Modeling the Time Variability of SDSS Stripe 82 Quasars as a Damped
  Random Walk
  We model the time variability of ~9,000 spectroscopically confirmed quasars
in SDSS Stripe 82 as a damped random walk. Using 2.7 million photometric
measurements collected over 10 years, we confirm the results of Kelly et al.
(2009) and Koz{\l}owski et al. (2010) that this model can explain quasar light
curves at an impressive fidelity level (0.01-0.02 mag). The damped random walk
model provides a simple, fast [O(N) for N data points], and powerful
statistical description of quasar light curves by a characteristic time scale
(tau) and an asymptotic rms variability on long time scales (SF_inf). We
searched for correlations between these two variability parameters and physical
parameters such as luminosity and black hole mass, and rest-frame wavelength.
We find that tau increases with increasing wavelength with a power law index of
0.17, remains nearly constant with redshift and luminosity, and increases with
increasing black hole mass with power law index of 0.21+/-0.07. The amplitude
of variability is anti-correlated with the Eddington ratio, which suggests a
scenario where optical fluctuations are tied to variations in the accretion
rate. The radio-loudest quasars have systematically larger variability
amplitudes by about 30%, when corrected for the other observed trends, while
the distribution of their characteristic time scale is indistinguishable from
that of the full sample. We do not detect any statistically robust differences
in the characteristic time scale and variability amplitude between the full
sample and the small subsample of quasars detected by ROSAT. Our results
provide a simple quantitative framework for generating mock quasar light
curves, such as currently used in LSST image simulations. (abridged)
