Abstract
The dark compact object at the centre of the Milky Way is well established to be a supermassive black hole with mass M-center dot similar to 4.3 x 10(6) M-circle dot, 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) (less than or similar to) m(s less than or similar to) 10(-18) eV, our Markov chain Monte Carlo analysis shows no evidence for such a cloud, placing an upper bound M-cloud (less than or similar to) 0.1 % M-center dot 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.

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

Abstract
Young, low-mass brown dwarfs orbiting early-type stars, with low mass ratios (q less than or similar to 0.01), appear to be intrinsically rare and present a formation dilemma: could a handful of these objects be the highest-mass outcomes of planetary formation channels (bottom up within a protoplanetary disk), or are they more representative of the lowest-mass failed binaries (formed via disk fragmentation or core fragmentation)? Additionally, their orbits can yield model-independent dynamical masses, and when paired with wide wavelength coverage and accurate system age estimates, can constrain evolutionary models in a regime where the models have a wide dispersion depending on the initial conditions. We present new interferometric observations of the 16 Myr substellar companion HD 136164 Ab (HIP 75056 Ab) made with the Very Large Telescope Interferometer (VLTI)/GRAVITY and an updated orbit fit including proper motion measurements from the Hipparcos-Gaia Catalog of Accelerations. We estimate a dynamical mass of 35 +/- 10 M-J (q similar to 0.02), making HD 136164 Ab the youngest substellar companion with a dynamical mass estimate. The new mass and newly constrained orbital eccentricity (e = 0.44 +/- 0.03) and separation (22.5 +/- 1 au) could indicate that the companion formed via the low-mass tail of the initial mass function. Our atmospheric fit to a SPHINX M-dwarf model grid suggests a subsolar C/O ratio of 0.45 and 3 x solar metallicity, which could indicate formation in a circumstellar disk via disk fragmentation. Either way, the revised mass estimate likely excludes bottom-up formation via core accretion in a circumstellar disk. HD 136164 Ab joins a select group of young substellar objects with dynamical mass estimates; epoch astrometry from future Gaia data releases will constrain the dynamical mass of this crucial object further.

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

Abstract
This paper proposes a multiple-lens receiver scheme to increase the misalignment tolerance of an underwater optical wireless communications link between an autonomous underwater vehicle (AUV) and a sensor plane. An accurate model of photon propagation based on the Monte Carlo simulation is presented which accounts for the lens(es) photon refraction at the sensor interface and angular misalignment between the emitter and receiver. The results show that the ideal divergence of the beam of the emitter is around 15 degrees for a 1 m transmission length, increasing to 22 degrees for a shorter distance of 0.5 m but being independent of the water turbidity. In addition, it is concluded that a seven-lense scheme is approximately three times more tolerant to offset than a single lens. A random forest machine learning algorithm is also assessed for its suitability to estimate the offset and angle of the AUV in relation to the fixed sensor, based on the power distribution of each lens, in real time. The algorithm is able to estimate the offset and angular misalignment with a mean square error of 5 mm (6 mm) and 0.157 rad (0.174 rad) for a distance between the transmitter and receiver of 1 m and 0.5 m, respectively.