A low viscosity relatively thick twisted disk in a supermassive binary black hole as a potential model of OJ 287

Abstract

In this Paper we consider twisted accretion disks in supermassive binary black hole by analytical and numerical means. It is assumed that the disk orbiting around the more massive rotating component and that the disk rings are inclined with respect to the orbital plane. We use orbital parameters of the binary often employed in the precessing massive (PM) model of the well-known blazar OJ 287. Unlike our previous investigation of a similar problem, here we consider disks with both small and relatively large relative thicknesses $\delta=h/r$, where $h$ is the disk's height at a typical radius $r$, as well as a range of values of the viscosity parameter, $\alpha$, including the cases when $\alpha \lesssim \delta$. Similar to our previous results, we find that the twisted disk relaxes to a quasi-stationary state in the frame precessing with the Lense-Thirring frequency of the orbit. However, its shape is qualitatively different from that corresponding to the case of $\delta=10^{-3}$ and $\alpha=0.1$ considered in our previous work. In a disk with $\delta=10^{-3}$ but $\alpha \le 2\cdot 10^{-2}$, we find the new effect of generation of a twisting spiral wave near the resonance between a forcing frequency associated with the presence of the secondary and the Lense-Thirring frequency of a particular disk ring defined in the precessing frame. We propose an analytic theory of it, which is in a good agreement with our numerical results. This effect leads to multiple crossings of the orbit with the disk per one orbital period, which contradicts the PM model. When $\delta \gtrsim 0.1$, a typical disk's inclination within the orbit of the binary is smaller than that of the orbit which results in only two crossings of the orbit with the disk per one orbital period. We suggest that the additional heating of the disk gas by the secondary-disk collisions may result in $\delta \sim 0.1$.