Simulations of dense planetary rings. III. Self-gravitating identical particles.
Simulations of dense planetary rings. III. Self-gravitating identical particles.
复制标题
密集行星环的模拟。
DOI：
10.1006/icar.1995.1157
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发表时间：
1995
期刊：
影响因子：
3.2
通讯作者：
H. Salo
中科院分区：
文献类型：
--
作者：
H. Salo
摘要 通过局部模拟研究了碰撞环系统的动力学行为，其中包括粒子之间的相互引力。采用涉及多达数千个相同粒子的直接力计算，参数值适合土星环。研究了影响碰撞稳态的不同因素，包括两个粒子的引力相遇、集体朱利安-托姆尾迹的形成，甚至粒子群的发展。这些模拟表明，平衡径向速度色散 c x 往往由单独产生最大随机运动的因素主导。在非引力粒子的恢复系数 ϵ 恒定的情况下，平衡 c x 永远不会超过 r Ω 的几倍，其中 r 是粒子半径，Ω 是轨道角速度。由于自引力，即使表面密度很小，引力相遇很快就会占主导地位，并且 c x 接近单个粒子的逃逸速度。随着表面密隐含的 c x ≈ ( r /1 m ) 0.2 cm s -1 与基于密度波阻尼的估计定性一致。天王星环预计也会出现引力尾迹。原则上，对应于值 ϵ ≥ 0.6 的速度相关耗散将抑制尾流结构。然而，土星A环的方位不对称性有力地支持了尾流的存在，模拟的20°-25°的俯仰角与观测所需的高度一致。这一一致性表明，该环中 ϵ 的有效值比最近固体冰球之间撞击的实验室实验所暗示的更接近于零。同样，假设合理的密度和耗散，当前的模拟表明，对于土星环，集体尾迹开始在距离该行星 a ≥ 125,000 公里处退化为实际的粒子群。在约 140,000 公里之外，这样的团块似乎非常稳定。模拟骨料的 r p ≈ 0.7-0.9，其中 r p 是骨料相对于其 Hill 半径的短轴半径。
Abstract The dynamical behavior of collisional ring systems is studied via a local simulation which includes mutual gravitational forces between particles. Direct force calculations involving up to a few thousand identical particles are employed, with parameter values appropriate to Saturn's rings. Different factors affecting the collisional steady state are studied, including two-particle gravitational encounters, the formation of collective Julian-Toomre wakes, and even the development of particle groups. These simulations indicate that the equilibrium radial velocity dispersion c x tends to be dominated by that factor which alone would yield the largest random motion. In the case of a constant coefficient of restitution ϵ among nongravitating particles, the equilibrium c x never exceeds a few times r Ω, where r is the particle radius and Ω is the orbital angular velocity. With self-gravity, gravitational encounters soon dominate, even when the surface density is small, and c x is then close to the escape speed from individual particles. With increased surface density, scattering by collective wakes becomes yet more important, and c x corresponds to the Toomre parameter Q T ≈ 2. For Saturn's A-ring this implies a multilayered structure with strongly enhanced velocity dispersion, c x , reaching values ≈15rΩ for surface densities ≈500 kg m -2 . The implied c x ≈ ( r /1 m ) 0.2 cm s -1 agrees qualitatively with estimates based on the damping of density waves. Gravitational wakes are also expected for the rings of Uranus. In principle, velocity-dependent dissipation corresponding to values ϵ ≥ 0.6 would suppress the wake structure. However, the azimuthal asymmetry of Saturn's A-ring gives strong support to the existence of wakes, with the simulated pitch angles of order 20°-25° being in good agreement with those required by observations. This agreement suggests that the effective values of ϵ in that ring is closer to zero than implied by recent laboratory experiments of impacts between solid ice balls. Likewise, assuming reasonable densities and dissipation, the present simulations indicate for Saturn's rings that the collective wakes begin to degrade into actual particle groups at distances a ≥ 125,000 km from that planet. Beyond a ≈ 140,000 km, such clumps seem to be very stable. The simulated aggregates have r p ≈ 0.7-0.9, where r p is the minor axis radius of the agregate relative to its Hill's radius.