包括新生盘、旋进和扁率的基于共振项的模型：对GJ 876的应用
A resonant-term-based model including a nascent disk, precession, and oblateness: application to GJ 876
摘要：
研究两颗共振行星围绕一颗恒星或两颗共振卫星围绕一颗行星的轨道运行，往往依赖于一些共振和长期的条款，以获得系统的动力学演化的代表性定量描述。我们提出了一个半解析模型，跟踪轨道演化的任何两个共振机构在第一至第四阶偏心率或倾斜为基础的共振为主的共振和世俗的参数的用户的选择。通过考虑天平动宽度随不同轨道参数的变化，我们确定了引起不同共振“深度”的相空间区域，并提出了模型天平动轮廓的方法。我们将该模型应用于GJ 876太阳系外行星系统，量化相关的共振和长期的贡献的相对重要性，从而评估的善良的共同近似表示系统的假定占主导地位的条款。我们通过揭示二阶而非一阶解产生的不自然的天平动中心，并通过证明真正的轨道解位于三阶和四阶解之间的某个地方，来强调使用“阶”作为轨道解精度度量的危险。我们还提出了用于将扰动从中心体扁率和岁差，和原行星或原卫星薄盘间隙，到一个共振系统的公式。我们量化这些贡献的GJ 876系统，从而突出的条件必须存在的多行星系外系统受到这些因素的显着影响。我们发现，足够大的磁盘可能会将共振天平动转换为循环，这样的磁盘诱导的签名可能会为未来的系外行星系统的研究提供限制。
英文摘要：
Investigations of two resonant planets orbiting a star or two resonant satellites orbiting a planet often rely on a few resonant and secular terms in order to obtain a representative quantitative description of the system's dynamical evolution. We present a semianalytic model which traces the orbital evolution of any two resonant bodies in a first- through fourth-order eccentricity or inclination-based resonance dominated by the resonant and secular arguments of the user's choosing. By considering the variation of libration width with different orbital parameters, we identify regions of phase space which give rise to different resonant ''depths,'' and propose methods to model libration profiles. We apply the model to the GJ 876 extrasolar planetary system, quantify the relative importance of the relevant resonant and secular contributions, and thereby assess the goodness of the common approximation of representing the system by just the presumably dominant terms. We highlight the danger in using ''order'' as the metric for accuracy in the orbital solution by revealing the unnatural libration centers produced by the second-order, but not first-order, solution, and by demonstrating that the true orbital solution lies somewhere ''in-between'' the third- and fourth-order solutions. We also present formulas used to incorporate perturbations from central-body oblateness and precession, and a protoplanetary or protosatellite thin disk with gaps, into a resonant system. We quantify these contributions to the GJ 876 system, and thereby highlight the conditions which must exist for multi-planet exosystems to be significantly influenced by such factors. We find that massive enough disks may convert resonant libration into circulation; such disk-induced signatures may provide constraints for future studies of exoplanet systems.
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