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We present new VLTI/GRAVITY near-infrared interferometric measurements of the angular size of the innermost hot dust continuum for 14 type 1 AGNs. The angular sizes are resolved on scales of ~0.7 mas and the inferred ring radii range from 0.028 to 1.33 pc, comparable to those reported previously and a factor 10-20 smaller than the mid-infrared sizes in the literature. Combining our new data with previously published values, we compile a sample of 25 AGN with bolometric luminosity ranging from $10^{42}$ to $10^{47} \rm erg~s^{-1}$, with which we study the radius-luminosity (R-L) relation for the hot dust structure. Our interferometric measurements of radius are offset by a factor 2 from the equivalent relation derived through reverberation mapping. Using a simple model to explore the dust structure's geometry, we conclude that this offset can be explained if the 2 um emitting surface has a concave shape. Our data show that the slope of the relation is in line with the canonical $R \propto L^{0.5}$ when using an appropriately non-linear correction for bolometric luminosity. In contrast, using optical luminosity or applying a constant bolometric correction to it results in a significant deviation in the slope, suggesting a potential luminosity dependence on the spectral energy distribution. Over four orders of magnitude in luminosity, the intrinsic scatter around the R-L relation is 0.2 dex, suggesting a tight correlation between innermost hot dust structure size and the AGN luminosity., Comment: 14 pages, 5 figures, 4 tables, accepted for publication in A&A

Since 2019, GRAVITY has provided direct observations of giant planets and brown dwarfs at separations of down to 95 mas from the host star. Some of these observations have provided the first direct confirmation of companions previously detected by indirect techniques (astrometry and radial velocities). We want to improve the observing strategy and data reduction in order to lower the inner working angle of GRAVITY in dual-field on-axis mode. We also want to determine the current limitations of the instrument when observing faint companions with separations in the 30-150 mas range. To improve the inner working angle, we propose a fiber off-pointing strategy during the observations to maximize the ratio of companion-light-to-star-light coupling in the science fiber. We also tested a lower-order model for speckles to decouple the companion light from the star light. We then evaluated the detection limits of GRAVITY using planet injection and retrieval in representative archival data. We compare our results to theoretical expectations. We validate our observing and data-reduction strategy with on-sky observations; first in the context of brown dwarf follow-up on the auxiliary telescopes with HD 984 B, and second with the first confirmation of a substellar candidate around the star Gaia DR3 2728129004119806464. With synthetic companion injection, we demonstrate that the instrument can detect companions down to a contrast of $8\times 10^{-4}$ ($\Delta \mathrm{K}= 7.7$ mag) at a separation of 35 mas, and a contrast of $3\times 10^{-5}$ ($\Delta \mathrm{K}= 11$ mag) at 100 mas from a bright primary (K<6.5), for 30 min exposure time. With its inner working angle and astrometric precision, GRAVITY has a unique reach in direct observation parameter space. This study demonstrates the promising synergies between GRAVITY and Gaia for the confirmation and characterization of substellar companions., Comment: 16 pages, 14 figures. Submitted to A&A

With four companions at separations from 16 to 71 au, HR 8799 is a unique target for direct imaging, presenting an opportunity for the comparative study of exoplanets with a shared formation history. Combining new VLTI/GRAVITY observations obtained within the ExoGRAVITY program with archival data, we perform a systematic atmospheric characterisation of all four planets. We explore different levels of model flexibility to understand the temperature structure, chemistry and clouds of each planet using both petitRADTRANS atmospheric retrievals and fits to self-consistent radiative-convective equilibrium models. Using Bayesian Model Averaging to combine multiple retrievals, we find that the HR 8799 planets are highly enriched in metals, with [M/H] $\gtrsim$1, and have stellar to super-stellar C/O ratios. The C/O ratio increases with increasing separation from $0.55^{+0.12}_{-0.10}$ for d to $0.78^{+0.03}_{-0.04}$ for b, with the exception of the innermost planet which has a C/O ratio of $0.87\pm0.03$. By retrieving a quench pressure and using a disequilibrium chemistry model we derive vertical mixing strengths compatible with predictions for high-metallicity, self-luminous atmospheres. Bayesian evidence comparisons strongly favour the presence of HCN in HR 8799 c and e, as well as CH$_{4}$ in HR 8799 c, with detections at $>5\sigma$ confidence. All of the planets are cloudy, with no evidence for patchiness. The clouds of c, d and e are best fit by silicate clouds lying above a deep iron cloud layer, while the clouds of the cooler HR 8799 b are more likely composed of Na$_{2}$S. With well defined atmospheric properties, future exploration of this system is well positioned to unveil further detail in these planets, extending our understanding of the composition, structure, and formation history of these siblings., Comment: 45 pages, 25 figures, accepted by Astronomy & Astrophysics

Precise mass constraints are vital for the characterisation of brown dwarfs and exoplanets. Here we present how the combination of data obtained by Gaia and GRAVITY can help enlarge the sample of substellar companions with measured dynamical masses. We show how the Non-Single-Star (NSS) two-body orbit catalogue contained in Gaia DR3 can be used to inform high-angular-resolution follow-up observations with GRAVITY. Applying the method presented in this work to eight Gaia candidate systems, we detect all eight predicted companions, seven of which were previously unknown and five are of a substellar nature. Among the sample is Gaia DR3 2728129004119806464 B, which - detected at an angular separation of (34.01 $\pm$ 0.15) mas from the host - is the closest substellar companion ever imaged. This translates to a semi-major axis of (0.938 $\pm$ 0.023) AU. WT 766 B, detected at a greater angular separation, was confirmed to be on an orbit exhibiting an even smaller semi-major axis of (0.676 $\pm$ 0.008) AU. The GRAVITY data were then used to break the host-companion mass degeneracy inherent to the Gaia NSS orbit solutions as well as to constrain the orbital solutions of the respective target systems. Knowledge of the companion masses enabled us to further characterise them in terms of their ages, effective temperatures, and radii via the application of evolutionary models. The inferred ages exhibit a distinct bias towards values younger than what is to be expected based on the literature. The results serve as an independent validation of the orbital solutions published in the NSS two-body orbit catalogue and show that the combination of astrometric survey missions and high-angular-resolution direct imaging holds great promise for efficiently increasing the sample of directly imaged companions in the future, especially in the light of Gaia's upcoming DR4 and the advent of GRAVITY+., Comment: Accepted for publication in Astronomy and Astrophysics

