TILARA: Template-Independent Line-by-line Algorithm for Radial velocity Analysis. I. Description of the code and application on a Sun-like star

This paper introduces TILARA, a novel template-independent, line-by-line algorithm for deriving precise radial velocities that effectively mitigates biases from reference spectra and demonstrates performance comparable to existing methods when applied to ESPRESSO observations of the Sun-like star HD 102365.

The Gist

Here is an explanation of the paper, translated into everyday language with some creative analogies.

The Big Picture: Listening to a Star's Heartbeat

Imagine you are trying to listen to a single violin playing a melody in the middle of a massive, chaotic orchestra. The violin is the planet you are looking for, and the orchestra is the star. The problem is that the orchestra (the star) is constantly changing its tune due to its own "noise"—sunspots, magnetic storms, and surface bubbling (granulation).

For decades, astronomers have tried to hear that tiny violin by using a template. Think of a template like a "perfect sheet music" of what the star should sound like. They compare the live recording to the sheet music. If the live recording is slightly out of tune, they assume the violin (the planet) is pulling it.

The Problem: Sometimes, the star's "sheet music" changes so fast or is so messy that you can't write a perfect template. If you try to force a comparison, you get confused and miss the planet.

The Solution: Enter TILARA.

What is TILARA?

TILARA stands for Template-Independent Line-by-Line Algorithm for Radial velocity Analysis.

That's a mouthful, so let's break it down with an analogy:

Imagine you are trying to find a specific person in a crowded room (the star's spectrum) by looking at their face.

• The Old Way (Template Matching): You have a photo of what that person usually looks like. You scan the crowd, looking for someone who matches the photo. If the person puts on a hat or the lighting changes, you might lose them or get confused.
• The TILARA Way: Instead of looking at the whole face at once, TILARA looks at one single feature at a time. It says, "Okay, let's just track the left eye of every person in the room. Then, let's track the nose. Then the mouth."

TILARA doesn't need a "perfect photo" of the star. It picks thousands of specific, tiny dark lines in the star's light (like individual notes in a song) and measures the speed of each one independently.

How Does It Work? (The 4-Step Recipe)

The paper describes a four-step process to get the most accurate speed measurement possible:

1. The Shopping List (Selection): First, the code goes to a "reference library" (in this case, a high-quality recording of our own Sun) and picks a curated list of the best, most stable "notes" (spectral lines) to track. It's like making a shopping list of the most reliable ingredients for a recipe.
2. The Measurement (ARES): It uses a tool called ARES to find those specific notes in the target star's light. It measures exactly where each note is located.
3. The Speed Calculation: It calculates how fast each note is moving toward or away from us using the Doppler effect (the same reason a siren sounds higher when it comes toward you).
4. The "Bouncer" (Outlier Rejection): This is the magic part. In a crowd, some people might be wearing masks or moving weirdly (noise, stellar activity).
   • Sigma-Clipping: This is like a bouncer who says, "If your speed is way too crazy compared to everyone else, you're out." It simply throws away the weird data points.
   • Down-Weighting: This is a more polite bouncer. It says, "You're moving a bit weirdly, so we'll listen to you, but we won't trust you as much as the calm people." It gives less "voting power" to the noisy lines.

Why Is This a Big Deal?

The authors tested this new code on a star called HD 102365 (a star very similar to our Sun) using data from the ESPRESSO telescope, which is one of the most precise instruments in the world.

Here is what they found:

• It works just as well as the old methods: TILARA found the star's speed with the same precision as the traditional "template" methods.
• It's more flexible: Because it doesn't need a perfect "sheet music" template, it can work even when the star is acting up or when we don't have enough data to build a template.
• It's ready for the future: The paper mentions a future telescope called PoET that will look at the Sun up close (disk-resolved). When you look at the Sun up close, the surface is so messy and changing that you cannot make a template. TILARA is built specifically to handle this chaos.

The "Sun" of the Story

The team tried to find a planet around HD 102365 that was previously thought to exist (a Neptune-sized planet). Using TILARA, they couldn't find it. This suggests that the "planet" signal was likely just the star acting up (noise), not a real planet. This is a great example of how TILARA helps separate the "violin" from the "orchestra noise."

The Bottom Line

TILARA is a new, smarter way to measure how fast stars are moving.

Instead of trying to match the whole star to a perfect picture, it listens to thousands of tiny, individual "notes" in the star's light. It ignores the noisy ones and averages out the calm ones. This makes it incredibly robust, especially for the future of astronomy where we will be studying the messy, churning surfaces of stars in high definition.

It's like moving from trying to guess a song by humming the whole melody to a super-precise instrument that listens to every single string on the guitar to tell you exactly how the musician is playing.

Technical Summary

Here is a detailed technical summary of the paper "TILARA: Template-Independent Line-by-line Algorithm for Radial velocity Analysis."

1. Problem Statement

Precise Radial Velocity (RV) measurements are critical for exoplanet detection, particularly for Earth-like planets requiring precisions of $\sim10$ cm s$^{-1}$. Current standard methods rely heavily on template matching or Cross-Correlation Functions (CCF), which require a stable reference spectrum. These approaches face significant limitations:

• Template Dependency: Creating a high Signal-to-Noise (S/N) template is difficult for variable stars, stars with sparse data, or when observing time spans are short (leading to interpolation errors and telluric contamination).
• Future Observations: Upcoming instruments like the Paranal solar ESPRESSO Telescope (PoET) will perform disk-resolved solar observations. In these cases, the stellar surface varies so rapidly (granulation, sunspots) that a stable reference template cannot be constructed, breaking the fundamental assumption of template-matching methods.
• Existing Line-by-Line (LBL) Limitations: While LBL methods exist to probe stellar activity, most still rely on template matching to derive individual line RVs, inheriting the same biases. Furthermore, many existing LBL codes define "lines" as segments between local maxima rather than physically distinct absorption features, limiting their ability to resolve blended lines.

