Rotational Spectral Unmixing of Exoplanets: Degeneracies between Surface Colors and Geography

TL;DR

This paper explores the mathematical degeneracies in unmixing exoplanet spectra, revealing limitations and potential constraints in identifying surface compositions from disk-integrated light.

Contribution

It demonstrates the degeneracy between surface colors and geography in spectral unmixing and proposes constraints based on albedo limits to improve surface identification.

Findings

Degeneracy exists between surface colors and spatial distribution.

Constraints from albedo limits can help recover surface spectra.

Surface identification is easier with larger coverage and extreme spectral values.

Abstract

Unmixing the disk-integrated spectra of exoplanets provides hints about heterogeneous surfaces that we cannot directly resolve in the foreseeable future. It is particularly important for terrestrial planets with diverse surface compositions like Earth. Although previous work on unmixing the spectra of Earth from disk-integrated multi-band light curves appeared successful, we point out a mathematical degeneracy between the surface colors and their spatial distributions. Nevertheless, useful constraints on the spectral shape of individual surface types may be obtained from the premise that albedo is everywhere between 0 and 1. We demonstrate the degeneracy and the possible constraints using both mock data based on a toy model of Earth, as well as real observations of Earth. Despite the severe degeneracy, we are still able to recover an approximate albedo spectrum for an ocean. In general, we find that surfaces are easier to identify when they cover a large fraction of the planet and when their spectra approach zero or unity in certain bands.