ON THE MIGRATION OF JUPITER AND SATURN: CONSTRAINTS FROM LINEAR MODELS OF SECULAR RESONANT COUPLING WITH THE TERRESTRIAL PLANETS
ON THE MIGRATION OF JUPITER AND SATURN: CONSTRAINTS FROM LINEAR MODELS OF SECULAR RESONANT COUPLING WITH THE TERRESTRIAL PLANETS
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DOI：
10.1088/0004-637x/745/2/143
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发表时间：
2012-02-01
影响因子：
4.9
通讯作者：
Lin, D. N. C.
中科院分区：
文献类型：
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作者：
Agnor, Craig B.;Lin, D. N. C.
我们研究了木星和土星的后期发散迁移可能会扰动类地行星。利用一个改进的长期模型，我们确定了木星和土星的nu（5）频率与类地行星的四个拱点本征频率（g（1 - 4））之间的六个长期共振。我们推导出解析上限的偏心率和轨道迁移时间尺度的木星和土星时，这些共振遇到，以避免扰动的偏心率的类地行星的值大于所观察到的。由于j = 2，3的地球本征模的振幅很小，g（2）-nu（5）和g（3）-nu（5）共振对巨行星迁移提供了最强的约束。如果木星和土星的迁移与它们现在的偏心率相当，那么具有小行星驱动迁移的指数时间尺度特征的平滑迁移（τ类似于5 - 10百万年）将使类地行星的偏心率扰动到远远超过观测值的值。如果木星的偏心率在迁移时期很小，这种激发可能会减轻，迁移非常迅速（e。例如，在一个实施例中，τ小于或类似于0.5Myr，可能通过行星-行星散射或不稳定性驱动的迁移）或观测到的j = 2，3地球模式的小偏心率振幅是由几个大振幅贡献的低概率抵消引起的。轨道积分的结果显示，极短的迁移时间尺度（τ <0.5百万年），不稳定性驱动的迁移的特征，也可能扰动类地行星的偏心率的数量与它们的观测值相当。我们讨论了这些限制的相对时间的类地行星形成，巨行星迁移，和所谓的月球晚重轰炸的起源3.9 +/-0.1 Ga前的影响。我们认为，满足这些动力学约束的最简单的方法可能是任何巨行星迁移的大部分在太阳系历史的第一个30 - 100万年完成。
We examine how the late divergent migration of Jupiter and Saturn may have perturbed the terrestrial planets. Using a modified secular model we have identified six secular resonances between the nu(5) frequency of Jupiter and Saturn and the four apsidal eigenfrequencies of the terrestrial planets (g(1-4)). We derive analytic upper limits on the eccentricity and orbital migration timescale of Jupiter and Saturn when these resonances were encountered to avoid perturbing the eccentricities of the terrestrial planets to values larger than the observed ones. Because of the small amplitudes of the j = 2, 3 terrestrial eigenmodes the g(2)-nu(5) and g(3)-nu(5) resonances provide the strongest constraints on giant planet migration. If Jupiter and Saturn migrated with eccentricities comparable to their present-day values, smooth migration with exponential timescales characteristic of planetesimal-driven migration (tau similar to 5-10 Myr) would have perturbed the eccentricities of the terrestrial planets to values greatly exceeding the observed ones. This excitation may be mitigated if the eccentricity of Jupiter was small during the migration epoch, migration was very rapid (e. g., tau less than or similar to 0.5Myr perhaps via planet-planet scattering or instability-driven migration) or the observed small eccentricity amplitudes of the j = 2, 3 terrestrial modes result from low probability cancellation of several large amplitude contributions. Results of orbital integrations show that very short migration timescales (tau < 0.5 Myr), characteristic of instability-driven migration, may also perturb the terrestrial planets' eccentricities by amounts comparable to their observed values. We discuss the implications of these constraints for the relative timing of terrestrial planet formation, giant planet migration, and the origin of the so-called Late Heavy Bombardment of the Moon 3.9 +/- 0.1 Ga ago. We suggest that the simplest way to satisfy these dynamical constraints may be for the bulk of any giant planet migration to be complete in the first 30-100 Myr of solar system history.