Abstract
Context. The GRAVITY beam-combiner at the Very Large Telescope Interferometer has recently made important contributions to many different fields of astronomy, from observations of the Galactic centre to the study of massive stars, young stellar objects, exoplanet atmospheres, and active galactic nuclei. These achievements were only made possible by the development of several key technologies, including the development of reliable and high-performance fringe trackers. These systems compensate for disturbances ranging from atmospheric turbulence to vibrations in the optical system, enabling long exposures and ensuring the stability of interferometric measurements. Aims. As part of the ongoing GRAVITY+ upgrade of the Very Large Telescope Interferometer infrastructure, we aim to improve the performance of the GRAVITY fringe tracker, and to enable its use by other instruments. Methods. We modified the group-delay controller to consistently maintain tracking in the white-light fringe, which is characterised by a minimum group delay. Additionally, we introduced a novel approach in which fringe-tracking is performed in the non-observable optical path length state-space using a covariance-weighted Kalman filter and an auto-regressive model of the disturbance. We outline this new state-space representation and the formalism we used to propagate the state vector and generate the control signal. While our approach is presented specifically in the context of GRAVITY/GRAVITY+, it can easily be adapted to other instruments or interfero-metric facilities. Results. We successfully demonstrate phase-delay tracking within a single fringe, with any spurious phase jumps detected and corrected in less than 100 ms. We also report a significant performance improvement, as shown by a reduction of similar to 30 to 40% in phase residuals, and a much better behaviour under sub-optimal atmospheric conditions. Compared to what was observed in 2019, the median residuals have decreased from 150 nm to 100 nm on the Auxiliary Telescopes and from 250 nm to 150 nm on the Unit Telescopes. Conclusions. The improved phase-delay tracking combined with white-light fringe tracking means that from now on, the GRAVITY fringe tracker can be used by other instruments operating in different wavebands. The only limitation remains the need for an adjustment of the optical path dispersion.

Abstract
Studying the orbital motion of stars around Sagittarius A* in the Galactic center provides a unique opportunity to probe the gravitational potential near the supermassive black hole at the heart of our Galaxy. Interferometric data obtained with the GRAVITY instrument at the Very Large Telescope Interferometer (VLTI) since 2016 has allowed us to achieve unprecedented precision in tracking the orbits of these stars. GRAVITY data have been key to detecting the in-plane, prograde Schwarzschild precession of the orbit of the star S2 that is predicted by general relativity. By combining astrometric and spectroscopic data from multiple stars, including S2, S29, S38, and S55 - for which we have data around their time of pericenter passage with GRAVITY - we can now strengthen the significance of this detection to an approximately 10 sigma confidence level. The prograde precession of S2's orbit provides valuable insights into the potential presence of an extended mass distribution surrounding Sagittarius A*, which could consist of a dynamically relaxed stellar cusp comprising old stars and stellar remnants, along with a possible dark matter spike. Our analysis, based on two plausible density profiles - a power-law and a Plummer profile - constrains the enclosed mass within the orbit of S2 to be consistent with zero, establishing an upper limit of approximately 1200 M-circle dot with a 1 sigma confidence level. This significantly improves our constraints on the mass distribution in the Galactic center. Our upper limit is very close to the expected value from numerical simulations for a stellar cusp in the Galactic center, leaving little room for a significant enhancement of dark matter density near Sagittarius A*.

Abstract
We resolve the multiple images of the binary-lens microlensing event ASASSN-22av using the GRAVITY instrument of the Very Large Telescope Interferometer (VLTI). The light curves show weak binary-lens perturbations, complicating the analysis, but the joint modeling with the VLTI data breaks several degeneracies, arriving at a strongly favored solution. Thanks to precise measurements of the angular Einstein radius theta E = 0.724 +/- 0.002 mas and microlens parallax, we determine that the lens system consists of two M dwarfs with masses of M 1 = 0.258 +/- 0.008 M circle dot and M 2 = 0.130 +/- 0.007 M circle dot, a projected separation of r perpendicular to = 6.83 +/- 0.31 au, and a distance of D L = 2.29 +/- 0.08 kpc. The successful VLTI observations of ASASSN-22av open up a new path for studying intermediate-separation (i.e., a few astronomical units) stellar-mass binaries, including those containing dark compact objects such as neutron stars and stellar-mass black holes.

