A Statistical Method to Search for Recoiling Supermassive Black Holes in
  Active Galactic Nuclei
  We propose an observational test for gravitationally recoiling supermassive
black holes (BHs) in active galactic nuclei, based on a correlation between the
velocities of BHs relative to their host galaxies, |\Delta v|, and their
obscuring dust column densities, \Sigma_{dust} (both measured along the line of
sight). We use toy models for the distribution of recoil velocities, BH
trajectories, and the geometry of obscuring dust tori in galactic centres, to
simulate 2.5x10^5 random observations of recoiling quasars. BHs with recoil
velocities comparable to the escape velocity from the galactic centre remain
bound to the nucleus, and do not fully settle back to the centre of the torus
due to dynamical friction in a typical quasar lifetime. We find that |\Delta v|
and \Sigma_ {dust} for these BHs are positively correlated. For obscured
(\Sigma_{dust}>0) and for partially obscured (0<\Sigma_{dust}<~2.3 g/m^2)
quasars with |\Delta v|>=45 km/s, the sample correlation coefficient between
log10(|\Delta v|) and \Sigma_{dust} is r_{45} = 0.28+/-0.02 and r_{45} =
0.13+/-0.02, respectively. Allowing for random +/-100 km/s errors in |\Delta v|
unrelated to the recoil dilutes the correlation for the partially obscured
quasars to r_{45} = 0.026+/-0.004 measured between |\Delta v| and
\Sigma_{dust}. A random sample of >~3,500 obscured quasars with |\Delta v|>=45
km/s would allow rejection of the no-correlation hypothesis with 3 sigma
significance 95% of the time. Finally, we find that the fraction of obscured
quasars, F_{obs}(|\Delta v|), decreases with |\Delta v| from F_{obs}(<10
km/s)>~0.8 to F_{obs}(>10^3 km/s)<~0.4. This predicted trend can be compared to
the observed fraction of type II quasars, and can further test combinations of
recoil, trajectory, and dust torus models.
