Characterizing Earth analogs may require a moderate or high-resolution spectrograph

Abstract: A primary goal of the Habitable Worlds Observatory (HWO) is to detect and measure the abundance of biosignature molecules, such as water (H2O) and oxygen (O2), in the atmosphere of Earth analogs. This is expected to require deep spectroscopic observations lasting hundreds of hours per planet. In this context, it is essential to optimize the spectral resolution of the spectrograph to both maximize the number of planets that can be studied over the lifetime of the mission, and also to reduce the risks of false detections. The purpose of this work is to provide a framework to explore the spectral resolution design trade-space for HWO. This framework must be valid and comparable across all spectral resolutions from low (R<100) to high resolutions (R>10,000), and account for the spectral correlation of the residual starlight (i.e., speckle noise chromaticity). Leveraging the concept of "template matching", we develop a simulation toolkit based on the Python package EXOSIMS to compute the detection significance of planets and molecules. We then simulate observations of Earth analogs around 164 stars using representative mission parameters to explore the effects of the detector noise and the correlated speckle noise floor. Our findings suggest that a moderate or high resolution spectrograph (R>1,000) will provide higher sensitivity to critical molecules compared to a low resolution spectroscopy mode (e.g., R~140). The correlated speckle noise may also entirely suppress our ability to detect bio-signatures at low spectral resolutions. We conclude that a more comprehensive study combined with detailed models of its stability, and other sources of correlated noise, is necessary to fully explore the trade space of spectral resolution and detectability of key species.

• The paper demonstrates that spectrographs with R > 1,000 can mitigate correlated noise issues that diminish biosignature signals in Earth analog observations.
• It employs a template-matching maximum-likelihood framework incorporating both correlated and uncorrelated noise to robustly estimate signal-to-noise ratios.
• Simulation results indicate that detecting molecules like O₂ reliably requires moderate-to-high resolution, guiding key design trade-offs for future exoplanet missions.

Moderate or High-Resolution Spectroscopy as a Requirement for Earth-Analog Characterization

Introduction

The detection and characterization of biosignature molecules such as H$_2$O and O$_2$ in the atmospheres of terrestrial exoplanets is a central scientific goal for upcoming flagship direct-imaging missions like NASA's Habitable Worlds Observatory (HWO). The prevailing instrument architecture for such missions has historically emphasized low spectral resolution (e.g., $R \sim 140$) to mitigate photon noise and detector noise penalties due to the extremely low flux ratios of Earth-analogs in reflected light. However, this work presents a rigorous statistical and simulation-driven framework that challenges the paradigm of exclusively low-resolution spectroscopy. Instead, it demonstrates that correlated noise—particularly chromatic speckle residuals—can severely limit biosignature detectability at low resolution, and that moderate-to-high spectral resolution ($R > 1,000$) may not only confer increased robustness, but may even become a necessity when observational systematics are realistically considered (2604.17554).

Statistical Framework for S/N Estimation

The paper formulates a template-matching signal-to-noise ratio (S/N) approach, applicable at arbitrary spectral resolution and incorporating both uncorrelated (shot, background, detector) and correlated (speckle, systematics) noise sources. This is accomplished via a maximum-likelihood fit of a spectral template to simulated data, treating the noise as a Gaussian process with both diagonal and off-diagonal covariance terms.

The broadband (planet detection) S/N and the molecular-specific S/N (after subtracting the continuum envelope) are both computed through this template-matching formalism. In addition, a high-pass filtered molecular S/N is defined, which quantifies the detectability of narrow molecular features after low-frequency (broadband) correlated noise is removed. These definitions provide a consistent, information-theoretic measure of detectability that is valid from $R \sim 20$ to $R > 10,000$.

Importance of Correlated Noise: Covariance and Impact

The study underscores that correlated noise—especially residual starlight due to imperfect PSF subtraction, wavefront instability, fringing, and spectral systematics—cannot be ignored, particularly at low spectral resolution where molecular features occur on similar scales as the correlated systematics. As illustrated in (Figure 1):

Figure 1: Covariance model exhibiting both uncorrelated (diagonal) and correlated (off-diagonal) noise components, with parameters chosen to reflect realistic instrument stability and starlight suppression characteristics.

A Gaussian covariance kernel is adopted, parameterized by a noise floor (set by post-processing gain and coronagraph suppression) and a correlation length scale (typically on the order of 10 nm, comparable to the width of oxygen absorption bands). This model captures the broad, variable spectral baseline below which molecular detection S/N quickly collapses if the spectral resolution is too low relative to the correlation scale.

Simulation Environment and Assumptions

The authors implement the framework within the EXOSIMS simulation platform, generating a synthetic survey of 164 target stars with one Earth analog each, drawing on the ExEP HWO star list. Critical assumptions include a LUVOIR-analog aperture (7.87 m), realistic coronagraph and spectrograph throughputs (see Figure 2), and detector noise models that reflect current and near-future instrument capabilities.

Figure 2: Throughput assumptions for coronagraphy, showing differential transmission for planet flux and background sources (zodiacal/exozodiacal light).