Dual-field interferometric observations with VLTI/GRAVITY sometimes require the use of a "binary calibrator", a binary star whose individual components remain unresolved by the interferometer, with a separation between 400 and 2000 mas for observations with the Units Telescopes (UTs), or 1200 to 3000 mas for the Auxiliary Telescopes (ATs). The separation vector also needs to be predictable to within 10 mas for proper pointing of the instrument. Up until now, no list of properly vetted calibrators was available for dual-field observations with VLTI/GRAVITY on the UTs. Our objective is to compile such a list, and make it available to the community. We identify a list of candidates from the Washington Double Star (WDS) catalogue, all with appropriate separations and brightness, scattered over the Southern sky. We observe them as part of a dedicated calibration programme, and determine whether these objects are true binaries (excluding higher multiplicities resolved interferometrically but unseen by imaging), and extract measurements of the separation vectors. We combine these new measurements with those available in the WDS to determine updated orbital parameters for all our vetted calibrators. We compile a list of 13 vetted binary calibrators for observations with VLTI/GRAVITY on the UTs, and provide orbital estimates and astrometric predictions for each of them. We show that our list guarantees that there are always at least two binary calibrators at airmass < 2 in the sky over the Paranal observatory, at any point in time. Any Principal Investigator wishing to use the dual-field mode of VLTI/GRAVITY with the UTs can now refer to this list to select an appropriate calibrator. We encourage the use of "whereistheplanet" to predict the astrometry of these calibrators, which seamlessly integrates with "p2Gravity" for VLTI/GRAVITY dual-field observing material preparation., Comment: 16 pages, 6 figures. Submitted to A&A

3C84 is a nearby radio source with a complex total intensity structure, showing linear polarisation and spectral patterns. A detailed investigation of the central engine region necessitates the use of VLBI above the hitherto available maximum frequency of 86GHz. Using ultrahigh resolution VLBI observations at the highest available frequency of 228GHz, we aim to directly detect compact structures and understand the physical conditions in the compact region of 3C84. We used EHT 228GHz observations and, given the limited (u,v)-coverage, applied geometric model fitting to the data. We also employed quasi-simultaneously observed, multi-frequency VLBI data for the source in order to carry out a comprehensive analysis of the core structure. We report the detection of a highly ordered, strong magnetic field around the central, SMBH of 3C84. The brightness temperature analysis suggests that the system is in equipartition. We determined a turnover frequency of $\nu_m=(113\pm4)$GHz, a corresponding synchrotron self-absorbed magnetic field of $B_{SSA}=(2.9\pm1.6)$G, and an equipartition magnetic field of $B_{eq}=(5.2\pm0.6)$G. Three components are resolved with the highest fractional polarisation detected for this object ($m_\textrm{net}=(17.0\pm3.9)$%). The positions of the components are compatible with those seen in low-frequency VLBI observations since 2017-2018. We report a steeply negative slope of the spectrum at 228GHz. We used these findings to test models of jet formation, propagation, and Faraday rotation in 3C84. The findings of our investigation into different flow geometries and black hole spins support an advection-dominated accretion flow in a magnetically arrested state around a rapidly rotating supermassive black hole as a model of the jet-launching system in the core of 3C84. However, systematic uncertainties due to the limited (u,v)-coverage, however, cannot be ignored., Comment: 15 pages, 6 figures, published in A&A

Tight relationships exist in the local universe between the central stellar properties of galaxies and the mass of their supermassive black hole. These suggest galaxies and black holes co-evolve, with the main regulation mechanism being energetic feedback from accretion onto the black hole during its quasar phase. A crucial question is how the relationship between black holes and galaxies evolves with time; a key epoch to probe this relationship is at the peaks of star formation and black hole growth 8-12 billion years ago (redshifts 1-3). Here we report a dynamical measurement of the mass of the black hole in a luminous quasar at a redshift of 2, with a look back time of 11 billion years, by spatially resolving the broad line region. We detect a 40 micro-arcsecond (0.31 pc) spatial offset between the red and blue photocenters of the H$\alpha$ line that traces the velocity gradient of a rotating broad line region. The flux and differential phase spectra are well reproduced by a thick, moderately inclined disk of gas clouds within the sphere of influence of a central black hole with a mass of 3.2x10$^{8}$ solar masses. Molecular gas data reveal a dynamical mass for the host galaxy of 6x10$^{11}$ solar masses, which indicates an under-massive black hole accreting at a super-Eddington rate. This suggests a host galaxy that grew faster than the supermassive black hole, indicating a delay between galaxy and black hole formation for some systems., Comment: 5 pages Main text, 8 figures, 2 tables, to be published in Nature, under embargo until 29 January 2024 16:00 (London)

The broad-line region (BLR) of active galactic nuclei (AGNs) traces gas close to the central supermassive black hole (BH). Recent reverberation mapping (RM) and interferometric spectro-astrometry data have enabled detailed investigations of the BLR structure and dynamics, as well as estimates of the BH mass. These exciting developments motivate comparative investigations of BLR structures using different broad emission lines. In this work, we have developed a method to simultaneously model multiple broad lines of the BLR from a single-epoch spectrum. We apply this method to the five strongest broad emission lines (H$\alpha$, H$\beta$, H$\gamma$, Pa$\beta$, and He $I\;\lambda$5876) in the UV-to-NIR spectrum of NGC 3783, a nearby Type I AGN which has been well studied by RM and interferometric observations. Fixing the BH mass to the published value, we fit these line profiles simultaneously to constrain the BLR structure. We find that the differences between line profiles can be explained almost entirely as being due to different radial distributions of the line emission. We find that using multiple lines in this way also enables one to measure some important physical parameters, such as the inclination angle and virial factor of the BLR. The ratios of the derived BLR time lags are consistent with the expectation of theoretical model calculations and RM measurements., Comment: 16 pages, 9 figures, 4 tables, accepted for publication in A&A

