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S. Lacour

Publications and source records attributed to S. Lacour.

At least 55 records · Page 3Linked to original sources
arXiv2024

Single-mode waveguides for GRAVITY II. Single-mode fibers and Fiber Control Unit

The 2nd generation VLTI instrument GRAVITY is a two-field infrared interferometer operating in the K band between 1.97 and 2.43 $μ$m with either the four 8 m or the four 1.8 m telescopes of the Very Large Telescope (VLT). Beams collected by the telescopes are corrected with adaptive optics systems and the fringes are stabilized with a fringe-tracking system. A metrology system allows the measurement of internal path lengths in order to achieve high-accuracy astrometry. High sensitivity and high interferometric accuracy are achieved thanks to (i) correction of the turbulent phase, (ii) the use of low-noise detectors, and (iii) the optimization of photometric and coherence throughput. Beam combination and most of the beam transport are performed with single-mode waveguides in vacuum and at low temperature. In this paper, we present the functions and performance achieved with weakly birefringent standard single-mode fiber systems in GRAVITY. Fibered differential delay lines (FDDLs) are used to dynamically compensate for up to 6 mm of delay between the science and reference targets. Fibered polarization rotators allow us to align polarizations in the instrument and make the single-mode beam combiner close to polarization neutral. The single-mode fiber system exhibits very low birefringence (less than 23°), very low attenuation (3.6-7 dB/km across the K band), and optimized differential dispersion (less than 2.04 $μ$rad cm2 at zero extension of the FDDLs). As a consequence, the typical fringe contrast losses due to the single-mode fibers are 6% to 10% in the lowest-resolution mode and 5% in the medium- and high-resolution modes of the instrument for a photometric throughput of the fiber chain of the order of 90%. There is no equivalent of this fiber system to route and modally filter beams with delay and polarization control in any other K-band beamcombiner.

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arXiv2024

The size-luminosity relation of local active galactic nuclei from interferometric observations of the broad-line region

By using the GRAVITY instrument with the near-infrared (NIR) Very Large Telescope Interferometer (VLTI), the structure of the broad (emission-)line region (BLR) in active galactic nuclei (AGNs) can be spatially resolved, allowing the central black hole (BH) mass to be determined. This work reports new NIR VLTI/GRAVITY interferometric spectra for four type 1 AGNs (Mrk 509, PDS 456, Mrk 1239, and IC 4329A) with resolved broad-line emission. Dynamical modelling of interferometric data constrains the BLR radius and central BH mass measurements for our targets and reveals outflow-dominated BLRs for Mrk 509 and PDS 456. We present an updated radius-luminosity (R-L) relation independent of that derived with reverberation mapping (RM) measurements using all the GRAVITY-observed AGNs. We find our R-L relation to be largely consistent with that derived from RM measurements except at high luminosity, where BLR radii seem to be smaller than predicted. This is consistent with RM-based claims that high Eddington ratio AGNs show consistently smaller BLR sizes. The BH masses of our targets are also consistent with the standard $M_\mathrm{BH}$-$σ_*$ relation. Model-independent photocentre fitting shows spatial offsets between the hot dust continuum and the BLR photocentres (ranging from $\sim$17 $μ$as to 140 $μ$as) that are generally perpendicular to the alignment of the red- and blueshifted BLR photocentres. These offsets are found to be related to the AGN luminosity and could be caused by asymmetric K-band emission of the hot dust, shifting the dust photocentre. We discuss various possible scenarios that can explain this phenomenon.

