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Direct measurements of the masses of supermassive black holes (SMBHs) are keyto understanding their growth and constrain their symbiotic relationship totheir host galaxies. However, current methods used to directly measure blackhole masses in active quasars become challenging or impossible beyond$z\gtrsim0.2$. Spectroastrometry (SA) measures the spatial centroid of anobject's spectrum as a function of wavelength, delivering angular resolutionfar better than the point-spread function (PSF) for high signal-to-noise ratioobservations. We observed the luminous quasar SDSS J212329.47--005052.9 at$z=2.279$ with the aim of resolving its $\sim100\mu\mathrm{as}$ H$\alpha$ broademission-line region (BLR), and present the first SA constraints on the sizeand kinematic structure of the BLR. Using a novel pipeline to extract the SAsignal and reliable uncertainties, we achieved a centroiding precision of$\simeq100\mu\mathrm{as}$, or $>2000\times$ smaller than the $K$-bandAO-corrected PSF, yielding a tentative $3.2\sigma$ detection of an SA signalfrom the BLR. Modeling the BLR emission as arising from an inclined rotatingdisk with a mixture of coherent and random motions we constrain$r_\mathrm{BLR}=454^{+565}_{-162}\,\mu\mathrm{as}$($3.71^{+4.65}_{-1.28}\,\mathrm{pc}$), providing a $95\%$ confidence upperlimit on the black hole mass $M_\mathrm{BH}\,\sin^2\,i \leq1.8\times10^9\,\mathrm{M}_\odot$. Our results agree with the $r_\mathrm{BLR}-L$relation measured for lower-$z$ quasars, but expands its dynamic range by anorder of magnitude in luminosity. We did not detect the potentially stronger SAsignal from the narrow-line region, but discuss in detail why it may be absent.Already with existing instrumentation, SA can deliver $\sim6\times$ smalleruncertainties ($\sim15\,\mu\mathrm{as}$) than achieved here, enabling$\sim10\%$ measurements of SMBH masses in high-$z$ quasars.

astrophysical journal/the astrophysical journal

Spatially Resolving the Kinematics of the $\lesssim 100\,\mu$as Quasar  Broad-line Region Using Spectroastrometry II. The First Tentative Detection  in a Luminous Quasar at $z=2.3$