The dark compact object at the centre of the Milky Way is well established to be a supermassive black hole with mass $M_{\bullet} \sim 4.3 \cdot 10^6 \, M_{\odot}$, but the nature of its environment is still under debate. In this work, we used astrometric and spectroscopic measurements of the motion of the star S2, one of the closest stars to the massive black hole, to determine an upper limit on an extended mass composed of a massive vector field around Sagittarius A*. For a vector with effective mass $10^{-19} \, \rm eV \lesssim m_s \lesssim 10^{-18} \, \rm eV$, our Markov Chain Monte Carlo analysis shows no evidence for such a cloud, placing an upper bound $M_{\rm cloud} \lesssim 0.1\% M_{\bullet}$ at $3\sigma$ confidence level. We show that dynamical friction exerted by the medium on S2 motion plays no role in the analysis performed in this and previous works, and can be neglected thus., Comment: 9 pages, 5 figures, accepted to MNRAS

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 {\mu}as. 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., Comment: Accepted by A&A

We apply image moment invariant analysis to total intensity and polarimetric images calculated from general relativistic magnetohydrodynamic simulations of accreting black holes. We characterize different properties of the models in our library by their invariant distributions and their evolution in time. We show that they are highly sensitive to different physical effects present in the system which allow for model discrimination. We propose a new model scoring method based on image moment invariants that is uniformly applicable to total intensity and polarimetric images simultaneously. The method does not depend on the type of images considered and its application to other non-ring like images (e.g., jets) is straight forward., Comment: 17 pages, 19 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society (MNRAS)

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., Comment: 10 pages, 12 figures. Accepted for publication in A&A

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., Comment: Published on MNRAS. References added

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), Comment: 11 pages, 6 figures, published in A $\&$ A

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$\beta$ 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., Comment: Accepted for publication in A&A; 11 pages, 5 figures, 3 tables

The stars orbiting the compact radio source Sgr A* in the Galactic Centre are precision probes of the gravitational field around the closest massive black hole. In addition to adaptive optics assisted astrometry (with NACO / VLT) and spectroscopy (with SINFONI / VLT, NIRC2 / Keck and GNIRS / Gemini) over three decades, since 2016/2017 we have obtained 30-100 mu-as astrometry with the four-telescope interferometric beam combiner GRAVITY / VLTI reaching a sensitivity of mK = 20 when combining data from one night. We present the simultaneous detection of several stars within the diffraction limit of a single telescope, illustrating the power of interferometry. The new data for the stars S2, S29, S38 and S55 yield significant accelerations between March and July 2021, as these stars pass the pericenters of their orbits between 2018 and 2023. This allows for a high-precision determination of the gravitational potential around Sgr A*. Our data are in excellent agreement with general relativity orbits around a single central point mass, M = 4.30 x 10^6 M_sun with a precision of about +-0.25%. We improve the significance of our detection of the Schwarzschild precession in the S2 orbit to 7 sigma. Assuming plausible density profiles, an extended mass component inside S2's apocentre (= 0.23" or 2.4 x 10^4 R_S) must be 3000 M_sun (1 sigma), or 0.1% of M. Adding the enclosed mass determinations from 13 stars orbiting Sgr A* at larger radii, the innermost radius at which the excess mass beyond Sgr A* tentatively is seen is r = 2.5" >= 10x the apocentre of S2. This is in full harmony with the stellar mass distribution (including stellar-mass black holes) obtained from the spatially resolved luminosity function., Comment: published in A&A

Stellar orbits at the Galactic Center provide a very clean probe of the gravitational potential of the supermassive black hole. They can be studied with unique precision, beyond the confusion limit of a single telescope, with the near-infrared interferometer GRAVITY. Imaging is essential to search the field for faint, unknown stars on short orbits which potentially could constrain the black hole spin. Furthermore, it provides the starting point for astrometric fitting to derive highly accurate stellar positions. Here, we present $\mathrm{G^R}$, a new imaging tool specifically designed for Galactic Center observations with GRAVITY. The algorithm is based on a Bayesian interpretation of the imaging problem, formulated in the framework of information field theory and building upon existing works in radio-interferometric imaging. Its application to GRAVITY observations from 2021 yields the deepest images to date of the Galactic Center on scales of a few milliarcseconds. The images reveal the complicated source structure within the central $100\,\mathrm{mas}$ around Sgr A*, where we detected the stars S29 and S55 and confirm S62 on its trajectory, slowly approaching Sgr A*. Furthermore, we were able to detect S38, S42, S60, and S63 in a series of exposures for which we offset the fiber from Sgr A*. We provide an update on the orbits of all aforementioned stars. In addition to these known sources, the images also reveal a faint star moving to the west at a high angular velocity. We cannot find any coincidence with any known source and, thus, we refer to the new star as S300. From the flux ratio with S29, we estimate its K-band magnitude as $m_\mathrm{K}\left(\mathrm{S300}\right)\simeq 19.0 - 19.3$. Images obtained with CLEAN confirm the detection., Comment: 24 pages, 14 figures

We aim to demonstrate that the presence and mass of an exoplanet can now be effectively derived from the astrometry of another exoplanet. We combined previous astrometry of $\beta$ Pictoris b with a new set of observations from the GRAVITY interferometer. The orbital motion of $\beta$ Pictoris b is fit using Markov chain Monte Carlo simulations in Jacobi coordinates. The inner planet, $\beta$ Pictoris c, was also reobserved at a separation of 96\,mas, confirming the previous orbital estimations. From the astrometry of planet b only, we can (i) detect the presence of $\beta$ Pictoris c and (ii) constrain its mass to $10.04^{+4.53}_{-3.10}\,M_{\rm Jup}$. If one adds the astrometry of $\beta$ Pictoris c, the mass is narrowed down to $9.15^{+1.08}_{-1.06}\,M_{\rm Jup}$. The inclusion of radial velocity measurements does not affect the orbital parameters significantly, but it does slightly decrease the mass estimate to $8.89^{+0.75}_{-0.75}\,M_{\rm Jup}$. With a semimajor axis of $2.68\pm0.02$\,au, a period of $1221\pm15$ days, and an eccentricity of $0.32\pm0.02$, the orbital parameters of $\beta$ Pictoris c are now constrained as precisely as those of $\beta$ Pictoris b. The orbital configuration is compatible with a high-order mean-motion resonance (7:1). The impact of the resonance on the planets' dynamics would then be negligible with respect to the secular perturbations, which might have played an important role in the eccentricity excitation of the outer planet., Comment: Accepted in A&A Letter

