Madigan Ann-Marie, Zderic Alexander, McCourt Michael, Fleisig Jacob
JILA and Department of Astrophysical and Planetary Sciences, CU Boulder, Boulder, CO 80309, USA.
Astronomy Department, Broida Hall, University of California, Santa Barbara, CA 93106, USA.
Astron J. 2018 Oct;156(4). doi: 10.3847/1538-3881/aad95c. Epub 2018 Sep 6.
Axisymmetric disks of eccentric Kepler orbits are vulnerable to an instability that causes orbits to exponentially grow in inclination, decrease in eccentricity, and cluster in their angle of pericenter. Geometrically, the disk expands to a cone shape that is asymmetric about the mid-plane. In this paper, we describe how secular gravitational torques between individual orbits drive this "inclination instability". We derive growth timescales for a simple two-orbit model using a Gauss -ring code, and generalize our result to larger systems with -body simulations. We find that two-body relaxation slows the growth of the instability at low and that angular phase coverage of orbits in the disk is important at higher . As → ∞, the e-folding timescale converges to that expected from secular theory.
偏心开普勒轨道的轴对称盘容易受到一种不稳定性的影响，这种不稳定性会导致轨道倾角呈指数增长、偏心率减小，并在近日点角度上聚集。从几何角度看，盘会扩展成一个关于中平面不对称的圆锥形状。在本文中，我们描述了各个轨道之间的长期引力扭矩如何驱动这种“倾角不稳定性”。我们使用高斯环代码推导了一个简单双轨道模型的增长时间尺度，并通过多体模拟将结果推广到更大的系统。我们发现，两体弛豫在低密度时会减缓不稳定性的增长，而在高密度时盘内轨道的角相位覆盖很重要。当密度趋于无穷大时，指数衰减时间尺度收敛到长期理论预期的值。
