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arXiv 2005.06498astro-ph.EPastro-ph.SR
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确定周双星轨道根数的数值方法及其在周双星行星和冥王星-冥卫一卫星中的应用

A Numerical Method for Determining the Elements of Circumbinary Orbits and Its Application to Circumbinary Planets and the Satellites of Pluto-Charon

Jason Man Yin Woo, Man Hoi Lee

摘要:

围绕双星系统运行的行星和卫星存在于太阳系和太阳系外的行星系中。它们的轨道可能与开普勒轨道有很大的不同,如果它们接近双星,并且次级与初级质量比很高。环双星轨道的正确描述是在行星频率$κ_0$下的自由偏心率$e_{\rm free}$,在平均运动$n_0$下的强迫偏心率$e_{\rm forced}$,以及由双星势的非轴对称分量强迫的更高频率的振荡。我们表明,这些条款的振幅和频率的精确数值,可以提取从数值轨道积分,通过应用快速傅立叶变换(FFT)的圆柱体之间的距离circumbinary对象和二进制的质量质心作为时间的函数。我们将这种方法应用到三个开普勒环联行星和冥王星的卫星冥卫一。对于冥王星-冥卫一的卫星冥河,$κ_0$和$e_{\rm free}$的FFT结果分别与一阶解析值和Showalter & Hamilton(2015)报告的值有显著差异。我们发现,$κ_0$的偏差可能是由于3:1平均运动共振的影响,并讨论了较低的值$e_{\rm free}$的影响。

英文摘要:

Planets and satellites orbiting a binary system exist in the solar system and extrasolar planetary systems. Their orbits can be significantly different from Keplerian orbits, if they are close to the binary and the secondary-to-primary mass ratio is high. A proper description of a circumbinary orbit is in terms of the free eccentricity $e_{\rm free}$ at the epicyclic frequency $κ_0$, forced eccentricity $e_{\rm forced}$ at the mean motion $n_0$, and oscillations at higher frequencies forced by the non-axisymmetric components of the binary's potential. We show that accurate numerical values for the amplitudes and frequencies of these terms can be extracted from numerical orbit integrations by applying fast Fourier transformation (FFT) to the cylindrical distance between the circumbinary object and the center of mass of the binary as a function of time. We apply this method to three Kepler circumbinary planets and the satellites of Pluto-Charon. For the satellite Styx of Pluto-Charon, the FFT results for $κ_0$ and $e_{\rm free}$ differ significantly from the first-order analytic value and the value reported by Showalter & Hamilton (2015), respectively. We show that the deviation in $κ_0$ is likely due to the effect of the 3:1 mean-motion resonance and discuss the implications of the lower value for $e_{\rm free}$.

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