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A. -M. Lagrange

Publications and source records attributed to A. -M. Lagrange.

At least 91 records · Page 5Linked to original sources

ODEA: Orbital Dynamics in a complex Evolving Architecture -- Application to the planetary system HD 106906

Mixed-variable symplectic integrators are widely used in orbital dynamics. However, they have been developed for Solar system-type architectures, and can not handle evolving hierarchy, in particular in systems with two or more stellar components. Such configuration may have occurred in the history of HD 106906, a tight pair of F-type stars surrounded by a debris disk and a planetary-mass companion on a wide orbit. We present the new algorithm ODEA, based on the symplectic algorithm SWIFT HJS, that can model any system (binary,...) with unstable architecture. We study the peculiar system HD 106906 as a testcase for the code. We define and compute a criterion based on acceleration ratios to indicate when the initial hierarchy is not relevant anymore. A new hierarchy is then computed. The code is applied to study the two fly-bys that occurred on system HD 106906, recently evidenced by De Rosa & Kalas (2019), to determine if they could account for the wide orbit of the planet. Thousands of simulations have been performed to account for the uncertainty on the perturbers coordinates and velocities. The algorithm is able to handle any change of hierarchy, temporary or not. We used it to fully model HD 106906 encounters. The simulations confirm that the fly-bys could have stabilized the planet orbit, and show that it can account for the planet probable misalignment with respect to the disk plane as well as the disk morphology. However, that requires a small distance at closest approach (< 0.05 pc), and this configuration is not guaranteed. ODEA is a very good choice for the study of non-Solar type architecture. It can now adapt to an evolving hierarchy, and is thus suitable to study capture of planets and dust. Further observations of the perturbers, in particular their radial velocity, are required to conclude on the effects of the fly-by on system HD 106906.

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The detection and characterisation of 54 massive companions with the SOPHIE spectrograph -- 7 new brown dwarfs and constraints on the BD desert

Brown-dwarfs are substellar objects with masses intermediate between planets and stars within about 13-80Mjup. While isolated BDs are most likely produced by gravitational collapse in molecular clouds down to masses of a few Mjup, a non-negligible fraction of low-mass companions might be formed through the planet formation channel in protoplanetary disks. The upper mass limit of objects formed within disks is still observationally unknown, the main reason being the strong dearth of BD companions at orbital periods shorter than 10 years, a.k.a. the BD desert. To address this question, we aim at determining the best statistics of secondary companions within the 10-100Mjup range and within 10 au from the primary star, while minimising observational bias. We made an extensive use of the RV surveys of FGK stars below 60pc distance to the Sun and in the northern hemisphere performed with the SOPHIE spectrograph at the Observatoire de Haute-Provence. We derived the Keplerian solutions of the RV variations of 54 sources. Public astrometric data of the Hipparcos and Gaia missions allowed constraining the mass of the companion for most sources. We introduce GASTON, a new method to derive inclination combining RVs Keplerian and astrometric excess noise from Gaia DR1. We report the discovery of 12 new BD candidates. For 5 of them, additional astrometric data led to revise their mass in the M-dwarf regime. Among the 7 remaining objects, 4 are confirmed BD companions, and 3 others are likely in this mass regime. We also report the detection of 42 M-dwarfs within 90Mjup-0.52Msun. The resulting Msin(i)-P distribution of BD candidates shows a clear drop in the detection rate below 80-day orbital period. Above that limit, the BD desert reveals rather wet, with a uniform distribution of the Msin(i). We derive a minimum BD-detection frequency around Solar-like stars of 2.0+/-0.5%.

