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

Viacheslav V. Zhuravlev ^*

Pavel B. Ivanov^†

Sternberg Astronomical Institute, Lomonosov Moscow State University, Universitetskij Prospect, 13, Moscow 119234, Russia

P.N. Lebedev Physical Institute, 53 Leninsky Prospect, Moscow 119991, Russia

^*Contact author: v.jouravlev@gmail.com
^†Contact author: pavel000astrophysics@gmail.com

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Phys. Rev. D 113, 123027 – Published 10 June, 2026

DOI: https://doi.org/10.1103/g635-y8vr

Abstract

In this paper we consider twisted accretion disks in supermassive binary black holes by analytical and numerical means. It is assumed that the disk is 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, which are often employed in the so-called precessing massive (PM) model of the activity of the well-known blazar OJ 287. In particular, the orbit is assumed to have a large eccentricity around 0.7, and the ratio of the mass of the secondary component to the primary is around $10^{- 2}$ . Unlike our previous investigation of a similar problem, here we consider disks with both small and relatively large relative thicknesses $δ = h / r$ , where $h$ is the disk’s height at a typical radius $r$ , as well as a range of values of the viscosity parameter, $α$ , including the cases when $α ≲ δ$ . The influence of the secondary black hole on the disk is treated using the formalism proposed by us elsewhere, which is based on the double averaging procedure of the secondary’s gravitational field. Similar to our previous results, we find that the twisted disk relaxes relatively quickly to a quasistationary 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 $δ = 10^{- 3}$ and $α = 0.1$ considered in our previous work. When $δ \sim 10^{- 3}$ the shape of the disk of any viscosity is largely determined by the resonance between a forcing frequency associated with the presence of the secondary and the Lense-Thirring frequency of a particular disk ring calculated in the precessing frame. In addition to the effect determining the shape of the $α = 0.1$ disk considered by us earlier, we find the new effect of the generation of a twisting spiral wave near the resonance in a disk with $α \leq 2 \times 10^{- 2}$ . We propose an analytic theory, which is in quite good agreement with our numerical results. For all cases, the typical disk’s inclinations with respect to the equatorial plane are of the order of or larger than the orbital inclination. This leads to multiple crossings of the orbit with the disk per one orbital period, which contradicts the PM model, where only two crossings per orbital period are required. When $δ ≳ 0.1$ , a typical disk’s inclination within the orbit of the binary turns out to be smaller than that of the orbit. We provide a qualitative analytical analysis, which confirms this conclusion. In this case there are only two crossings of the orbit with the disk per one orbital period. On the other hand, qualitative estimates allow us to suggest that the additional heating of the disk gas by the secondary-disk collisions may result in $δ \sim 0.1$ . Thus, we suggest that in the framework of the PM model of OJ 287, the disk should be relatively thick, with $δ \sim 0.1$ . This could lead to a modification of the theoretical spectrum of the source.

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

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