Probing the Optical/UV Continuum Variability of Active Galactic Nuclei with the Damped Random Walk Model
Optical/UV continuum variability over baselines of up to 20 yr is investigated using the damped random walk (DRW) model for 1214 active galactic nuclei (AGNs) compiled from Y. Shen et al. and C. J. Burke et al. Among these, 115 AGNs with reliable DRW fitting and unbiased DRW parameters (timescale $τ_{2500}$ and amplitude $σ_{2500}$ at the rest-frame 2500~Å) are used to examine the relations between the variability and the accretion properties. We found a significant correlation of $τ_{2500}$ with black hole mass ($M_{\rm BH}$) and dimensionless accretion rate ($\dot{\mathscr{M}}$) of the form $τ_{2500} \propto M_{\rm BH}^{0.50\pm0.07} \dot{\mathscr{M}}^{0.27\pm0.04}$, while the dependence on the continuum luminosity at 5100~Å and redshift becomes insignificant after controlling for $M_{\rm BH}$. $τ_{2500}$ also correlate with the mass accretion rate ($\dot{M}$) as $τ_{2500} \propto \dot{M}^{0.41\pm0.04}$, which is consistent with the thermal timescale expected from the standard thin-disk model within $3σ$ uncertainties; while the average value is consistent with the expectations of the model, the scatter in the relation can be due to differences in the viscosity parameter ($α$) or in disk temperature profiles. Assuming that \tauuv\ corresponds to the accretion disk thermal timescale, the disk-emitting radius at rest-frame 2500~Å ($R_{2500}$) is found to correlate with $M_{\rm BH}$ as $R_{2500} \propto M_{\rm BH}^{0.53\pm0.05}$. Using the microlensing-based $R_{2500}-M_{\rm BH}$ relation of C. W. Morgan et al., $α$ is statistically estimated to be $0.04\pm0.01$.