青蛙的护理和喂养
Care and feeding of frogs
摘要：
“螺旋桨”是土星A环的特征，与打开部分间隙的小卫星有关。它们表现出非开普勒运动（Tiscareno 2010）;观测最好的螺旋桨“Blériot”的经度残差与周期约为4年的正弦曲线一致。Pan和Chiang（2010年）提出螺旋桨小卫星在与共轨环材料的“青蛙共振”中进行自由振动。通过与限制性三体问题的类比，他们将共轨物质视为在旋转坐标系中静止的物质，而忽略了非共轨物质。在这里，我们使用简单的数值实验来扩展青蛙模型，包括反馈由于差距的运动，和阻力与Lindblad磁盘扭矩，导致I型迁移。由于小卫星产生了间隙，我们期望间隙质心跟踪小卫星，但只有在时间延迟t_diff之后，环粒子从与小卫星结合到间隙结束的时间。我们发现，青蛙的天平动可以持续只有当t_diff超过青蛙天平动周期P_lib，如果从Lindblad扭矩阻尼平衡驱动从共轨扭矩。如果t_diff << P_lib，则振动幅度衰减为零。在Blériot的情况下，蛙共振模型可以再现观测到的天平动周期Plib ~ 4 yr。然而，我们简单的反馈处方表明，Blériot的t_diff ~ 0.01P_lib，这与观测到的260 km的天平动振幅不一致。我们敦促更准确地处理反馈，以测试我们的玩具模型的假设。
英文摘要：
"Propellers" are features in Saturn's A ring associated with moonlets that open partial gaps. They exhibit non-Keplerian motion (Tiscareno 2010); the longitude residuals of the best-observed propeller, "Blériot," appear consistent with a sinusoid of period ~4 years. Pan and Chiang (2010) proposed that propeller moonlets librate in "frog resonances" with co-orbiting ring material. By analogy with the restricted three-body problem, they treated the co-orbital material as stationary in the rotating frame and neglected non-co-orbital material. Here we use simple numerical experiments to extend the frog model, including feedback due to the gap's motion, and drag associated with the Lindblad disk torques that cause Type I migration. Because the moonlet creates the gap, we expect the gap centroid to track the moonlet, but only after a time delay t_diff, the time for a ring particle to travel from conjunction with the moonlet to the end of the gap. We find that frog librations can persist only if t_diff exceeds the frog libration period P_lib, and if damping from Lindblad torques balances driving from co-orbital torques. If t_diff << P_lib, then the libration amplitude damps to zero. In the case of Blériot, the frog resonance model can reproduce the observed libration period P_lib ~ 4 yr. However, our simple feedback prescription suggests that Blériot's t_diff ~ 0.01P_lib, which is inconsistent with the observed libration amplitude of 260 km. We urge more accurate treatments of feedback to test the assumptions of our toy models.
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