2：1共振径向速度轨道与偏心轨道的分离及对HD 27894的个例研究
Disentangling 2:1 resonant radial velocity orbits from eccentric ones and a case study for HD 27894
摘要：
在径向速度观测中，如果数据稀疏且测量精度不足以区分这些模型，则一对接近2：1轨道共振的太阳系外行星可能被误解为单个偏心行星。我们确定了所谓的单行星RV检测系统的比例，其中2：1共振对行星也是一个可行的模型，并解决了模型如何可以解开的问题。通过模拟，我们量化了应用错误模型所产生的失配。模型的替代品说明使用假设的单行星系统HD 27894，我们还研究了近2：1共振解的动力学稳定性。从拟合的单行星开普勒周围的数据分散，我们发现，对于$254$假定的单行星系统的$74\% $，2：1共振对不能被排除作为一个可行的模型，因为错误的模型所造成的误差小于分散。对于$187$恒星，$χ^2$ -概率可用于拒绝开普勒模型，对于恒星的$54\% $，置信度为$95\% $，对于恒星的$39\% $，置信度为$99.9\% $。对于HD 27894来说，当增加一颗低质量的行星时，得到了相当大的拟合改进，这颗行星的轨道周期接近已知木星的一半。动力学分析表明，该系统是稳定的，当两个行星最初被放置在圆形轨道。对于完全开普勒轨道，只有当内行星的偏心率被限制在$<0.3$时，才能得到稳定的系统。应该仔细检查据称RV检测到的单行星系统的很大一部分，以确定包含近2：1共振行星对的系统的比例。了解这些系统的丰度将使我们能够修正太阳系外行星的偏心率分布，并为行星系统的形成提供直接的约束。
英文摘要：
In radial velocity observations, a pair of extrasolar planets near a 2:1 orbital resonance can be misinterpreted as a single eccentric planet, if data are sparse and measurement precision insufficient to distinguish between these models. We determine the fraction of alleged single-planet RV detected systems for which a 2:1 resonant pair of planets is also a viable model and address the question of how the models can be disentangled. By simulation we quantified the mismatch arising from applying the wrong model. Model alternatives are illustrated using the supposed single-planet system HD 27894 for which we also study the dynamical stability of near-2:1 resonant solutions. From the data scatter around the fitted single-planet Keplerians, we find that for $74\% $ of the $254$ putative single-planet systems, a 2:1 resonant pair cannot be excluded as a viable model, since the error due to the wrong model is smaller than the scatter. For $187$ stars $χ^2$-probabilities can be used to reject the Keplerian models with a confidence of $95\% $ for $54\% $ of the stars and with $99.9\% $ for $39\% $ of the stars. For HD 27894 a considerable fit improvement is obtained when adding a low-mass planet near half the orbital period of the known Jovian planet. Dynamical analysis demonstrates that this system is stable when both planets are initially placed on circular orbits. For fully Keplerian orbits a stable system is only obtained if the eccentricity of the inner planet is constrained to $<0.3$. A large part of the allegedly RV detected single-planet systems should be scrutinized in order to determine the fraction of systems containing near-2:1 resonant pairs of planets. Knowing the abundance of such systems will allow us to revise the eccentricity distribution for extrasolar planets and provide direct constraints for planetary system formation.
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