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Spatially resolved spectroscopy of the debris disk HD 32297: Further evidence of small dust grains

Spectro-photometry of debris disks in total intensity and polarimetry can provide new insight into the properties of the dust grains therein (size distribution and optical properties). We aim to constrain the morphology of the highly inclined debris disk HD 32297. We also intend to obtain spectroscopic and polarimetric measurements to retrieve information on the particle size distribution within the disk for certain grain compositions. We observed HD 32297 with SPHERE in Y, J, and H bands in total intensity and in J band in polarimetry. The observations are compared to synthetic models of debris disks and we developed methods to extract the photometry in total intensity overcoming the data-reduction artifacts, namely the self-subtraction. The spectro-photometric measurements averaged along the disk mid-plane are then compared to model spectra of various grain compositions. These new images reveal the very inner part of the system as close as 0.15". The disk image is mostly dominated by the forward scattering making one side (half-ellipse) of the disk more visible, but observations in total intensity are deep enough to also detect the back side for the very first time. The images as well as the surface brightness profiles of the disk rule out the presence of a gap as previously proposed. We do not detect any significant asymmetry between the northeast and southwest sides of the disk. The spectral reflectance features a "gray to blue" color which is interpreted as the presence of grains far below the blowout size. The presence of sub-micron grains in the disk is suspected to be the result of gas drag and/or "avalanche mechanisms". The blue color of the disk could be further investigated with additional total intensity and polarimetric observations in K and H bands respectively to confirm the spectral slope and the fraction of polarization.

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Constraining the properties of HD 206893 B. A combination of radial velocity, direct imaging, and astrometry data

High contrast imaging enables the determination of orbital parameters for substellar companions (planets, brown dwarfs) from the observed relative astrometry and the estimation of model and age-dependent masses from their observed magnitudes or spectra. Combining astrometric positions with radial velocity gives direct constraints on the orbit and on the dynamical masses of companions. A brown dwarf was discovered with the VLT/SPHERE instrument in 2017, which orbits at $\sim$ 11 au around HD 206893. Its mass was estimated between 12 and 50 $M_{Jup}$ from evolutionary models and its photometry. However, given the significant uncertainty on the age of the system and the peculiar spectrophotometric properties of the companion, this mass is not well constrained. We aim at constraining the orbit and dynamical mass of HD 206893 B. We combined radial velocity data obtained with HARPS spectra and astrometric data obtained with the high contrast imaging VLT/SPHERE and VLT/NaCo instruments, with a time baseline less than three years. We then combined those data with astrometry data obtained by Hipparcos and Gaia with a time baseline of 24 years. We used a MCMC approach to estimate the orbital parameters and dynamical mass of the brown dwarf from those data. We infer a period between 21 and 33° and an inclination in the range 20-41° from pole-on from HD 206893 B relative astrometry. The RV data show a significant RV drift over 1.6 yrs. We show that HD 206893 B cannot be the source of this observed RV drift as it would lead to a dynamical mass inconsistent with its photometry and spectra and with Hipparcos and Gaia data. An additional inner (semimajor axis in the range 1.4-2.6 au) and massive ($\sim$ 15 $M_{Jup}$) companion is needed to explain the RV drift, which is compatible with the available astrometric data of the star, as well as with the VLT/SPHERE and VLT/NaCo nondetection.

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Determining mass limits around HD163296 through SPHERE direct imaging data

HD163296 is a Herbig Ae/Be star known to host a protoplanetary disk with a ringed structure. To explain the disk features, previous works proposed the presence of planets embedded into the disk. We have observed HD163296 with the near-infrared (NIR) branch of SPHERE composed by IRDIS and IFS with the aim to put tight constraints on the presence of substellar companions around this star. Despite the low rotation of the field of view during our observation we were able to put upper mass limits of few M_Jup around this object. These limits do not allow to give any definitive conclusion about the planets proposed through the disk characteristics. On the other hand, our results seem to exclude the presence of the only candidate proposed until now using direct imaging in the NIR even if some caution has to be taken considered the different wavelength bands of the two observations.

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Constraints on HD113337 fundamental parameters and planetary system. Combining long-base visible interferometry, disk imaging and high-contrast imaging

