[论文解读] The dynamical evolution of close-in binary systems formed by a super-Earth and its host star. Case of the Kepler-21 system

Luna, Santiago, Navone, Hugo+1 more|arXiv (Cornell University)|Jul 24, 2019

Stellar, planetary, and galactic studies被引用 2

一句话总结

本文提出了一种正则化长期形式化方法，用于建模近轨道超级海卫系统中潮汐力与三轴性驱动的动力学演化，以开普勒-21b为例。结果表明，潮汐力与三轴性力矩显著影响轨道与自转演化，潮汐锁定时间对流变参数极为敏感，且确认由于内部强烈耗散，开普勒-21b很可能处于同步自转状态。

ABSTRACT

The aim of this work is to develop a formalism for the study of the secular evolution of a binary system which includes interaction due to the tides that each body imparts on the other. We also consider the influence of the $J_2$-related secular terms on the orbital evolution and the torque, caused by the triaxiality, on the rotational evolution, both of which are associated only to one of the bodies. We apply these set of equations to the study of the orbital and rotational evolution of a binary system composed of a rocky planet and its host star in order to characterize the dynamical evolution at work, particularly near spin-orbit resonances. We used the equations of motion that give the time evolution of the orbital elements and the spin rates of each body to study the time evolution of the Kepler-21 system as an example of how the formalism that we have developed can be applied. We obtained a set of equations of motion without singularities for vanishing eccentricities and inclinations. This set gives, on one hand, the time evolution of the orbital elements due to the tidal potentials generated by both members of the system as well as the triaxiality of one of them. On the other hand, it gives the time evolution of the stellar spin rate due to the corresponding tidal torque and of the planet's rotation angle due to both the tidal and triaxiality-induced torques. We found that for the parameters and the initial conditions explored here, the tidally and triaxiality-induced modifications of the tidal modes can be more significative than expected and that the time of tidal synchronization strongly depends on the values of the rheological parameters.

研究动机与目标

• 为具有相互潮汐作用与三轴性的双星系统，发展一种无奇点的长期轨道与自转演化形式化方法。
• 建模一颗超级海卫与其恒星的动力学演化，重点关注自转-轨道共振与潮汐锁定。
• 评估潮汐耗散与J2相关长期项对轨道元素与自转速率的影响。
• 评估行星三轴性在自转演化与共振捕获中的作用。

提出的方法

• 基于Boué & Efroimsky (2019)的潮汐与三轴势，推导轨道元素与自转速率的长期运动方程。
• 通过流变模型（如麦克斯韦粘弹性模型）引入潮汐耗散，适用于恒星与行星。
• 包含J2相关长期项以描述轨道进动，以及三轴性引起的力矩以描述行星自转演化。
• 使用在偏心率与倾角趋近零时有效的正则化方程，避免数值奇点。
• 对开普勒-21系统进行全方程组的数值积分，采用真实初始条件。
• 应用基于观测约束与理论模型推导的流变参数与物理属性。

实验结果

研究问题

• RQ1 相互潮汐作用与行星三轴性如何共同影响近轨道超级海卫系统的轨道与自转演化？
• RQ2 开普勒-21b的潮汐锁定时间尺度是多少？其对流变参数的敏感性如何？
• RQ3 J2相关长期项与三轴性引起的力矩在多大程度上影响轨道进动与自转演化？
• RQ4 系统是否可能长期捕获在高于同步的自转-轨道共振状态？其决定因素是什么？
• RQ5 潮汐力与三轴性力矩如何改变开普勒-21系统中的近日点与交点进动速率？

主要发现

• 该形式化方法成功避免了偏心率或倾角趋近零时的奇点，实现了稳定的数值积分。
• 潮汐模式受潮汐与三轴性共同修正的影响，比以往认为的更为显著，尤其在共振附近。
• 潮汐锁定时间对流变参数极为敏感，不同粘度下可能相差数个数量级。
• 由于内部强烈耗散导致麦克斯韦松弛时间缩短，开普勒-21b很可能处于1:1自转-轨道同步状态。
• 开普勒-21的轨道倾角演化具有反直觉特征且依赖于系统参数，潮汐相互作用可能使i1增加或减少，取决于参数组合。
• 轨道衰减与圆化时间尺度为上限值，当行星接近洛希极限时因更强潮汐力而增加。