作为Keplerian圆盘翘曲动力学模型的非线性共振环面振荡
Nonlinear resonant torus oscillations as a model of Keplerian disc warp dynamics
摘要：
对扭曲圆盘的观测突出了扭曲在各种天体物理环境中的普遍存在。这已经被理解曲速演化动力学的理论努力所补充。尽管作出了重大努力，以了解动态的翘曲盘，以前的工作未能解决可以说是最普遍的制度-非线性翘曲开普勒光盘的轨道，周转和垂直振荡频率之间的共振。在这项工作中，我们实现了一种新的非线性环模型，最近开发的Fairbairn和Ogilvie，作为一个框架来理解这种共振翘曲动力学。在这里，我们发现两个不同的非线性制度的翘曲幅度增加。最初，我们发现一个光滑的调制理论，它描述了翘曲演化的平均拉格朗日振荡的垂直运动的磁盘。这暗示了在一个广义的世俗框架下连接以前的翘曲理论的可能性。当翘曲幅度超过一个临界值时，这个临界值与我们的环的纵横比的平方根成比例，圆盘进入一个弹跳状态，每个轨道有两次极端的垂直压缩。我们开发了一个脉冲理论，预测特殊的逆行和逆行进动翘曲的解决方案，这是确定使用我们的完整方程组的数值。这样的解决方案强调的非线性垂直振荡盘内的基本激活，并可能有重要的影响，能量和翘曲耗散。未来的工作应该在翘曲圆盘内部流动结构的详细数值研究中寻找这种行为。
英文摘要：
Observations of distorted discs have highlighted the ubiquity of warps in a variety of astrophysical contexts. This has been complemented by theoretical efforts to understand the dynamics of warp evolution. Despite significant efforts to understand the dynamics of warped discs, previous work fails to address arguably the most prevalent regime -- nonlinear warps in Keplerian discs for which there is a resonance between the orbital, epicyclic and vertical oscillation frequencies. In this work, we implement a novel nonlinear ring model, developed recently by Fairbairn and Ogilvie, as a framework for understanding such resonant warp dynamics. Here we uncover two distinct nonlinear regimes as the warp amplitude is increased. Initially we find a smooth modulation theory which describes warp evolution in terms of the averaged Lagrangian of the oscillatory vertical motions of the disc. This hints towards the possibility of connecting previous warp theory under a generalised secular framework. Upon the warp amplitude exceeding a critical value, which scales as the square root of the aspect-ratio of our ring, the disc enters into a bouncing regime with extreme vertical compressions twice per orbit. We develop an impulsive theory which predicts special retrograde and prograde precessing warped solutions, which are identified numerically using our full equation set. Such solutions emphasise the essential activation of nonlinear vertical oscillations within the disc and may have important implications for energy and warp dissipation. Future work should search for this behaviour in detailed numerical studies of the internal flow structure of warped discs.
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