Surface Mapping of Earth-like Exoplanets using Single Point Light Curves

Summary

The protocol extracts information from light curves of exoplanets and constructs their surface maps. It uses light curves of Earth, which serves as a proxy exoplanet, to demonstrate the approach.

Abstract

Spatially resolving exoplanet features from single-point observations is essential for evaluating the potential habitability of exoplanets. The ultimate goal of this protocol is to determine whether these planetary worlds harbor geological features and/or climate systems. We present a method of extracting information from multi-wavelength single-point light curves and retrieving surface maps. It uses singular value decomposition (SVD) to separate sources that contribute to light curve variations and infer the existence of partially cloudy climate systems. Through analysis of the time series obtained from SVD, physical attributions of principal components (PCs) could be inferred without assumptions of any spectral properties. Combining with viewing geometry, it is feasible to reconstruct surface maps if one of the PCs are found to contain surface information. Degeneracy originated from convolution of the pixel geometry and spectrum information determines the quality of reconstructed surface maps, which requires the introduction of regularization. For the purpose of demonstrating the protocol, multi-wavelength light curves of Earth, which serves as a proxy exoplanet, are analyzed. Comparison between the results and the ground truth is presented to show the performance and limitation of the protocol. This work provides a benchmark for future generalization of exoplanet applications.

Introduction

Identifying habitable worlds is one of the ultimate goals in astrobiology¹. Since the first detection², more than 4000 exoplanets have been confirmed to date³ with a number of Earth analogs (e.g., TRAPPIST-1e)⁴. These planets have orbital and planetary properties similar to those of Earth, and therefore are potentially habitable. Evaluating their habitability from limited observations is essential in this context. Based on the knowledge of life on Earth, geological and climate systems are critical to habitability, which can therefore serve as biosignatures. In principle, fe....

Protocol

1. Programming setup

1. Set up the programming environment for the attached code. A computer with Linux operating system is required, as the healpy package is not available on Windows. The code is not computationally expensive, so a normal personal computer can handle the protocol.
2. Follow the instruction (https://docs.anaconda.com/anaconda/install/linux/) to install Anaconda with Python 3.7 onto the system, then use the following commands in terminal to set up the programming environment:
   $ conda create --name myenv python=3.7
   $ conda activate myenv
   $ conda install anaconda
   $ conda install healpy
   NOTE: These steps ....

Results

We use multi-wavelength single-point light curves of Earth to demonstrate the protocol, and compare the results with the ground truth to evaluate the quality of surface mapping. Observation used here is obtained by DSCOVR/EPIC, which is a satellite located near the first Lagrangian point (L1) between Earth and Sun taking images at ten wavelengths of the sunlit face of Earth. Two years (2016 and 2017) of observations are used for this demonstration, which are the same as those in Jiang et al. (2018)¹²

Discussion

One critical requirement of the protocol is the feasibility of extracting surface information from light curves, which depends on the cloud coverage. In step 3.5.1, the relative values of the PCs may be different among exoplanets. In the case of Earth, the first two PCs dominate the light curve variations, and correspond to surface-independent clouds and surface (Fan et al. 2019)¹³. They have comparable singular values so that the surface information can be separated following steps 3.5.2 and 3.5........

Materials

Name	Company	Catalog Number	Comments
Python 3.7 with anaconda and healpy packages			Other programming environments (e.g., IDL or MATLAB) also work.