HD113337 is a Main-Sequence F6V field star more massive than the Sun, hosting one (possibly two) radial velocity (RV) giant planet(s) and a cold debris disk (marked by an infrared excess). We used the VEGA interferometer on the CHARA array to measure HD113337 angular diameter, and derived its linear radius using the Gaia parallax. We computed the bolometric flux to derive its effective temperature and luminosity, and we estimated its mass and age using evolutionary tracks. We used Herschel images to partially resolve the outer disk, and high-contrast images of HD113337 with the LBTI to probe the 10-80 au separation range. Finally, we combined the deduced contrast maps with previous RV of the star using the MESS2 software to bring upper mass limits on possible companions at all separations up to 80 au, taking advantage of the constraints on the age and inclination (brought by the fundamental parameter analysis and the disk imaging, respectively). We derive a limb-darkened angular diameter of 0.386 $\pm$ 0.009 mas that converts into a linear radius of 1.50 $\pm$ 0.04 solar radius. The fundamental parameter analysis leads to an effective temperature of 6774 $\pm$ 125 K, and to two possible age solutions: one young within 14-21 Myr and one old within 0.8-1.7 Gyr. We partially resolve the known outer debris disk and model its emission. Our best solution corresponds to a radius of 85 $\pm$ 20 au, an extension of 30 $\pm$ 20 au and an inclination within 10-30 degrees for the outer disk. The combination of imaging contrast limits, published RV, and our new age and inclination solutions leads to a first possible estimation of the true masses of the planetary companions: $\sim 7_{-2}^{+4}$ Jupiter masses for HD113337 b (confirmed companion), and $\sim 16_{-3}^{+10}$ Jupiter masses for HD113337 c (candidate). We also constrain possible additional companions at larger separations.

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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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Unexpectedly strong effect of supergranulation on the detectability of Earth twins orbiting Sun-like stars with radial velocities

Magnetic activity and surface flows at different scales pertub radial velocity measurements. This affects the detectability of low-mass exoplanets. In these flows, the effect of supergranulation is not as well characterized as the other flows, and we wish to estimate its effect on the detection of Earth-like planets in the habitable zone of Sun-like stars. We produced time series of radial velocities due to oscillations, granulation, and supergranulation, and estimated the detection limit for a G2 star and a period of 300 days. We also studied in detail the behavior of the power when the signal of a 1 Mearth planet was superposed on the signal from the stellar flows. We find that the detection rate does not reach 100% except for the supergranulation level we assume, which is still optimistic, and for an excellent sampling. We conclude that with current knowledge, it is a very challenging task to find Earth twins around Sun-like stars with our current capabilities.

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Two cold belts in the debris disk around the G-type star NZ Lup

Planetary systems hold the imprint of the formation and of the evolution of planets especially at young ages, and in particular at the stage when the gas has dissipated leaving mostly secondary dust grains. The dynamical perturbation of planets in the dust distribution can be revealed with high-contrast imaging in a variety of structures. SPHERE, the high-contrast imaging device installed at the VLT, was designed to search for young giant planets in long period, but is also able to resolve fine details of planetary systems at the scale of astronomical units in the scattered-light regime. As a young and nearby star, NZ Lup was observed in the course of the SPHERE survey. A debris disk had been formerly identified with HST/NICMOS. We observed this system in the near-infrared with the camera in narrow and broad band filters and with the integral field spectrograph. High contrasts are achieved by the mean of pupil tracking combined with angular differential imaging algorithms. The high angular resolution provided by SPHERE allows us to reveal a new feature in the disk which is interpreted as a superimposition of two belts of planetesimals located at stellocentric distances of $\sim$85 and $\sim$115\,au, and with a mutual inclination of about 5$\degb$. Despite the very high inclination of the disk with respect to the line of sight, we conclude that the presence of a gap, that is, a void in the dust distribution between the belts, is likely. We discuss the implication of the existence of two belts and their relative inclination with respect to the presence of planets.

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Activity time series of old stars from late F to early K. I. Simulating radial velocity, astrometry, photometry, and chromospheric emission

Solar simulations and observations show that the detection of long-period Earth-like planets is expected to be very difficult with radial velocity techniques in the solar case because of activity. The inhibition of the convective blueshift in active regions (which is then dominating the signal) is expected to decrease toward lower mass stars, which would provide more suitable conditions. In this paper we build synthetic time series to be able to precisely estimate the effects of activity on exoplanet detectability for stars with a wide range of spectral type (F6-K4) and activity levels (old main-sequence stars). We simulated a very large number of realistic time series of radial velocity, chromospheric emission, photometry, and astrometry. We built a coherent grid of stellar parameters that covers a wide range in the (B-V, LogR'HK) space based on our current knowledge of stellar activity, to be able to produce these time series. We describe the model and assumptions in detail. We present first results on chromospheric emission. We find the average LogR'HK to correspond well to the target values that are expected from the model, and observe a strong effect of inclination on the average LogR'HK (over time) and its long-term amplitude. This very large set of synthetic time series offers many possibilities for future analysis, for example, for the parameter effect, correction method, and detection limits of exoplanets.

