Dynamical Modeling of the C iv Broad Line Region of the z = 2.805 Multiply Imaged Quasar SDSS J2222+2745

We present the first ever models of a broad line region (BLR) at the peak of active galactic nucleus (AGN) activity using the multiply imaged z = 2.805 quasar SDSS J2222+2745. The modeled data consist of monthly spectra covering the broad C iv emission line over a 5.3 yr baseline. The models suggest a thick disk BLR that is inclined by ∼40° to the observer's line of sight and with an emissivity weighted median radius of $r_{median}={33.0}_{-2.1}^{+2.4}$ light days. The kinematics are dominated by near-circular Keplerian motion with the remainder inflowing. The rest-frame lag one would measure from the models is ${\tau }_{median}={36.4}_{-1.8}^{+1.8}$ days, which is consistent with measurements based on cross-correlation. We show a possible geometry and transfer function based on the model fits and find that the model-produced velocity-resolved lags are consistent with those from cross-correlation. We measure a black hole mass of ${log}_{10}\left(M_{BH}/M_{\odot }\right)={8.31}_{-0.06}^{+0.07}$, which requires a scale factor of ${log}_{10}\left(f_{mean,\sigma }\right)={0.20}_{-0.07}^{+0.09}$. This is the most precise M _BH measurement for any AGN at cosmological distances and it demonstrates that the precision required for BH-host coevolution studies is attainable.