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Improving the Precision of Line-by-Line Radial Velocities: A Data-Driven Iterative Algorithm for Spectral Line Selection

This paper introduces FLARES, an iterative, data-driven algorithm that optimizes spectral line selection for extreme-precision radial velocity measurements, achieving a significantly lower RMS of 1.122 m/s with just 24 lines compared to traditional cross-correlation and other benchmark methods.

Original authors: Kanishk Pandey, Eric A. Ford, Joseph M. Salzer, Jessi Cisewski-Kehe, Lily L. Zhao, Arvind F. Gupta, Michael L. Palumbo III, Ryan C. Terrien, Evan Fitzmaurice, Brady Barth, Jason T. Wright, Cullen H. B

Published 2026-06-30

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CC BY 4.0

Original authors: Kanishk Pandey, Eric A. Ford, Joseph M. Salzer, Jessi Cisewski-Kehe, Lily L. Zhao, Arvind F. Gupta, Michael L. Palumbo III, Ryan C. Terrien, Evan Fitzmaurice, Brady Barth, Jason T. Wright, Cullen H. Blake, Suvrath Mahadevan, Arpita Roy, Joe P. Ninan, Gudmundur Stefansson, Paul Robertson, Christian Schwab, Daniel M. Krolikowski, Leonardo A. Paredes

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Cosmic Detective's Problem: Finding a Whisper in a Storm

Imagine you are trying to hear a single person whispering a secret across a crowded, noisy stadium. That is the challenge astronomers face when looking for Earth-like planets. These planets are tiny and far away, tugging on their stars so gently that the star's movement is like a whisper—only about 10 centimeters per second.

However, the "stadium" (the star itself) is incredibly noisy. The star has sunspots, magnetic storms, and boiling gas on its surface that create "shouts" and "rumblings" (stellar activity) that are much louder than the planet's whisper. Traditional methods try to listen to the whole stadium at once, averaging out all the noise. But sometimes, the loudest shouts drown out the whisper entirely.

The New Strategy: The "Line-by-Line" Approach

This paper introduces a new way to listen. Instead of treating the star's light as one big blur, the researchers looked at 3,830 individual "lines" in the star's spectrum. Think of these lines as individual instruments in an orchestra. Some instruments (lines) are very sensitive to the crowd's noise (stellar activity), while others are steady and reliable.

The researchers used a powerful telescope called NEID to watch our own Sun for over a year. They measured how much each of these 3,830 "instruments" wobbled.

The Solution: FLARES (The Smart Filter)

The team developed a new algorithm called FLARES (Filtering Lines for Accurate Radial-velocity Exoplanet Search). You can think of FLARES as a very strict, smart editor for a noisy choir.

Here is how FLARES works, step-by-step:

The Initial Crowd: They started with all 3,830 lines. The "noise" (measured as Root Mean Square or RMS) was about 2.0 meters per second. This is still too loud to hear the planet's whisper.
The Iterative Cut: FLARES doesn't just guess which lines to keep. It plays a game of "musical chairs" but in reverse.
- It looks at every line and asks: "If I remove this line, does the overall noise go down?"
- It checks many different "traits" for each line: How deep is the line? Is it near the edge of the detector? Does it wiggle in sync with the Sun's rotation?
- It picks the line that, when removed, makes the remaining group the quietest.
- It repeats this process thousands of times, cutting out the "bad actors" one by one.
The Result: After removing the noisy lines, FLARES was left with just 24 lines. These 24 lines were the "super-singers" of the group. When the team listened only to these 24, the noise dropped dramatically to 1.12 meters per second.

Why This Matters

The paper compares FLARES to other methods:

Random Selection: If you just picked 24 lines at random, the noise would still be high (around 2.0 m/s).
The "Deepest Lines" Method: Picking lines that are physically "deeper" in the star's atmosphere helped a bit, but not as much as FLARES.
The "Best Performers" Method (BLARES): This method picked lines that historically wobbled the least. It got the noise down to about 1.45 m/s.
FLARES: By using a combination of many different clues (like a detective using fingerprints, alibis, and motive), FLARES got the noise down to 1.12 m/s.

The "Goldilocks" Lines

The paper discovered that the best lines (the ones FLARES kept) have specific characteristics:

They are deep (strong signals).
They are located in the center of the telescope's detector (avoiding the messy edges).
They are not correlated with the Sun's magnetic activity (they don't dance to the star's stormy tune).
They are found in the redder part of the light spectrum.

The Bottom Line

The researchers proved that by carefully selecting only the most stable "instruments" in the star's light, they can significantly reduce the noise. While they haven't yet reached the theoretical limit of silence (which would be near zero noise), they have built a much quieter room.

This means that in the future, when we point these telescopes at other stars, we might finally be able to hear the "whisper" of an Earth-like planet without being drowned out by the star's own "shouts." The paper confirms that this method is robust; even if you run the algorithm 100 times with slight random changes, it consistently finds the same high-quality group of lines.

In short: FLARES is a smart filter that throws away the noisy parts of a star's light, leaving behind a crystal-clear signal that makes it easier to find new worlds.

