Are the Variability Properties of the Kepler AGN Light Curves Consistent with a Damped Random Walk?

We test the consistency of active galactic nuclei (AGN) optical flux variability with the $\textit{damped random walk}$ (DRW) model. Our sample consists of 20 multi-quarter $\textit{Kepler}$ AGN light curves including both Type 1 and 2 Seyferts, radio-loud and -quiet AGN, quasars, and blazars. $\textit{Kepler}$ observations of AGN light curves offer a unique insight into the variability properties of AGN light curves because of the very rapid ($11.6-28.6$ min) and highly uniform rest-frame sampling combined with a photometric precision of $1$ part in $10^{5}$ over a period of 3.5 yr. We categorize the light curves of all 20 objects based on visual similarities and find that the light curves fall into 5 broad categories. We measure the first order structure function of these light curves and model the observed light curve with a general broken power-law PSD characterized by a short-timescale power-law index $\gamma$ and turnover timescale $\tau$. We find that less than half the objects are consistent with a DRW and observe variability on short timescales ($\sim 2$ h). The turnover timescale $\tau$ ranges from $\sim 10-135$ d. Interesting structure function features include pronounced dips on rest-frame timescales ranging from $10-100$ d and varying slopes on different timescales. The range of observed short-timescale PSD slopes and the presence of dip and varying slope features suggests that the DRW model may not be appropriate for all AGN. We conclude that AGN variability is a complex phenomenon that requires a more sophisticated statistical treatment.