A general model of resonance capture in planetary systems: first- and second-order resonances
A general model of resonance capture in planetary systems: first- and second-order resonances
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DOI：
10.1111/j.1365-2966.2011.18201.x
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发表时间：
2010-12
影响因子：
4.8
通讯作者：
A. Mustill;M. Wyatt
中科院分区：
文献类型：
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作者：
A. Mustill;M. Wyatt
平均运动共振是我们太阳系和太阳系外行星系统的共同特征。当物体的轨道半长轴改变时，例如当它们迁移通过原行星盘时，它们可以被困在共振中。我们使用一个哈密顿模型彻底调查的捕获行为的第一和第二阶共振。使用这种方法，所有相同阶数的共振都可以用一个方程来描述，并通过适当的缩放来应用于特定的共振。我们专注于一个物体是无质量的测试粒子而另一个是大质量行星的极限。我们量化捕获到共振的概率取决于行星和粒子的相对迁移率，以及粒子的偏心率。共振捕获失败的高迁移率，并具有更高的偏心率，虽然对于某些迁移率，捕获概率峰值在一个有限的偏心率降低的概率。更大质量的行星可以捕获更高偏心率和迁移率的粒子。我们还计算了被捕获粒子的天平动振幅和天平动中心的偏移量，以及如果没有捕获，偏心率的变化。初始偏心率越大，天平动振幅越大。该模型允许一个完整的描述粒子的行为，因为它连续遇到几个共振。包含积分网格输出的数据文件将在线提供。我们讨论了几种情况下的影响：（一）行星迁移通过气体盘捕获其他行星或微行星的共振：我们发现，与经典的处方I型迁移，捕获到二阶共振是不可能的，和较低质量的行星或那些远离星星应该捕获物体在一阶共振更接近行星比高质量的行星或那些更接近星星。如果迁移速度足够快，行星就不会把任何物体困在它的共振中。我们认为，目前的天平动振幅的行星可能是他们的偏心率在捕获时代的签名，与高天平动振幅表明高偏心率（例如HD 128311）。(ii)行星迁移通过碎片盘：我们发现由此产生的动力学结构强烈依赖于迁移率和星子偏心率。将其转换为空间结构，我们预计块状度将从e = 0.01的显著水平降低到e = 0.1的不存在。(iii)通过坡印廷-罗伯逊（PR）阻力的尘埃迁移：我们预测，火星应该有自己的共振环的粒子捕获黄道带云，捕获概率是地球的25%，与公布的上限共振环一致。总之，利用汉密尔顿模型可以快速解释太阳系外行星和柯伊伯带天体的共振特性，并可以快速生成碎片盘结构的合成图像，这将有助于预测和解释阿塔卡马大型毫米波阵列（阿尔马）、达尔文/类地行星探测器（TPF）或类似飞行任务所拍摄的盘图像。（减）
Mean motion resonances are a common feature of both our own Solar system and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semimajor axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first- and second-order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a massive planet. We quantify how the probability of capture into a resonance depends on the relative migration rate of the planet and particle, and the particle's eccentricity. Resonant capture fails for high migration rates, and has decreasing probability for higher eccentricities, although for certain migration rates, capture probability peaks at a finite eccentricity. More massive planets can capture particles at higher eccentricities and migration rates. We also calculate libration amplitudes and the offset of the libration centres for captured particles, and the change in eccentricity if capture does not occur. Libration amplitudes are higher for larger initial eccentricity. The model allows for a complete description of a particle's behaviour as it successively encounters several resonances. Data files containing the integration grid output will be available online. We discuss implications for several scenarios: (i) Planet migration through gas discs trapping other planets or planetesimals in resonances: we find that, with classical prescriptions for Type I migration, capture into second-order resonances is not possible, and lower mass planets or those further from the star should trap objects in first-order resonances closer to the planet than higher mass planets or those closer to the star. For fast enough migration, a planet can trap no objects into its resonances. We suggest that the present libration amplitude of planets may be a signature of their eccentricities at the epoch of capture, with high libration amplitudes suggesting high eccentricity (e.g. HD 128311). (ii) Planet migration through a debris disc: we find the resulting dynamical structure depends strongly both on migration rate and on planetesimal eccentricity. Translating this to spatial structure, we expect clumpiness to decrease from a significant level at e ≲ 0.01 to non-existent at e ≳ 0.1. (iii) Dust migration through Poynting-Robertson (PR) drag: we predict that Mars should have its own resonant ring of particles captured from the zodiacal cloud, and that the capture probability is ≲25 per cent that of the Earth, consistent with published upper limits for its resonant ring. To summarize, the Hamiltonian model will allow quick interpretation of the resonant properties of extrasolar planets and Kuiper Belt Objects, and will allow synthetic images of debris disc structures to be quickly generated, which will be useful for predicting and interpreting disc images made with Atacama Large Millimeter Array (ALMA), Darwin/Terrestrial Planet Finder (TPF) or similar missions. (Less)