Abstract
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 on 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.

Abstract
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 flares to six. Of all flares, two are well covered 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. First, we find that the combination of polarization period and measured flare radius of around nine gravitational radii (9R(g) similar to 1.5R(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 x 10(6) M-circle dot 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. Second, 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. Finally, both the position angle on the 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 '' from Sgr A*, in agreement with recent simulations.

Abstract
Aims. The goal of this work is to characterize the polarization effects of the beam path of the Very Large Telescope Interferometer (VLTI) and the GRAVITY beam combiner instrument. This is useful for two reasons: 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. Methods. By combining a model of the VLTI light path and its mirrors and dedicated experimental data, we constructed a full polarization model of the VLTI Unit Telescopes (UTs) and the GRAVITY instrument. We first characterized all telescopes together to construct a universal UT calibration model for polarized targets with the VLTI. We then expanded the model to include the differential birefringence between the UTs. With this, we were able to constrain the systematic errors and the contrast loss for highly polarized targets. Results. Along with this paper, we have published a standalone Python package that can be used to calibrate the instrumental effects on polarimetric observations. This enables the community to use GRAVITY with the UTs to observe targets in a polarimetric observing mode. We demonstrate the calibration model with the Galactic Center star IRS 16C. For this source, we were able to constrain the polarization degree to within 0.4% and the polarization angle to within 5 degrees while being consistent with the literature values. 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 degrees, corresponding to an astrometric error of 10 mu as. Conclusions. With this work, we enable the use by the community of the polarimetric mode with GRAVITY/UTs and outline the steps necessary to observe and calibrate polarized targets with GRAVITY. 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.

Abstract
Stars form by accreting material from their surrounding disks. There is a consensus that matter flowing through the disk is channelled onto the stellar surface by the stellar magnetic field. This is thought to be strong enough to truncate the disk close to the corotation radius, at which the disk rotates at the same rate as the star. Spectro-interferometric studies in young stellar objects show that hydrogen emission (a well known tracer of accretion activity) mostly comes from a region a few milliarcseconds across, usually located within the dust sublimation radius(1-3). The origin of the hydrogen emission could be the stellar magnetosphere, a rotating wind or a disk. In the case of intermediate-mass Herbig AeBe stars, the fact that Brackett gamma (Br gamma) emission is spatially resolved rules out the possibility that most of the emission comes from the magnetosphere(4-6)because the weak magnetic fields (some tenths of a gauss) detected in these sources(7,8)result in very compact magnetospheres. In the case of T Tauri sources, their larger magnetospheres should make them easier to resolve. The small angular size of the magnetosphere (a few tenths of a milliarcsecond), however, along with the presence of winds(9,10)make the interpretation of the observations challenging. Here we report optical long-baseline interferometric observations that spatially resolve the inner disk of the T Tauri star TW Hydrae. We find that the near-infrared hydrogen emission comes from a region approximately 3.5 stellar radii across. This region is within the continuum dusty disk emitting region (7 stellar radii across) and also within the corotation radius, which is twice as big. This indicates that the hydrogen emission originates in the accretion columns (funnel flows of matter accreting onto the star), as expected in magnetospheric accretion models, rather than in a wind emitted at much larger distance (more than one astronomical unit). The size of the inner disk of the T Tauri star TW Hydrae is determined using optical long-baseline interferometric observations, indicating that hydrogen emission comes from a region approximately 3.5 stellar radii across.

Abstract
Context. eta Car is one of the most intriguing luminous blue variables in the Galaxy. Observations and models of the X-ray, ultraviolet, optical, and infrared emission suggest a central binary in a highly eccentric orbit with a 5.54 yr period residing in its core. 2D and 3D radiative transfer and hydrodynamic simulations predict a primary with a dense and slow stellar wind that interacts with the faster and lower density wind of the secondary. The wind-wind collision scenario suggests that the secondary's wind penetrates the primary's wind creating a low-density cavity in it, with dense walls where the two winds interact. However, the morphology of the cavity and its physical properties are not yet fully constrained. Aims. We aim to trace the inner similar to 5-50 au structure of eta Car's wind-wind interaction, as seen through Br gamma and, for the first time, through the He i 2s-2p line. Methods. We have used spectro-interferometric observations with the K-band beam-combiner GRAVITY at the VLTI. The analyses of the data include (i) parametrical model-fitting to the interferometric observables, (ii) a CMFGEN model of the source's spectrum, and (iii) interferometric image reconstruction. Results. Our geometrical modeling of the continuum data allows us to estimate its FWHM angular size close to 2 mas and an elongation ratio epsilon = 1.06 +/- 0.05 over a PA = 130 degrees +/- 20 degrees. Our CMFGEN modeling of the spectrum helped us to confirm that the role of the secondary should be taken into account to properly reproduce the observed Br gamma and He i lines. Chromatic images across the Br gamma line reveal a southeast arc-like feature, possibly associated to the hot post-shocked winds flowing along the cavity wall. The images of the He i 2s-2p line served to constrain the 20 mas (similar to 50 au) structure of the line-emitting region. The observed morphology of He i suggests that the secondary is responsible for the ionized material that produces the line profile. Both the Br gamma and the He i 2s-2p maps are consistent with previous hydrodynamical models of the colliding wind scenario. Future dedicated simulations together with an extensive interferometric campaign are necessary to refine our constraints on the wind and stellar parameters of the binary, which finally will help us predict the evolutionary path of eta Car.

Abstract
Aims. To date, infrared interferometry at best achieved contrast ratios of a few times 10(-4) on bright targets. GRAVITY, with its dual-field mode, is now capable of high contrast observations, enabling the direct observation of exoplanets. We demonstrate the technique on HR 8799, a young planetary system composed of four known giant exoplanets. Methods. We used the GRAVITY fringe tracker to lock the fringes on the central star, and integrated off-axis on the HR 8799 e planet situated at 390 mas from the star. Data reduction included post-processing to remove the flux leaking from the central star and to extract the coherent flux of the planet. The inferred K band spectrum of the planet has a spectral resolution of 500. We also derive the astrometric position of the planet relative to the star with a precision on the order of 100 mu as. Results. The GRAVITY astrometric measurement disfavors perfectly coplanar stable orbital solutions. A small adjustment of a few degrees to the orbital inclination of HR 8799 e can resolve the tension, implying that the orbits are close to, but not strictly coplanar. The spectrum, with a signal-to-noise ratio of approximate to 5 per spectral channel, is compatible with a late- type L brown dwarf. Using Exo-REM synthetic spectra, we derive a temperature of 1150 +/- 50 K and a surface gravity of 10(4.3 +/- 0.3) cm s(2). This corresponds to a radius of 1.17(-0.11)(+0.13) R-Jup and a mass of 10(-4)(+7) M-Jup, which is an independent confirmation of mass estimates from evolutionary models. Our results demonstrate the power of interferometry for the direct detection and spectroscopic study of exoplanets at close angular separations from their stars.