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