2021ApJ...919...31B

Direct measurements of the masses of supermassive black holes are key to understanding their growth and constraining their symbiotic relationship to their host galaxies. However, current methods used to directly measure black hole masses in active quasars become challenging or impossible beyond z >= 0.2. Spectroastrometry (SA) measures the spatial centroid of an object's spectrum as a function of wavelength, delivering angular resolution far better than the point-spread function (PSF) for high signal-to-noise ratio observations. We observed the luminous quasar SDSS J212329.47-005052.9 at z = 2.279 with the aim of resolving its ∼100 µas Hα broad emission-line region (BLR) and present the first SA constraints on the size and kinematic structure of the BLR. Using a novel pipeline to extract the SA signal and reliable uncertainties, we achieved a centroiding precision of ≃100 µas, or >2000x smaller than the K-band AO-corrected PSF, yielding a tentative 3.2σ detection of an SA signal from the BLR. Modeling the BLR emission as arising from an inclined rotating disk with a mixture of coherent and random motions we constrain r_BLR=454_–162⁺⁵⁶⁵µas (3.71_–1.28^+4.65pc), providing a 95% confidence upper limit on the black hole mass M_BHsin²i≤ 1.8×10⁹M_☉. Our results agree with the r_BLR-L relation measured for lower-z quasars but expands its dynamic range by an order of magnitude in luminosity. We did not detect the potentially stronger SA signal from the narrow-line region but discuss in detail why it may be absent. Already with existing instrumentation, SA can deliver ∼6x smaller uncertainties (∼15 µas) than achieved here, enabling ∼10% measurements of supermassive black hole masses in high-z quasars.