Misaligned gas discs around eccentric black-hole binaries and implications for the final-parsec problem

We investigate the evolution of low mass (Md /Mb = 0.005) misaligned gaseous discs around eccentric supermassive black hole (SMBH) binaries. These are expected to form from randomly oriented accretion events onto a SMBH binary formed in a galaxy merger. When expanding the interaction terms between the binary and a circular ring to quadrupole order and averaging over the binary orbit, we expect four non-precessing disc orientations: aligned or counter-aligned with the binary, or polar orbits around the binary eccentricity vector with either sense of rotation. All other orientations precess around either of these, with the polar precession dominating for high eccentricity. These expectations are borne out by smoothed particle hydrodynamics simulations of initially misaligned viscous circumbinary discs, resulting in the formation of polar rings around highly eccentric binaries in contrast to the co-planar discs around circular binaries. Moreover, we observe disc tearing and violent interactions between differentially precessing rings in the disc significantly disrupting the disc structure and causing gas to fall onto the binary with little angular momentum. While accretion from a polar disc may not promote SMBH binary coalescence (solving the `final-parsec problem'), ejection of this infalling low-angular momentum material via gravitational slingshot is a possible mechanism to reduce the binary separation. Moreover, this process acts on dynamical rather than viscous time scales, and so is much faster.