Bayesian Dynamic Mapping of an Exo-Earth from Photometric Variability

Abstract

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.

arXiv comment23 pages, 13 figures, accepted for publication in ApJ. The code is available online at https://github.com/HajimeKawahara/sot . The retrieved dynamic map of a real light curve of the Earth (movie) can be viewed at https://www.youtube.com/watch?v=rGMWbAUAv4Y

References in corpus (17)

• emcee: The MCMC Hammer
• The NumPy array: a structure for efficient numerical computation
• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Alien Maps of an Ocean-Bearing World
• Characterization of extrasolar terrestrial planets from diurnal photometric variability
• Colors of a Second Earth: Estimating the fractional areas of ocean, land, and vegetation of Earth-like exoplanets
• Mapping Earth Analogs from Photometric Variability: Spin-Orbit Tomography for Planets in Inclined Orbits
• Global Mapping of Earth-like Exoplanets from Scattered Light Curves
• Mapping Clouds and Terrain of Earth-like Planets from Photometric Variability: Demonstration with Planets in Face-on Orbits
• Using Deep Space Climate Observatory Measurements to Study the Earth as An Exoplanet
• Inferring Planetary Obliquity Using Rotational & Orbital Photometry
• Earth as an Exoplanet: A Two-dimensional Alien Map
• exocartographer: A Bayesian Framework for Mapping Exoplanets in Reflected Light
• Frequency Modulation of Directly Imaged Exoplanets: Geometric Effect as a Probe of Planetary Obliquity
• Global Mapping of an Exo-Earth using Sparse Modeling
• Global Mapping of the Surface Composition on an Exo-Earth using Color Variability
• Obliquity of an Earth-like planet from frequency modulation of its direct imaged lightcurve: mock analysis from general circulation model simulation

Cited by in corpus (6)

• Analytic Light Curves in Reflected Light: Phase Curves, Occultations, and Non-Lambertian Scattering for Spherical Planets and Moons
• Mapping the Surface of Partially Cloudy Exoplanets is Hard
• Water versus land on temperate rocky planets
• Planet cartography with neural learned regularization
• Global Mapping of Surface Composition on an Exo-Earth Using Sparse Modeling
• Exoplanet Cartography using Convolutional Neural Networks