It has been observed that many relativistic jets display a kind of cork-screw-like precession. Numerical simulations has suggested that such kind of precession may originate from the precession of the disk. In this work, we introduce an analytical model to describe the precession and split of a tilted, geometrically thin disk. We consider the Lense-Thirring effect from the central (primary) black hole (BH) and the gravitational effect from the companion (secondary) BH far away from the center, both of which could induce the precession of the accretion disk around the spin axis of central black hole. We propose the splitting conditions that when the rate of viscous diffusion cannot catch up with the dynamical frequency at a certain layer of fluid, the disk would split into two parts which precess independently. We presume that the precessions of the inner and outer disks are in accord with the rotation and precession of jet, respectively. By matching the frequencies of the disks to the observed frequencies of jet in the cork-screw-like precession and considering the splitting condition, we are allowed to read four parameters, the innermost radius (r _in), the outermost radius (r _out) of the disk, the initial splitting radius (r _sp,0), and the inflow speed magnitude (β), of the disk. We apply this model to OJ 287. Moreover, considering the inward shrinking of the disks, we find the time variation of the precession angle of jet. This time variation presents a unique feature of our model, which could be distinguishable in the future observation.

中文翻译：

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倾斜的、几何薄的吸积盘的进动和分裂：一项分析研究


据观察，许多相对论性喷流表现出一种螺旋形进动。数值模拟表明这种进动可能源于圆盘的进动。在这项工作中，我们引入了一个分析模型来描述倾斜的几何薄盘的进动和分裂。我们考虑来自中心（主）黑洞（BH）的透镜-蒂林效应和来自远离中心的伴星（次）黑洞（BH）的引力效应，这两者都可能引起吸积盘绕自转轴的进动的中心黑洞。我们提出了分裂条件，即当粘性扩散速率无法赶上某一层流体的动态频率时，圆盘将分裂成独立进动的两部分。我们假设内盘和外盘的进动分别与射流的自转和进动一致。通过将圆盘的频率与螺旋状进动中观察到的射流频率相匹配并考虑分裂条件，我们可以读取四个参数，即最内半径（ r_在) 中，最外层半径 ( r_出）的圆盘，初始分裂半径（ r _sp,0 ) 和圆盘的流入速度大小 (β)。我们将此模型应用于OJ 287。此外，考虑到圆盘的向内收缩，我们发现了射流进动角的时间变化。这种时间变化呈现出我们模型的独特特征，可以在未来的观察中区分出来。