环双星盘动力学的解析与数值方法——II：倾斜盘
Analytical and Numerical Methods for Circumbinary Disk Dynamics -- II: Inclined Disks
AI总结：
本文通过二维流体力学模拟与解析分析，研究倾斜环双星盘中双星力矩与黏滞力矩的分布及中心空隙稳定性，发现倾角接近45度时系统无法达到准稳态，并揭示了力矩平衡缺失或随时间振荡的构型，为理解超大质量黑洞双星的引力波与电磁对应体提供依据。
摘要：
（节略）为深入了解超大质量黑洞双星对环双星吸积盘的动力影响，我们研究了该盘中的双星力矩密度和黏滞力矩密度，重点关注最终密度分布，尤其是双星与盘内边缘之间中心空隙的大小和稳定性。我们仅限于简化情形：一个无质量黏滞薄吸积盘，受到轨道平面相对于盘面倾斜的双星系统引力势的影响。如果轨道平面与盘并非同时形成，或者黑洞自旋角动量相对于盘轨道角动量方向错位，从而使双星能够进动到倾斜取向，则轨道平面可能是倾斜的。我们采用二维牛顿流体力学模拟来考察两个模型参数的影响：双星质量比以及双星与盘之间的倾角。我们研究它们对密度和力矩分布的影响。在解析方法中，我们考虑了由非对称倾斜双星引力势对开普勒圆轨道的微扰效应所引发的本轮稳定性。通过模拟，我们观察到某些构型从未达到准稳态，即经过多个轨道平均后的密度剖面不会稳定。这种不稳定性发生在倾角接近45度时。此外，我们还识别出一些构型，其中动力学力矩密度与黏滞力矩密度之间从未存在持续平衡，以及该平衡位置在黏滞时标上振荡或表现出其他随时间变化行为的情形。这些发现对于理解超大质量黑洞双星预期的引力波信号和电磁对应体具有重要意义。
英文摘要：
(Abridged) To gain insight into the dynamical influence of a supermassive black hole binary on a circumbinary accretion disk, we investigate the binary and viscous torque densities throughout such a disk, with emphasis on the final density distribution, particularly the size and stability of the central gap between the binary and the inner edge of the disk. We limit ourselves to the simplified case of a massless viscous thin accretion disk under the influence of the gravitational potential from a binary system whose orbital plane is inclined relative to the disk. The orbital plane could be inclined if it is not coeval with the disk, or the black holes have spin angular momentum misaligned with respect to the disk's orbital angular momentum, so that the binary can precess to an inclined orientation. We employ 2D Newtonian hydrodynamics simulations to examine the influence of two model parameters: the mass ratio of the binary and the inclination angle between the binary and the disk. We investigate their impact on the density and torque distribution. In our analytical approach, we consider the stability of epicycles induced by the perturbative effect of the asymmetric inclined binary gravitational potential on Keplerian circular orbits. Through our simulations, we observe that certain configurations never attain a quasi-steady state, where the density profile averaged over many orbits stabilizes. This instability occurs when the inclination is close to 45 degrees. Furthermore, we identify configurations where there is never a persistent balance between the dynamical and viscous torque densities, as well as cases where the location of this balance oscillates or exhibits other time-dependent behavior over viscous timescales. These findings have implications for understanding both the expected gravitational-wave signal and electromagnetic counterparts from supermassive black hole binaries.
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