Bayesian Dynamic Mapping of an Exo-Earth from Photometric Variability


Observed 8-day mean cloud fraction (top), the retrieved mean snapshot (bottom), for three different dates in January, May, and September in 2016 (from left to right). The range of the color bar is commonly fixed to -0.75 – 0 to compare three snapshot with each other. We note that the pixel value can be negative because these are the mapping of PC1, not albedo

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 ∼3×106 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.

Hajime Kawahara, Kento Masuda
Comments: 23 pages, 13 figures, accepted for publication in ApJ. The code is available online at this https URL . The retrieved dynamic map of a real light curve of the Earth (movie) can be viewed at this https URL
Subjects: Earth and Planetary Astrophysics (astro-ph.EP); Instrumentation and Methods for Astrophysics (astro-ph.IM); Methodology (stat.ME)
Cite as: arXiv:2007.13096 [astro-ph.EP] (or arXiv:2007.13096v1 [astro-ph.EP] for this version)
Submission history
From: Hajime Kawahara
[v1] Sun, 26 Jul 2020 10:34:40 UTC (4,055 KB)
https://arxiv.org/abs/2007.13096
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