CONDITION FOR CAPTURE INTO FIRST-ORDER MEAN MOTION RESONANCES AND APPLICATION TO CONSTRAINTS ON THE ORIGIN OF RESONANT SYSTEMS
CONDITION FOR CAPTURE INTO FIRST-ORDER MEAN MOTION RESONANCES AND APPLICATION TO CONSTRAINTS ON THE ORIGIN OF RESONANT SYSTEMS
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DOI：
10.1088/0004-637x/775/1/34
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发表时间：
2013-07
期刊：
影响因子：
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通讯作者：
M. Ogihara;H. Kobayashi
中科院分区：
文献类型：
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作者：
M. Ogihara;H. Kobayashi
我们用数值模拟的方法研究了在不同参数范围内捕获到一阶平均运动共振的条件。特别是，我们重点推导了捕获到2：1共振的临界迁移时间标度；还对近距离共振(例如3：2)进行了额外的数值实验。我们发现，临界迁移时间尺度是由行星与恒星的质量比决定的，其依赖关系呈现指数−为4/3的幂定律行为。这种依赖关系也得到了简单的解析论证的支持。我们还发现，具有等质量物体的系统的临界迁移时间标度比限制问题中的要短；例如，对于两个等质量物体之间的2：1共振，临界时间标度减小了10倍。此外，利用所得到的公式，包含一阶公度的观测系统的起源受到了约束。假设成对的行星最初形成时彼此完全分开，然后经历会聚的迁移，并在共振中被捕获，则可能有一些系外行星经历了快速的轨道迁移。对于近距离共振系统，共振对之间的差异迁移时间尺度可以很好地约束；进一步表明，几个系外行星经历了等于甚至超过线性理论预测的I型迁移速率的迁移。这意味着它们中的一些可能是在原位形成的。未来的观测和我们的模型的使用将使我们能够从统计上确定原行星盘中的典型迁移速度。
We investigate the condition for capture into first-order mean motion resonances using numerical simulations with a wide range of various parameters. In particular, we focus on deriving the critical migration timescale for capture into the 2:1 resonance; additional numerical experiments for closely spaced resonances (e.g., 3:2) are also performed. We find that the critical migration timescale is determined by the planet-to-stellar mass ratio, and its dependence exhibits power-law behavior with index −4/3. This dependence is also supported by simple analytic arguments. We also find that the critical migration timescale for systems with equal-mass bodies is shorter than that in the restricted problem; for instance, for the 2:1 resonance between two equal-mass bodies, the critical timescale decreases by a factor of 10. In addition, using the obtained formula, the origin of observed systems that include first-order commensurabilities is constrained. Assuming that pairs of planets originally form well separated from each other and then undergo convergent migration and are captured in resonances, it is possible that a number of exoplanets experienced rapid orbital migration. For systems in closely spaced resonances, the differential migration timescale between the resonant pair can be constrained well; it is further suggested that several exoplanets underwent migration that can equal or even exceed the type I migration rate predicted by the linear theory. This implies that some of them may have formed in situ. Future observations and the use of our model will allow us to statistically determine the typical migration speed in a protoplanetary disk.