Off-nucleus active galactic nuclei (AGN) can be signposts of inspiraling supermassive black holes (SMBHs) on galactic scales, or accreting SMBHs recoiling after the coalescence of a SMBH binary or slingshot from three-body interactions. Because of the stochastic variability of AGN, the measured photocenter of an unresolved AGN-host system will display astrometric jitter that depends on the off-nucleus distance of the AGN, the total photometric variability of the system, and the AGN-host contrast. Here we use the precision astrometry from Gaia DR2 to constrain the off-nucleus population of a low-redshift (0.3<z<0.8) sample of unobscured broad-line AGN drawn from the SDSS with significant host contribution and photometric variability. We find that Gaia DR2 already provides strong constraints on the projected off-nucleus distance in the sub-kpc regime at these redshifts: 99%, 90% and 40% of AGN must be well-centered to <1 kpc, <500 pc and <100 pc, respectively. Limiting the sample to the most variable subset constrains >99% of AGN to be well-centered below 500 parsec. These results suggest that genuine off-nucleus AGN (offset by > a few hundred pc) must be rare at low redshift. Future Gaia releases of time series of photocenter and flux measurements, improved treatments for extended sources and longer baselines will further tighten these constraints, and enable a systematic full-sky search for rare off-nucleus AGN on ~ 10-1000 pc scales.
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