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Hint of curvature in the orbital motion of the exoplanet 51 Eridani b using 3 years of VLT/SPHERE monitoring

Context. The 51 Eridani system harbors a complex architecture with its primary star forming a hierarchical system with the binary GJ 3305AB at a projected separation of 2000 au, a giant planet orbiting the primary star at 13 au, and a low-mass debris disk around the primary star with possibly a cold component and a warm component inferred from the spectral energy distribution. Aims. We aim to better constrain the orbital parameters of the known giant planet. Methods. We monitored the system over three years from 2015 to 2018 with the VLT/SPHERE exoplanet imaging instrument. Results. We measure an orbital motion for the planet of ~130 mas with a slightly decreasing separation (~10 mas) and find a hint of curvature. This potential curvature is further supported at 3$σ$ significance when including literature GPI astrometry corrected for calibration systematics. Fits of the SPHERE and GPI data using three complementary approaches provide broadly similar results. The data suggest an orbital period of 32$^{+17}_{-9}$ yr (i.e. 12$^{+4}_{-2}$ au in semi-major axis), an inclination of 133$^{+14}_{-7}$ deg, an eccentricity of 0.45$^{+0.10}_{-0.15}$, and an argument of periastron passage of 87$^{+34}_{-30}$ deg [mod 180 deg]. The time at periastron passage and the longitude of node exhibit bimodal distributions because we do not detect yet if the planet is accelerating or decelerating along its orbit. Given the inclinations of the planet's orbit and of the stellar rotation axis (134-144 deg), we infer alignment or misalignment within 18 deg for the star-planet spin-orbit. Further astrometric monitoring in the next 3-4 years is required to confirm at a higher significance the curvature in the planet's motion, determine if the planet is accelerating or decelerating on its orbit, and further constrain its orbital parameters and the star-planet spin-orbit.

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First direct detection of an exoplanet by optical interferometry; Astrometry and K-band spectroscopy of HR8799 e

To date, infrared interferometry at best achieved contrast ratios of a few times $10^{-4}$ on bright targets. GRAVITY, with its dual-field mode, is now capable of high contrast observations, enabling the direct observation of exoplanets. We demonstrate the technique on HR8799, a young planetary system composed of four known giant exoplanets. We used the GRAVITY fringe tracker to lock the fringes on the central star, and integrated off-axis on the HR8799e planet situated at 390 mas from the star. Data reduction included post-processing to remove the flux leaking from the central star and to extract the coherent flux of the planet. The inferred K band spectrum of the planet has a spectral resolution of 500. We also derive the astrometric position of the planet relative to the star with a precision on the order of 100$\,μ$as. The GRAVITY astrometric measurement disfavors perfectly coplanar stable orbital solutions. A small adjustment of a few degrees to the orbital inclination of HR 8799 e can resolve the tension, implying that the orbits are close to, but not strictly coplanar. The spectrum, with a signal-to-noise ratio of $\approx 5$ per spectral channel, is compatible with a late-type L brown dwarf. Using Exo-REM synthetic spectra, we derive a temperature of $1150\pm50$\,K and a surface gravity of $10^{4.3\pm0.3}\,$cm/s$^{2}$. This corresponds to a radius of $1.17^{+0.13}_{-0.11}\,R_{\rm Jup}$ and a mass of $10^{+7}_{-4}\,M_{\rm Jup}$, which is an independent confirmation of mass estimates from evolutionary models. Our results demonstrate the power of interferometry for the direct detection and spectroscopic study of exoplanets at close angular separations from their stars.

