翘曲天体物理盘的局部和全局动力学
Local and global dynamics of warped astrophysical discs
摘要：
天体物理学的圆盘在系统中出现错位时，或者当一个平的圆盘被外力弄得不稳定时，就会发生翘曲。翘曲圆盘的形状和质量分布的演变不仅受到外部影响的驱动，而且还受到通过圆盘传递角动量的内部扭矩的驱动。这种扭矩取决于由与翘曲相关的振荡压力梯度驱动的内部流动，以及在较小尺度上操作的物理过程，这可能包括不稳定性和湍流。我们介绍了一个本地模型的详细研究翘曲盘。本文从Goldreich & Lynden-Bell的剪切单出发，通过坐标变换，给出了轨道平面的振荡几何。这种翘曲的剪切片（或盒）适用于流体动力学、磁流体力学等的分析和计算处理，并且它可以用来计算驱动盘的大规模演化的内部扭矩。局部模型中最简单的流体动力学状态是以轨道频率振荡的水平均匀层流。这些对应的非线性解决方案中发现的翘曲盘在以前的工作Ogilvie，我们提出了一个替代的推导和推广的理论。在配套文件中，我们表明，这些层流往往是线性不稳定的，特别是如果光盘是近开普勒和低粘度。局部模型可以用于在未来的工作中，以确定翘曲盘的流体动力学不稳定性的非线性结果，以及它与其他如磁旋转不稳定性的相互作用。
英文摘要：
Astrophysical discs are warped whenever a misalignment is present in the system, or when a flat disc is made unstable by external forces. The evolution of the shape and mass distribution of a warped disc is driven not only by external influences but also by an internal torque, which transports angular momentum through the disc. This torque depends on internal flows driven by the oscillating pressure gradient associated with the warp, and on physical processes operating on smaller scales, which may include instability and turbulence. We introduce a local model for the detailed study of warped discs. Starting from the shearing sheet of Goldreich & Lynden-Bell, we impose the oscillating geometry of the orbital plane by means of a coordinate transformation. This warped shearing sheet (or box) is suitable for analytical and computational treatments of fluid dynamics, magnetohydrodynamics, etc., and it can be used to compute the internal torque that drives the large-scale evolution of the disc. The simplest hydrodynamic states in the local model are horizontally uniform laminar flows that oscillate at the orbital frequency. These correspond to the nonlinear solutions for warped discs found in previous work by Ogilvie, and we present an alternative derivation and generalization of that theory. In a companion paper we show that these laminar flows are often linearly unstable, especially if the disc is nearly Keplerian and of low viscosity. The local model can be used in future work to determine the nonlinear outcome of the hydrodynamic instability of warped discs, and its interaction with others such as the magnetorotational instability.
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