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arXiv2024

The GRAVITY young stellar object survey XII. The hot gas disk component in Herbig Ae/Be stars

The region of protoplanetary disks closest to a star (within 1-2\,au) is shaped by a number of different processes, from accretion of the disk material onto the central star to ejection in the form of winds and jets. Optical and near-IR emission lines are potentially good tracers of inner disk processes if very high spatial and/or spectral resolution are achieved. In this paper, we exploit the capabilities of the VLTI-GRAVITY near-IR interferometer to determine the location and kinematics of the hydrogen emission line Bracket gamma. We present VLTI-GRAVITY observations of the Bracket gamma line for a sample of 26 stars of intermediate mass (HAEBE), the largest sample so far analysed with near-IR interferometry. The Bracket gamma line was detected in 17 objects. The emission is very compact (in most cases only marginally resolved), with a size of 10-30R* (1-5 mas). About half of the total flux comes from even smaller regions, which are unresolved in our data. For eight objects, it was possible to determine the position angle (PA) of the line-emitting region, which is generally in agreement with that of the inner-dusty disk emitting the K-band continuum. The position-velocity pattern of the Bracket gamma line-emitting region of the sampled objects is roughly consistent with Keplerian rotation. The exception is HD~45677, which shows more extended emission and more complex kinematics. The most likely scenario for the Bracket gamma origin is that the emission comes from an MHD wind launched very close to the central star, in a region well within the dust sublimation radius. An origin in the bound gas layer at the disk surface cannot be ruled out, while accreting matter provides only a minor fraction of the total flux. These results show the potential of near-IR spectro-interferometry to study line emission in young stellar objects.

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arXiv2024

Dynamics of the Beta Pictoris planetary system and its falling evaporating bodies

For decades, the spectral variations of Beta Pictoris have been modelled as the result of the evaporation of exocomets close to the star, termed falling evaporating bodies (FEBs). Resonant perturbations by a giant planet have been proposed to explain the dynamical origin of these stargrazers. The disk is now known to harbour two giant planets, Beta Pic b and c, orbiting the star at 9.9 au and 2.7 au. While the former almost matches the planet formerly suspected, the discovery of the latter complicates the picture. We first question the stability of the two-planet system. Then we investigate the dynamics of a disk of planetesimals orbiting the star with both planets to check the validity of the FEB generation mechanism. Symplectic N-body simulations are used to determine which regions of the planetesimal disk are dynamically stable. Then we focus on regions where disk particles are able to reach high eccentricities thanks to resonant mechanisms. The first result is that the system is dynamically stable. Both planets may temporarily fall in 7:1 mean motion resonance (MMR). Then, simulations reveal that the whole region extending between ~1.5 au and ~25 au is unstable to planetary perturbations. However, a disk below 1.5 au survives, which appears to constitute an active source of FEBs via high-order MMRs with Beta Pic c. Beta Pic b acts as a distant perturber that helps sustain the whole process. These simulations rule out the preceding FEB generation mechanism model, which placed their origin at around 4-5 au. Conversely, FEBs are likely to originate from a region much further in and related to MMRs with Beta Pic c. That mechanism also appears to last longer, as new planetesimals are able to continuously enter the MMRs and evolve towards the FEB state. Subsequently, the physical nature of the FEBs may differ from that previously thought, and presumably may not be icy.

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arXiv2023

The GRAVITY young stellar object survey: XI. Imaging the hot gas emission around the Herbig Ae star HD 58647

We aim to investigate the origin of the HI Br$γ$ emission in young stars by using GRAVITY to image the innermost region of circumstellar disks, where important physical processes such as accretion and winds occur. With high spectral and angular resolution, we focus on studying the continuum and the HI Br$γ$-emitting area of the Herbig star HD58647. Using VLTI-GRAVITY, we conducted observations of HD58647 with both high spectral and high angular resolution. Thanks to the extensive $uv$ coverage, we were able to obtain detailed images of the circumstellar environment at a sub-au scale, specifically capturing the continuum and the Br$γ$-emitting region. Through the analysis of velocity-dispersed images and photocentre shifts, we were able to investigate the kinematics of the HI Br$γ$-emitting region. The recovered continuum images show extended emission where the disk major axis is oriented along a position angle of 14\degr. The size of the continuum emission at 5-sigma levels is $\sim$ 1.5 times more extended than the sizes reported from geometrical fitting (3.69 mas $\pm$ 0.02 mas). This result supports the existence of dust particles close to the stellar surface, screened from the stellar radiation by an optically thick gaseous disk. Moreover, for the first time with GRAVITY, the hot gas component of HD58647 traced by the Br$γ$ ,has been imaged. This allowed us to constrain the size of the Br$γ$-emitting region and study the kinematics of the hot gas; we find its velocity field to be roughly consistent with gas that obeys Keplerian motion. The velocity-dispersed images show that the size of the hot gas emission is from a more compact region than the continuum (2.3 mas $\pm$ 0.2 mas). Finally, the line phases show that the emission is not entirely consistent with Keplerian rotation, hinting at a more complex structure in the hot gaseous disk.

