Varstrometry for Off-nucleus and Dual sub-Kpc AGN (VODKA): Methodology
  and Initial Results with Gaia DR2
  Gaia's milli-arcsec (mas) astrometric precision allows systematic
identification of optically-selected sub-kpc dual active galactic nuclei (AGN),
off-nucleus AGN, and small-scale lensed quasars by `varstrometry' -- where
variability-induced astrometric jitter, i.e., temporal displacements of
photocenter in unresolved sources, can be reasonably well detected or
constrained. This approach extends systematic searches for small-scale
($\gtrsim$ mas) dual and off-nucleus AGN to poorly explored regime between
$\sim 10$ pc and $\sim 1$ kpc, with Gaia's full sky coverage and depth to
$G\sim 21$. We outline the general principles of this method and calculate the
expected astrometric signals from the full time series of photocenter
measurements and light curves. We demonstrate the feasibility of varstrometry
by using Gaia DR2 data on a sample of variable pre-main sequence stars with
known close companions. We find that extended host galaxies have a significant
impact on the accuracy of astrometric and photometric variability in Gaia DR2,
a situation to be improved in future Gaia releases. Using spectroscopically
confirmed SDSS quasars, we present several examples of candidate sub-kpc
off-nucleus or dual AGN selected from Gaia DR2. We discuss the merits and
limitations of this method and follow-up strategy for promising candidates. We
highlight Gaia's potential of systematically discovering and characterizing the
sub-kpc off-nucleus and dual AGN population in the entire optical sky.
