Examining AGN UV/optical Variability Beyond the Simple Damped Random Walk

We present damped harmonic oscillator (DHO) light-curve modeling for a sample of 12,714 spectroscopically confirmed quasars in the Sloan Digital Sky Survey Stripe 82 region. DHO is a second-order continuous-time autoregressive moving-average (CARMA) process, which can be fully described using four independent parameters: a natural oscillation frequency (${\omega }_0$), a damping ratio ($\xi$), a characteristic perturbation timescale (${\tau }_{\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{b}}$), and an amplitude for the perturbing white noise (${\sigma }_{ϵ}$). The asymptotic variability amplitude of a DHO process is quantified by ${\sigma }_{\mathrm{D}\mathrm{H}\mathrm{O}}$ – a function of ${\omega }_0$, $\xi$, ${\tau }_{\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{b}}$, and ${\sigma }_{ϵ}$. We find that both ${\tau }_{\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{b}}$ and ${\sigma }_{ϵ}$ follow different dependencies with rest-frame wavelength (${\lambda }_{\mathrm{R}\mathrm{F}}$) on either side of 2500 \AA, whereas ${\sigma }_{\mathrm{D}\mathrm{H}\mathrm{O}}$ follows a single power-law relation with ${\lambda }_{\mathrm{R}\mathrm{F}}$. After correcting for wavelength dependence, ${\sigma }_{\mathrm{D}\mathrm{H}\mathrm{O}}$ exhibits anti-correlations with both the Eddington ratio and the black hole mass, while ${\tau }_{\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{b}}$ – with a typical value of days in the rest-frame – shows an anti-correlation with the bolometric luminosity. Modeling AGN variability as a DHO offers more insight into the workings of accretion disks close to the supermassive black holes (SMBHs) at the center of AGN. The newly discovered short-term variability (characterized by ${\tau }_{\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{b}}$ and ${\sigma }_{ϵ}$) and its correlation with bolometric luminosity pave the way for new algorithms that will derive fundamental properties (e.g., Eddington ratio) of AGN using photometric data alone.