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arXiv2023

VLTI/GRAVITY Provides Evidence the Young, Substellar Companion HD 136164 Ab formed like a "Failed Star"

Young, low-mass Brown Dwarfs orbiting early-type stars, with low mass ratios ($q\lesssim0.01$), appear intrinsically rare and present a formation dilemma: could a handful of these objects be the highest mass outcomes of ``planetary" formation channels (bottom up within a protoplanetary disk), or are they more representative of the lowest mass ``failed binaries" (formed via disk fragmentation, or core fragmentation)? Additionally, their orbits can yield model-independent dynamical masses, and when paired with wide wavelength coverage and accurate system age estimates, can constrain evolutionary models in a regime where the models have a wide dispersion depending on initial conditions. We present new interferometric observations of the $16\,\mathrm{Myr}$ substellar companion HD~136164~Ab (HIP~75056~Ab) with VLTI/GRAVITY and an updated orbit fit including proper motion measurements from the Hipparcos-Gaia Catalogue of Accelerations. We estimate a dynamical mass of $35\pm10\,\mathrm{M_J}$ ($q\sim0.02$), making HD~136164~Ab the youngest substellar companion with a dynamical mass estimate. The new mass and newly constrained orbital eccentricity ($e=0.44\pm0.03$) and separation ($22.5\pm1\,\mathrm{au}$) could indicate that the companion formed via the low-mass tail of the Initial Mass Function. Our atmospheric fit to the \texttt{SPHINX} M-dwarf model grid suggests a sub-solar C/O ratio of $0.45$, and $3\times$ solar metallicity, which could indicate formation in the circumstellar disk via disk fragmentation. Either way, the revised mass estimate likely excludes ``bottom-up" formation via core accretion in the circumstellar disk. HD~136164~Ab joins a select group of young substellar objects with dynamical mass estimates; epoch astrometry from future \textit{Gaia} data releases will constrain the dynamical mass of this crucial object further.

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arXiv2023

Polarization analysis of the VLTI and GRAVITY

The goal of this work is to characterize the polarization effects of the VLTI and GRAVITY. This is needed to calibrate polarimetric observations with GRAVITY for instrumental effects and to understand the systematic error introduced to the astrometry due to birefringence when observing targets with a significant intrinsic polarization. By combining a model of the VLTI light path and its mirrors and dedicated experimental data, we construct a full polarization model of the VLTI UTs and the GRAVITY instrument. We first characterize all telescopes together to construct a UT calibration model for polarized targets. We then expand the model to include the differential birefringence. With this, we can constrain the systematic errors for highly polarized targets. Together with this paper, we publish a standalone Python package to calibrate the instrumental effects on polarimetric observations. This enables the community to use GRAVITY to observe targets in a polarimetric observing mode. We demonstrate the calibration model with the galactic center star IRS 16C. For this source, we can constrain the polarization degree to within 0.4 % and the polarization angle within 5 deg while being consistent with the literature. Furthermore, we show that there is no significant contrast loss, even if the science and fringe-tracker targets have significantly different polarization, and we determine that the phase error in such an observation is smaller than 1 deg, corresponding to an astrometric error of 10 μas. With this work, we enable the use of the polarimetric mode with GRAVITY/UTs and outline the steps necessary to observe and calibrate polarized targets. We demonstrate that it is possible to measure the intrinsic polarization of astrophysical sources with high precision and that polarization effects do not limit astrometric observations of polarized targets.

