Spectral Ratio Analysis: probing of a new suite of stellar activity indicators as a tool for astrophysical noise mitigation

Technical Summary: Spectral Ratio Analysis for Astrophysical Noise Mitigation

Problem Statement
The detection and confirmation of low-mass, long-period, and Earth-analogue planets via radial-velocity (RV) measurements are currently hindered by stellar activity noise. While thousands of exoplanets have been discovered, the "Earth twin" remains elusive. Stellar magnetic activity, particularly the presence of faculae (plage), suppresses convective blueshift in the stellar photosphere, inducing apparent RV signals that mimic planetary orbits. Existing mitigation techniques often rely on chromospheric activity indicators (e.g., the $\log R'_{HK}$ index) or cross-correlation function (CCF) parameters (e.g., Bisector Span, FWHM). However, these proxies trace chromospheric variability or global line-shape changes, which may not accurately reflect the photospheric line distortions where RVs are actually measured. This disconnect limits the ability to distinguish between planetary and stellar signals, especially for quiet, Sun-like stars where faculae dominate the noise.

Methodology
This study introduces and validates a technique called Spectral Ratio Analysis (SRA) to isolate activity-driven changes directly within stellar photospheric absorption lines. The methodology involves the following steps:

1. Target Selection: The authors analyzed archival HARPS spectrograph data for 14 relatively inactive G- and K-type stars exhibiting magnetic activity cycles. Selection criteria ensured long observational baselines (>4 years), high signal-to-noise ratios (SNR > 100 per observation, >150 for nightly averages, >500 for seasonal averages), and sufficient sampling of both high- and low-activity phases.
2. Data Preparation: Spectra were corrected for barycentric motion, secular acceleration, and known planetary signals (using allesfitter to re-model orbital solutions). Telluric lines were masked.
3. Spectral Ratio Construction: For each star, high-activity spectra were divided by a low-activity template spectrum (the seasonally averaged spectrum with the lowest activity level). This process generates ratio spectra where activity-induced features appear as apparent emission peaks or distortions.
4. Systematic Correction: The authors identified and corrected for systematic "ripple" structures in the ratio spectra (amplitudes of 0.05–1%, likely caused by thin-film interference in the calibration unit) using a wavelength-dependent sinusoidal model.
5. Feature Identification: An automated algorithm identified hundreds of activity-sensitive spectral features in the ratio spectra based on amplitude variability (pixels exceeding twice the weighted noise level) and clustering. Gaussian fits were applied to extract the amplitude and velocity shift of each feature.
6. Metric Derivation: Two global metrics were derived for each star: the SRAFeature amplitude (weighted average of feature amplitudes) and the SRAFeature shift (weighted average of velocity shifts).
7. Benchmarking: The performance of these SRA indicators was compared against classical proxies ($\log R'_{HK}$, CCF BIS, CCF FWHM) using:
   • Linear regression models to fit CCF RVs.
   • Random forest regression to determine indicator importance.
   • Planetary injection recovery tests (injecting fake planetary signals into $\alpha$ Cen B data) to assess noise mitigation limits.

Key Contributions

• Proof-of-Concept for SRA: Demonstrates that SRA can successfully isolate hundreds of photospheric features sensitive to stellar activity across a sample of 14 stars, providing a direct link between photospheric line behavior and RV variability.
• New Activity Indicators: Introduces a vector-like approach to activity monitoring, utilizing both the magnitude (amplitude) and direction (velocity shift) of photospheric line distortions, as opposed to scalar chromospheric indices.
• Public Atlas: Released a comprehensive online atlas containing the SRA spectra, identified features, and associated metadata for the 14 stars, facilitating future line-by-line analyses and magnetohydrodynamic simulations.

Results

• Correlations with Activity:
  • Amplitude: The SRAFeature amplitude shows a strong positive correlation with $\log R'_{HK}$ over both nightly and seasonal timescales. However, this correlation weakens for earlier-type (hotter) stars, suggesting a potential decoupling between photospheric and chromospheric responses in these stars.
  • Velocity Shift: No strong correlation exists between SRAFeature velocity shifts and $\log R'_{HK}$ on nightly timescales (consistent with rotational modulation of active regions). However, a moderate positive correlation emerges on seasonal timescales for cooler stars. The authors speculate this may indicate a long-term variation in the magnitude of convective blueshift suppression as the magnetic cycle progresses.
• RV Mitigation Performance:
  • SRA-derived indicators outperform classical proxies in explaining RV variability. In linear regression models, SRA reduced the RMS of RV residuals by up to a factor of two compared to $\log R'_{HK}$ for stars with high SNR (>300).
  • Random forest analysis identified the SRAFeature velocity shift as the most important predictor of RV variations for the majority of the sample (8 out of 14 stars), significantly outperforming $\log R'_{HK}$, BIS, and FWHM.
  • Planetary Recovery: In injection tests on $\alpha$ Cen B, SRA-based corrections successfully recovered injected planetary signals of 1–2 m s$^{-1}$ that were undetectable after correcting with $\log R'_{HK}$. However, the technique is sensitive to significant Doppler shifts; if planetary signals are not removed prior to SRA, the technique may inadvertently track the planetary signal rather than stellar noise.
• Limitations: The efficacy of SRA is dependent on high SNR (effective SNR > 300) and high-cadence sampling. The current analysis used a simplified "global metric" approach (collapsing hundreds of features into two averages), which the authors acknowledge discards rich feature-specific information.

Significance and Claims
The paper presents SRA as a promising tool for improving astrophysical noise mitigation in the search for Earth-analogue planets. By deriving indicators directly from photospheric lines, SRA offers a more physically direct connection to the sources of RV perturbations than chromospheric proxies. The authors claim that the velocity information contained in SRA features acts as a "vector quantity," providing directional information about active regions that scalar indices lack.

The study concludes that while the current implementation is a proof-of-concept that simplifies complex line-profile variations, the results demonstrate that SRA indicators can capture RV variability better than traditional methods by up to a factor of two. The authors emphasize that future work is required to fully exploit the diverse morphologies and temporal evolutions of the identified features, but the direct link established between photospheric line behavior and stellar-induced RV variability offers a viable path toward more robust noise mitigation strategies.