Abstract
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 similar to 9 gravitational radii with an inclination of i similar to 140 degrees. The emitting region must be compact and less than similar to 5 gravitational radii in diameter. We place a further limit on the out-of-plane motion during the flare.

Abstract
Context. The inner regions of the discs of high-mass young stellar objects (HMYSOs) are still poorly known due to the small angular scales and the high visual extinction involved.Aims. We deploy near-infrared spectro-interferometry to probe the inner gaseous disc in HMYSOs and investigate the origin and physical characteristics of the CO bandhead emission (2.3-2.4 mu m).Methods. We present the first GRAVITY/VLTI observations at high spectral (R=4000) and spatial (mas) resolution of the CO overtone transitions in NGC 2024 IRS 2.Results. The continuum emission is resolved in all baselines and is slightly asymmetric, displaying small closure phases (<= 8 degrees). Our best ellipsoid model provides a disc inclination of 34 degrees +/- 1 degrees, a disc major axis position angle (PA) of 166 degrees +/- 1 degrees, and a disc diameter of 3.99 +/- 0.09 mas (or 1.69 +/- 0.04 au, at a distance of 423 pc). The small closure phase signals in the continuum are modelled with a skewed rim, originating from a pure inclination effect. For the first time, our observations spatially and spectrally resolve the first four CO bandheads. Changes in visibility, as well as differential and closure phases across the bandheads are detected. Both the size and geometry of the CO-emitting region are determined by fitting a bidimensional Gaussian to the continuum-compensated CO bandhead visibilities. The CO-emitting region has a diameter of 2.74 +/-(0.08)(0.07) +/- 0.07 0.08 mas (1.16 +/- 0.03 au), and is located in the inner gaseous disc, well within the dusty rim, with inclination and PA matching the dusty disc geometry, which indicates that both dusty and gaseous discs are coplanar. Physical and dynamical gas conditions are inferred by modelling the CO spectrum. Finally, we derive a direct measurement of the stellar mass of M-* similar to 14.7(-3.6)(+2)M(circle dot) M * similar to 14 . 7 - 3.6 + 2 M circle dot by combining our interferometric and spectral modelling results.

Abstract
Context. Close young binary stars are unique laboratories for the direct measurement of pre-main-sequence (PMS) stellar masses and their comparison to evolutionary theoretical models. At the same time, a precise knowledge of their orbital parameters when still in the PMS phase offers an excellent opportunity for understanding the influence of dynamical effects on the morphology and lifetime of the circumstellar as well as circumbinary material. Aims. The young T Tauri star WW Cha was recently proposed to be a close binary object with strong infrared and submillimeter excess associated with circum-system emission, which makes it dynamically a very interesting source in the above context. The goal of this work is to determine the astrometric orbit and the stellar properties of WW Cha using multi-epoch interferometric observations. Methods. We derive the relative astrometric positions and flux ratios of the stellar companion in WW Cha from the interferometric model fitting of observations made with the VLTI instruments AMBER, PIONIER, and GRAVITY in the near-infrared from 2011 to 2020. For two epochs, the resulting uv-coverage in spatial frequencies permits us to perform the first image reconstruction of the system in the K band. The positions of nine epochs are used to determine the orbital elements and the total mass of the system. Combining the orbital solution with distance measurements from Gaia DR2 and the analysis of evolutionary tracks, we constrain the mass ratio. Results. We find the secondary star orbiting the primary with a period of T = 206.55 days, a semimajor axis of a = 1.01 au, and a relatively high eccentricity of e = 0.45. The dynamical mass of M-tot = 3.20 M-circle dot can be explained by a mass ratio between similar to 0.5 and 1, indicating an intermediate-mass T Tauri classification for both components. The orbital angular momentum vector is in close alignment with the angular momentum vector of the outer disk as measured by ALMA and SPHERE, resulting in a small mutual disk inclination. The analysis of the relative photometry suggests the presence of infrared excess surviving in the system and likely originating from truncated circumstellar disks. The flux ratio between the two components appears variable, in particular in the K band, and may hint at periods of triggered higher and lower accretion or changes in the disks' structures. Conclusions. The knowledge of the orbital parameters, combined with a relatively short period, makes WW Cha an ideal target for studying the interaction of a close young T Tauri binary with its surrounding material, such as time-dependent accretion phenomena. Finding WW Cha to be composed of two (probably similar) stars led us to reevaluate the mass of WW Cha, which had been previously derived under the assumption of a single star. This work illustrates the potential of long baseline interferometry to precisely characterize close young binary stars separated by a few astronomical units. Finally, when combined with radial velocity measurements, individual stellar masses can be derived and used to calibrate theoretical PMS models.