2. Methodology: The TILARA Code

The authors introduce TILARA (Template-Independent Line-by-line Algorithm for Radial velocity Analysis), a code designed to extract RVs without a pre-constructed flux template. It operates in conjunction with ARES (a code for measuring spectral line parameters) and linesearcher. The workflow consists of four main steps:

Step 1: Selection of Reference Lines

• Instead of a full spectral template, TILARA uses a curated list of reference wavelengths.
• Process: linesearcher identifies candidate features in a reference spectrum (e.g., solar spectra) to provide initial wavelength and depth estimates. ARES then refines these by fitting Gaussian profiles to determine precise central wavelengths, Equivalent Widths (EW), Full Width at Half Maximum (FWHM), and depths.
• Filtering: A statistical selection process (using $\sigma_{NMAD}$ and median metrics) filters out unstable lines, blends, and noise, resulting in a robust reference line list (e.g., 4,454 lines for the solar case).

Step 2: Line Characterization (ARES)

• The reference line list is applied to the target star's spectra.
• ARES measures the central wavelength of each line in every observation.
• Key Feature: Unlike many LBL codes, ARES can fit multiple Gaussian components within blended features if they are separable, allowing TILARA to measure true individual absorption components rather than blended segments.

Step 3: RV and Error Calculation

• RV Calculation: The RV for each line ($RV_l$) is calculated using the classical Doppler formula based on the shift between the observed center ($\lambda_{obs}$) and the reference center ($\lambda_{ref}$).
• Error Estimation: The paper adopts the formalism of Bouchy et al. (2001). To ensure consistency across observations with varying S/N, the authors construct a "master spectrum" (median of all observations) to define the wavelength intervals and flux gradients ($dF/d\lambda$) for error calculation. These fixed intervals are then scaled by the flux ratio of the master spectrum to the individual observation.

Step 4: Outlier Rejection and Weighting

To mitigate the impact of noisy or activity-affected lines, TILARA offers two configurable strategies:

1. Sigma-Clipping: Iteratively removes lines with inconsistent RV errors or anomalously high temporal variability (standard deviation across the time series).
2. Down-Weighting (Lorentzian Fit): Instead of hard rejection, this method assigns weights to lines based on their temporal stability.
   • The distribution of line-by-line RV standard deviations is modeled using a truncated Lorentzian function.
   • Lines in the "heavy tail" (high variability) are down-weighted, while stable lines retain full weight.
   • This approach avoids the bias of assuming a zero-centered distribution (common in template-matching residuals) and accounts for intrinsic line-dependent offsets.

3. Key Contributions

• Template Independence: TILARA eliminates the need for a fixed flux template, making it uniquely suited for disk-resolved solar observations (PoET) and variable stars where templates are unfeasible.
• Physical Line Resolution: By leveraging ARES, it measures true individual absorption components, distinguishing it from methods that treat blended regions as single entities.
• Flexible Outlier Handling: The implementation of a truncated Lorentzian down-weighting scheme provides a robust, probabilistic method to handle stellar activity and instrumental outliers without discarding entire spectra.
• Modularity: The code is designed to be adaptable to different stellar types and instruments, with a user-provided line list capability.

4. Results

The code was tested on 520 ESPRESSO observations of the Sun-like star HD 102365 (a G-type star with low activity).

• Performance Comparison: TILARA was compared against CCF (official pipeline), s-BART (template matching), ARVE, and LBL (Artigau et al.).
  • Precision: TILARA achieved a standard deviation of 0.94 m s$^{-1}$ (down-weighting mode) for ESPRESSO 18 data, comparable to or slightly better than the CCF (0.89 m s$^{-1}$) and other state-of-the-art pipelines.
  • Error Bars: TILARA produced slightly tighter average error bars than competing methods.
• Injection-Recovery Tests: Synthetic planetary signals ($K=10$ m s$^{-1}$ and $K=2$ m s$^{-1}$) were injected into the data. TILARA successfully recovered both signals with high accuracy, demonstrating its sensitivity and robustness.
• HD 102365 b Re-evaluation: A periodogram analysis of the TILARA-derived RVs showed no significant signal at the previously reported 122.1-day period of the candidate planet HD 102365 b (above the 1% False Alarm Probability), supporting recent findings that the planet's existence is dubious with current ESPRESSO data.
• Consistency: Both sigma-clipping and down-weighting modes yielded consistent results, with down-weighting showing slightly reduced scatter.

5. Significance and Future Prospects

• Enabling PoET Science: TILARA is the first tool specifically designed to handle the unique challenges of disk-resolved solar observations, where the spectrum changes too rapidly for traditional template matching.
• Activity Mitigation: By isolating individual lines, TILARA allows astronomers to study how specific physical properties (formation height, magnetic sensitivity) correlate with RV variations, aiding in the separation of stellar activity from planetary signals.
• Complementary Tool: While template matching remains superior when a high-quality, stable template exists, TILARA provides a necessary, robust alternative for variable targets and future high-spatial-resolution instruments.
• Open Source: The code, solar line list, and documentation are publicly available, encouraging adaptation for other instruments and stellar populations.

In conclusion, TILARA represents a significant step forward in high-precision RV analysis, offering a template-free, line-by-line framework that bridges the gap between current spectroscopic capabilities and the demands of future solar and exoplanet research.