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arXiv 1809.05490astro-ph.EPastro-ph.GA
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用新的先验方法改进不完整轨道的轨道估计--从黑洞到行星的应用

Improving Orbit Estimates for Incomplete Orbits with a New Approach to Priors -- with Applications from Black Holes to Planets

K. Kosmo O'Neil, G. D. Martinez, A. Hees, A. M. Ghez, T. Do, G. Witzel, Q. Konopacky, E. E. Becklin, D. S. Chu, J. Lu, K. Matthews, S. Sakai

摘要:

我们提出了一种新的方法贝叶斯先验概率分布(先验),可以提高低相位覆盖轨道,其中数据覆盖不到约40%的轨道的轨道解决方案。在低相位覆盖的情况下,例如银河系中心的恒星轨道或直接成像的系外行星,数据具有低约束力,因此先验可能会使参数估计产生偏差,并产生低估的置信区间。在轨道拟合中通常假设的均匀先验,因此是臭名昭著的。我们提出了一个新的基于观测的先验范式,是基于均匀的观测。我们比较性能的可观测的先验和普遍假设的统一先验使用银河系中心和直接成像的系外行星(HR 8799)的数据。基于可观测的先验可以将模型参数中的偏差减少两倍,并且有助于避免对具有小于约40%相位覆盖的模拟的置信区间的低估。在这个阈值以上,具有足够相位覆盖的物体的轨道解,如S 0 -2,在银河系中心具有全相位覆盖的短周期恒星,与以前发表的结果一致。在这个阈值以下,基于观测的先验限制了先验优势区域中的先验影响,并增加了数据影响。使用基于观测的先验,HR 8799的轨道分析有利于较低的偏心率轨道,并提供了更有力的证据,表明这四颗行星有一个一致的倾角约30度,在1西格玛。该分析还考虑到共面性的可能性。我们提出的指标,以量化改进的轨道估计与不同的先验,使可观测的先验框架可以测试和实施其他低相位覆盖轨道。

英文摘要:

We propose a new approach to Bayesian prior probability distributions (priors) that can improve orbital solutions for low-phase-coverage orbits, where data cover less than approximately 40% of an orbit. In instances of low phase coverage such as with stellar orbits in the Galactic center or with directly-imaged exoplanets, data have low constraining power and thus priors can bias parameter estimates and produce under-estimated confidence intervals. Uniform priors, which are commonly assumed in orbit fitting, are notorious for this. We propose a new observable-based prior paradigm that is based on uniformity in observables. We compare performance of this observable-based prior and of commonly assumed uniform priors using Galactic center and directly-imaged exoplanet (HR 8799) data. The observable-based prior can reduce biases in model parameters by a factor of two and helps avoid under-estimation of confidence intervals for simulations with less than about 40% phase coverage. Above this threshold, orbital solutions for objects with sufficient phase coverage such as S0-2, a short-period star at the Galactic center with full phase coverage, are consistent with previously published results. Below this threshold, the observable-based prior limits prior influence in regions of prior dominance and increases data influence. Using the observable-based prior, HR 8799 orbital analyses favor lower eccentricity orbits and provide stronger evidence that the four planets have a consistent inclination around 30 degrees to within 1-sigma. This analysis also allows for the possibility of coplanarity. We present metrics to quantify improvements in orbital estimates with different priors so that observable-based prior frameworks can be tested and implemented for other low-phase-coverage orbits.

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