Abstract
The correlation between the broad line region radius and continuum luminosity
($R-L$ relation) of active galactic nuclei (AGN) is critical for single-epoch
mass estimates of supermassive black holes (SMBHs). At $z \sim 1-2$, where AGN
activity peaks, the $R-L$ relation is constrained by the reverberation mapping
(RM) lags of the Mg II line. We present 25 Mg II lags from the Australian Dark
Energy Survey (OzDES) RM project based on six years of monitoring. We define
quantitative criteria to select good lag measurements and verify their
reliability with simulations based on both the damped random walk stochastic
model and the re-scaled, re-sampled versions of the observed lightcurves of
local, well-measured AGN. Our sample significantly increases the number of Mg
II lags and extends the $R-L$ relation to higher redshifts and luminosities.
The relative iron line strength $\mathcal{R}_{\rm Fe}$ has little impact on the
$R-L$ relation. The best-fit Mg II $R-L$ relation has a slope $\alpha = 0.39
\pm 0.08$ with an intrinsic scatter $\sigma_{\rm rl} = 0.15^{+0.03}_{-0.02}$.
The slope is consistent with previous measurements and shallower than the
H$\beta$ $R-L$ relation. The intrinsic scatter of the new $R-L$ relation is
substantially smaller than previous studies and comparable to the intrinsic
scatter of the H$\beta$ $R-L$ relation. Our new $R-L$ relation will enable more
precise single-epoch mass estimates and SMBH demographic studies at cosmic
noon.