Revisiting Stochastic Variability of AGNs with Structure Functions

Discrepancies between reported structure function (SF) slopes and their overall flatness as compared to expectations from the damped random walk (DRW) model, which generally well describes the variability of active galactic nuclei (AGNs), have triggered us to study this problem in detail. We review common AGN variability observables and identify their most common problems. Equipped with this knowledge, we study ~9000 r-band AGN light curves from Stripe 82 of the Sloan Digital Sky Survey, using SFs described by stochastic processes with the power exponential covariance matrix of the signal. We model the "subensemble" SFs in the redshift-absolute magnitude bins with the full SF equation (including the turnover and the noise part) and a single power law (SPL; in the "red noise regime" after subtracting the noise term). The distribution of full-equation SF (SPL) slopes peaks at gamma = 0.55 +/- 0.08 (0.52 +/- 0.06) and is consistent with the DRW model. There is a hint of a weak correlation of gamma with the luminosity and a lack of correlation with the black hole mass. The typical decorrelation timescale in the optical is tau = 0.97 +/- 0.46 year. The SF amplitude at one year obtained from the SPL fitting is SF_0 = 0.22 +/- 0.06 mag and is overestimated because the SF is already at the turnover part, so the true value is SF_0 = 0.20 +/- 0.06 mag. The asymptotic variability is SF_\infty = 0.25 +/- 0.06 mag. It is strongly anticorrelated with both the luminosity and the Eddington ratio and is correlated with the black hole mass. The reliability of these results is fortified with Monte Carlo simulations.