LIGO--Virgo correlations between mass ratio and effective inspiral spin:
  testing the active galactic nuclei channel
  Observations by LIGO--Virgo of binary black hole mergers suggest a possible
anti-correlation between black hole mass ratio ($q=m_{2}/m_{1}$) and the
effective inspiral spin parameter $\chi_{\rm eff}$, the mass-weighted spin
projection onto the binary orbital angular momentum (Callister et al. 2021). We
show that such an anti-correlation can naturally occur for binary black holes
assembled in active galactic nuclei (AGN) due to spherical and planar
symmetry-breaking effects. We describe a phenomenological model in which: 1)
heavier black holes live in the AGN disk and tend to spin up into alignment
with the disk; 2) lighter black holes with random spin orientations live in the
nuclear spheroid; 3) the AGN disk is dense enough to rapidly capture a fraction
of the spheroid component. but small in radial extent to limit the number of
bulk disk mergers; 4) migration within the disk is non-uniform, likely
disrupted by feedback from migrators or disk turbulence; 5) dynamical
encounters in the disk are common and preferentially disrupt binaries that are
retrograde around their center of mass, particularly at stalling orbits, or
traps. This model may explain trends in LIGO--Virgo data while offering
falsifiable predictions. Comparisons of predictions in ($q,\chi_{\rm eff}$)
parameter space for the different channels may allow us to distinguish their
fractional contributions to the observed merger rates.
