Probing BLR dynamics with single-epoch line profiles

The broad-line region (BLR) of active galactic nuclei (AGN) can be used as an important probe of the mass of the central supermassive black hole (BH). Recent GRAVITY observations are able to spatially resolve the BLR and measure the BH mass by modeling the differential phase and the broad-line profile. Combining GRAVITY angular size measurements of the BLR with time lag observations from reverberation mapping (RM) studies, which can be used to determine the BLR physical size, one can constrain the geometric distance of the AGN, thus providing a promising cosmological probe of the universe from low to intermediate redshifts. However, these two techniques are often based on the measurements of different broad lines which creates complications as RM measurements show tentative evidence that the BLR sizes differ between different line profiles. In this work, we investigate the profiles of four broad emission lines of NGC 3783 concurrently measured by X-SHOOTER in ultra-violet, optical, and near-infrared. Once fixing the BH mass, which is well measured by GRAVITY and RM, we can constrain the BLR structure by fitting the line profiles simultaneously with the dynamical model. We find the different asymmetry of independent line profiles can be explained by the same BLR geometry with different radial distributions of line emission. In addition, we determine that several physical parameters such as the inclination angle, BLR radius, and virial factor of the BLR can be well constrained. We find the BLR radii of H-alpha and H-gamma to be similar, measuring to be about 1.5 times larger than those of H-beta and Pa-beta. We expect these methods to be useful in providing further constraints on both the geometry and dynamics of the BLR for larger samples of AGNs for which RM data are not currently available.