Secular Spin–Orbit Resonances of Black Hole Binaries in AGN Disks

The spin-orbit misalignment of stellar-mass black hole (sBH) binaries provide important constraints on the formation channels merging sBHs. Here, we study role secular resonance in evolution a sBH binary component around supermassive BH (SMBH) an AGN disk. We consider sBH's spin-precession due to $J_2$ moment introduced by circum-sBH disk within warping/breaking radius find that (obliquity) can be excited via between binary's orbital nodal precession and driven massive Using $\alpha$-disk model with Bondi-Hoyle-Lyttleton accretion, resonances typically occur for semi-major axis $1$AU, at distance $\sim 1000$AU $10^7$\msun SMBH. lead high obliquities, broad distribution spin-spin misalignments. However, note accretion is much higher than Eddington which results spin being too low trigger resonances. Thus, quite rare sBHs disks.