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A search for accreting young companions embedded in circumstellar disks: High-contrast H$α$ imaging with VLT/SPHERE

Aims: We want to detect and quantify observables related to accretion processes occurring locally in circumstellar disks, which could be attributed to young forming planets. We focus on objects known to host protoplanet candidates and/or disk structures thought to be the result of interactions with planets. Methods: We analyzed observations of 6 young stars (age $3.5-10$ Myr) and their surrounding environments with the SPHERE/ZIMPOL instrument on the VLT in the H$α$ filter (656 nm) and a nearby continuum filter (644.9 nm). Results: We re-detect the known accreting M-star companion HD142527 B with the highest published signal to noise to date in both H$α$ and the continuum. We derive new astrometry ($r = 62.8^{+2.1}_{-2.7}$ mas and $\text{PA} = (98.7\,\pm1.8)^\circ$) and photometry ($Δ$N_Ha=$6.3^{+0.2}_{-0.3}$ mag, $Δ$B_Ha=$6.7\pm0.2$ mag and $Δ$Cnt_Ha=$7.3^{+0.3}_{-0.2}$ mag) for the companion in agreement with previous studies, and estimate its mass accretion rate ($\dot{M}\approx1-2\,\times10^{-10}\,M_\odot\text{ yr}^{-1}$). A faint point-like source around HD135344 B (SAO206462) is also investigated, but a second deeper observation is required to reveal its nature. No other companions are detected. In the framework of our assumptions we estimate detection limits at the locations of companion candidates around HD100546, HD169142 and MWC758 and calculate that processes involving H$α$ fluxes larger than $\sim8\times10^{-14}-10^{-15}\,\text{erg/s/cm}^2$ ($\dot{M}>10^{-10}-10^{-12}\,M_\odot\text{ yr}^{-1}$) can be excluded. Furthermore, flux upper limits of $\sim10^{-14}-10^{-15}\,\text{erg/s/cm}^2$ ($\dot{M}<10^{-11}-10^{-12}\,M_\odot \text{ yr}^{-1}$) are estimated within the gaps identified in the disks surrounding HD135344B and TW Hya.

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Exploring the RCrA environment with SPHERE: Discovery of a new stellar companion

Aims. R Coronae Australis (R CrA) is the brightest star of the Coronet nebula of the Corona Australis (CrA) star forming region. It has very red colors, probably due to dust absorption and it is strongly variable. High contrast instruments allow for an unprecedented direct exploration of the immediate circumstellar environment of this star. Methods. We observed R CrA with the near-IR channels (IFS and IRDIS) of SPHERE at VLT. In this paper, we used four different epochs, three of them from open time observations while one is from the SPHERE guaranteed time. The data were reduced using the DRH pipeline and the SPHERE Data Center. On the reduced data we implemented custom IDL routines with the aim to subtract the speckle halo.We have also obtained pupil-tracking H-band (1.45-1.85 micron) observations with the VLT/SINFONI near-infrared medium-resolution (R~3000) spectrograph. Results. A companion was found at a separation of 0.156" from the star in the first epoch and increasing to 0.18400 in the final one. Furthermore, several extended structures were found around the star, the most noteworthy of which is a very bright jet-like structure North-East from the star. The astrometric measurements of the companion in the four epochs confirm that it is gravitationally bound to the star. The SPHERE photometry and the SINFONI spectrum, once corrected for extinction, point toward an early M spectral type object with a mass between 0.3 and 0.55 M?. The astrometric analyis provides constraints on the orbit paramenters: e~0.4, semi-major axis at 27-28 au, inclination of ~ 70° and a period larger than 30 years. We were also able to put constraints of few MJup on the mass of possible other companions down to separations of few tens of au.

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Investigating the presence of two belts in the HD 15115 system

