Statistical evidence for massive black hole recoils in active galactic nuclei

We search for a population-level signature of gravitational-wave recoiling supermassive black holes: a positive correlation between dust obscuration and the magnitude of the line-of-sight velocity offset of broad emission lines relative to the host. Using the SDSS DR16 quasar catalogue, we estimate the velocity offset, $\Delta v$, as the difference between the broad H$\beta$ redshift and a noise-weighted redshift from narrow lines ([O iii] 5007, [O ii] 3728, and Ca ii 3934). We adopt the redshift-relative colour excess $\Delta (g-i)$ as a proxy for dust column density. Analysing $\sim 10^{5}$ quasars that meet basic spectral quality requirements, we find a modest but highly significant positive correlation between $|\Delta v|$ and $\Delta (g-i)$ (Spearman $r\simeq 0.12$ and Pearson $r\simeq 0.13$, with $p\ll 10^{-10}$ in both cases). The fraction of highly obscured quasars increases with $|\Delta v|$, indicating that the correlation is driven by a dust-reddened subpopulation. The result is robust to the choice of minimum $|\Delta v|$ threshold and to the line redshift estimator (peak vs. centroid). As expected, the correlation is largely absent when velocity offsets are computed between narrow emission lines. We find systematic differences between redshifted and blueshifted subsamples, which may point to residual velocity biases or additional physical effects (e.g. winds, inflows, orientation-dependent obscuration, or asymmetric broad-line regions). Recoiling massive black holes provide a natural explanation for the observed correlation, but alternative scenarios should be explored. If confirmed, this would enable population-level constraints on massive black hole merger rates, recoil dynamics, and active galactic nuclei disc properties.