The Bardeen–Petterson effect in accreting supermassive black hole binaries: a systematic approach

Disc-driven migration is a key evolutionary stage of supermassive black hole binaries hosted in gas-rich galaxies. Besides promoting the inspiral, viscous interactions tend to align the spins of the black holes with the orbital angular momentum of the disc. We present a critical and systematic investigation of this problem, also known as the Bardeen–Petterson effect. We design a new iterative scheme to solve the non-linear dynamics of warped accretion discs under the influence of both relativistic frame dragging and binary companion. We characterize the impact of the disc ‘critical obliquity’, which marks regions of the parameter space where stationary solutions do not exist. We find that black hole spins reach either complete alignment or a critical configuration. Reaching the critical obliquity might imply that the disc breaks as observed in hydrodynamical simulations. Our findings are important to predict the spin configurations with which supermassive black hole binaries enter their gravitational-wave driven regime and become detectable by LISA.