Earth Analogs in Reflected Light: Insights from Early Spectral Characterization in Unconstrained Orbits

TL;DR

Direct-imaging of Earth-like exoplanets with reflected light faces degeneracies from restricted spectral coverage and noise. Using the rfast retrieval tool, the authors simulate 17 free parameters for an Earth-analog across multiple bandpasses and S/N, including an 'early spectrum' regime before orbit constraints, to quantify what can be learned. They find that broad spectral coverage, particularly Visible+NIR, yields the strongest constraints on $f_{H_2O}$, $f_{O_2}$, and $f_{O_3}$, surface pressure, clouds, and atmospheric temperature, while $f_{N2}$ remains unconstrained and radius/mass require external orbital priors; consequently, radius and mass are poorly constrained without orbit information. The study argues for mission designs that maximize spectral breadth (parallel multi-band instruments and wider bandpasses) and adopt a spectrum-first strategy, which can guide target prioritization and optimize the scientific return of early Earth-analog characterization, as encapsulated by the flux relation $F_{ m p}/F_{ m s} = A_{ m g} \,\Phi(\alpha)\left(R_{ m p}/a\right)^2$.

Abstract

A next generation of space-based observatories aims to detect and characterize potentially Earth-like exoplanets around Sun-like stars using reflected light spectroscopy. However, it remains unclear how such direct imaging observations$-$limited in spectral coverage and signal-to-noise ratio (S/N)$-$translate into constraints on atmospheric composition and habitability. Coronagraphs used for high-contrast imaging typically operate over narrow bandpasses, and exposure time limits can restrict data quality. To optimize observing strategies and instrument design, we use our atmospheric retrieval tool, $\texttt{rfast}$, to assess the performance of a $\mathit{Habitable\ Worlds\ Observatory}$-type mission across different spectral bandpasses ("Red", "Blue", "Visible", "NIR", and their combination) and S/N levels (10, 15, and 20; from moderate to moderate-high observation quality) in retrieving a wide range of 17 atmospheric, surface, bulk, and orbital parameters of a habitable Earth analog. We outline the observation requirements for each parameter and the detection capabilities of each case, within a novel scenario where spectral data are taken "early", prior to achieving orbit constraints (which may require repeat visits to a system). For coronagraph-restricted and NIR-only bandpasses, most of the limited retrievable information is already captured at S/N = 10, with little improvement at higher S/N. For broader spectral coverage, the quality and quantity of retrieved information improve with increasing S/N, but combining visible and NIR ranges provides the most comprehensive characterization, even at moderate S/N. To maximize returns, wider spectral coverage should be prioritized over improving S/N when spectral access is limited.

Figures (10)

• Figure 1: Schematic of the rfast retrieval framework. Boxes denote model inputs and outputs, while circles represent components of the framework. Here, the "observed" spectrum is a synthetic observation of an Earth analog, generated using Earth-based fiducial parameters (see \ref{['tab:retrieved_pars']}).
• Figure 2: Model-generated (synthetic) reflected light spectrum of our fiducial case (plain line): an Earth-like planet at quadrature (i.e., at a planetary phase angle $\alpha=90$°; see \ref{['tab:retrieved_pars']} for fiducial input values), and assuming grey cloud properties (dashed line), which notably do not capture the absorption feature of water ice clouds near 1.6 $\upmu$m. The colored areas indicate the spectral imprints of the gas species by showing the difference between the baseline spectrum (plain line) and the flux measured if they were absent from the atmosphere and replaced with Ar, the background gas. The top of the figure indicates the spectral ranges considered, along with their resolving power $res = \lambda/\delta\lambda$ (\ref{['tab:retrieval_grid']}): Blue ($\rm \lambda = [0.43 - 0.53]~\upmu m$, $res = 140$) & Red ($\rm \lambda = [0.87 - 1.05]~\upmu m$, $res = 140$) bandpasses, Visible ($\rm \lambda = [0.45 - 1]~\upmu m$, $res = 140$) & near-infrared (NIR; $\rm \lambda = [1 - 1.80]~\upmu m$, $res = 70$) bandpasses (together denoted vNIR), or Red, Visible, and NIR bandpasses observed individually. The error bars represent the nonrandomized, wavelength-independent noise levels corresponding to specific signal-to-noise ratios (S/N), set at the lower bound of each spectral coverage (see \ref{['sec:appendix_SNR']} and \ref{['fig:spectrum_SNR']}): $\rm \lambda_0 = 0.43~\upmu m$ for the Blue & Red bandpass, $\rm \lambda_0 = 0.45~\upmu m$ for the Visible and Visible & NIR spectral ranges, $\rm \lambda_0 = 0.87~\upmu m$ for the Red bandpass, and $\rm \lambda_0 = 1.00~\upmu m$ for the NIR bandpass.
• Figure 3: Posterior distributions of gas abundances obtained from observations in different color-coded spectral coverages at signal-to-noise ratios (S/N) of 10 (left side of the split-violins, without contour lines), 15 (right side, with dashed contours), and 20 (right side, with solid contours). From top to bottom: (left column) molecular nitrogen, molecular oxygen, water vapor, (right column) carbon dioxide, methane, and ozone. The horizontal dashed lines spanning each violin row indicate Earth-like input values, while the dashed lines within the violins show the 25th, 50th, and 75th percentiles of the data (the first quartile, median, and third quartile, respectively). The density has been normalized across all kernel density plots so that each has the same area.
• Figure 4: Posterior distributions of surface and atmospheric condition parameters obtained from observations in different color-coded spectral coverages at signal-to-noise ratios (S/N) of 10 (left side of the split-violins, without contour lines), 15 (right side, with dashed contours), and 20 (right side, with solid contours). From top to bottom: surface pressure, atmospheric temperature, and surface albedo. The horizontal dashed lines spanning each violin row indicate Earth-like input values, while the dashed lines within the violins show the 25th, 50th, and 75th percentiles of the data (the first quartile, median, and third quartile, respectively). The density has been normalized across all kernel density plots so that each has the same area.
• Figure 5: Posterior distributions of cloud properties obtained from observations in different color-coded spectral coverages at signal-to-noise ratios (S/N) of 10 (left side of the split-violins, without contour lines), 15 (right side, with dashed contours), and 20 (right side, with solid contours). From top to bottom: (left column) cloud-top pressure, thickness, (right column) optical depth, and cloudiness fraction. The horizontal dashed lines spanning each violin row indicate Earth-like input values, while the dashed lines within the violins show the 25th, 50th, and 75th percentiles of the data (the first quartile, median, and third quartile, respectively). The density has been normalized across all kernel density plots so that each has the same area.