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arXiv 1105.4696astro-ph.EP
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根据Keck和HARPS最新径向速度数据得出的GJ876太阳系外行星系统的轨道结构

Orbital structure of the GJ876 extrasolar planetary system, based on the latest Keck and HARPS radial velocity data

Roman V. Baluev

备注：
36 pages, 11 figures, 3 tables; Accepted to Celestial Mechanics and Dynamical Astronomy
发表信息：
Celest. Mech. Dyn. Astron., 2011, V. 111 (1-2), P. 235-266; Erratum: Celest. Mech. Dyn. Astron., 2013, V.117 (2), P. 215
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摘要：

我们使用完整的径向速度数据阵列，包括最近公布的HARPS和凯克天文台集，来描述的行星系的轨道结构绕GJ 876。首先，我们提出并详细描述了一种快速的方法来拟合摄动轨道配置，基于积分的灵敏度方程推导出的原始$N$体问题的方程。此外，我们发现，这是不令人满意的处理现有的径向速度数据的GJ 876在传统的白噪声模型，因为实际的噪声出现自相关（并显示非白色的频谱）。这种相关性的时间尺度大约是几天，相关噪声的贡献大约是2 m/s（即，类似于Keck数据中的内部误差水平）。我们提出了一个变化的最大似然算法来估计系统的轨道配置，考虑到红噪声的影响。特别是，我们发现，在以前的研究中获得的最里面的行星\emph{d}的非零轨道偏心率，很可能是一个错误解释的红噪声的数据。除了某些轨道参数的偏移外，红噪声还使得拟合不确定度被系统地低估（而在传统的白噪声模型中，它们被处理）。此外，我们表明，最外层的行星的轨道偏心率实际上是不确定的，虽然有界的$\sim 0.2$。最后，我们调查可能的轨道非共面性的系统，并限制行星\emph{b}和\emph{c}轨道之间的相互倾斜的$5^\circ-15^\circ$，根据相互轨道节点的角位置。

英文摘要：

We use full available array of radial velocity data, including recently published HARPS and Keck observatory sets, to characterize the orbital configuration of the planetary system orbiting GJ876. First, we propose and describe in detail a fast method to fit perturbed orbital configuration, based on the integration of the sensitivity equations inferred by the equations of the original $N$-body problem. Further, we find that it is unsatisfactory to treat the available radial velocity data for GJ876 in the traditional white noise model, because the actual noise appears autocorrelated (and demonstrates non-white frequency spectrum). The time scale of this correlation is about a few days, and the contribution of the correlated noise is about 2 m/s (i.e., similar to the level of internal errors in the Keck data). We propose a variation of the maximum-likelihood algorithm to estimate the orbital configuration of the system, taking into account the red noise effects. We show, in particular, that the non-zero orbital eccentricity of the innermost planet \emph{d}, obtained in previous studies, is likely a result of misinterpreted red noise in the data. In addition to offsets in some orbital parameters, the red noise also makes the fit uncertainties systematically underestimated (while they are treated in the traditional white noise model). Also, we show that the orbital eccentricity of the outermost planet is actually ill-determined, although bounded by $\sim 0.2$. Finally, we investigate possible orbital non-coplanarity of the system, and limit the mutual inclination between the planets \emph{b} and \emph{c} orbits by $5^\circ-15^\circ$, depending on the angular position of the mutual orbital nodes.

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