The angular size of the broad line region (BLR) of the nearby active galactic nucleus (AGN) NGC 3783 has been spatially resolved by recent observations with VLTI/GRAVITY. A reverberation mapping (RM) campaign has also recently obtained high quality light curves and measured the linear size of the BLR in a way that is complementary to the GRAVITY measurement. The size and kinematics of the BLR can be better constrained by a joint analysis that combines both GRAVITY and RM data. This, in turn, allows us to obtain the mass of the supermassive black hole in NGC3783 with an accuracy that is about a factor of two better than that inferred from GRAVITY data alone. We derive $M_\mathrm{BH}=2.54_{-0.72}^{+0.90}\times 10^7\,M_\odot$. Finally, and perhaps most notably, we are able to measure a geometric distance to NGC 3783 of $39.9^{+14.5}_{-11.9}$ Mpc. We are able to test the robustness of the BLR-based geometric distance with measurements based on the Tully-Fisher relation and other indirect methods. We find the geometric distance is consistent with other methods within their scatter. We explore the potential of BLR-based geometric distances to directly constrain the Hubble constant, $H_0$, and identify differential phase uncertainties as the current dominant limitation to the $H_0$ measurement precision for individual sources., Comment: 9 pages and 5 figures in main text, Accepted for publication in A&A

We report the time-resolved spectral analysis of a bright near-infrared and moderate X-ray flare of Sgr A*. We obtained light curves in the $M$-, $K$-, and $H$-bands in the mid- and near-infrared and in the $2-8~\mathrm{keV}$ and $2-70~\mathrm{keV}$ bands in the X-ray. The observed spectral slope in the near-infrared band is $\nu L_\nu\propto \nu^{0.5\pm0.2}$; the spectral slope observed in the X-ray band is $\nu L_\nu \propto \nu^{-0.7\pm0.5}$. We tested synchrotron and synchrotron self-Compton (SSC) scenarios. The observed near-infrared brightness and X-ray faintness, together with the observed spectral slopes, pose challenges for all models explored. We rule out a scenario in which the near-infrared emission is synchrotron emission and the X-ray emission is SSC. A one-zone model in which both the near-infrared and X-ray luminosity are produced by SSC and a model in which the luminosity stems from a cooled synchrotron spectrum can explain the flare. In order to describe the mean SED, both models require specific values of the maximum Lorentz factor $\gamma_{max}$, which however differ by roughly two orders of magnitude: the SSC model suggests that electrons are accelerated to $\gamma_{max}\sim 500$, while cooled synchrotron model requires acceleration up to $\gamma_{max}\sim5\times 10^{4}$. The SSC scenario requires electron densities of $10^{10}~\mathrm{cm^{-3}}$ much larger than typical ambient densities in the accretion flow, and thus require in an extraordinary accretion event. In contrast, assuming a source size of $1R_s$, the cooled synchrotron scenario can be realized with densities and magnetic fields comparable with the ambient accretion flow. For both models, the temporal evolution is regulated through the maximum acceleration factor $\gamma_{max}$, implying that sustained particle acceleration is required to explain at least a part of the temporal evolution of the flare., Comment: accepted for publication in Astronomy & Astrophysics; preview abstract shortened due to arXiv requirements

We aim to reveal the nature of the reddest known substellar companion HD 206893 B by studying its near-infrared colors and spectral morphology and by investigating its orbital motion. We fit atmospheric models for giant planets and brown dwarfs and perform spectral retrievals with petitRADTRANS and ATMO on the observed GRAVITY, SPHERE, and GPI spectra of HD 206893 B. To recover its unusual spectral features, we include additional extinction by high-altitude dust clouds made of enstatite grains in the atmospheric model fits. We also infer the orbital parameters of HD 206893 B by combining the $\sim 100~\mu\text{as}$ precision astrometry from GRAVITY with data from the literature and constrain the mass and position of HD 206893 C based on the Gaia proper motion anomaly of the system. The extremely red color and the very shallow $1.4~\mu\text{m}$ water absorption feature of HD 206893 B can be fit well with the adapted atmospheric models and spectral retrievals. Altogether, our analysis suggests an age of $\sim 3$-$300~\text{Myr}$ and a mass of $\sim 5$-$30~\text{M}_\text{Jup}$ for HD 206893 B, which is consistent with previous estimates but extends the parameter space to younger and lower-mass objects. The GRAVITY astrometry points to an eccentric orbit ($e = 0.29^{+0.06}_{-0.11}$) with a mutual inclination of $< 34.4~\text{deg}$ with respect to the debris disk of the system. While HD 206893 B could in principle be a planetary-mass companion, this possibility hinges on the unknown influence of the inner companion on the mass estimate of $10^{+5}_{-4}~\text{M}_\text{Jup}$ from radial velocity and Gaia as well as a relatively small but significant Argus moving group membership probability of $\sim 61\%$. However, we find that if the mass of HD 206893 B is $< 30~\text{M}_\text{Jup}$, then the inner companion HD 206893 C should have a mass between $\sim 8$-$15~\text{M}_\text{Jup}$., Comment: 28 pages, 19 figures, accepted for publication in A&A

