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 \sim 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 \pm 0.08 ( 0.52 \pm 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 \pm 0.46 year .
The SF amplitude at one year obtained from the SPL fitting is SF _ { 0 } = 0.22 \pm 0.06 mag and is overestimated because the SF is already at the turnover part , so the true value is SF _ { 0 } = 0.20 \pm 0.06 mag .
The asymptotic variability is SF _ { \infty } = 0.25 \pm 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 .