Spatially Resolving the Kinematics of the <100 {\mu}as Quasar Broad Line Region using Spectroastrometry

The broad line region (BLR) of luminous active galactic nuclei (AGN) is a prominent observational signature of the accretion flow around supermassive black holes, which can be used to measure their masses (M_BH) over cosmic history. Due to the <100 {\mu}as angular size of the BLR, current direct constraints on BLR kinematics are limited to those provided by reverberation mapping studies, which are most efficiently carried out on low-luminosity L and low-redshift z AGN. We analyze the possibility to measure the BLR size and study its kinematic structure using spectroastrometry, whereby one measures the spatial position centroid of emission line photons as a function of velocity. We calculate the expected spectroastrometric signal of a rotation-dominated BLR for various assumptions about the ratio of random to rotational motions, and the radial distribution of the BLR gas. We show that for hyper-luminous quasars at z < 2.5, the size of the low-ionization BLR can already be constrained with existing telescopes and adaptive optics systems, thus providing a novel method to spatially resolve the kinematics of the accretion flow at 10^3 -- 10^4 gravitational radii, and measure M_BH at the high-L end of the AGN family. With a 30m-class telescope, BLR spectroastrometry should be routinely detectable for much fainter quasars out to z ~ 6, and for various emission lines. This will enable kinematic M_BH measurements as a function of luminosity and redshift, providing a compelling science case for next generation telescopes.