Global Mapping of the Surface Composition on an Exo-Earth using Color Variability

Abstract

Photometric variation of a directly imaged planet contains information on both the geography and spectra of the planetary surface. We propose a novel technique that disentangles the spatial and spectral information from the multi-band reflected light curve. This will enable us to compose a two-dimensional map of the surface composition of a planet with no prior assumption on the individual spectra, except for the number of independent surface components. We solve the unified inverse problem of the spin-orbit tomography and spectral unmixing by generalizing the non-negative matrix factorization (NMF) using a simplex volume minimization method. We evaluated our method on a toy cloudless Earth and observed that the new method could accurately retrieve the geography and unmix spectral components. Furthermore, our method is also applied to the real-color variability of the Earth as observed by Deep Space Climate Observatory (DSCOVR). The retrieved map explicitly depicts the actual geography of the Earth and unmixed spectra capture features of the ocean, continents, and clouds. It should be noted that, the two unmixed spectra consisting of the reproduced continents resemble those of soil and vegetation.

arXiv comment20 pages, 14 figures, accepted for publication in ApJ. The code is available online at https://github.com/HajimeKawahara/sot. updated to match the published version

References in corpus (21)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications
• 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
• Identifying the rotation rate and the presence of dynamic weather on extrasolar Earth-like planets from photometric observations
• Mapping Earth Analogs from Photometric Variability: Spin-Orbit Tomography for Planets in Inclined Orbits
• Global Mapping of Earth-like Exoplanets from Scattered Light Curves
• Detecting Ocean Glint on Exoplanets Using Multiphase Mapping
• Lightcurves of Stars & Exoplanets: Estimating Inclination, Obliquity, and Albedo
• Colors of a Second Earth II: Effects of Clouds on Photometric Characterization of Earth-like Exoplanets
• Determining Reflectance Spectra of Surfaces and Clouds on Exoplanets
• 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
• Algorithms and Comparisons of Non-negative Matrix Factorization with Volume Regularization for Hyperspectral Unmixing
• 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
• Rotational Spectral Unmixing of Exoplanets: Degeneracies between Surface Colors and Geography
• Analytic Reflected Lightcurves for Exoplanets

Cited by in corpus (9)

• Global Mapping of an Exo-Earth using Sparse Modeling
• Earth as a Proxy Exoplanet: Deconstructing and Reconstructing Spectrophotometric Light Curves
• Bayesian Dynamic Mapping of an Exo-Earth from Photometric Variability
• Analytic Light Curves in Reflected Light: Phase Curves, Occultations, and Non-Lambertian Scattering for Spherical Planets and Moons
• Measuring the variability of directly imaged exoplanets using vector Apodizing Phase Plates combined with ground-based differential spectrophotometry
• The pale blue dot: using the Planetary Spectrum Generator to simulate signals from hyper realistic exo-Earths
• 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