Detector and astrophysical noise components are comprehensively modeled, and 400-hour integrations are adopted as the baseline for signal-to-noise calculations for faint Earth-analogs. Figure 3 illustrates the typical distribution of photon counts and key noise terms for such an observation:

Figure 3: Exemplar mock exoEarth spectrum for a G2V target at 14 pc, showing the relative magnitude of planet signal and various noise components at $R = 1,000$.

Numerical Results and Exploration of Trade Space

Spectral Resolution vs. Noise Sources

A primary result is the quantification of S/N as a function of spectral resolution and dominant noise source (Figure 4). At low $R$, molecular and planet detection S/N are suppressed by correlated noise if not adequately modeled and subtracted. Specifically, with a correlated noise floor of $10^{-11}$ (for a $10^{-10}$ starlight suppression coronagraph), the median broadband S/N drops from $_2$0 (detector-noise limited) to $_2$1 (correlated noise-limited).

Figure 4: S/N for various diagnostic definitions (per bin, template-matching, molecular, high-pass-filtered) for 164 HWO targets as a function of $_2$2 and detector noise.

Detector noise only dominates at $_2$3 for current best-in-class EMCCD detectors. In the regime where correlated noise is dominant, high-pass filtering becomes essential for robust molecular detection. The high-pass filtered molecular S/N becomes independent of correlated noise amplitude, depending only on the uncorrelated photon and detector noise.

Requirements for Biosignature Discovery

Figure 5 (and analogously Figure 6) demonstrates that unless correlated noise floors are suppressed to $_2$4 or below, biosignature S/N (for O$_2$5 specifically) vanishes with $_2$6. This provides a strong quantitative justification for either improved wavefront error control, or adoption of moderate/high $_2$7 modes to shift molecular information content above the correlated noise correlation length scale.

Figure 5: O$_2$8 molecular S/N as a function of $_2$9, detector noise, and correlated noise floor, revealing the resolution threshold below which biosignature detectability collapses for realistic instrument systematics.

Furthermore, the study shows that improvements in either raw coronagraphic suppression or post-processing gain (see Figure 6) can be traded against each other, but both are functionally equivalent in their impact on correlated noise-limited performance.

Figure 6: Trade-off between coronagraph suppression and post-processing gain on O$R \sim 140$0 detectability, highlighting the interplay between system stability and instrument architecture.

The conceptual design space is summarized in Figure 7, showing the qualitative optimization: correlated noise dominates at low $R \sim 140$1, detector noise at high $R \sim 140$2, implying an optimal $R \sim 140$3 between $R \sim 140$4 and $R \sim 140$5 under plausible scenarios.

Figure 7: Schematic of the spectral resolution trade-off: correlated noise sets a lower bound on $R \sim 140$6 for molecular detection, while detector noise sets an upper bound beyond which S/N declines for fixed total observation time.

Implications for Mission Design and Future Directions

The results presented indicate that persistent use of exclusively low-resolution spectrographs for Earth-analog characterization would pose substantial risks of false negatives in biosignature searches and could even preclude detection if correlated noise cannot be suppressed far below current laboratory or spaceflight levels. Moderate/high-resolution spectrographs ($R \sim 140$7), in contrast, offer superior robustness to correlated systematics, enable more effective template-matching and cross-correlation techniques, and facilitate richer science cases including measurement of precise planetary velocities, rotational modulation, and trace species detection.

Key quantitative findings include:

• A moderate to high $R \sim 140$8 ($R \sim 140$9) spectrograph increases the median O$R > 1,000$0 S/N over low-$R > 1,000$1 modes by a factor of several, contingent upon correlated noise floor.
• Even at 400-hour integrations, detector noise typically does not dominate the noise budget for current EMCCDs until $R > 1,000$2; at higher $R > 1,000$3, ultra-low noise detectors become essential.
• If correlated noise floor for a $R > 1,000$4 starlight suppression system cannot be suppressed below $R > 1,000$5–$R > 1,000$6, low-$R > 1,000$7 biosignature detection becomes unviable.

These results strongly recommend that future instrument trade studies and yield calculations for flagship exoplanet missions adopt comprehensive covariance modeling, resist the temptation to focus solely on S/N per bin metrics, and include moderate-to-high $R > 1,000$8 options as baseline instrument modes. The statistical framework also needs to be extended for retrieval accuracy on atmospheric abundances, not just detection S/N.

Progress towards zero-noise detectors and improved coronagraphic stability can further relax design constraints and provide multiplicative science returns.

Conclusion

This work forcefully demonstrates that the canonical approach of low-resolution spectroscopy for exoEarth characterization is vulnerable to systemic, correlated noise sources that are inherent to high-contrast imaging. A moderate or high-resolution spectrograph is not merely advantageous but may be operationally necessary to ensure biosignature detectability and robust avoidance of false positives/negatives. These findings have clear implications for the architectural design, operational modes, and performance validation of future missions targeting Earth-analog spectroscopy (2604.17554). As instrument designs mature, covariant noise modeling and end-to-end information-theoretic analyses must become standard practice in mission planning.