On the evolution of a twisted thin accretion disc in eccentric inclined supermassive binary black holes

We propose a model of a twisted accretion disc around a Kerr black hole interacting with a secondary black hole of a smaller mass on an inclined eccentric orbit. We use parameters of the system, which may be appropriate for the so-called 'precessing massive' model of OJ 287. We calculate expressions for torque exerted on the disc by the secondary and a contribution of the secondary to the apsidal precession of disc elements by a double averaging procedure over the periods of the secondary and the disc elements. These expressions are used at all scales of interest, including the ones inside the binary orbit. We calculate numerically the evolution of the disc tilt and twist assuming a flat initial configuration. We consider the disc aspect ratio $h/r=10^{-3}$, a rather large viscosity parameter $\alpha=0.1$ and several values of the primary rotational parameter, $\chi$. We find that, after a few periods of Lense-Thirring precession of the orbit, the disc relaxes to a quasi-stationary configuration in the precessing frame with a non-trivial distribution of the disc inclination angle, $\beta$, over the radial scale. We propose an analytic model for this configuration. We show that the presence of the twisted disc leads to multiple crossings of the disc by the secondary per one orbital period, with time periods between the crossings being different from the flat disc model. Our results should be taken into account in the modelling of OJ 287. They can also be applied to similar sources.