GCIRS 7, the brightest star in the Galactic central parsec, formed $6\pm2$ Myr ago together with dozens of massive stars in a disk orbiting the central black-hole. It has been argued that GCIRS 7 is a pulsating body, on the basis of photometric variability. We present the first medium-resolution ($R=500$), K-band spectro-interferometric observations of GCIRS 7, using the GRAVITY instrument with the four auxiliary telescopes of the ESO VLTI. We looked for variations using two epochs, namely 2017 and 2019. We find GCIRS 7 to be moderately resolved with a uniform-disk photospheric diameter of $\theta^*_\text{UD}=1.55 \pm 0.03$ mas ($R^*_\text{UD}=1368 \pm 26$ $R_\odot$) in the K-band continuum. The narrow-band uniform-disk diameter increases above 2.3 $\mu$m, with a clear correlation with the CO band heads in the spectrum. This correlation is aptly modeled by a hot ($T_\text{L}=2368\pm37$ K), geometrically thin molecular shell with a diameter of $\theta_\text{L}=1.74\pm0.03$ mas, as measured in 2017. The shell diameter increased ($\theta_\text{L}=1.89\pm0.03$ mas), while its temperature decreased ($T_\text{L}=2140\pm42$ K) in 2019. In contrast, the photospheric diameter $\theta^*_\text{UD}$ and the extinction up to the photosphere of GCIRS 7 ($A_{\mathrm{K}_\mathrm{S}}=3.18 \pm 0.16$) have the same value within uncertainties at the two epochs. In the context of previous interferometric and photo-spectrometric measurements, the GRAVITY data allow for an interpretation in terms of photospheric pulsations. The photospheric diameter measured in 2017 and 2019 is significantly larger than previously reported using the PIONIER instrument ($\theta_*=1.076 \pm 0.093$ mas in 2013 in the H band). The parameters of the photosphere and molecular shell of GCIRS 7 are comparable to those of other red supergiants that have previously been studied using interferometry., Comment: 12 pages, 11 figures, 3 tables. Accepted for publication in Astronomy and Astrophysics (A&A)

Using general relativistic magnetohydrodynamic simulations of accreting black holes, we show that a suitable subtraction of the linear polarization per pixel from total intensity images can enhance the photon ring features. We find that the photon ring is typically a factor of $\simeq 2$ less polarized than the rest of the image. This is due to a combination of plasma and general relativistic effects, as well as magnetic turbulence. When there are no other persistently depolarized image features, adding the subtracted residuals over time results in a sharp image of the photon ring. We show that the method works well for sample, viable GRMHD models of Sgr A* and M87*, where measurements of the photon ring properties would provide new measurements of black hole mass and spin, and potentially allow for tests of the "no-hair" theorem of general relativity., Comment: 13 pages, 12 figures, accepted for publication in MNRAS

Using VLTI/GRAVITY and SINFONI data, we investigate the sub-pc gas and dust structure around the nearby type 1 AGN hosted by NGC 3783. The K-band coverage of GRAVITY uniquely allows a simultaneous analysis of the size and kinematics of the broad line region (BLR), the size and structure of the near-IR continuum emitting hot dust, and the size of the coronal line region (CLR). We find the BLR probed through broad Br$\gamma$ emission is well described by a rotating, thick disk with a radial distribution of clouds peaking in the inner region. In our BLR model the physical mean radius of 16 light days is nearly twice the 10 day time lag that would be measured, which matches very well the 10 day time lag that has been measured by reverberation mapping. We measure a hot dust FWHM size of 0.74 mas (0.14 pc) and further reconstruct an image of the hot dust which reveals a faint (5% of the total flux) offset cloud which we interpret as an accreting cloud heated by the central AGN. Finally, we directly measure the FWHM size of the nuclear CLR as traced by the [CaVIII] and narrow Br$\gamma$ line. We find a FWHM size of 2.2 mas (0.4 pc), fully in line with the expectation of the CLR located between the BLR and narrow line region. Combining all of these measurements together with larger scale near-IR integral field unit and mid-IR interferometry data, we are able to comprehensively map the structure and dynamics of gas and dust from 0.01--100 pc., Comment: 20 pages and 18 figures in main text, Accepted for publication in A&A

The GRAVITY instrument on the ESO VLTI pioneers the field of high-precision near-infrared interferometry by providing astrometry at the $10 - 100\,\mu$as level. Measurements at such high precision crucially depend on the control of systematic effects. Here, we investigate how aberrations introduced by small optical imperfections along the path from the telescope to the detector affect the astrometry. We develop an analytical model that describes the impact of such aberrations on the measurement of complex visibilities. Our formalism accounts for pupil-plane and focal-plane aberrations, as well as for the interplay between static and turbulent aberrations, and successfully reproduces calibration measurements of a binary star. The Galactic Center observations with GRAVITY in 2017 and 2018, when both Sgr A* and the star S2 were targeted in a single fiber pointing, are affected by these aberrations at a level of less than 0.5 mas. Removal of these effects brings the measurement in harmony with the dual beam observations of 2019 and 2020, which are not affected by these aberrations. This also resolves the small systematic discrepancies between the derived distance $R_0$ to the Galactic Center reported previously.

Combining adaptive optics and interferometric observations results in a considerable contrast gain compared to single-telescope, extreme AO systems. Taking advantage of this, the ExoGRAVITY project is a survey of known young giant exoplanets located in the range of 0.1'' to 2'' from their stars. The observations provide astrometric data of unprecedented accuracy, being crucial for refining the orbital parameters of planets and illuminating their dynamical histories. Furthermore, GRAVITY will measure non-Keplerian perturbations due to planet-planet interactions in multi-planet systems and measure dynamical masses. Over time, repetitive observations of the exoplanets at medium resolution ($R=500$) will provide a catalogue of K-band spectra of unprecedented quality, for a number of exoplanets. The K-band has the unique properties that it contains many molecular signatures (CO, H$_2$O, CH$_4$, CO$_2$). This allows constraining precisely surface gravity, metallicity, and temperature, if used in conjunction with self-consistent models like Exo-REM. Further, we will use the parameter-retrieval algorithm petitRADTRANS to constrain the C/O ratio of the planets. Ultimately, we plan to produce the first C/O survey of exoplanets, kick-starting the difficult process of linking planetary formation with measured atomic abundances., Comment: SPIE 2020, invited talk

We present K-band interferometric observations of the PDS 70 protoplanets along with their host star using VLTI/GRAVITY. We obtained K-band spectra and 100 $\mu$as precision astrometry of both PDS 70 b and c in two epochs, as well as spatially resolving the hot inner disk around the star. Rejecting unstable orbits, we found a nonzero eccentricity for PDS 70 b of $0.17 \pm 0.06$, a near-circular orbit for PDS 70 c, and an orbital configuration that is consistent with the planets migrating into a 2:1 mean motion resonance. Enforcing dynamical stability, we obtained a 95% upper limit on the mass of PDS 70 b of 10 $M_\textrm{Jup}$, while the mass of PDS 70 c was unconstrained. The GRAVITY K-band spectra rules out pure blackbody models for the photospheres of both planets. Instead, the models with the most support from the data are planetary atmospheres that are dusty, but the nature of the dust is unclear. Any circumplanetary dust around these planets is not well constrained by the planets' 1-5 $\mu$m spectral energy distributions (SEDs) and requires longer wavelength data to probe with SED analysis. However with VLTI/GRAVITY, we made the first observations of a circumplanetary environment with sub-au spatial resolution, placing an upper limit of 0.3~au on the size of a bright disk around PDS 70 b., Comment: 30 pages, 9 figures, Accepted for publication in AJ

