密集多行星系统中的三体共振重叠
Three Body Resonance Overlap in Closely Spaced Multiple Planet Systems
摘要：
计算了共面低偏心率多行星系统零阶三体共振强度。在一个数值积分，我们说明，缓慢移动的拉普拉斯角匹配的变化，在三个机构与外部的两个机构在同一方向上移动，内部的一个在相反的方向移动，从两个量，在三体共振中守恒的预期。当行星际距离小于一阶单位因子乘以行星质量的四分之一次方时，推导出了三体共振重叠的等质量紧密系统的共振重叠判据.我们发现，三体共振是足够密集的占半长轴的数值积分中看到的紧密间隔系统的漂移，他们可能是这些系统的不稳定性的原因。对于重叠区以外的行星际分离，稳定时间尺度显著增加。粗略估计的离心率和半长轴的扩散系数取决于行星质量和行星际间距的高次幂。先前拟合稳定性或交叉时间尺度的指数依赖性可能是由于积分中可能的参数和时间的有限范围以及扩散速率对这些量的强幂律依赖性。
英文摘要：
We compute the strengths of zero-th order (in eccentricity) three-body resonances for a co-planar and low eccentricity multiple planet system. In a numerical integration we illustrate that slowly moving Laplace angles are matched by variations in semi-major axes among three bodies with the outer two bodies moving in the same direction and the inner one moving in the opposite direction, as would be expected from the two quantities that are conserved in the three-body resonance. A resonance overlap criterion is derived for the closely and equally spaced, equal mass system with three-body resonances overlapping when interplanetary separation is less than an order unity factor times the planet mass to the one quarter power. We find that three-body resonances are sufficiently dense to account for wander in semi-major axis seen in numerical integrations of closely spaced systems and they are likely the cause of instability of these systems. For interplanetary separations outside the overlap region, stability timescales significantly increase. Crudely estimated diffusion coefficients in eccentricity and semi-major axis depend on a high power of planet mass and interplanetary spacing. An exponential dependence previously fit to stability or crossing timescales is likely due to the limited range of parameters and times possible in integration and the strong power law dependence of the diffusion rates on these quantities.
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