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arXiv2023

The GRAVITY fringe tracker

The GRAVITY instrument has been commissioned on the VLTI during 2016 and is now available to the astronomical community. It is the first optical interferometer capable of observing sources as faint as magnitude 19 in K-band. This is possible thanks to the fringe tracker which compensates the differential piston based on measurements of a brighter off-axis astronomical reference source. The goal of this paper is to consign the main developments made in the context of the GRAVITY fringe tracker. This could serve as basis for future fringe tracking systems. The paper therefore covers all aspects of the fringe tracker, from hardware, to control software and on-sky observations. Special emphasis is placed on the interaction between the group delay controller and the phase delay controller. The group delay control loop is a simple but robust integrator. The phase delay controller is a state-space control loop based on an auto-regressive representation of the atmospheric and vibrational perturbations. A Kalman filter provides optimal determination of the state of the system. The fringe tracker shows good tracking performance on sources with coherent K magnitudes of 11 on the UTs and 9.5 on the ATs. It can track fringes with an SNR level of 1.5 per DIT, limited by photon and background noises. On the ATs, during good seeing conditions, the optical path delay residuals can be as low as 75 nm root mean square. On the UTs, the performance is limited to around 250 nm because of structural vibrations.

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arXiv2023

First VLTI/GRAVITY Observations of HIP 65426 b: Evidence for a Low or Moderate Orbital Eccentricity

Giant exoplanets have been directly imaged over orders of magnitude of orbital separations, prompting theoretical and observational investigations of their formation pathways. In this paper, we present new VLTI/GRAVITY astrometric data of HIP 65426 b, a cold, giant exoplanet which is a particular challenge for most formation theories at a projected separation of 92 au from its primary. Leveraging GRAVITY's astrometric precision, we present an updated eccentricity posterior that disfavors large eccentricities. The eccentricity posterior is still prior-dependent, and we extensively interpret and discuss the limits of the posterior constraints presented here. We also perform updated spectral comparisons with self-consistent forward-modeled spectra, finding a best fit ExoREM model with solar metallicity and C/O=0.6. An important caveat is that it is difficult to estimate robust errors on these values, which are subject to interpolation errors as well as potentially missing model physics. Taken together, the orbital and atmospheric constraints paint a preliminary picture of formation inconsistent with scattering after disk dispersal. Further work is needed to validate this interpretation. Analysis code used to perform this work is available at https://github.com/sblunt/hip65426.

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arXiv2023

VLTI/GRAVITY Observations and Characterization of the Brown Dwarf Companion HD 72946 B

Tension remains between the observed and modeled properties of substellar objects, but objects in binary orbits, with known dynamical masses can provide a way forward. HD 72946 B is a recently imaged brown dwarf companion to the nearby, solar type star. We achieve $\sim100~μ\mathrm{as}$ relative astrometry of HD 72946 B in the K-band using VLTI/GRAVITY, unprecedented for a benchmark brown dwarf. We fit an ensemble of measurements of the orbit using orbitize! and derive a strong dynamical mass constraint $\mathrm{M_B}=69.5\pm0.5~\mathrm{M_{Jup}}$ assuming a strong prior on the host star mass $\mathrm{M_A}=0.97\pm0.01~\mathrm{M_\odot}$ from an updated stellar analysis. We fit the spectrum of the companion to a grid of self-consistent BT-Settl-CIFIST model atmospheres, and perform atmospheric retrievals using petitRADTRANS. A dynamical mass prior only marginally influences the sampled distribution on effective temperature, but has a large influence on the surface gravity and radius, as expected. The dynamical mass alone does not strongly influence retrieved pressure-temperature or cloud parameters within our current retrieval setup. Independent of cloud prescription and prior assumptions, we find agreement within $\pm2\,σ$ between the C/O ratio of the host ($0.52\pm0.05)$ and brown dwarf ($0.43$ to $0.63$), as expected from a molecular cloud collapse formation scenario, but our retrieved metallicities are implausibly high ($0.6-0.8$) in light of an excellent agreement of the data with the solar abundance model grid. Future work on our retrieval framework will seek to resolve this tension. Additional study of low surface-gravity objects is necessary to assess the influence of a dynamical mass prior on atmospheric analysis.

