PLANETS NEAR MEAN-MOTION RESONANCES
PLANETS NEAR MEAN-MOTION RESONANCES
复制标题
DOI：
10.1088/0004-637x/770/1/24
复制
发表时间：
2012-11
期刊：
影响因子：
--
通讯作者：
C. Petrovich;R. Malhotra;S. Tremaine
中科院分区：
文献类型：
--
作者：
C. Petrovich;R. Malhotra;S. Tremaine
开普勒任务发现的多行星系统表现出以下特征：接近一阶平均运动共振的行星对更喜欢在名义共振外的轨道，而避免在共振内的轨道。我们探索了行星形成的一个极其简单的动力学模型，在这个模型中，行星的质量以规定的速率增长，没有轨道迁移或耗散。在两种极限情况下，我们开发了该模型的解析版本：行星质量相对于特征共振振动时间快速或缓慢增长。在这两种情况下，系统的周期比分布在共振周围形成了一种特征的不对称峰谷结构，在质量上与开普勒样品中观察到的相似。我们用三体问题的数值积分验证了这一结果。我们表明，对于观测到的峰谷结构最强的3:2共振，我们的简单模型与平均行星质量20-100 M⊕的观测结果一致。这个预测的质量范围比少数几个开普勒行星测量到的质量范围要高至少三倍，但这种差异的部分原因可能是动力学模型的过度简化或行星质量-半径关系的不确定性。
The multiple-planet systems discovered by the Kepler mission exhibit the following feature: planet pairs near first-order mean-motion resonances prefer orbits just outside the nominal resonance, while avoiding those just inside the resonance. We explore an extremely simple dynamical model for planet formation, in which planets grow in mass at a prescribed rate without orbital migration or dissipation. We develop an analytic version of this model for two-planet systems in two limiting cases: the planet mass grows quickly or slowly relative to the characteristic resonant libration time. In both cases, the distribution of systems in period ratio develops a characteristic asymmetric peak–trough structure around the resonance, qualitatively similar to that observed in the Kepler sample. We verify this result with numerical integrations of the three-body problem. We show that for the 3 : 2 resonance, where the observed peak–trough structure is strongest, our simple model is consistent with the observations for a range of mean planet masses 20–100 M⊕. This predicted mass range is higher—by at least a factor of three—than the range expected from the few Kepler planets with measured masses, but part of this discrepancy could be due to oversimplifications in the dynamical model or uncertainties in the planetary mass–radius relation.