[论文解读] Highly inclined and eccentric massive planets I: Planet-disc interactions

Bertram Bitsch, A. Crida+2 more|Repository of the University of Namur|May 31, 2013

Astrophysics and Star Formation Studies参考文献 41被引用 46

一句话总结

本论文利用NIRVANA代码的3D流体动力学模拟，研究了大质量、高倾角行星与原行星盘的相互作用。推导出偏心率和倾角的实证阻尼公式，作为行星质量、偏心率和倾角的函数，表明高质​​量行星在最终阻尼前可与盘发生科瓦伊循环，导致中平面迁移，并在倾角降低后出现偏心率激发。

ABSTRACT

In the Solar System, planets have a small inclination with respect to the equatorial plane of the Sun, but there is evidence that in extrasolar systems the inclination can be very high. This spin-orbit misalignment is unexpected, as planets form in a protoplanetary disc supposedly aligned with the stellar spin. Planet-planet interactions are supposed to lead to a mutual inclination, but the effects of the protoplanetary disc are still unknown. We investigate therefore planet-disc interactions for planets above 1M_Jup. We check the influence of the inclination i, eccentricity e, and mass M_p of the planet. We perform 3D numerical simulations of protoplanetary discs with embedded high-mass planets. We provide damping formulae for i and e as a function of i, e, and M_p that fit the numerical data. For highly inclined massive planets, the gap opening is reduced, and the damping of i occurs on time-scales of the order of 10^-4 deg/yr M_disc/(0.01 M_star) with the damping of e on a smaller time-scale. While the inclination of low planetary masses (<5M_Jup) is always damped, large planetary masses with large i can undergo a Kozai-cycle with the disc. These Kozai-cycles are damped in time. Eccentricity is generally damped, except for very massive planets (M_p = 5M_Jup) where eccentricity can increase for low inclinations. The dynamics tends to a final state: planets end up in midplane and can then, over time, increase their eccentricity as a result of interactions with the disc. The interactions with the disc lead to damping of i and e after a scattering event of high-mass planets. If i is sufficiently reduced, the eccentricity can be pumped up because of interactions with the disc. If the planet is scattered to high inclination, it can undergo a Kozai-cycle with the disc that makes it hard to predict the exact movement of the planet and its orbital parameters at the dispersal of the disc.

研究动机与目标

• 理解原行星盘如何影响高轨道倾角大质量行星的倾角与偏心率。
• 确定行星-盘相互作用是否能在大质量、高倾角系统中导致倾角与偏心率的阻尼或激发。
• 推导倾角与偏心率的实证阻尼定律，作为行星质量、偏心率与倾角的函数。
• 研究盘诱导的科瓦伊循环在大质量、倾斜行星动力学演化中的作用。

提出的方法

• 使用显式/隐式NIRVANA代码进行3D流体动力学模拟，采用等温状态方程。
• 固定大质量行星的轨道元素（最高达5 M_Jup），以隔离盘相互作用的影响。
• 通过球坐标网格单元对盘的角动量与偏心率进行质量加权平均，以计算全局倾角与偏心率演化。
• 将局部角动量矢量从球坐标系转换至笛卡尔坐标系，以实现一致的全局平均。
• 从倾角与偏心率演化的时间序列数据中推导阻尼 timescales。
• 利用洛伦兹共振理论与增长率分析（γ）估算偏心率增加的潜力，假设盘的偏心率可忽略不计。

实验结果

研究问题

• RQ1 盘如何阻尼高轨道倾角大质量行星的倾角？
• RQ2 倾角与偏心率阻尼 timescales 对行星质量、偏心率与倾角的依赖关系如何？
• RQ3 行星-盘相互作用是否会导致大质量行星的偏心率增长，特别是在低倾角情况下？
• RQ4 高质​​量、高倾角行星是否与盘发生科瓦伊型循环？若发生，其阻尼机制如何？
• RQ5 在盘消散后，初始具有高倾角与高偏心率的大质量行星的最终轨道构型是什么？

主要发现

• 对于大质量行星，倾角阻尼 timescales 约为每 (M_disc / 0.01 M_*) 10^-4 deg/year。偏心率阻尼发生在更短 timescales。
• 对于质量低于5 M_Jup的行星，倾角始终被阻尼；然而，对于高倾角下的更高质量行星，可发生与盘的科瓦伊循环，且随时间被阻尼。
• 偏心率通常被阻尼，但对于接近5 M_Jup且倾角较低的行星，由于盘驱动的共振效应，偏心率可能增加。
• 对于高度倾斜的大质量行星，间隙打开显著减弱，削弱了标准的II型迁移机制。
• 在倾角被阻尼后，行星向中平面迁移，并可能因持续的盘相互作用而随后经历偏心率激发。
• 所推导的倾角与偏心率阻尼公式为建模具有轨道倾角的大质量行星迁移提供了预测性框架。