Variability-based AGN selection using image subtraction in the SDSS and
  LSST era
  With upcoming all sky surveys such as LSST poised to generate a deep digital
movie of the optical sky, variability-based AGN selection will enable the
construction of highly-complete catalogs with minimum contamination. In this
study, we generate $g$-band difference images and construct light curves for
QSO/AGN candidates listed in SDSS Stripe 82 public catalogs compiled from
different methods, including spectroscopy, optical colors, variability, and
X-ray detection. Image differencing excels at identifying variable sources
embedded in complex or blended emission regions such as Type II AGNs and other
low-luminosity AGNs that may be omitted from traditional photometric or
spectroscopic catalogs. To separate QSOs/AGNs from other sources using our
difference image light curves, we explore several light curve statistics and
parameterize optical variability by the characteristic damping timescale
($\tau$) and variability amplitude. By virtue of distinguishable variability
parameters of AGNs, we are able to select them with high completeness of 93.4%
and efficiency (i.e., purity) of 71.3%. Based on optical variability, we also
select highly variable blazar candidates, whose infrared colors are consistent
with known blazars. One third of them are also radio detected. With the X-ray
selected AGN candidates, we probe the optical variability of X-ray detected
optically-extended sources using their difference image light curves for the
first time. A combination of optical variability and X-ray detection enables us
to select various types of host-dominated AGNs. Contrary to the AGN unification
model prediction, two Type II AGN candidates (out of 6) show detectable
variability on long-term timescales like typical Type I AGNs. This study will
provide a baseline for future optical variability studies of extended sources.
