The VLT Interferometric Measurements of Active Galactic Nuclei: Effects of Angular Momentum Distributions of Clouds in the Broad-line Region

A few months ago, GRAVITY at the Very Large Telescope Interferometry revealed the structure and kinematics of the broad-line region (BLR) of 3C 273. GRAVITY works with an unprecedented high spatial resolution through spectroastrometry where centers of photons at different wavelengths (lambda-photoncenters) of active galactic nuclei are measured by differential phase curves (DPCs) in the wavelength range of the broad Paschen alpha line. Since Doppler effects govern wavelength shifts of photons sensitively depending on the degree of the ordered rotation (R-0) of clouds in the BLR, the DPCs are expected to be a function of R-0. Distributions of the angular momenta of clouds in the BLR could be determined by the formation processes of the BLR; however, R-0 is a totally unknown parameter so far. In this paper, we show that the DPC is sensitive to this free parameter, and R-0 should be taken into account for GRAVITY measurements of the BLR. It is then expected that joint observations of reverberation mapping campaigns and GRAVITY will allow us to obtain complete information about the structure and kinematics of the BLR, including the degree of ordered rotation of clouds, offering an opportunity to reveal the formation of the BLR, either from the tidal capture of clumps in the torus or from winds that developed from accretion disks.