Short time-scale optical variability properties of the largest AGN sample observed with Kepler/K2

We present the first short time-scale ($\sim$hours to days) optical variability study of a large sample of Active Galactic Nuclei (AGN) observed with the Kepler/K2 mission. The sample contains 252 AGN observed over four campaigns with $\sim 30$ minute cadence selected from the Million Quasar Catalogue with R magnitude $< 19$. We performed time series analysis to determine their variability properties by means of the power spectral densities (PSDs) and applied Monte Carlo techniques to find the best model parameters that fit the observed power spectra. A power-law model is sufficient to describe all the PSDs of our sample. A variety of power-law slopes were found indicating that there is not a universal slope for all AGN. We find that the rest-frame amplitude variability in the frequency range of $6\times10^{-6}-10^{-4}$ Hz varies from $1-10$ % with an average of 1.7 %. We explore correlations between the variability amplitude and key parameters of the AGN, finding a significant correlation of rest-frame short-term variability amplitude with redshift. We attribute this effect to the known "bluer when brighter" variability of quasars combined with the fixed bandpass of Kepler data. This study also enables us to distinguish between Seyferts and Blazars and confirm AGN candidates. For our study we have compared results obtained from light curves extracted using different aperture sizes and with and without de-trending. We find that limited de-trending of the optimal photometric precision light curve is the best approach, although some systematic effects still remain present.