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arXiv 2007.13096astro-ph.EPastro-ph.IMstat.ME
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根据光度变化进行外地球的贝叶斯动态制图

Bayesian Dynamic Mapping of an Exo-Earth from Photometric Variability

Hajime Kawahara, Kento Masuda

摘要:

直接成像的地外地球的光度变化传达了其表面的空间信息,可用于检索行星的二维地形和轴向倾斜(自旋轨道层析成像)。在这项研究中,我们放松了静态地理的假设,并提出了一个计算易处理的框架,适用于随时间变化的地理动态自旋轨道层析成像。首先,静态自旋轨道层析成像的贝叶斯框架重新使用高斯先验的贝叶斯逆问题的解析表达式。然后,我们通过时域中的高斯过程将这个分析框架扩展到时变框架,并提出解析表达式,使从地理,轴向倾斜,自旋旋转周期和高斯过程先验中的超参数的全联合后验分布进行有效采样。因此,对于总共$\sim 3 \times 10^6$参数,膝上型计算机仅需要0.3秒来采样一个以具有3,072个像素和1,024个时间网格的其他参数为条件的后验动态图。我们应用我们的动态映射方法的玩具模型,发现随时间变化的地理准确检索随着轴向倾斜和自旋旋转周期。此外,我们演示了使用动态自旋轨道层析成像与一个真正的多色光变曲线的地球观测深空气候观测。我们发现,从主成分分析的主导成分得到的快照大致捕捉到了地球上晴朗天空和多云地区的大尺度季节性变化。

英文摘要:

Photometric variability of a directly imaged exo-Earth conveys spatial information on its surface and can be used to retrieve a two-dimensional geography and axial tilt of the planet (spin-orbit tomography). In this study, we relax the assumption of the static geography and present a computationally tractable framework for dynamic spin-orbit tomography applicable to the time-varying geography. First, a Bayesian framework of static spin-orbit tomography is revisited using analytic expressions of the Bayesian inverse problem with a Gaussian prior. We then extend this analytic framework to a time-varying one through a Gaussian process in time domain, and present analytic expressions that enable efficient sampling from a full joint posterior distribution of geography, axial tilt, spin rotation period, and hyperparameters in the Gaussian-process priors. Consequently, it only takes 0.3 s for a laptop computer to sample one posterior dynamic map conditioned on the other parameters with 3,072 pixels and 1,024 time grids, for a total of $\sim 3 \times 10^6$ parameters. We applied our dynamic mapping method on a toy model and found that the time-varying geography was accurately retrieved along with the axial-tilt and spin rotation period. In addition, we demonstrated the use of dynamic spin-orbit tomography with a real multi-color light curve of the Earth as observed by the Deep Space Climate Observatory. We found that the resultant snapshots from the dominant component of a principle component analysis roughly captured the large-scale, seasonal variations of the clear-sky and cloudy areas on the Earth.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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