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arXiv2023

Using the motion of S2 to constrain scalar clouds around SgrA*

The motion of S2, one of the stars closest to the Galactic Centre, has been measured accurately and used to study the compact object at the centre of the Milky Way. It is commonly accepted that this object is a supermassive black hole but the nature of its environment is open to discussion. Here, we investigate the possibility that dark matter in the form of an ultralight scalar field ``cloud'' clusters around Sgr~A*. We use the available data for S2 to perform a Markov Chain Monte Carlo analysis and find the best-fit estimates for a scalar cloud structure. Our results show no substantial evidence for such structures. When the cloud size is of the order of the size of the orbit of S2, we are able to constrain its mass to be smaller than $0.1\%$ of the central mass, setting a strong bound on the presence of new fields in the galactic centre.

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arXiv2023

Polarimetry and Astrometry of NIR Flares as Event Horizon Scale, Dynamical Probes for the Mass of Sgr A*

We present new astrometric and polarimetric observations of flares from Sgr A* obtained with GRAVITY, the near-infrared interferometer at ESO's Very Large Telescope Interferometer (VLTI), bringing the total sample of well-covered astrometric flares to four and polarimetric ones to six, where we have for two flares good coverage in both domains. All astrometric flares show clockwise motion in the plane of the sky with a period of around an hour, and the polarization vector rotates by one full loop in the same time. Given the apparent similarities of the flares, we present a common fit, taking into account the absence of strong Doppler boosting peaks in the light curves and the EHT-measured geometry. Our results are consistent with and significantly strengthen our model from 2018: We find that a) the combination of polarization period and measured flare radius of around nine gravitational radii ($9 R_g \approx 1.5 R_{ISCO}$, innermost stable circular orbit) is consistent with Keplerian orbital motion of hot spots in the innermost accretion zone. The mass inside the flares' radius is consistent with the $4.297 \times 10^6 \; \text{M}_\odot$ measured from stellar orbits at several thousand $R_g$. This finding and the diameter of the millimeter shadow of Sgr A* thus support a single black hole model. Further, b) the magnetic field configuration is predominantly poloidal (vertical), and the flares' orbital plane has a moderate inclination with respect to the plane of the sky, as shown by the non-detection of Doppler-boosting and the fact that we observe one polarization loop per astrometric loop. Moreover, c) both the position angle on sky and the required magnetic field strength suggest that the accretion flow is fueled and controlled by the winds of the massive, young stars of the clockwise stellar disk 1-5 arcsec from Sgr A*, in agreement with recent simulations.

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arXiv2023

Where intermediate-mass black holes could hide in the Galactic Centre: A full parameter study with the S2 orbit

In the Milky Way the central massive black hole, SgrA*, coexists with a compact nuclear star cluster that contains a sub-parsec concentration of fast-moving young stars called S-stars. Their location and age are not easily explained by current star formation models, and in several scenarios the presence of an intermediate-mass black hole (IMBH) has been invoked. We use GRAVITY astrometric and SINFONI, KECK, and GNIRS spectroscopic data of S2 to investigate whether a second massive object could be present deep in the Galactic Centre (GC) in the form of an IMBH binary companion to SgrA*. To solve the three-body problem, we used a post-Newtonian framework and consider two types of settings: (i) a hierarchical set-up where the star S2 orbits the SgrA* - IMBH binary and (ii) a non-hierarchical set-up where the IMBH trajectory lies outside the S2 orbit. In both cases we explore the full 20-dimensional parameter space by employing a Bayesian dynamic nested sampling method. For the hierarchical case we find: IMBH masses > 2000 Msun on orbits with smaller semi-major axes than S2 are largely excluded. For the non-hierarchical case the parameter space contains several pockets of valid IMBH solutions. However, a closer analysis of their impact on the resident stars reveals that IMBHs on semi-major axes larger than S2 tend to disrupt the S-star cluster in less than a million years. This makes the existence of an IMBH among the S-stars highly unlikely. The current S2 data do not formally require the presence of an IMBH. If an IMBH hides in the GC, it has to be either a low-mass IMBH inside the S2 orbit that moves on a short and significantly inclined trajectory or an IMBH with a semi-major axis >1". We provide the parameter maps of valid IMBH solutions in the GC and discuss the general structure of our results. (abridged)

