Reverberation mapping 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 analyze the independent BLR structure constraints given by super-resolving
differential interferometry. We developed a three-dimensional BLR model to
compute all differential interferometry and reverberation mapping signals. We
extrapolate realistic noises from our successful observations of the QSO 3C273
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 reverberation mapping mass-luminosity fits. We
evaluate the number of QSOs accessible to measures 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.Comment: 19 pages, 14 figures, accepted by MNRAS on December 5, 201