The spin of the supermassive black hole that resides at the Galactic Centre can in principle be measured by accurate measurements of the orbits of stars that are much closer to SgrA* than S2, the orbit of which recently provided the measurement of the gravitational redshift and the Schwarzschild precession. The GRAVITY near-infrared interferometric instrument combining the four 8m telescopes of the VLT provides a spatial resolution of 2-4 mas, breaking the confusion barrier for adaptive-optics-assisted imaging with a single 8-10m telescope. We used GRAVITY to observe SgrA* over a period of six months in 2019 and employed interferometric reconstruction methods developed in radio astronomy to search for faint objects near SgrA*. This revealed a slowly moving star of magnitude 18.9 in K band within 30mas of SgrA*. The position and proper motion of the star are consistent with the previously known star S62, which is at a substantially larger physical distance, but in projection passes close to SgrA*. Observations in August and September 2019 easily detected S29, with K-magnitude of 16.6, at approximately 130 mas from SgrA*. The planned upgrades of GRAVITY, and further improvements in the calibration, hold the promise of finding stars fainter than magnitude 19 at K., Comment: 12 pages, 11 figures, published in A&A. Here we updated Fig. 1 with the latest motions laws of the S-stars as obtained from VLT/NACO observations until end 2019

Radial velocity monitoring has revealed the presence of moving broad emission lines in some quasars, potentially indicating the presence of a sub-parsec binary system. Phase-referenced, near-infrared interferometric observations could map out the binary orbit by measuring the photocenter difference between a broad emission line and the hot dust continuum. We show that astrometric data over several years may be able to detect proper motions and accelerations, confirming the presence of a binary and constraining system parameters. The brightness, redshifts, and astrometric sizes of current candidates are well matched to the capabilities of the upgraded VLTI/GRAVITY+ instrument, and we identify a first sample of 10 possible candidates. The astrometric signature depends on the morphology and evolution of hot dust emission in supermassive black hole binary systems. Measurements of the photocenter offset may reveal binary motion whether the hot dust emission region is fixed to the inner edge of the circumbinary disk, or moves in response to the changing irradiation pattern from an accreting secondary black hole., Comment: 17 pages, 6 figures, ApJ, in press

Methods used to detect giant exoplanets can be broadly divided into two categories: indirect and direct. Indirect methods are more sensitive to planets with a small orbital period, whereas direct detection is more sensitive to planets orbiting at a large distance from their host star. %, and thus on long orbital period. This dichotomy makes it difficult to combine the two techniques on a single target at once. Simultaneous measurements made by direct and indirect techniques offer the possibility of determining the mass and luminosity of planets and a method of testing formation models. Here, we aim to show how long-baseline interferometric observations guided by radial-velocity can be used in such a way. We observed the recently-discovered giant planet $\beta$ Pictoris c with GRAVITY, mounted on the Very Large Telescope Interferometer (VLTI). This study constitutes the first direct confirmation of a planet discovered through radial velocity. We find that the planet has a temperature of $T = 1250\pm50$\,K and a dynamical mass of $M = 8.2\pm0.8\,M_{\rm Jup}$. At $18.5\pm2.5$\,Myr, this puts $\beta$ Pic c close to a 'hot start' track, which is usually associated with formation via disk instability. Conversely, the planet orbits at a distance of 2.7\,au, which is too close for disk instability to occur. The low apparent magnitude ($M_{\rm K} = 14.3 \pm 0.1$) favours a core accretion scenario. We suggest that this apparent contradiction is a sign of hot core accretion, for example, due to the mass of the planetary core or the existence of a high-temperature accretion shock during formation., Comment: 10 pages

We present new near-infrared VLTI/GRAVITY interferometric spectra that spatially resolve the broad Br$\gamma$ emission line in the nucleus of the active galaxy IRAS 09149-6206. We use these data to measure the size of the broad line region (BLR) and estimate the mass of the central black hole. Using an improved phase calibration method that reduces the differential phase uncertainty to 0.05 degree per baseline across the spectrum, we detect a differential phase signal that reaches a maximum of ~0.5 degree between the line and continuum. This represents an offset of ~120 $\mu$as (0.14 pc) between the BLR and the centroid of the hot dust distribution traced by the 2.3 $\mu$m continuum. The offset is well within the dust sublimation region, which matches the measured ~0.6 mas (0.7 pc) diameter of the continuum. A clear velocity gradient, almost perpendicular to the offset, is traced by the reconstructed photocentres of the spectral channels of the Br$\gamma$ line. We infer the radius of the BLR to be ~65 $\mu$as (0.075 pc), which is consistent with the radius-luminosity relation of nearby active galactic nuclei derived based on the time lag of the H$\beta$ line from reverberation mapping campaigns. Our dynamical modelling indicates the black hole mass is $\sim 1\times10^8\,M_\odot$, which is a little below, but consistent with, the standard $M_{\rm BH}$-$\sigma_*$ relation., Comment: Accepted for publication in A&A. 14 pages, 11 figures in main text

We study the time-variable linear polarisation of Sgr A* during a bright NIR flare observed with the GRAVITY instrument on July 28, 2018. Motivated by the time evolution of both the observed astrometric and polarimetric signatures, we interpret the data in terms of the polarised emission of a compact region ('hotspot') orbiting a black hole in a fixed, background magnetic field geometry. We calculated a grid of general relativistic ray-tracing models, created mock observations by simulating the instrumental response, and compared predicted polarimetric quantities directly to the measurements. We take into account an improved instrument calibration that now includes the instrument's response as a function of time, and we explore a variety of idealised magnetic field configurations. We find that the linear polarisation angle rotates during the flare, which is consistent with previous results. The hotspot model can explain the observed evolution of the linear polarisation. In order to match the astrometric period of this flare, the near horizon magnetic field is required to have a significant poloidal component, which is associated with strong and dynamically important fields. The observed linear polarisation fraction of $\simeq 30\%$ is smaller than the one predicted by our model ($\simeq 50\%$). The emission is likely beam depolarised, indicating that the flaring emission region resolves the magnetic field structure close to the black hole., Comment: 13 pages, 14 figures, to be published in A&A

