[论文解读] Stability of the co-orbital resonance under dissipation: Application to its evolution in protoplanetary discs

A. Leleu, Gavin A. L. Coleman+1 more|arXiv (Cornell University)|Jan 22, 2019

Astrophysics and Star Formation Studies参考文献 3被引用 4

一句话总结

本文在原行星盘中针对通用耗散与质量演化，推导出共轨系外行星的稳定性判据，表明迁移与盘致力可使拉格朗日平衡点稳定或不稳定。关键结果表明，领先的大质量行星与共振链可稳定共轨构型，而向内迁移与质量不对称性则会增大 librations 振幅，可能导致行星脱离共振或增加偏心率与倾角，从而降低凌星可探测性。

ABSTRACT

Despite the existence of co-orbital bodies in the solar system, and the prediction of the formation of co-orbital planets by planetary system formation models, no co-orbital exoplanets (also called trojans) have been detected thus far. In this paper we investigate how a pair of co-orbital exoplanets would fare during their migration in a protoplanetary disc. To this end, we computed a stability criterion of the Lagrangian equilibria L4 and L5 under generic dissipation and slow mass evolution. Depending on the strength and shape of these perturbations, the system can either evolve towards the Lagrangian equilibrium, or tend to increase its amplitude of libration, possibly all the way to horseshoe orbits or even exiting the resonance. We estimated the various terms of our criterion using a set of hydrodynamical simulations, and show that the dynamical coupling between the disc perturbations and both planets have a significant impact on the stability: the structures induced by each planet in the disc perturb the dissipative forces applied on the other planets over each libration cycle. Amongst our results on the stability of co-orbitals, several are of interest to constrain the observability of such configurations: long-distance inward migration and smaller leading planets tend to increase the libration amplitude around the Lagrangian equilibria, while leading massive planets and belonging to a resonant chain tend to stabilise it. We also show that, depending on the strength of the dissipative forces, both the inclination and the eccentricity of the smaller of the two co-orbitals can be significantly increased during the inward migration of the co-orbital pair, which can have a significant impact on the detectability by transit of such configurations.

研究动机与目标

• 理解在原行星盘中经历 I 型与 II 型迁移时共轨系外行星的稳定性。
• 识别在盘致耗散与质量吸积作用下，共轨构型（L4/L5）被稳定或破坏的条件。
• 评估迁移、质量不对称性与共振链对 librations 振幅、偏心率与倾角演化的影响。
• 在演化盘条件下，评估通过凌星与径向速度方法探测共轨系外行星的可行性。
• 量化盘结构与行星-盘相互作用对共轨系统长期存续的影响。

提出的方法

• 为共轨共振在共面圆轨道情形下，基于通用耗散与缓慢质量演化，发展了一种可积解析模型。
• 基于迁移的破坏性与质量吸积的稳定性之间的平衡，推导出拉格朗日平衡点（L4/L5）的稳定性判据。
• 利用行星-盘相互作用的流体动力学模拟校准模型，以估算力矩与耗散项。
• 在具有不同盘轮廓与行星质量的演化原行星盘中，模拟长期演化过程。
• 分析行星质量比、迁移方向与共振链对共轨稳定性与轨道元素演化的影响。
• 使用解析与基于模拟的估计方法，研究倾角与偏心率的演化。

实验结果

研究问题

• RQ1 在何种条件下，向内迁移会稳定或破坏原行星盘中的共轨构型？
• RQ2 盘致力矩与质量吸积如何影响共轨行星的 librations 振幅？
• RQ3 行星质量比与共振链在稳定或破坏 L4/L5 拉格朗日平衡点中起何作用？
• RQ4 共轨迁移过程中偏心率与倾角如何演化，其对凌星可探测性有何影响？
• RQ5 共轨系统是否能维持足够长的稳定时间，以通过凌星计时变异或径向速度测量被探测到？

主要发现

• 向内迁移与质量不对称性倾向于增大 librations 振幅，可能导致共轨行星从蝌蚪轨道转变为马蹄轨或脱离共振状态。
• 领先的大质量行星显著稳定共轨构型，降低被抛射或脱离共振的风险。
• 当存在第三颗行星的共振链时，可稳定原本不稳定的共轨系统，即使忽略螺旋臂扰动的影响。
• 质量吸积可稳定共轨行星，但该效应在早期迁移阶段最强，随时间减弱。
• 在向内迁移过程中，偏心率与倾角可能显著激发，尤其当盘阻尼较弱时，导致凌星概率降低。
• 具有相互倾角的共轨系统可能沿 m1I1 = m2I2, Ω1 = Ω2 + π 方向形成，尤其当较高质量行星形成深隙时，可降低可探测性。