arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0810.4076astro-ph
收藏

具有Turbulence、相互作用和阻尼的太阳系外行星系统中的平均运动共振

Mean Motion Resonances in Extrasolar Planetary Systems with Turbulence, Interactions, and Damping

Daniel Lecoanet, Fred C. Adams, Anthony M. Bloch

摘要:

本文继续了前人关于湍流对系外行星系统平均运动共振影响的研究。在形成行星的圆盘中预计会出现湍流,这些波动会影响共振配置。本文通过考虑行星之间的相互作用和磁盘可能施加的阻尼效应如何影响结果,扩展了以前的工作。这些物理过程的研究使用三种方法:数值积分的三体问题与额外的强迫由于湍流,模型方程,减少问题的随机驱动的振荡器,和福克-普朗克方程描述的时间演化的合奏系统。通过这种结合的方法,我们阐明了湍流如何从平均运动共振中去除太阳系外行星系统的物理学。正如预期的那样,具有足够大阻尼(耗散)的系统可以保持共振,尽管湍流强迫。在没有强阻尼的情况下,这些系统的合奏表现出两种制度的行为,其中的束缚态的分数作为幂律或指数下降。这两种类型的行为都可以通过本文开发的模型来理解。对于行星间具有弱相互作用的系统,模型简化为随机摆,束缚态的分数按幂律减小。对于高度相互作用的系统,动力学更加复杂,束缚态的分数呈指数下降。我们展示了行星间的相互作用如何导致Fokker-Planck方程中的漂移项,并解释了这种指数行为。除了澄清所涉及的物理过程,本文加强了发现,湍流意味着平均运动共振应该是罕见的。

英文摘要:

This paper continues previous work on the effects of turbulence on mean motion resonances in extrasolar planetary systems. Turbulence is expected to arise in the disks that form planets, and these fluctuations act to compromise resonant configurations. This paper extends previous work by considering how interactions between the planets and possible damping effects imposed by the disk affect the outcomes. These physical processes are studied using three approaches: numerical integrations of the 3-body problem with additional forcing due to turbulence, model equations that reduce the problem to stochastically driven oscillators, and Fokker-Planck equations that describe the time evolution of an ensemble of systems. With this combined approach, we elucidate the physics of how turbulence can remove extrasolar planetary systems from mean motion resonance. As expected, systems with sufficiently large damping (dissipation) can maintain resonance, in spite of turbulent forcing. In the absence of strong damping, ensembles of these systems exhibit two regimes of behavior, where the fraction of the bound states decreases as a power-law or as an exponential. Both types of behavior can be understood through the model developed herein. For systems with weak interactions between planets, the model reduces to a stochastic pendulum, and the fraction of bound states decreases as a power-law. For highly interactive systems, the dynamics are more complicated and the fraction of bound states decreases exponentially. We show how planetary interactions lead to drift terms in the Fokker-Planck equation and account for this exponential behavior. In addition to clarifying the physical processes involved, this paper strengthens the finding that turbulence implies that mean motions resonances should be rare.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