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arXiv2023

The Enhanced Resolution Imager and Spectrograph for the VLT

ERIS, the Enhanced Resolution Imager and Spectrograph, is an instrument that both extends and enhances the fundamental diffraction limited imaging and spectroscopy capability for the VLT. It replaces two instruments that were being maintained beyond their operational lifetimes, combines their functionality on a single focus, provides a new wavefront sensing module for natural and laser guide stars that makes use of the Adaptive Optics Facility, and considerably improves on their performance. The observational modes ERIS provides are integral field spectroscopy at 1-2.5 μm, imaging at 1-5 μm with several options for high contrast imaging, and longslit spectroscopy at 3-4 μm, The instrument is installed at the Cassegrain focus of UT4 at the VLT and, following its commissioning during 2022, has been made available to the community.

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arXiv2023

Direct discovery of the inner exoplanet in the HD206893 system. Evidence for deuterium burning in a planetary-mass companion

Long term precise radial velocity (RV) monitoring of the nearby star HD206893, as well as anomalies in the system proper motion, have suggested the presence of an additional, inner companion in the system. Here we describe the results of a multi-epoch search for the companion responsible for this RV drift and proper motion anomaly using the VLTI/GRAVITY instrument. Utilizing information from ongoing precision RV measurements with the HARPS spectrograph, as well as Gaia host star astrometry, we report a high significance detection of the companion HD206893c over three epochs, with clear evidence for Keplerian orbital motion. Our astrometry with $\sim$50-100 $μ$arcsec precision afforded by GRAVITY allows us to derive a dynamical mass of 12.7$^{+1.2}_{-1.0}$ M$_{\rm Jup}$ and an orbital separation of 3.53$^{+0.08}_{-0.06}$ au for HD206893c. Our fits to the orbits of both companions in the system utilize both Gaia astrometry and RVs to also provide a precise dynamical estimate of the previously uncertain mass of the B component, and therefore derive an age of $155\pm15$ Myr. We find that theoretical atmospheric/evolutionary models incorporating deuterium burning for HD206893c, parameterized by cloudy atmospheres provide a good simultaneous fit to the luminosity of both HD206893B and c. In addition to utilizing long-term RV information, this effort is an early example of a direct imaging discovery of a bona fide exoplanet that was guided in part with Gaia astrometry. Utilizing Gaia astrometry is expected to be one of the primary techniques going forward to identify and characterize additional directly imaged planets. Lastly, this discovery is another example of the power of optical interferometry to directly detect and characterize extrasolar planets where they form at ice-line orbital separations of 2-4\,au.

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arXiv2022

Chasing extreme planetary architectures: I- HD196885Ab, a super-Jupiter dancing with two stars?