Technical Summary: Improving the Precision of Line-by-Line Radial Velocities

Problem Statement
The detection of Earth-mass planets in the habitable zone of Sun-like stars requires extreme-precision radial velocity (EPRV) measurements with amplitudes as low as $\approx 10$ cm s $^{-1}$ . However, stellar variability (e.g., spots, faculae, granulation, p-mode oscillations) and instrumental systematics introduce quasi-periodic RV noise often exceeding 1 m s $^{-1}$ , obscuring planetary signals. While standard Cross-Correlation Function (CCF) methods average spectral information, they lose critical line-shape details that could distinguish activity-induced signals from true Doppler shifts. Line-by-Line (LBL) analyses preserve this information but face challenges in selecting optimal spectral lines from large lists, as not all lines contribute equally to RV precision; many are susceptible to activity, telluric contamination, or detector edge effects.

Methodology
The authors analyzed 383 days of high-cadence NEID solar observations (February 2021 – June 2025), measuring LBL RVs for 3,830 spectral lines. The workflow involved:

Data Processing: Daily-averaged spectra were constructed using Gaussian Processes to mitigate short-timescale variability and increase Signal-to-Noise Ratio (SNR).
Line Vetting: An initial vetting procedure removed 1,021 lines that exhibited significant deviations from the weighted RV time series, primarily due to telluric contamination (red orders) and instrumental artifacts following a Laser Frequency Comb (LFC) upgrade. This left a curated list of 2,809 lines.
Benchmarking: Several baseline line-selection strategies were tested:
- Random: Selecting random subsets.
- BLARES: Iteratively removing lines with the highest LBL RV RMS.
- Depth-based: Iteratively removing the shallowest lines (based on the hypothesis that deeper lines form higher in the atmosphere and are less sensitive to convective blueshift inhibition).
FLARES Algorithm: The authors introduced FLARES (Filtering Lines for Accurate Radial-velocity Exoplanet Search), an iterative, data-driven algorithm. Unlike previous methods that rely on a single metric, FLARES evaluates 14 distinct line metrics across five categories: stellar activity (e.g., correlation with Ca II HK, ACF at 28 days), atomic parameters (excitation energy, oscillator strength, Landé factor), damping parameters, instrumental effects (SNR, wavelength, pixel position, ACF at 365 days), and morphology (depth, width).
- Mechanism: At each iteration, the algorithm identifies a pool of candidate lines with extreme values for each metric. It temporarily removes candidates to evaluate the resulting weighted RV RMS of the remaining set. The line whose removal yields the greatest reduction in RV RMS is permanently discarded. This greedy approach continues until a single line remains.
Validation: The robustness of FLARES was assessed via 100 Monte Carlo simulations to quantify reproducibility. Additionally, "nearest-neighbor" line lists were constructed to test if lines with similar physical properties to the FLARES-selected set could replicate the performance.

Key Results

Baseline Performance: Using all 2,809 vetted lines, the LBL approach achieved an RV Root Mean Square (RMS) of 2.012 m s $^{-1}$ , comparable to the 2.129 m s $^{-1}$ achieved by a standard CCF approach.
Benchmark Comparison:
- BLARES (RMS-based selection) reduced the RMS to 1.457 m s $^{-1}$ using 27 lines.
- FLARESdepth (depth-based selection) reduced the RMS to 1.630 m s $^{-1}$ using $\approx$ 150 lines.
- FLARES (multi-metric selection) achieved the lowest RMS of 1.122 m s $^{-1}$ using only 24 lines.
Metric Influence: The algorithm was most sensitive to detector pixel position (427 removals) and correlation with Ca II HK (360 removals). Activity-related metrics dominated the early iterations, while other categories (atomic, instrumental, morphology) were removed more uniformly in later stages.
Properties of Optimal Lines: The best 100 lines selected by FLARES were characterized by greater depth, higher SNR, central detector positions (avoiding order edges), weaker correlation with Ca II HK, and longer wavelengths (redder orders).
Robustness: Monte Carlo simulations showed that the RV RMS is highly reproducible (dispersion $\le$ 0.1 m s $^{-1}$ ) even with only 20–30 lines remaining. The Jaccard similarity between subsets from different simulations indicated that $\approx$ 60% of the best lines are consistently selected across runs.
Nearest-Neighbor Test: Line lists constructed to match the physical properties of the FLARES-selected lines (FLARES MC NN) performed better than random selection and similarly to BLARES ( $\approx$ 1.51 m s $^{-1}$ ) but did not match the performance of the actual FLARES selection ( $\approx$ 1.12 m s $^{-1}$ ). This suggests FLARES identifies specific, non-trivial combinations of line properties that simple property matching cannot fully replicate.

Significance and Claims
The paper claims that FLARES successfully identifies subsets of spectral lines that are intrinsically less sensitive to stellar activity, instrumental systematics, and telluric contamination. By iteratively removing lines based on a multi-metric framework, the algorithm significantly improves RV precision compared to standard CCF methods and single-metric selection strategies.

The authors emphasize that while the results are derived from solar data, the FLARES framework offers a general, automated approach for constructing optimal line lists for other stars. They note that traditional CCF methods often use fixed line lists transferred between stars, whereas FLARES can adapt to the specific activity signals and atmospheric properties of different stellar types. The work also highlights that the "greedy" nature of the algorithm is a limitation, as it may miss global optima, but it offers a computationally efficient alternative to global searches. The authors conclude that while FLARES has not yet reached the photon-noise limit ( $\sim$ 0.05 m s $^{-1}$ ), it demonstrates that data-driven line selection is a viable path toward mitigating stellar noise in EPRV surveys.