Abstract
This work focuses on active galactic nuclei (AGNs) and on 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 simply be 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 they are also more time efficient than those needed to resolve the BLR with OI. The primary goal of this work is to demonstrate a measuring of the BH mass based on the dust-continuum size with our first calibration of the R-BLR-R-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 of measuring BH masses for a large sample of AGNs in the low-redshift Universe.

Abstract
Context. T Tauri stars are known to be the cradle of planet formation. Most exoplanets discovered to date lie at the very inner part of the circumstellar disk (<1 au). The innermost scale of young stellar objects is therefore a compelling region to be addressed, and long-baseline interferometry is a key technique to unveil their mysteries. Aims. We aim to spatially and spectrally resolve the innermost scale (<= 1 au) of the young stellar system CI Tau to constrain the inner disk properties and better understand the magnetospheric accretion phenomenon. Methods. The high sensitivity offered by the combination of the four 8-m class telescopes of the Very Large Telescope Interferometer (VLTI) allied with the high spectral resolution (R similar to 4000) of the K-band beam combiner GRAVITY offers a unique capability to probe the sub-au scale of the CI Tau system, tracing both dust (continuum) and gas (Br gamma line) emission regions. We developed a physically motivated geometrical model to fit the interferometric observables - visibilities and closure phases (CP) - and constrained the physical properties of the inner dusty disk. The continuum-corrected pure line visibilities have been used to estimate the size of the Hydrogen Br gamma emitting region. Results. From the K-band continuum study, we report a highly inclined (i similar to 70 degrees) resolved inner dusty disk, with an inner edge located at a distance of 21 +/- 2 R-star from the central star, which is significantly larger than the dust sublimation radius (R-sub = 4.3 to 8.6 R-star). The inner disk appears misaligned compared to the outer disk observed by ALMA and the non-zero closure phase indicates the presence of an asymmetry that could be reproduced with an azimuthally modulated ring with a brighter south-west side. From the differential visibilities across the Br gamma line, we resolved the line-emitting region, and measured a size of 4.8(-1.0)(+0.8) R-star. Conclusions. The extended inner disk edge compared to the dust sublimation radius is consistent with the claim of an inner planet, CI Tau b, orbiting close in. The inner-outer disk misalignment may be induced by gravitational torques or magnetic warping. The size of the Br gamma emitting region is consistent with the magnetospheric accretion process. Assuming it corresponds to the magnetospheric radius, it is significantly smaller than the co-rotation radius (R-cor = 8.8 +/- 1.3 R-star), which suggests an unstable accretion regime that is consistent with CI Tau being a burster.

Abstract
Context. In the Milky Way the central massive black hole, Sgr A*, 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.Aims. We use GRAVITY astrometric and SINFONI, KECK, and GNIRS spectroscopic data of S2, the best known S-star, 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 Sgr A*.Methods. 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 Sgr A*-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.Results. For the hierarchical case we find the strongest constraints: IMBH masses > 2000 M-circle dot on orbits with smaller semi-major axes than S2 are largely excluded. For the non-hierarchical case, the chaotic nature of the problem becomes significant: 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.Conclusions. 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 and how future observations can help to put even stronger constraints on the properties of IMBHs in the GC.

Abstract
Tension remains between the observed and modeled properties of substellar objects, but objects in binary orbits, with known dynamical masses, can provide a way forward. HD 72946 B is a recently imaged brown dwarf companion to a nearby, solar-type star. We achieve similar to 100 mu as relative astrometry of HD 72946 B in the K band using VLTI/GRAVITY, unprecedented for a benchmark brown dwarf. We fit an ensemble of measurements of the orbit using orbitize! and derive a strong dynamical mass constraint M B = 69.5 +/- 0.5 M Jup assuming a strong prior on the host star mass M A = 0.97 +/- 0.01 M circle dot from an updated stellar analysis. We fit the spectrum of the companion to a grid of self-consistent BT-Settl-CIFIST model atmospheres, and perform atmospheric retrievals using petitRADTRANS. A dynamical mass prior only marginally influences the sampled distribution of effective temperature, but has a large influence on the surface gravity and radius, as expected. The dynamical mass alone does not strongly influence retrieved pressure-temperature or cloud parameters within our current retrieval setup. Independently of the cloud prescription and prior assumptions, we find agreement within +/- 2 sigma between the C/O of the host (0.52 +/- 0.05) and brown dwarf (0.43-0.63), as expected from a molecular cloud collapse formation scenario, but our retrieved metallicities are implausibly high (0.6-0.8) in light of the excellent agreement of the data with the solar-abundance model grid. Future work on our retrieval framework will seek to resolve this tension. Additional study of low surface gravity objects is necessary to assess the influence of a dynamical mass prior on atmospheric analysis.

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
Giant exoplanets have been directly imaged over orders of magnitude of orbital separations, prompting theoretical and observational investigations of their formation pathways. In this paper, we present new VLTI/GRAVITY astrometric data of HIP 65426 b, a cold, giant exoplanet which is a particular challenge for most formation theories at a projected separation of 92 au from its primary. Leveraging GRAVITY's astrometric precision, we present an updated eccentricity posterior that disfavors large eccentricities. The eccentricity posterior is still prior dependent, and we extensively interpret and discuss the limits of the posterior constraints presented here. We also perform updated spectral comparisons with self-consistent forward-modeled spectra, finding a best-fit ExoREM model with solar metallicity and C/O = 0.6. An important caveat is that it is difficult to estimate robust errors on these values, which are subject to interpolation errors as well as potentially missing model physics. Taken together, the orbital and atmospheric constraints paint a preliminary picture of formation inconsistent with scattering after disk dispersal. Further work is needed to validate this interpretation. Analysis code used to perform this work is available on GitHub: https://github.com/sblunt/hip65426.