垂直振荡吸积盘中的不稳定性和翘曲
Instability and warping in vertically oscillating accretion discs
AI总结：
本文利用准二维和三维剪切盒模型研究垂直振荡吸积盘的耗散与能量学，发现纯垂直振荡盘会参数不稳定地激发惯性波，其中弯曲波最为重要，其非线性激波可阻尼振荡并伴随能量回流。
摘要：
许多吸积盘已被发现是畸变的：要么由于系统中的错位而翘曲，要么由于轨道偏心率或双星伴星的潮汐变形而呈非圆形。翘曲的、偏心的和潮汐畸变的盘并不处于垂直流体静力学平衡状态，因此在垂直于盘的方向上表现出垂直振荡，这一现象在圆形和平坦盘中是不存在的。在极端情况下，这种垂直运动表现为气体的垂直“弹跳”，可能导致激波和加热，正如最近的全球数值模拟中所观测到的那样。在本文中，我们通过准二维和完全三维的流体动力学局部（剪切盒）模型来分离垂直盘振荡的力学机制。为了确定振荡过程中起作用的数值耗散和物理耗散机制，我们首先研究非受迫振荡，考察初始振荡幅度以及分辨率、边界条件和垂直盒尺寸对振荡耗散和能量学的影响。然后，我们通过引入一个随时间变化的引力势来驱动振荡。一个关键结果是，即使是一个纯粹垂直振荡的盘也会（参数性地）不稳定，从而产生惯性波，我们通过线性稳定性分析证实了这一点。其中最重要的具有弯曲波的特征，其径向波长取决于垂直振荡的频率。不稳定性的非线性阶段表现出激波，这些激波会阻尼振荡，尽管能量也可以从弯曲波流回垂直振荡。
英文摘要：
Many accretion discs have been found to be distorted: either warped due a misalignment in the system, or non-circular as a result of orbital eccentricity or tidal deformation by a binary companion. Warped, eccentric, and tidally distorted discs are not in vertical hydrostatic equilibrium, and thus exhibit vertical oscillations in the direction perpendicular to the disc, a phenomenon that is absent in circular and flat discs. In extreme cases, this vertical motion is manifested as a vertical `bouncing' of the gas, potentially leading to shocks and heating, as observed in recent global numerical simulations. In this paper we isolate the mechanics of vertical disc oscillations by means of quasi-2D and fully 3D hydrodynamic local (shearing-box) models. To determine the numerical and physical dissipation mechanisms at work during an oscillation we start by investigating unforced oscillations, examining the effect of initial oscillation amplitude, as well as resolution, boundary conditions, and vertical box size on the dissipation and energetics of the oscillations. We then drive the oscillations by introducing a time-dependent gravitational potential. A key result is that even a purely vertically oscillating disc is (parametrically) unstable to developing inertial waves, as we confirm through a linear stability analysis. The most important of these has the character of a bending wave, whose radial wavelength depends on the frequency of the vertical oscillation. The nonlinear phase of the instability exhibits shocks, which dampen the oscillations, although energy can also flow from the bending wave back to the vertical oscillation.
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