Black hole mass of a quiescent galaxy hosting a Type 1 AGN at z=2.09: Implications for black hole - galaxy co-evolution and AGN quenching at high redshift

We report a characterization of an X-ray-detected quiescent galaxy at $z=2.09$, named COS-XQG1, using JWST/NIRCam and NIRSpec data. This galaxy is detected in Chandra imaging, suggesting the presence of an AGN with a high black hole accretion rate of $\dot{M}_{\rm BH}=0.22\pm0.03\, {\rm M_\odot yr^{-1}}$. Using multi-wavelength photometry from X-ray to sub-millimeter, including the latest JWST imaging, we confirm that COS-XQG1 is massive ($M_\star = (1.6\pm0.2)\times10^{11}\, M_\odot$) and quiescent (${\rm sSFR}<10^{-10}\, {\rm yr^{-1}}$) as reported previously, even considering the contribution from AGN emission. Noticeably, COS-XQG1 displays a broad H$\beta$ and H$\alpha$ emission component with a full width at half maximum of $4365^{+81}_{-81}\, {\rm km\, s^{-1}}$ in its NIRSpec spectrum, which is typical of Type 1 AGNs. The line width and luminosity of the broad H$\alpha$ emission give a black hole mass of $\log{(M_{\rm BH}/M_\odot)} = 8.43\pm0.02\, (\pm 0.5)$. With a stellar velocity dispersion measurement ($\sigma_\star=238\pm32\, {\rm km\, s^{-1}}$), we find that this galaxy is consistent with the local relations in the $M_{\rm BH} - \sigma_\star$ and $M_{\rm BH}- M_\star$ planes, which might suggest that massive quiescent galaxies at $z\geq2$ have already been mature in terms of both stellar and black hole masses and will not evolve significantly. In addition, image 2D-decomposition analysis finds that this galaxy comprises disk and point source components. The latter is likely the composition of an AGN and a stellar bulge. Based on a comparison with numerical simulations, we expect that COS-XQG1 will evolve into a typical quiescent galaxy with lower AGN activity by redshift 0. This study shows the usefulness of X-ray-detected quiescent galaxies in investigating the co-evolution between SMBHs and galaxies in the early Universe.