Local and global dynamics of eccentric astrophysical discs
Local and global dynamics of eccentric astrophysical discs
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偏心天体物理盘的局部和全局动力学
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Barker
中科院分区：
文献类型：
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作者：
G. Ogilvie;A. Barker
我们制定了偏心圆盘的局部动力学模型，其中主要运动由椭圆开普勒轨道组成。该模型是众所周知的剪切板的推广，适用于偏心盘局部动力学的分析和计算研究。它在水平维度上是空间均匀的，但具有以轨道频率振荡的时间依赖性几何形状。我们展示了局部模型中应力张量的某些平均值如何确定圆盘形状和质量分布的大规模演化。局部模型最简单的解决方案是由圆盘（通常是非线性）垂直振荡组成的层流。由于偏心轨道周围垂直重力加速度的变化，以及在某些情况下由于与偏心梯度相关的轨道速度场的发散，偏心盘缺乏垂直静水平衡。我们讨论了层流解决方案的属性，表明它们可以在偏心率大于 0.5 左右时表现出极端压缩行为，特别是在等温的圆盘中。我们还推导出了偏心盘的线性演化方程，该方程是在没有剪切粘度的情况下由层流得出的。在一篇配套论文中，我们表明这些解决方案是线性不稳定的，并且我们确定了相关的增长率和不稳定模式。
We formulate a local dynamical model of an eccentric disc in which the dominant motion consists of elliptical Keplerian orbits. The model is a generalization of the well-known shearing sheet, and is suitable for both analytical and computational studies of the local dynamics of eccentric discs. It is spatially homogeneous in the horizontal dimensions but has a time-dependent geometry that oscillates at the orbital frequency. We show how certain averages of the stress tensor in the local model determine the large-scale evolution of the shape and mass distribution of the disc. The simplest solutions of the local model are laminar flows consisting of a (generally non-linear) vertical oscillation of the disc. Eccentric discs lack vertical hydrostatic equilibrium because of the variation of the vertical gravitational acceleration around the eccentric orbit, and in some cases because of the divergence of the orbital velocity field associated with an eccentricity gradient. We discuss the properties of the laminar solutions, showing that they can exhibit extreme compressional behaviour for eccentricities greater than about 0.5, especially in discs that behave isothermally. We also derive the linear evolutionary equations for an eccentric disc that follow from the laminar flows in the absence of a shear viscosity. In a companion paper we show that these solutions are linearly unstable and we determine the associated growth rates and unstable modes.