Large-amplitude Sgr A* near-infrared flares result from energy injection into electrons near the black hole event horizon. Astrometry data show continuous rotation of the emission region during bright flares, and corresponding rotation of the linear polarization angle. One broad class of physical flare models invokes magnetic reconnection. Here we show that such a scenario can arise in a general relativistic magnetohydrodynamic simulation of a magnetically arrested disc. Saturation of magnetic flux triggers eruption events, where magnetically dominated plasma is expelled from near the horizon and forms a rotating, spiral structure. Dissipation occurs via reconnection at the interface of the magnetically dominated plasma and surrounding fluid. This dissipation is associated with large increases in near-infrared emission in models of Sgr A*, with durations and amplitudes consistent with the observed flares. Such events occur at roughly the timescale to re-accumulate the magnetic flux from the inner accretion disc, 10h for Sgr A*. We study near-infrared observables from one sample event to show that the emission morphology tracks the boundary of the magnetically dominated region. As the region rotates around the black hole, the near-infrared centroid and linear polarization angle both undergo continuous rotation, similar to the behavior seen in Sgr A* flares., Comment: revised version, MNRAS, in press

The Galactic Center black hole Sagittarius A* is a variable NIR source that exhibits bright flux excursions called flares. The low-flux density turnover of the flux distribution is below the sensitivity of current single-aperture telescopes. We use the unprecedented resolution of the GRAVITY instrument at the VLTI. Our light curves are unconfused, overcoming the confusion limit of previous photometric studies. We analyze the light curves using standard statistical methods and obtain the flux distribution. We find that the flux distribution of SgrA* turns over at a median flux density of (1.1\pm0.3)mJy. We measure the percentiles of the flux distribution and use them to constrain the NIR K-band SED. Furthermore, we find that the flux distribution is intrinsically right-skewed to higher flux density in log space. Flux densities below 0.1mJy are hardly ever observed. In consequence, a single powerlaw or lognormal distribution does not suffice to describe the observed flux distribution in its entirety. However, if one takes into account a power law component at high flux densities, a lognormal distribution can describe the lower end of the observed flux distribution. We confirm the RMS-flux relation for Sgr~A* and find it to be linear for all flux densities in our observation. We conclude that Sgr~A* has two states: the bulk of the emission is generated in a lognormal process with a well-defined median flux density and this quiescent emission is supplemented by sporadic flares that create the observed power law extension of the flux distribution.

The star S2 orbiting the compact radio source Sgr A* is a precision probe of the gravitational field around the closest massive black hole (candidate). Over the last 2.7 decades we have monitored the star's radial velocity and motion on the sky, mainly with the SINFONI and NACO adaptive optics (AO) instruments on the ESO VLT, and since 2017, with the four-telescope interferometric beam combiner instrument GRAVITY. In this paper we report the first detection of the General Relativity (GR) Schwarzschild Precession (SP) in S2's orbit. Owing to its highly elliptical orbit (e = 0.88), S2's SP is mainly a kink between the pre-and post-pericentre directions of motion ~ +- 1 year around pericentre passage, relative to the corresponding Kepler orbit. The superb 2017-2019 astrometry of GRAVITY defines the pericentre passage and outgoing direction. The incoming direction is anchored by 118 NACO-AO measurements of S2's position in the infrared reference frame, with an additional 75 direct measurements of the S2-Sgr A* separation during bright states ('flares') of Sgr A*. Our 14-parameter model fits for the distance, central mass, the position and motion of the reference frame of the AO astrometry relative to the mass, the six parameters of the orbit, as well as a dimensionless parameter f_SP for the SP (f_SP = 0 for Newton and 1 for GR). From data up to the end of 2019 we robustly detect the SP of S2, del phi = 12' per orbital period. From posterior fitting and MCMC Bayesian analysis with different weighting schemes and bootstrapping we find f_SP = 1.10 +- 0.19. The S2 data are fully consistent with GR. Any extended mass inside S2's orbit cannot exceed ~ 0.1% of the central mass. Any compact third mass inside the central arcsecond must be less than about 1000 M_sun., Comment: accepted to A&A

Realistic synthetic observations of theoretical source models are essential for our understanding of real observational data. In using synthetic data, one can verify the extent to which source parameters can be recovered and evaluate how various data corruption effects can be calibrated. These studies are important when proposing observations of new sources, in the characterization of the capabilities of new or upgraded instruments, and when verifying model-based theoretical predictions in a comparison with observational data. We present the SYnthetic Measurement creator for long Baseline Arrays (SYMBA), a novel synthetic data generation pipeline for Very Long Baseline Interferometry (VLBI) observations. SYMBA takes into account several realistic atmospheric, instrumental, and calibration effects. We used SYMBA to create synthetic observations for the Event Horizon Telescope (EHT), a mm VLBI array, which has recently captured the first image of a black hole shadow. After testing SYMBA with simple source and corruption models, we study the importance of including all corruption and calibration effects. Based on two example general relativistic magnetohydrodynamics (GRMHD) model images of M87, we performed case studies to assess the attainable image quality with the current and future EHT array for different weather conditions. The results show that the effects of atmospheric and instrumental corruptions on the measured visibilities are significant. Despite these effects, we demonstrate how the overall structure of the input models can be recovered robustly after performing calibration steps. With the planned addition of new stations to the EHT array, images could be reconstructed with higher angular resolution and dynamic range. In our case study, these improvements allowed for a distinction between a thermal and a non-thermal GRMHD model based on salient features in reconstructed images., Comment: 20 pages, 15 figures, accepted for publication in A&A