Abstract
Context. A low-mass companion potentially in the brown dwarf mass regime was discovered on a similar to 12 yr orbit (similar to 5.5 au) around HD 167665 using radial velocity (RV) monitoring. Joint RV-astrometry analyses confirmed that HD 167665B is a brown dwarf with precisions on the measured mass of similar to 4-9%. Brown dwarf companions with measured mass and luminosity are valuable for testing formation and evolutionary models. However, its atmospheric properties and luminosity are still unconstrained, preventing detailed tests of evolutionary models. Aims. We further characterize the HD 167665 system by measuring the luminosity and refining the mass of its companion and reassessing the stellar age. Methods. We present new high-contrast imaging data of the star and of its close-in environment from SPHERE and GRAVITY, which we combined with RV data from CORALIE and HIRES and astrometry from HIPPARCOS and Gaia. Results. The analysis of the host star properties indicates an age of 6.20 +/- 1.13 Gyr. GRAVITY reveals a point source near the position predicted from a joint fit of RV data and HIPPARCOS-Gaia proper motion anomalies. Subsequent SPHERE imaging confirms the detection and reveals a faint point source of contrast of Delta H2 = 10.95 +/- 0.33 mag at a projected angular separation of similar to 180 mas. A joint fit of the high-contrast imaging, RV, and HIPPARCOS intermediate astrometric data together with the Gaia astrometric parameters constrains the mass of HD 167665B to similar to 1.2%, 60.3 +/- 0.7 M-J. The SPHERE colors and spectrum point to an early or mid-T brown dwarf of spectral type T4(-2)(+1). Fitting the SPHERE spectrophotometry and GRAVITY spectrum with synthetic spectra suggests an effective temperature of similar to 1000-1150 K, a surface gravity of similar to 5.0-5.4 dex, and a bolometric luminosity log(L/L-circle dot)=-4.892(-0.028)(+0.024) dex. The mass, luminosity, and age of the companion can only be reproduced within 3 sigma by the hybrid cloudy evolutionary models of Saumon & Marley (2008, ApJ, 689, 1327), whereas cloudless evolutionary models underpredict its luminosity.

Abstract
We present new Very Large Telescope Interferometer (VLTI)/GRAVITY near-infrared interferometric measurements of the angular size of the innermost hot dust continuum for 14 type 1 active galactic nuclei (AGNs). The angular sizes are resolved on scales of similar to 0.7 mas and the inferred ring radii range from 0.028 to 1.33 pc, comparable to those reported previously and a factor of 10-20 smaller than the mid-infrared sizes in the literature. Combining our new data with previously published values, we compiled a sample of 25 AGNs with bolometric luminosity ranging from 10(42) to 10(47) erg s(-1), with which we studied the radius-luminosity (R - L) relation for the hot dust structure. Our interferometric measurements of radius are offset by a factor of 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 mu m emitting surface has a concave shape. Our data show that the slope of the relation is in line with the canonical R proportional to 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 the innermost hot dust structure size and the AGN luminosity.

Abstract
Context. Dual-field interferometric observations with VLTI/GRAVITY sometimes require the use of a binary calibrator. This is a binary star whose individual components remain unresolved by the interferometer, with a separation between 400 and 2000 mas for observations with the Unit Telescopes (UTs), or 1200-3000 mas for the Auxiliary Telescopes (ATs). The separation vector also needs to be predictable to within 10 mas for a proper pointing of the instrument. Aims. No list of properly vetted calibrators was available so far 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. Methods. We identified a list of candidates from the Washington Double Star (WDS) catalogue, all with appropriate separations and brightness, scattered over the southern sky. We observed them as part of a dedicated calibration programme, determined whether these objects were true binaries (excluding higher multiplicities resolved interferometrically, but unseen by imaging), and extracted measurements of the separation vectors. We combined these new measurements with those available in the WDS to determine updated orbital parameters for all our vetted calibrators. Results. We compiled a list of 13 vetted binary calibrators for observations with VLTI/GRAVITY on the UTs, and we provide orbital estimates and astrometric predictions for each of them. We show that our list guarantees that there are always two binary calibrators at least at an airmass < 2 in the sky over the Paranal observatory at any point in time. Conclusions. 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.