Resolving the black hole sphere of influence in a hyper-luminous obscured quasar at redshift 4.6

Supermassive black holes (SMBHs) imprint gravitational signatures on the matter within their sphere of influence (SoI). Nuclear gas dynamics can hence be used to accurately measure the mass of an SMBH, yet such measurements remain elusive in the early Universe. We report the first dynamical measurement of an SMBH mass at $z >$ 2, based on high spatial resolution observations of the [C II] emission line that resolve the SoI in an obscured quasar at $z$ = 4.6. The velocity dispersion rises radially toward the center, requiring the presence of a 6.3$~\pm~0.14$ $\times$ 10$^9~\rm M_{\odot}$ SMBH. We propose that obscured quasars allow [C II] survivability in the inner regions, and may be ideal targets for increasing dynamical SMBH mass estimates in the early Universe.