论文标题
扭曲光盘的非线性行为围绕中心对象具有四极矩
Nonlinear behaviour of warped discs around a central object with a quadrupole moment
论文作者
论文摘要
低粘度翘曲的椎间盘的非线性行为知之甚少。我们验证了一种非线性弯曲波理论，其中流体柱通过直接的3D流体动力学模拟进行仿射转化。我们采用了二阶Godunov型方案，无线有限质量（MFM），以及具有高达128m颗粒的平滑颗粒流体动力学方法（SPH）方法。对于中度的非线性，MFM很好地维持了仿射模型预测的稳定的非线性翘曲，用于围绕具有四倍矩的中心对象倾斜的无粘性盘。但是，SPH中的数值耗散非常严重，即使MFM表现良好的分辨率，即使是低振幅非线性翘曲也会降解。低振幅任意扭曲倾向于向非线性稳态发展。但是，当我们的薄圆盘中没有这种状态，当外倾角超过约14度时，薄圆盘中没有角度半厚度H/r = 0.02。经线破裂并在绝热模拟中重新连接，或者在等温模拟中分为不同的环体。断裂半径位于最极端的非线性变形的位置附近。参数不稳定性仅在我们的最高分辨率仿真中捕获，导致环结构可以用作二进制行星的孵化器。
The nonlinear behaviour of low-viscosity warped discs is poorly understood. We verified a nonlinear bending-wave theory, in which fluid columns undergo affine transformations, with direct 3D hydrodynamical simulations. We employed a second-order Godunov-type scheme, Meshless Finite Mass (MFM), and also the Smoothed Particle Hydrodynamics (SPH) method, with up to 128M particles. For moderate nonlinearity, MFM maintains well the steady nonlinear warp predicted by the affine model for a tilted inviscid disc around a central object with a quadrupole moment. However, numerical dissipation in SPH is so severe that even a low-amplitude nonlinear warp degrades at a resolution where MFM performs well. A low-amplitude arbitrary warp tends to evolve towards a nonlinear steady state. However, no such state exists in our thin disc with an angular semi-thickness H/R = 0.02 when the outer tilt angle is beyond about 14 degrees. The warp breaks tenuously and reconnects in adiabatic simulations, or breaks into distinct annuli in isothermal simulations. The breaking radius lies close to the location with the most extreme nonlinear deformation. Parametric instability is captured only in our highest-resolution simulation, leading to ring structures that may serve as incubators for planets around binaries.
