First-order mean motion resonances in two-planet systems: general analysis and observed systems
First-order mean motion resonances in two-planet systems: general analysis and observed systems
复制标题
双行星系统中的一阶平均运动共振：一般分析和观测系统
DOI：
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发表时间：
2018
影响因子：
4.8
通讯作者：
J. Papaloizou
中科院分区：
文献类型：
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作者：
C. Terquem;J. Papaloizou
本文主要研究两行星系统在一阶（q +1）：q $平均运动共振下的圆盘I型迁移。我们提出了一个详细的分析，适用于任何值的共振。在光滑收敛偏移的情况下，推导出平衡偏心率、平均运动和偏离精确共振的表达式。我们表明，这种偏离，不假设是小的，是这样的周期比通常超过，但也可以小于，$（q +1）/q。偏离精确共振作为时间的函数的系统开始在共振和发散迁移也计算。我们讨论了两个低质量行星接近一阶共振的观测系统。我们认为，数据是一致的，只有一小部分的系统已被捕获的共振。此外，当捕获确实发生时，它通常不是在通过盘的平滑会聚迁移期间，而是在行星到达盘内部之后。我们表明，虽然共振可能会被破坏时，内行星进入一个中心腔，这本身不能解释所观察到的分离的蔓延。破坏被发现导致系统移动内部的共振百分之几，或获得另一个共振。我们假设两个人口的低质量行星：一个小的广泛顺利迁移发生，和一个较大的，形成近似原位非常有限的迁移。
This paper focuses on two-planet systems in a first-order $(q+1):q$ mean motion resonance and undergoing type-I migration in a disc. We present a detailed analysis of the resonance valid for any value of $q$. Expressions for the equilibrium eccentricities, mean motions and departure from exact resonance are derived in the case of smooth convergent migration. We show that this departure, not assumed to be small, is such that period ratio normally exceeds, but can also be less than, $ (q+1)/q.$ Departure from exact resonance as a function of time for systems starting in resonance and undergoing divergent migration is also calculated. We discuss observed systems in which two low mass planets are close to a first-order resonance. We argue that the data are consistent with only a small fraction of the systems having been captured in resonance. Furthermore, when capture does happen, it is not in general during smooth convergent migration through the disc but after the planets reach the disc inner parts. We show that although resonances may be disrupted when the inner planet enters a central cavity, this alone cannot explain the spread of observed separations. Disruption is found to result in either the system moving interior to the resonance by a few percent, or attaining another resonance. We postulate two populations of low mass planets: a small one for which extensive smooth migration has occurred, and a larger one that formed approximately in-situ with very limited migration.