Abstract
Context. The nearby and young beta Pictoris system hosts a well resolved disk, a directly imaged massive giant planet orbiting at similar or equal to 9 au, as well as an inner planet orbiting at similar or equal to 2.7 au, which was recently detected through radial velocity (RV). As such, it offers several unique opportunities for detailed studies of planetary system formation and early evolution.Aims. We aim to further constrain the orbital and physical properties of beta Pictoris b and c using a combination of high contrast imaging, long base-line interferometry, and RV data. We also predict the closest approaches or the transit times of both planets, and we constrain the presence of additional planets in the system.Methods. We obtained six additional epochs of SPHERE data, six additional epochs of GRAVITY data, and five additional epochs of RV data. We combined these various types of data in a single Markov-chain Monte Carlo analysis to constrain the orbital parameters and masses of the two planets simultaneously. The analysis takes into account the gravitational influence of both planets on the star and hence their relative astrometry. Secondly, we used the RV and high contrast imaging data to derive the probabilities of presence of additional planets throughout the disk, and we tested the impact of absolute astrometry.Results. The orbital properties of both planets are constrained with a semi-major axis of 9.8 0.4 au and 2.7 +/- 0.02 au for b and c, respectively, and eccentricities of 0.09 +/- 0.1 and 0.27 +/- 0.07, assuming the HIPPARCOS distance. We note that despite these low fitting error bars, the eccentricity of beta Pictoris c might still be over-estimated. If no prior is provided on the mass of beta Pictoris b, we obtain a very low value that is inconsistent with what is derived from brightness-mass models. When we set an evolutionary model motivated prior to the mass of beta Pictoris b, we find a solution in the 10-11 M-Jup range. Conversely, beta Pictoris c's mass is well constrained, at 7.8 +/- 0.4 M-Jup, assuming both planets are on coplanar orbits. These values depend on the assumptions on the distance of the beta Pictoris system. The absolute astrometry HIPPARCOS-Gaia data are consistent with the solutions presented here at the 2 sigma level, but these solutions are fully driven by the relative astrometry plus RV data. Finally, we derive unprecedented limits on the presence of additional planets in the disk. We can now exclude the presence of planets that are more massive than about 2.5 M-Jup closer than 3 au, and more massive than 3.5 M-Jup between 3 and 7.5 au. Beyond 7.5 au, we exclude the presence of planets that are more massive than 1-2 M-Jup.Conclusions. Combining relative astrometry and RVs allows one to precisely constrain the orbital parameters of both planets and to give lower limits to potential additional planets throughout the disk. The mass of beta Pictoris c is also well constrained, while additional RV data with appropriate observing strategies are required to properly constrain the mass of beta Pictoris b.

Abstract
The Galactic center black hole Sagittarius A* is a variable near-infrared (NIR) source that exhibits bright flux excursions called flares. When flux from Sgr A* is detected, the light curve has been shown to exhibit red noise characteristics and the distribution of flux densities is non-linear, non-Gaussian, and skewed to higher flux densities. However, the low-flux density turnover of the flux distribution is below the sensitivity of current single-aperture telescopes. For this reason, the median NIR flux has only been inferred indirectly from model fitting, but it has not been directly measured. In order to explore the lowest flux ranges, to measure the median flux density, and to test if the previously proposed flux distributions fit the data, we use the unprecedented resolution of the GRAVITY instrument at the VLTI. We obtain light curves using interferometric model fitting and coherent flux measurements. Our light curves are unconfused, overcoming the confusion limit of previous photometric studies. We analyze the light curves using standard statistical methods and obtain the flux distribution. We find that the flux distribution of Sgr A* turns over at a median flux density of (1.1 +/- 0.3) mJy. We measure the percentiles of the flux distribution and use them to constrain the NIR K-band spectral energy distribution. Furthermore, we find that the flux distribution is intrinsically right-skewed to higher flux density in log space. Flux densities below 0.1 mJy are hardly ever observed. In consequence, a single powerlaw or lognormal distribution does not suffice to describe the observed flux distribution in its entirety. However, if one takes into account a power law component at high flux densities, a lognormal distribution can describe the lower end of the observed flux distribution. We confirm the rms-flux relation for Sgr A* and find it to be linear for all flux densities in our observation. We conclude that Sgr A* has two states: the bulk of the emission is generated in a lognormal process with a well-defined median flux density and this quiescent emission is supplemented by sporadic flares that create the observed power law extension of the flux distribution.

