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Abstract Tight relationships exist in the local Universe between the central stellar properties of galaxies and the mass of their supermassive black hole (SMBH)^1–3. These suggest that galaxies and black holes co-evolve, with the main regulation mechanism being energetic feedback from accretion onto the black hole during its quasar phase^4–6. A crucial question is how the relationship between black holes and galaxies evolves with time; a key epoch to examine this relationship is at the peaks of star formation and black hole growth 8–12 billion years ago (redshifts 1–3)⁷. Here we report a dynamical measurement of the mass of the black hole in a luminous quasar at a redshift of 2, with a look back in time of 11 billion years, by spatially resolving the broad-line region (BLR). We detect a 40-μas (0.31-pc) spatial offset between the red and blue photocentres of the Hα line that traces the velocity gradient of a rotating BLR. The flux and differential phase spectra are well reproduced by a thick, moderately inclined disk of gas clouds within the sphere of influence of a central black hole with a mass of 3.2 × 10⁸ solar masses. Molecular gas data reveal a dynamical mass for the host galaxy of 6 × 10¹¹ solar masses, which indicates an undermassive black hole accreting at a super-Eddington rate. This suggests a host galaxy that grew faster than the SMBH, indicating a delay between galaxy and black hole formation for some systems. 

The angular size of the broad line region (BLR) of the nearby active galactic nucleus NGC 3783 has been spatially resolved by recent observations with VLTI/GRAVITY. A reverberation mapping (RM) campaign has also recently obtained high quality light curves and measured the linear size of the BLR in a way that is complementary to the GRAVITY measurement. The size and kinematics of the BLR can be better constrained by a joint analysis that combines both GRAVITY and RM data. This, in turn, allows us to obtain the mass of the supermassive black hole in NGC 3783 with an accuracy that is about a factor of two better than that inferred from GRAVITY data alone. We derive M BH = 2.54 −0.72 +0.90 × 10 7 M ⊙ . Finally, and perhaps most notably, we are able to measure a geometric distance to NGC 3783 of 39.9 −11.9 +14.5 Mpc. We are able to test the robustness of the BLR-based geometric distance with measurements based on the Tully–Fisher relation and other indirect methods. We find the geometric distance is consistent with other methods within their scatter. We explore the potential of BLR-based geometric distances to directly constrain the Hubble constant, H 0 , and identify differential phase uncertainties as the current dominant limitation to the H 0 measurement precision for individual sources. 

Using VLTI/GRAVITY and SINFONI data, we investigate the subparsec gas and dust structure around the nearby type 1 active galactic nucleus (AGN) hosted by NGC 3783. The K -band coverage of GRAVITY uniquely allows simultaneous analysis of the size and kinematics of the broad line region (BLR), the size and structure of the near-infrared(near-IR)-continuum-emitting hot dust, and the size of the coronal line region (CLR). We find the BLR, probed through broad Br γ emission, to be well described by a rotating, thick disc with a radial distribution of clouds peaking in the inner region. In our BLR model, the physical mean radius of 16 light-days is nearly twice the ten-day time-lag that would be measured, which closely matches the ten-day time-lag that has been measured by reverberation mapping. We measure a hot dust full-width at half-maximum (FWHM) size of 0.74 mas (0.14 pc) and further reconstruct an image of the hot dust, which reveals a faint (5% of the total flux) offset cloud that we interpret as an accreting or outflowing cloud heated by the central AGN. Finally, we directly measure the FWHM size of the nuclear CLR as traced by the [Ca  VIII ] and narrow Br γ line. We find a FWHM size of 2.2 mas (0.4 pc), fully in line with the expectation of the CLR located between the BLR and narrow line region. Combining all of these measurements together with larger scale near-IR integral field unit and mid-IR interferometry data, we are able to comprehensively map the structure and dynamics of gas and dust from 0.01 to 100 pc. 

Aims.We aim to demonstrate that the presence and mass of an exoplanet can now be effectively derived from the astrometry of another exoplanet. Methods.We combined previous astrometry ofβPictoris b with a new set of observations from the GRAVITY interferometer. The orbital motion ofβPictoris b is fit using Markov chain Monte Carlo simulations in Jacobi coordinates. The inner planet,βPictoris c, was also reobserved at a separation of 96 mas, confirming the previous orbital estimations. Results.From the astrometry of planet b only, we can (i) detect the presence ofβPictoris c and (ii) constrain its mass to 10.04_−3.10^+4.53M_Jup. If one adds the astrometry ofβPictoris c, the mass is narrowed down to 9.15_−1.06^+1.08M_Jup. The inclusion of radial velocity measurements does not affect the orbital parameters significantly, but it does slightly decrease the mass estimate to 8.89_−0.75^+0.75M_Jup. With a semimajor axis of 2.68 ± 0.02 au, a period of 1221 ± 15 days, and an eccentricity of 0.32 ± 0.02, the orbital parameters ofβPictoris c are now constrained as precisely as those ofβPictoris b. The orbital configuration is compatible with a high-order mean-motion resonance (7:1). The impact of the resonance on the planets’ dynamics would then be negligible with respect to the secular perturbations, which might have played an important role in the eccentricity excitation of the outer planet. 

Context.Near-infrared interferometry has become a powerful tool for studying the orbital and atmospheric parameters of substellar companions. Aims.We aim to reveal the nature of the reddest known substellar companion HD 206893 B by studying its near-infrared colors and spectral morphology and by investigating its orbital motion. Methods.We fit atmospheric models for giant planets and brown dwarfs and perform spectral retrievals withpetitRADTRANSandATMOon the observed GRAVITY, SPHERE, and GPI spectra of HD 206893 B. To recover its unusual spectral features, first and foremost its extremely red near-infrared color, we include additional extinction by high-altitude dust clouds made of enstatite grains in the atmospheric model fits. However, forsterite, corundum, and iron grains predict similar extinction curves for the grain sizes considered here. We also infer the orbital parameters of HD 206893 B by combining the ~100 μas precision astrometry from GRAVITY with data from the literature and constrain the mass and position of HD 206893 C based on theGaiaproper motion anomaly of the system. Results.The extremely red color and the very shallow 1.4 μm water absorption feature of HD 206893 B can be fit well with the adapted atmospheric models and spectral retrievals. By comparison with AMES-Cond evolutionary tracks, we find that only some atmosphericmodels predict physically plausible objects. Altogether, our analysis suggests an age of ~ 3–300 Myr and a mass of ~ 5–30 M_Jupfor HD 206893 B, which is consistent with previous estimates but extends the parameter space to younger and lower-mass objects. The GRAVITY astrometry points to an eccentric orbit (e = 0.29_−0.11^+0.06) with a mutual inclination of <34.4 deg with respectto the debris disk of the system. Conclusions.While HD 206893 B could in principle be a planetary-mass companion, this possibility hinges on the unknown influence of the inner companion on the mass estimate of 10₋₄⁺⁵ M_Jupfrom radial velocity andGaiaas well as a relatively small but significant Argus moving group membership probability of ~ 61%. However, we find that if the mass of HD 206893 B is <30 M_Jup, then the inner companion HD 206893 C should have a mass between ~ 8–15 M_Jup. Finally, further spectroscopic or photometric observations at higher signal-to-noise and longer wavelengths are required to learn more about the composition and dust cloud properties of HD 206893 B.