The evolution of a supermassive binary caused by an accretion disc

The interaction between a massive binary and a non-self-gravitating circumbinary accretion disc is considered. The shape of the stationary twisted disc produced by the binary is calculated. It is shown that the inner part of the disc must lie in the binary orbital plane for any value of the viscosity. When the inner disc mid- lane is aligned with the binary orbital plane on the scales of interest and it rotates in the same sense as the binary, the modification to the disc structure and the rate of decay of the binary orbit, assumed circular, caused by tidal exchange of angular momentum with the disc, are calculated. It is shown that the modified disc structure is well described by a self-similar solution of the non-linear diffusion equation governing the evolution of the disc surface density. The calculated time-scale for decay of the binary orbit is always smaller than the ‘accretion’ time-scale tacc=m/M (m is the mass of the secondary component, and M is the disc accretion rate), and is determined by the ratio of the secondary mass m, assumed to be much smaller than the primary mass, the disc mass inside the initial binary orbit, and the form of viscosity in the disc.