A statistical method for detecting gravitational recoils of supermassive black holes in active galactic nuclei

We propose an observational test for gravitationally recoiling supermassive black holes in active galactic nuclei, based on a positive correlation between the velocities of black holes relative to their host galaxies, |Δv|, and their obscuring dust column densities, Σdust, both measured along the line of sight. Our findings using a set of toy models implemented to a Monte Carlo simulation imply that models of the galactic centre and of recoil dynamics can be tested by future observations of the potential Σdust–|Δv| correlation. We have also found that the fraction of obscured quasars decreases with |Δv|, for which the predicted trend can be compared to the observed fraction of type II quasars, and can further test combinations of models we may implement.