Abstract
The star S2 orbiting the compact radio source Sgr A* is a precision probe of the gravitational field around the closest massive black hole (candidate). Over the last 2.7 decades we have monitored the star's radial velocity and motion on the sky, mainly with the SINFONI and NACO adaptive optics (AO) instruments on the ESO VLT, and since 2017, with the four-telescope interferometric beam combiner instrument GRAVITY. In this Letter we report the first detection of the General Relativity (GR) Schwarzschild Precession (SP) in S2's orbit. Owing to its highly elliptical orbit (e=0.88), S2's SP is mainly a kink between the pre-and post-pericentre directions of motion approximate to +/- 1 year around pericentre passage, relative to the corresponding Kepler orbit. The superb 2017-2019 astrometry of GRAVITY defines the pericentre passage and outgoing direction. The incoming direction is anchored by 118 NACO-AO measurements of S2's position in the infrared reference frame, with an additional 75 direct measurements of the S2-Sgr A* separation during bright states ("flares") of Sgr A*. Our 14-parameter model fits for the distance, central mass, the position and motion of the reference frame of the AO astrometry relative to the mass, the six parameters of the orbit, as well as a dimensionless parameter f(SP) for the SP (f(SP)=0 for Newton and 1 for GR). From data up to the end of 2019 we robustly detect the SP of S2, delta phi approximate to 12 ' per orbital period. From posterior fitting and MCMC Bayesian analysis with different weighting schemes and bootstrapping we find f(SP)=1.10 +/- 0.19. The S2 data are fully consistent with GR. Any extended mass inside S2's orbit cannot exceed approximate to 0.1% of the central mass. Any compact third mass inside the central arcsecond must be less than about 1000 M-circle dot.

Abstract
We use VLTI/GRAVITY near-infrared interferometry measurements of eight bright type 1 AGN to study the size and structure of hot dust that is heated by the central engine. We partially resolve each source, and report Gaussian full width at half-maximum sizes in the range 0.3-0.8 mas. In all but one object, we find no evidence for significant elongation or asymmetry (closure phases less than or similar to 1 degrees). The narrow range of measured angular sizes is expected given the similar optical flux of our targets, and implies an increasing effective physical radius with bolometric luminosity, as found from previous reverberation and interferometry measurements. The measured sizes for Seyfert galaxies are systematically larger than for the two quasars in our sample when measured relative to the previously reported R & x2004;similar to & x2004;L-1/2 relationship, which is explained by emission at the sublimation radius. This could be evidence of an evolving near-infrared emission region structure as a function of central luminosity.

Abstract
We present near-infrared interferometric data on the Seyfert 2 galaxy NGC 1068, obtained with the GRAVITY instrument on the European Southern Observatory Very Large Telescope Interferometer. The extensive baseline coverage from 5 to 60 M lambda allowed us to reconstruct a continuum image of the nucleus with an unrivaled 0.2 pc resolution in the K-band. We find a thin ring-like structure of emission with a radius r=0.24 +/- 0.03 pc, inclination i=70 +/- 5 degrees, position angle PA=-50 +/- 4 degrees, and h/r< 0.14, which we associate with the dust sublimation region. The observed morphology is inconsistent with the expected signatures of a geometrically and optically thick torus. Instead, the infrared emission shows a striking resemblance to the 22 GHz maser disc, which suggests they share a common region of origin. The near-infrared spectral energy distribution indicates a bolometric luminosity of (0.4-4.7) x 10(45) erg s(-1), behind a large A(K)5.5 (A(V)approximate to 90) screen of extinction that also appears to contribute significantly to obscuring the broad line region.

Abstract
NU Ori is a massive spectroscopic and visual binary in the Orion Nebula Cluster, with four components: Aa, Ab, B, and C. The B0.5 primary (Aa) is one of the most massive B-type stars reported to host a magnetic field. We report the detection of a spectroscopic contribution from the C component in high-resolution ESPaDOnS spectra, which is also detected in a Very Large Telescope Interferometer data set. Radial velocity (RV) measurements of the inner binary (designated Aab) yield an orbital period of 14.3027(7) d. The orbit of the third component (designated C) was constrained using both RVs and interferometry. We find C to be on a mildly eccentric 476(1) d orbit. Thanks to spectral disentangling of mean line profiles obtained via least-squares deconvolution, we show that the Zeeman Stokes V signature is clearly associated with C, rather than Aa as previously assumed. The physical parameters of the stars were constrained using both orbital and evolutionary models, yielding M-Aa = 14.9 +/- 0.5 M-circle dot, M-Ab = 3.9 +/- 0.7 M-circle dot, and M-C = 7.8 +/- 0.7 M-circle dot. The rotational period obtained from longitudinal magnetic field (B-z) measurements is P-rot = 1.09468(7)d, consistent with previous results. Modelling of (B-z) indicates a surface dipole magnetic field strength of similar to 8 kG. NU Ori C has a magnetic field strength, rotational velocity, and luminosity similar to many other stars exhibiting magnetospheric Ha emission, and we find marginal evidence of emission at the expected level (similar to 1 per cent of the continuum).