Differential interferometry of QSO broad-line regions – I. Improving the reverberation mapping model fits and black hole mass estimates

Reverberation mapping (RM) estimates the size and kinematics of broad-line regions (BLR) in quasars and type I AGNs. It yields size–luminosity relation to make QSOs standard cosmological candles, and mass–luminosity relation to study the evolution of black holes and galaxies. The accuracy of these relations is limited by the unknown geometry of the BLR clouds distribution and velocities. We analyse the independent BLR structure constraints given by super-resolving differential interferometry. We developed a three-dimensional BLR model to compute all differential interferometry and RM signals. We extrapolate realistic noises from our successful observations of the QSO 3C 273 with AMBER on the VLTI. These signals and noises quantify the differential interferometry capacity to discriminate and measure BLR parameters including angular size, thickness, spatial distribution of clouds, local-to-global and radial-to-rotation velocity ratios, and finally central black hole mass and BLR distance. A Markov Chain Monte Carlo model-fit, of data simulated for various VLTI instruments, gives mass accuracies between 0.06 and 0.13?dex, to be compared to 0.44?dex for RM mass–luminosity fits. We evaluate the number of QSOs accessible to observe with current (AMBER), upcoming (GRAVITY) and possible (OASIS with new generation fringe trackers) VLTI instruments. With available technology, the VLTI could resolve more than 60 BLRs, with a luminosity range larger than four decades, sufficient for a good calibration of RM mass–luminosity laws, from an analysis of the variation of BLR parameters with luminosity.