Detecting extrasolar planets from stellar radial velocities using Bayesian evidence
Detecting extrasolar planets from stellar radial velocities using Bayesian evidence
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DOI：
10.1111/j.1365-2966.2011.18962.x
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发表时间：
2011-08-01
影响因子：
4.8
通讯作者：
Hobson, M. P.
中科院分区：
文献类型：
--
作者：
Feroz, F.;Balan, S. T.;Hobson, M. P.
恒星径向速度(RV)测量已被证明是探测太阳系外行星的一种非常成功的方法。由于存在多颗行星和轨道参数之间的各种简并，分析RV数据以确定太阳系外行星的参数是一项重大的统计挑战。确定观测数据支持的行星数量是一项更加困难的任务。贝叶斯模型选择通过计算具有不同行星数量的模型的边际后验概率，为这一问题提供了一个数学上严格的解决方案，但这种方法在太阳系外行星搜索中的使用受到了评估贝叶斯证据的计算成本的阻碍。然而，贝叶斯模型的选择有可能改善对现有观测数据的解释，并可能探测到尚未发现的行星。我们提出了一种新的有效的贝叶斯方法来确定太阳系外行星的数量，以及推断它们的轨道参数，而不必直接计算包含大量行星的模型的贝叶斯证据。取而代之的是，我们迭代地工作，并在每一次迭代中获得一个保守的下限，即在模型中包含另一颗行星的赔率比。我们将这种方法应用于包含一颗和两颗行星的模拟数据集，成功地恢复了正确的行星数量和可靠的轨道参数约束。我们还将我们的方法应用于HD 37124、47 Ursae Majoris和HD 10180的RV测量。对于HD 37124，我们确认目前的数据强烈支持三行星系统。我们发现了在大熊座47号存在第四颗行星的有力证据，但它的轨道周期可疑地接近一年，这让人对它的有效性产生了怀疑。对于HD 10180，我们找到了存在六行星系统的有力证据。
Stellar radial velocity (RV) measurements have proven to be a very successful method for detecting extrasolar planets. Analysing RV data to determine the parameters of the extrasolar planets is a significant statistical challenge owing to the presence of multiple planets and various degeneracies between orbital parameters. Determining the number of planets favoured by the observed data is an even more difficult task. Bayesian model selection provides a mathematically rigorous solution to this problem by calculating marginal posterior probabilities of models with different number of planets, but the use of this method in extrasolar planetary searches has been hampered by the computational cost of the evaluating Bayesian evidence. None the less, Bayesian model selection has the potential to improve the interpretation of existing observational data and possibly detect yet undiscovered planets. We present a new and efficient Bayesian method for determining the number of extrasolar planets, as well as for inferring their orbital parameters, without having to calculate directly the Bayesian evidence for models containing a large number of planets. Instead, we work iteratively and at each iteration obtain a conservative lower limit on the odds ratio for the inclusion of an additional planet into the model. We apply this method to simulated data sets containing one and two planets and successfully recover the correct number of planets and reliable constraints on the orbital parameters. We also apply our method to RV measurements of HD 37124, 47 Ursae Majoris and HD 10180. For HD 37124, we confirm that the current data strongly favour a three-planet system. We find strong evidence for the presence of a fourth planet in 47 Ursae Majoris, but its orbital period is suspiciously close to 1 yr, casting doubt on its validity. For HD 10180 we find strong evidence for a six-planet system.