-disk interactions suggest that planets may be responsible for a number of the sub-structures frequently observed in disks in both scattered light and dust thermal emission. Despite the ubiquity of these features, direct evidence of planets embedded in disks and of the specific interaction features like spiral arms within planetary gaps still remain rare. In this study we discuss recent observational results in the context of hydrodynamical simulations in order to infer the properties of a putative embedded planet in the cavity of a transition disk. We imaged the transition disk SR 21 in H-band in scattered light with SPHERE/IRDIS and in thermal dust emission with ALMA band 3 (3mm) observations at a spatial resolution of 0.1". We combine these datasets with existing band 9 (430um) and band 7 (870um) ALMA continuum data. The Band 3 continuum data reveals a large cavity and a bright ring peaking at 53 au strongly suggestive of dust trapping.The ring shows a pronounced azimuthal asymmetry, with a bright region in the north-west that we interpret as a dust over-density. A similarly-asymmetric ring is revealed at the same location in polarized scattered light, in addition to a set of bright spirals inside the mm cavity and a fainter spiral bridging the gap to the outer ring. These features are consistent with a number of previous hydrodynamical models of planet-disk interactions, and suggest the presence of a ~1 MJup planet at 44 au and PA=11°. This makes SR21 the first disk showing spiral arms inside the mm cavity, as well as one for which the location of a putative planet can be precisely inferred. With the location of a possible planet being well-constrained by observations, it is an ideal candidate for follow-up observations to search for direct evidence of a planetary companion still embedded in its disk.

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arXiv2019

SPHERE: the exoplanet imager for the Very Large Telescope

Observations of circumstellar environments to look for the direct signal of exoplanets and the scattered light from disks has significant instrumental implications. In the past 15 years, major developments in adaptive optics, coronagraphy, optical manufacturing, wavefront sensing and data processing, together with a consistent global system analysis have enabled a new generation of high-contrast imagers and spectrographs on large ground-based telescopes with much better performance. One of the most productive is the Spectro-Polarimetic High contrast imager for Exoplanets REsearch (SPHERE) designed and built for the ESO Very Large Telescope (VLT) in Chile. SPHERE includes an extreme adaptive optics system, a highly stable common path interface, several types of coronagraphs and three science instruments. Two of them, the Integral Field Spectrograph (IFS) and the Infra-Red Dual-band Imager and Spectrograph (IRDIS), are designed to efficiently cover the near-infrared (NIR) range in a single observation for efficient young planet search. The third one, ZIMPOL, is designed for visible (VIR) polarimetric observation to look for the reflected light of exoplanets and the light scattered by debris disks. This suite of three science instruments enables to study circumstellar environments at unprecedented angular resolution both in the visible and the near-infrared. In this work, we present the complete instrument and its on-sky performance after 4 years of operations at the VLT.

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arXiv2019

Optical polarized phase function of the HR\,4796A dust ring

The scattering properties of the dust originating from debris discs are still poorly known. The analysis of scattered light is however a powerful remote-sensing tool to understand the physical properties of dust particles orbiting other stars. Scattered light is indeed widely used to characterise the properties of cometary dust in the solar system. We aim to measure the morphology and scattering properties of the dust from the debris ring around HR4796A in polarised optical light. We obtained high-contrast polarimetric images of HR4796A in the wavelength range 600-900nm with the SPHERE / ZIMPOL instrument on the Very Large Telescope. We measured for the first time the polarised phase function of the dust in a debris system over a wide range of scattering angles in the optical. We confirm that it is incompatible with dust particles being compact spheres under the assumption of the Mie theory, and propose alternative scenarios compatible with the observations, such as particles with irregular surface roughness or aggregate particles.

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arXiv2018

Post conjunction detection of $β$ Pictoris b with VLT/SPHERE

With an orbital distance comparable to that of Saturn in the solar system, \bpic b is the closest (semi-major axis $\simeq$\,9\,au) exoplanet that has been imaged to orbit a star. Thus it offers unique opportunities for detailed studies of its orbital, physical, and atmospheric properties, and of disk-planet interactions. With the exception of the discovery observations in 2003 with NaCo at the Very Large Telescope (VLT), all following astrometric measurements relative to \bpic have been obtained in the southwestern part of the orbit, which severely limits the determination of the planet's orbital parameters. We aimed at further constraining \bpic b orbital properties using more data, and, in particular, data taken in the northeastern part of the orbit. We used SPHERE at the VLT to precisely monitor the orbital motion of beta \bpic b since first light of the instrument in 2014. We were able to monitor the planet until November 2016, when its angular separation became too small (125 mas, i.e., 1.6\,au) and prevented further detection. We redetected \bpic b on the northeast side of the disk at a separation of 139\,mas and a PA of 30$^{\circ}$ in September 2018. The planetary orbit is now well constrained. With a semi-major axis (sma) of $a = 9.0 \pm 0.5$ au (1 $σ$), it definitely excludes previously reported possible long orbital periods, and excludes \bpic b as the origin of photometric variations that took place in 1981. We also refine the eccentricity and inclination of the planet. From an instrumental point of view, these data demonstrate that it is possible to detect, if they exist, young massive Jupiters that orbit at less than 2 au from a star that is 20 pc away.