The Galactic center black hole candidate Sgr A* is the best target for studies of low-luminosity accretion physics, including with near-infrared and submillimeter wavelength long baseline interferometry experiments. Here we compare images and spectra generated from a parameter survey of general relativistic MHD simulations to a set of radio to near-infrared observations of Sgr A*. Our models span the limits of weak and strong magnetization and use a range of sub-grid prescriptions for electron heating. We find two classes of scenarios can explain the broad shape of the submillimeter spectral peak and the highly variable near-infrared flaring emission. Weakly magnetized "disk-jet" models where most of the emission is produced near the jet wall, consistent with past work, as well as strongly magnetized (magnetically arrested disk) models where hot electrons are present everywhere. Disk-jet models are strongly depolarized at submillimeter wavelengths as a result of strong Faraday rotation, inconsistent with observations of Sgr A*. We instead favor the strongly magnetized models, which provide a good description of the median and highly variable linear polarization signal. The same models can also explain the observed mean Faraday rotation measure and potentially the polarization signals seen recently in Sgr A* near-infrared flares., Comment: 20 pages, 17 figures, MNRAS in press

Infrared observations of Sgr A* probe the region close to the event horizon of the black hole at the Galactic center. These observations can constrain the properties of low-luminosity accretion as well as that of the black hole itself. The GRAVITY instrument at the ESO VLTI has recently detected continuous circular relativistic motion during infrared flares which has been interpreted as orbital motion near the event horizon. Here we analyze the astrometric data from these flares, taking into account the effects of out-of-plane motion and orbital shear of material near the event horizon of the black hole. We have developed a new code to predict astrometric motion and flux variability from compact emission regions following particle orbits. Our code combines semi-analytic calculations of timelike geodesics that allow for out-of-plane or elliptical motions with ray tracing of photon trajectories to compute time-dependent images and light curves. We apply our code to the three flares observed with GRAVITY in 2018. We show that all flares are consistent with a hotspot orbiting at R$\sim$9 gravitational radii with an inclination of $i\sim140^\circ$. The emitting region must be compact and less than $\sim5$ gravitational radii in diameter. We place a further limit on the out-of-plane motion during the flare., Comment: Accepted in A&A

Our objective is to estimate the C/O ratio in the atmosphere of beta Pictoris b and obtain an estimate of the dynamical mass of the planet, as well as to refine its orbital parameters using high-precision astrometry. We used the GRAVITY instrument with the four 8.2 m telescopes of the Very Large Telescope Interferometer to obtain K-band spectro-interferometric data on $\beta$ Pic b. We extracted a medium resolution (R=500) K-band spectrum of the planet and a high-precision astrometric position. We estimated the planetary C/O ratio using two different approaches (forward modeling and free retrieval) from two different codes (ExoREM and petitRADTRANS, respectively). Finally, we used a simplified model of two formation scenarios (gravitational collapse and core-accretion) to determine which can best explain the measured C/O ratio. Our new astrometry disfavors a circular orbit for $\beta$ Pic b ($e=0.15^{+0.05}_{-0.04}$). Combined with previous results and with Hipparcos/GAIA measurements, this astrometry points to a planet mass of $M = 12.7\pm{}2.2\,M_\mathrm{Jup}$. This value is compatible with the mass derived with the free-retrieval code petitRADTRANS using spectral data only. The forward modeling and free-retrieval approches yield very similar results regarding the atmosphere of beta Pic b. In particular, the C/O ratios derived with the two codes are identical ($0.43\pm{}0.05$ vs $0.43^{+0.04}_{-0.03}$). We argue that if the stellar C/O in $\beta$ Pic is Solar, then this combination of a very high mass and a low C/O ratio for the planet suggests a formation through core-accretion, with strong planetesimal enrichment., Comment: 14 pages + 7 page appendix, 7 figures, accepted for pulication

We present near-infrared interferometric data on the Seyfert 2 galaxy NGC 1068, obtained with the GRAVITY instrument on the European Southern Observatory Very Large Telescope Interferometer. The extensive baseline coverage from 5 to 60 M\lambda allowed us to reconstruct a continuum image of the nucleus with an unrivaled 0.2 pc resolution in the K-band. We find a thin ring-like structure of emission with a radius r = 0.24+/-0.03 pc, inclination i = 70+/-5 deg, position angle PA = -50+/-4 deg, and h/r < 0.14, which we associate with the dust sublimation region. The observed morphology is inconsistent with the expected signatures of a geometrically and optically thick torus. Instead, the infrared emission shows a striking resemblance to the 22 GHz maser disc, which suggests they share a common region of origin. The near-infrared spectral energy distribution indicates a bolometric luminosity of (0.4-4.7) x 10^45 erg/s, behind a large A_K ~ 5.5 (A_V ~ 90) screen of extinction that also appears to contribute significantly to obscuring the broad line region., Comment: Accepted for publication in Astronomy and Astrophysics. 13 pages with 7 figures

The formation and the evolution of protoplanetary disks are important stages in the lifetime of stars. The processes of disk evolution and planet formation are intrinsically linked. We spatially resolve with GRAVITY/VLTI in the K-band the sub au-scale region of 27 stars to gain statistical understanding of their properties. We look for correlations with stellar parameters, such as luminosity, mass, temperature and age. Our sample also cover a range of various properties in terms of reprocessed flux, flared or flat morphology, and gaps. We developed semi-physical geometrical models to fit our interferometric data. Our best models correspond to smooth and wide rings, implying that wedge-shaped rims at the dust sublimation edge are favored, as found in the H-band. The closure phases are generally non-null with a median value of ~10 deg, indicating spatial asymmetries of the intensity distributions. Multi-size grain populations could explain the closure phase ranges below 20-25 deg but other scenarios should be invoked to explain the largest ones. Our measurements extend the Radius-Luminosity relation to ~1e4 Lsun and confirm the significant spread around the mean relation observed in the H-band. Gapped sources exhibit a large N-to-K band size ratio and large values of this ratio are only observed for the members of our sample that would be older than 1 Ma, less massive, and with lower luminosity. In the 2 Ms mass range, we observe a correlation in the increase of the relative age with the transition from group II to group I, and an increase of the N-to-K size ratio. However, the size of the current sample does not yet permit us to invoke a clear universal evolution mechanism across the HAeBe mass range. The measured locations of the K-band emission suggest that these disks might be structured by forming young planets, rather than by depletion due to EUV, FUV, and X-ray photo-evaporation., Comment: Accepted for publication in A&A; 23 pages, 16 figures, 7 tables