Planet(s) in binaries are unique architectures for testing predictions of planetary formation and evolution theories in very hostile environments. We used the IRDIS dual-band imager of SPHERE at VLT, and the speckle interferometric camera HRCAM of SOAR, to acquire high-angular resolution images of HD 196885 AB between 2015 and 2020. Radial velocity observations have been extended over almost 40 yr extending the radial velocity measurements HD 196885 A and resolving both the binary companion and the inner giant planet HD 196885 Ab. Finally, we took advantage of the exquisite astrometric precision of the dual-field mode of VLTI/GRAVITY (down to 30 μas) to monitor the relative position of HD 196885 A and B to search for the 3.6 yr astrometric wobble of the circumprimary planet Ab imprinted on the binary separation. Our observations enable to accurately constrain the orbital properties of the binary HD 196885 AB, seen on an inclined and retrograde orbit (iAB = 120.43 deg) with a semi-major axis of 19.78 au, and an eccentricity of 0.417. The GRAVITY measurements confirm for the first time the nature of the inner planet HD 196885 Ab by rejecting all families of pole-on solutions in the stellar or brown dwarf masses. The most favored island of solutions is associated with a Jupiter-like planet (MAb = 3.39 MJup), with moderate eccentricity (eAaAb = 0.44), and inclination close to 143.04 deg. This results points toward a significant mutual inclination (Phi = 24.36 deg) between the orbital planes (relative to the star) of the binary companion B and the planet Ab. Our dynamical simulations indicate that the system is dynamically stable over time. Eccentricity and mutual inclination variations could be expected for moderate von Zipele Kozai Lidov cycles that may affect the inner planet.

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arXiv2022

Towards measuring supermassive black hole masses with interferometric observations of the dust continuum

This work focuses on active galactic nuclei (AGNs), and the relation between the sizes of the hot dust continuum and the broad-line region (BLR). We find that the continuum size measured using optical/near-infrared interferometry (OI) is roughly twice that measured by reverberation mapping (RM). Both OI and RM continuum sizes show a tight relation with the H$β$ BLR size with only an intrinsic scatter of 0.25 dex. The masses of supermassive black holes (BHs) can hence be simply derived from a dust size in combination with a broad line width and virial factor. Since the primary uncertainty of these BH masses comes from the virial factor, the accuracy of the continuum-based BH masses is close to those based on the RM measurement of the broad emission line. Moreover, the necessary continuum measurements can be obtained on a much shorter timescale than those required monitoring for RM, and are also more time efficient than those needed to resolve the BLR with OI. The primary goal of this work is to demonstrate measuring the BH mass based on the dust continuum size with our first calibration of the $R_\mathrm{BLR}$-$R_\mathrm{d}$ relation. The current limitation and caveats are discussed in detail. Future GRAVITY observations are expected to improve the continuum-based method and have the potential to measure BH masses for a large sample of AGNs in the low-redshift Universe.

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arXiv2022

The binary system of the spinning-top Be star Achernar

Achernar, the closest and brightest classical Be star, presents rotational flattening, gravity darkening, occasional emission lines due to a gaseous disk, and an extended polar wind. It is also a member of a close binary system with an early A-type dwarf companion. We aim to determine the orbital parameters of the Achernar system and to estimate the physical properties of the components. We monitored the relative position of Achernar B using a broad range of high angular resolution instruments of the VLT/VLTI (VISIR, NACO, SPHERE, AMBER, PIONIER, GRAVITY, and MATISSE) over a period of 13 years (2006-2019). These astrometric observations are complemented with a series of more than 700 optical spectra for the period from 2003 to 2016. We determine that Achernar B orbits the Be star on a seven-year period, eccentric orbit (e = 0.7255 +/- 0.0014) which brings the two stars within 2 au at periastron. The mass of the Be star is found to be mA = 6.0 +/- 0.6 Msun for a secondary mass of mB = 2.0 +/- 0.1 Msun. We find a good agreement of the parameters of Achernar A with the evolutionary model of a critically rotating star of 6.4 Msun at an age of 63 million years. We also identify a resolved comoving low-mass star, which leads us to propose that Achernar is a member of the Tucana-Horologium moving group. Achernar A is presently in a short-lived phase of its evolution following the turn-off, during which its geometrical flattening ratio is the most extreme. Considering the orbital parameters, no significant interaction occurred between the two components, demonstrating that Be stars may form through a direct, single-star evolution path without mass transfer. Since component A will enter the instability strip in a few hundred thousand years, Achernar appears to be a promising progenitor of the Cepheid binary systems.

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