We present new observations of the edge-on debris disk around HD 15115 (F star at 48.2 pc) obtained in the near-IR. We search for observational evidence for a second inner planetesimal ring in the system. We obtained total intensity and polarimetric data in the broad bands J and H and processed the data with differential imaging techniques achieving an angular resolution of about 40 mas. We observe an axisymmetric planetesimal belt with a radius of $\sim$2$''$, an inclination of $85.8^{\circ} \pm 0.7^{\circ}$ and position angle of 278.9$^{\circ} \pm 0.1^{\circ}$. A grid of models describing the spatial distribution of the grains in the disk is generated to constrain the geometric parameters of the disk and to explore the presence of a second belt. We perform a photometric analysis of the data and compare disk brightness in two bands in scattered and in polarized light. The analysis shows that the west side is $\sim$2.5 times brighter in total intensity than the east side in both bands, while for polarized light in the J band this ratio is only 1.25. The maximum polarization fraction is 15--20% at $r\sim$2.5$''$. We also find that the J - H color of the disk appears to be red for the radial separations $r\lesssim2''$ and is getting bluer for the larger separations. This apparent change of disk color from red to blue with an increasing radial separation could be explained by the decreasing average grain size with distance. The presence of an additional inner belt slightly inclined with respect to the main planetesimal belt is suspected from the polarized intensity image but the analysis and modeling presented here cannot establish a firm conclusion due to the faintness of the disk and its high inclination.

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SPHERE dynamical and spectroscopic characterization of HD142527B

We detect the accreting low-mass companion HD142527B at a separation of 73 mas (11.4 au) from the star. No other companions with mass greater than 10 MJ are visible in the field of view of IFS (\sim 100 au centered on the star) or in the IRDIS field of view (\sim 400 au centered on the star). Measurements from IFS, SAM IFS, and IRDIS suggest an M6 spectral type for HD142527B, with an uncertainty of one spectral subtype, compatible with an object of M=0.11 \pm 0.06 MSun and R=0.15 \pm 0.07 RSun. The determination of the mass remains a challenge using contemporary evolutionary models, as they do not account for the energy input due to accretion from infalling material. We consider that the spectral type of the secondary may also be earlier than the type we derived from IFS spectra. From dynamical considerations, we further constrain the mass to 0.26^{+0.16}_{-0.14} MSun , which is consistent with both our spectroscopic analysis and the values reported in the literature. Following previous methods, the lower and upper dynamical mass values correspond to a spectral type between M2.5 and M5.5 for the companion. By fitting the astrometric points, we find the following orbital parameters: a period of P=35-137 yr; an inclination of i=121-130 deg.; , a value of Omega=124-135 deg for the longitude of node, and an 68% confidence interval of \sim 18 - 57 au for the separation at periapsis. Eccentricity and time at periapsis passage exhibit two groups of values: \sim0.2-0.45 and \sim0.45-0.7 for e, and \sim 2015-2020 and \sim2020-2022 for T_0. While these orbital parameters might at first suggest that HD142527B is not the companion responsible for the outer disk truncation, a previous hydrodynamical analysis of this system showed that they are compatible with a companion that is able to produce the large cavity and other observed features.

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Spectral and orbital characterisation of the directly imaged giant planet HIP 65426 b

HIP 65426 b is a recently discovered exoplanet imaged during the course of the SPHERE-SHINE survey. Here we present new $L'$ and $M'$ observations of the planet from the NACO instrument at the VLT from the NACO-ISPY survey, as well as a new $Y-H$ spectrum and $K$-band photometry from SPHERE-SHINE. Using these data, we confirm the nature of the companion as a warm, dusty planet with a mid-L spectral type. From comparison of its SED with the BT-Settl atmospheric models, we derive a best-fit effective temperature of $T_{\text{eff}}=1618\pm7$ K, surface gravity $\log g=3.78^{+0.04}_{-0.03}$ and radius $R=1.17\pm0.04$ $R_{\text{J}}$ (statistical uncertainties only). Using the DUSTY and COND isochrones we estimate a mass of $8\pm1$ $M_{\text{J}}$. Combining the astrometric measurements from our new datasets and from the literature, we show the first indications of orbital motion of the companion (2.6$σ$ significance) and derive preliminary orbital constraints. We find a highly inclined orbit ($i=107^{+13}_{-10}$ deg) with an orbital period of $800^{+1200}_{-400}$ yr. We also report SPHERE sparse aperture masking observations that investigate the possibility that HIP 65426 b was scattered onto its current orbit by an additional companion at a smaller orbital separation. From this data we rule out the presence of brown dwarf companions with masses greater than 16 $M_{\text{J}}$ at separations larger than 3 AU, significantly narrowing the parameter space for such a companion.

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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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