A Method to Measure the Unbiased Decorrelation Timescale of the AGN
  Variable Signal from Structure Functions
  A simple, model-independent method to quantify the stochastic variability of
active galactic nuclei (AGNs) is the structure function (SF) analysis. If the
SF for the timescales shorter than the decorrelation timescale $\tau$ is a
single power-law and for the longer ones becomes flat (i.e., the white noise),
the auto-correlation function (ACF) of the signal can have the form of the
power exponential (PE). We show that the signal decorrelation timescale can be
measured directly from the SF as the timescale matching the amplitude 0.795 of
the flat SF part (at long timescales), and only then the measurement is
independent of the ACF PE power. Typically, the timescale has been measured at
an arbitrarily fixed SF amplitude, but as we prove, this approach provides
biased results because the AGN SF/PSD slopes, so the ACF shape, are not
constant and depend on either the AGN luminosity and/or the black hole mass. In
particular, we show that using such a method for the simulated SFs that include
a combination of empirically known dependencies between the AGN luminosity $L$
and both the SF amplitude and the PE power, and having no intrinsic $\tau-L$
dependence, produces a fake $\tau \propto L^\kappa$ relation with $0.3\lesssim
\kappa \lesssim 0.6$, that otherwise is expected from theoretical works
($\kappa \equiv 0.5$). Our method provides an alternative means for analyzing
AGN variability to the standard SF fitting. The caveats, for both methods, are
that the light curves must be sufficiently long (several years rest-frame) and
the ensemble SF assumes AGNs to have the same underlying variability process.
