Inclination evolution of protoplanetary discs around eccentric binaries

It is usually thought that viscous torque works to align a circumbinary disc with the binary's orbital plane. However, recent numerical simulations suggest that the disc may evolve to a configuration perpendicular to the binary orbit ('polar alignment) if the binary is eccentric and the initial disc-binary inclination is sufficiently large. We carry out a theoretical study on the long-term evolution of inclined discs around eccentric binaries, calculating the disc warp profile and dissipative torque acting on the disc. For discs with aspect ratio H/r larger than the viscosity parameter α, bending wave propagation effectively makes the disc precess as a quasi-rigid body, while viscosity acts on the disc warp and twist to drive secular evolution of the disc-binary inclination. We derive a simple analytic criterion (in terms of the binary eccentricity and initial disc orientation) for the disc to evolve towards polar alignment with the eccentric binary. When the disc has a non-negligible angular momentum compared to the binary, the final 'polar alignment' inclination angle is reduced from 90°. For typical protoplanetary disc parameters, the time-scale of the inclination evolution is shorter than the disc lifetime, suggesting that highly inclined discs and planets may exist orbiting eccentric binaries.