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arXiv2018

VLT/SPHERE astrometric confirmation and orbital analysis of the brown dwarf companion HR 2562 B

Context. A low-mass brown dwarf has been recently imaged around HR 2562 (HD 50571), a star hosting a debris disk resolved in the far infrared. Interestingly, the companion location is compatible with an orbit coplanar with the disk and interior to the debris belt. This feature makes the system a valuable laboratory to analyze the formation of substellar companions in a circumstellar disk and potential disk-companion dynamical interactions. Aims. We aim to further characterize the orbital motion of HR 2562 B and its interactions with the host star debris disk. Methods. We performed a monitoring of the system over ~10 months in 2016 and 2017 with the VLT/SPHERE exoplanet imager. Results. We confirm that the companion is comoving with the star and detect for the first time an orbital motion at high significance, with a current orbital motion projected in the plane of the sky of 25 mas (~0.85 au) per year. No orbital curvature is seen in the measurements. An orbital fit of the SPHERE and literature astrometry of the companion without priors on the orbital plane clearly indicates that its orbit is (quasi-)coplanar with the disk. To further constrain the other orbital parameters, we used empirical laws for a companion chaotic zone validated by N-body simulations to test the orbital solutions that are compatible with the estimated disk cavity size. Non-zero eccentricities (>0.15) are allowed for orbital periods shorter than 100 yr, while only moderate eccentricities up to ~0.3 for orbital periods longer than 200 yr are compatible with the disk observations. A comparison of synthetic Herschel images to the real data does not allow us to constrain the upper eccentricity of the companion.

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arXiv2018

GRAVITY chromatic imaging of Eta Car's core

Eta Car is one of the most intriguing luminous blue variables in the Galaxy. Observations and models at different wavelengths suggest a central binary with a 5.54 yr period residing in its core. 2D and 3D radiative transfer and hydrodynamic simulations predict a primary with a dense and slow stellar wind that interacts with the faster and lower density wind of the secondary. The wind-wind collision scenario suggests that the secondary's wind penetrates the primary's wind creating a low-density cavity in it, with dense walls where the two winds interact. We aim to trace the inner ~5-50 au structure of Eta Car's wind-wind interaction, as seen through BrG and, for the first time, through the He I 2s-2p line. We have used spectro-interferometric observations with GRAVITY at the VLTI. Our modeling of the continuum allows us to estimate its FWHM angular size close to 2 mas and an elongation ratio of 1.06 +/- 0.05 over a PA = 130 +/- 20 deg. Our CMFGEN modeling helped us to confirm that the role of the secondary should be taken into account to properly reproduce the observed BrG and He I lines. Chromatic images across BrG reveal a southeast arc-like feature, possibly associated to the hot post-shocked winds flowing along the cavity wall. The images of He I 2s-2p served to constrain the 20 mas structure of the line-emitting region. The observed morphology of He I suggests that the secondary is responsible for the ionized material that produces the line profile. Both the BrG and the He I 2s-2p maps are consistent with previous hydrodynamical models of the colliding wind scenario. Future dedicated simulations together with an extensive interferometric campaign are necessary to refine our constraints on the wind and stellar parameters of the binary, which finally will help us predict the evolutionary path of Eta Car.

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arXiv2018

The GJ 504 system revisited. Combining interferometric, radial velocity, and high contrast imaging data

The G-type star GJ504A is known to host a 3 to 35 MJup companion whose temperature, mass, and projected separation all contribute to make it a test case for the planet formation theories and for atmospheric models of giant planets and light brown dwarfs. We collected data from the CHARA interferometer, SOPHIE spectrograph, and VLT/SPHERE high contrast imager to revisit the properties of the system. We measure a radius of 1.35+/- 0.04Rsun for GJ504A which yields isochronal ages of 21+/-2Myr or 4.0+/-1.8Gyr for the system and line-of-sight stellar rotation axis inclination of $162.4_{-4.3}^{+3.8}$ degrees or $18.6_{-3.8}^{+4.3}$ degrees. We re-detect the companion in the Y2, Y3, J3, H2, and K1 dual band SPHERE images. The complete 1-4 $μ$m SED shape of GJ504b is best reproduced by T8-T9.5 objects with intermediate ages ($\leq1.5$Gyr), and/or unusual dusty atmospheres and/or super-solar metallicities. All six atmospheric models used yield $\mathrm{T_{eff}=550 \pm 50}$K for GJ504b and point toward a low surface gravity (3.5-4.0 dex). The accuracy on the metallicity value is limited by model-to-model systematics. It is not degenerate with the C/O ratio. We derive $\mathrm{log\:L/L_{\odot}=-6.15\pm0.15}$ dex for the companion compatible with masses of $\mathrm{M=1.3^{+0.6}_{-0.3}M_{Jup}}$ and $\mathrm{M=23^{+10}_{-9} M_{Jup}}$ for the young and old age ranges, respectively. The semi-major axis (sma) is above 27.8 au and the eccentricity lower than 0.55. The posterior on GJ~504b's orbital inclination suggests a misalignment with GJ~504A rotation axis. We combine the radial velocity and multi-epoch imaging data to exclude additional objects (90\% prob.) more massive than 2.5 and 30 $\mathrm{M_{Jup}}$ with sma in the range 0.01-80 au for the young and old system ages, respectively. The companion is in the envelope of the population of planets synthetized with our core-accretion model.

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