Abstract
Context. Protoplanetary disks drive some of the formation process (e.g., accretion, gas dissipation, formation of structures) of stars and planets. Understanding such physical processes is one of the most significant astrophysical questions. HD 163296 is an interesting young stellar object for which infrared and sub-millimeter observations have shown a prominent circumstellar disk with gaps plausibly created by forming planets. Aims. This study aims to characterize the morphology of the inner disk in HD 163296 with multi-epoch, near-infrared interferometric observations performed with GRAVITY at the Very Large Telescope Interferometer. Our goal is to depict the K-band (lambda(0) similar to 2.2 mu m) structure of the inner rim with milliarcsecond (sub-au) angular resolution. Our data is complemented with archival Precision Integrated-Optics Near-infrared Imaging ExpeRiment (H-band; lambda(0) similar to 1.65 mu m) data of the source. Methods. We performed a gradient descent parametric model fitting to recover the sub-au morphology of our source. Results. Our analysis shows the existence of an asymmetry in the disk surrounding the central star of HD 163296. We confirm variability of the disk structure in the inner similar to 2 mas (0.2 au). While variability of the inner disk structure in this source has been suggested by previous interferometric studies, this is the first time that it is confirmed in the H- and K-bands by using a complete analysis of the closure phases and squared visibilities over several epochs. Because of the separation from the star, position changes, and the persistence of this asymmetric structure on timescales of several years, we argue that it is probably a dusty feature (e.g., a vortex or dust clouds) made by a mixing of silicate and carbon dust and/or refractory grains, inhomogeneously distributed above the mid-plane of the disk.

Abstract
Context. Near-infrared interferometry has become a powerful tool for studying the orbital and atmospheric parameters of substellar companions. Aims. 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. Methods. 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, first and foremost its extremely red near-infrared color, we include additional extinction by high-altitude dust clouds made of enstatite grains in the atmospheric model fits. However, forsterite, corundum, and iron grains predict similar extinction curves for the grain sizes considered here. We also infer the orbital parameters of HD 206893 B by combining the similar to 100 mu 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. Results. The extremely red color and the very shallow 1.4 mu m water absorption feature of HD 206893 B can be fit well with the adapted atmospheric models and spectral retrievals. By comparison with AMES-Cond evolutionary tracks, we find that only some atmosphericmodels predict physically plausible objects. Altogether, our analysis suggests an age of similar to 3-300 Myr and a mass of similar to 5-30 M-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(-0.11)(+0.06)) with a mutual inclination of <34.4 deg with respect to the debris disk of the system. Conclusions. 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(-4)(+5) M-Jup from radial velocity and Gaia as well as a relatively small but significant Argus moving group membership probability of similar to 61%. However, we find that if the mass of HD 206893 B is M-Jup, then the inner companion HD 206893 C should have a mass between similar to 8-15 M-Jup. Finally, further spectroscopic or photometric observations at higher signal-to-noise and longer wavelengths are required to learn more about the composition and dust cloud properties of HD 206893 B.

Abstract
GRAVITY+ is the upgrade for GRAVITY and the Very Large Telescope Interferometer (VLTI) with wide-separation fringe tracking, new adaptive optics, and laser guide stars on all four 8 m Unit Telescopes (UTs) to enable ever-fainter, all-sky, high-contrast, milliarcsecond interferometry. Here we present the design and first results of the first phase of GRAVITY+, known as GRAVITY Wide. GRAVITY Wide combines the dual-beam capabilities of the VLTI and the GRAVITY instrument to increase the maximum separation between the science target and the reference star from 2 arcseconds with the 8 m UTs up to several 10 arcseconds, limited only by the Earth's turbulent atmosphere. This increases the sky-coverage of GRAVITY by two orders of magnitude, opening up milliarcsecond resolution observations of faint objects and, in particular, the extragalactic sky. The first observations in 2019-2022 include the first infrared interferometry of two redshift z similar to 2 quasars, interferometric imaging of the binary system HD 105913A, and repeat observations of multiple star systems in the Orion Trapezium Cluster. We find the coherence loss between the science object and fringe-tracking reference star well described by the turbulence of the Earth's atmosphere. We confirm that the larger apertures of the UTs result in higher visibilities for a given separation due to the broader overlap of the projected pupils on the sky and provide predictions for visibility loss as a function of separation to be used for future planning.