[论文解读] Dynamical rearrangement of super-Earths during disk dispersal I. Outline of the magnetospheric rebound model

Beibei Liu, Chris W. Ormel+1 more|UvA-DARE (University of Amsterdam)|Feb 7, 2017

Stellar, planetary, and galactic studies参考文献 81被引用 30

一句话总结

本文提出了磁层反弹模型，该模型认为在气体原行星盘消散期间，由于磁层空腔扩张驱动的外向迁移，动态重组了超级地球系统，使行星脱离平均运动共振。该模型表明，质量排序和恒星磁场所强决定最终的轨道周期比，从而调和了盘迁移理论与开普勒望远镜观测到的非共振超级地球系统之间的矛盾。

ABSTRACT

The Kepler mission has discovered that multiple close-in super-Earth planets are common around solar-type stars, but their period ratios do not show strong pile-ups near mean motion resonances (MMRs). One scenario is that super-Earths form in a gas-rich disk, and they interact gravitationally with the surrounding gas, inducing their orbital migration. Disk migration theory predicts, however, that planets would end up at resonant orbits due to their differential migration speed. Motivated by the discrepancy between observation and theory, we seek for a mechanism that moves planets out of resonances. We examine the orbital evolution of planet pairs near the magnetospheric cavity during the gas disk dispersal phase. Our study determines the conditions under which planets can escape resonances. We perform two-planet N-body simulations, varying the planet masses, stellar magnetic field strengths, disk accretion rates and gas disk depletion timescales. As planets migrate outward with the expanding magnetospheric cavity, their dynamical configurations can be rearranged. Migration of planets is substantial (minor) in a massive (light) disk. When the outer planet is more massive than the inner planet, the period ratio of two planets increases through outward migration. On the other hand, when the inner planet is more massive, the final period ratio tends to remain similar to the initial one. Larger stellar magnetic field strengths result in planets stopping their migration at longer periods. We highlight extit{magnetospheric rebound} as an important ingredient able to reconcile disk migration theory with observations. Even when planets are trapped into MMR during the early gas-rich stage, subsequent cavity expansion would induce substantial changes to their orbits, moving them out of resonance.

研究动机与目标

• 解决盘迁移理论预测共振捕获与开普勒观测显示极少超级地球处于平均运动共振之间的矛盾。
• 研究盘消散和磁层空腔扩张如何影响行星轨道构型，特别是在行星形成晚期阶段的影响。
• 确定行星脱离共振构型的条件，特别关注质量排序和恒星磁场所强的影响。
• 将该模型应用于开普勒-170和开普勒-180等真实系统，推断盘和恒星在盘消散时的参数。
• 提供一种机制，使超级地球能在原位形成或通过迁移形成，但仍能最终呈现非共振且与观测一致的轨道构型。

提出的方法

• 通过在磁层空腔与周围盘之间的界面处计算单边力矩，扩展了I型迁移理论。
• 使用新的力矩表达式进行双行星N体模拟，变化行星质量、盘吸积率（$\dot{M}_{\rm g}$）、盘耗散 timescales（$\tau_{\rm d}$）和恒星磁场所强（$B_\ast$）。
• 对行星-盘相互作用采用线性近似，并假设不形成间隙，适用于低质量超级地球（$M_{\rm p} \lesssim 10M_{\oplus}$）在湍流、高温盘中的情况。
• 将模型应用于开普勒-170和开普勒-180，通过拟合观测到的周期比，推断盘消散时的初始盘和恒星参数。
• 分析迁移 timescales 与空腔扩张 timescales 的相对关系，以评估动力学演化过程。
• 假设模拟全程保持希尔稳定性，确保双行星系统在盘消散后不发生动力学不稳定。

实验结果

研究问题

• RQ1 由扩张的磁层空腔引起的外向迁移能否解释开普勒超级地球中观测到的强共振聚集缺失？
• RQ2 行星的质量排序（内侧行星与外侧行星）如何影响空腔驱动迁移后的最终周期比？
• RQ3 恒星磁场所强在多大程度上影响超级地球的最终轨道位置？
• RQ4 磁层反弹模型能否重现已知系统（如开普勒-170和开普勒-180）的观测轨道构型？
• RQ5 为匹配多行星超级地球系统中观测到的周期比，盘消散时需要哪些盘和恒星参数？

主要发现

• 在质量较大的盘中（高 $\dot{M}_{\rm g}$，长 $\tau_{\rm d}$），外向迁移显著，但在轻质盘中（低 $\dot{M}_{\rm g}$，短 $\tau_{\rm d}$）可忽略，导致轨道变化极小。
• 当外侧行星质量大于内侧行星时，由于外向迁移，周期比显著增大，从而打破初始的共振构型。
• 当内侧行星质量更大时，最终周期比接近初始值，原始构型得以保持。
• 更强的恒星磁场所强导致更大的磁层空腔，使行星在更远的轨道周期处停止迁移。
• 该模型成功重现了开普勒-170和开普勒-180的观测轨道构型，使我们能够推断盘消散时的盘和恒星参数。
• 磁层反弹机制为超级地球在气体富集阶段形成但避免永久共振捕获提供了可行路径，调和了理论与开普勒观测结果。