The TESS All-Sky Rotation Survey: Periods for 944,056 Stars Within 500 pc

The paper presents the TESS All-Sky Rotation Survey (TARS), a new homogeneous catalog containing rotation periods for 944,056 stars within 500 pc that significantly expands the available data for stellar age and activity studies while introducing methods to correct period aliases and providing open-source tools for further analysis.

The Gist

Imagine the night sky as a massive, bustling city. For centuries, astronomers have been trying to map the "jobs" and "ages" of the stars in this city. One of the most important clues to a star's age and personality is how fast it spins. Just like a spinning top slows down as it loses energy, stars slow their rotation as they age.

However, measuring this spin is incredibly difficult. It's like trying to hear a whisper in a hurricane. The stars are far away, their light is faint, and the "wind" (instrument noise and data gaps) often drowns out the signal.

Enter TESS (the Transiting Exoplanet Survey Satellite), a space telescope that has been taking high-definition photos of almost the entire sky for several years. But TESS has a quirk: it takes pictures in "sectors" (like slices of a pie), and it only stares at each slice for about a month. This is like trying to figure out how long a song is by listening to only 30 seconds of it. If the song is short, you get it right. If the song is long, you might mistake a short loop for the whole tune.

This paper, by Andrew Boyle and his team, is the story of how they turned those 30-second snippets into a complete, all-sky playlist of 944,056 stars.

Here is the breakdown of their achievement, explained simply:

1. The Mission: A Cosmic Speedometer

The team wanted to build a catalog of how fast stars spin, but only for stars relatively close to us (within 500 light-years) and bright enough to see easily.

• The Scale: They looked at over 7.4 million stars.
• The Result: They successfully measured the spin rate for nearly 1 million stars.
• The Impact: Before this, we knew the spin rates for only a fraction of these stars. This new catalog increases our knowledge of nearby stars by 2.1 times (for the closest 100 light-years) and 3.7 times (for the whole 500 light-year neighborhood).

2. The Problem: The "Half-Period" Illusion

Because TESS only watches a star for a month, it often gets confused.

• The Analogy: Imagine a clock with a second hand. If you only look at the clock for 15 seconds, you might think the hand is moving backward or that it's a different, faster clock.
• The Reality: In astronomy, this is called an alias. If a star spins once every 10 days, TESS might think it spins every 5 days because it only saw half the cycle.
• The Fix: The team built a "smart detective" (a computer program using Random Forests, a type of AI) to spot these tricks. They taught the AI to recognize the difference between a real star spin and a fake signal caused by the telescope's own quirks (like the satellite dumping momentum or sunlight hitting the lens).

3. The Solution: The "TARS" Catalog

They named their project TARS (TESS All-Sky Rotation Survey). Think of TARS as a massive, organized library where every book is a star, and the "spine" of the book tells you exactly how fast it spins.

• The "Vetting" Process: Before adding a star to the library, they ran it through two security checks:
  1. The Systematics Check: "Is this signal real, or is it just telescope noise?" (99% accuracy).
  2. The Alias Check: "Is this the true spin, or just half of it?" (95% accuracy).
• The Magic Trick: Even though TESS usually can't see spins longer than 12 days, their new method allows them to reliably detect spins up to 25 days from a single month of data. It's like being able to guess the length of a 25-minute movie just by watching the first 15 minutes and knowing the plot structure.

4. What Did They Find?

With this massive new dataset, they discovered some cool patterns:

• The "Gap": They confirmed a mysterious "gap" in the rotation speeds of cool stars (like our Sun's cooler cousins). It's like a highway where cars suddenly stop driving at a certain speed. This helps astronomers understand how stars lose their spin over time.
• The "Fast Lane": They found that many of the fastest-spinning stars aren't actually single stars; they are binary stars (two stars orbiting each other) that are locked in a dance, forcing them to spin faster. It's like two ice skaters holding hands and spinning faster than they could alone.
• The "Kraft Break": They saw a clear line where stars change behavior. Hotter stars (above 6,600 Kelvin) spin differently than cooler ones, marking the point where a star's internal "engine" (convection) changes.

5. Why Should You Care?

• Finding Alien Worlds: If we want to find Earth-like planets, we need to know if their host star is calm or crazy. A fast-spinning, active star can blast a planet with radiation, making life impossible. This catalog helps us pick the "good" stars to look at.
• Time Travel: Since a star's spin tells us its age, this catalog is essentially a time machine. It helps us map out the history of our galaxy, showing us where young star clusters are and how our neighborhood has changed over billions of years.
• Open Source: The best part? They didn't keep the data to themselves. They made the entire catalog, the code, and the light curves (the raw data) available to anyone. It's like giving the whole world the keys to the library.

In a nutshell: This paper is a massive leap forward in our understanding of the universe. The team took a messy, incomplete set of space photos, used clever math and AI to clean it up, and handed us a pristine map of nearly a million spinning stars. It's a foundational tool that will help astronomers solve mysteries about stars, planets, and the history of our galaxy for decades to come.

Technical Summary

Here is a detailed technical summary of the paper "The TESS All-Sky Rotation Survey: Periods for 944,056 Stars Within 500 pc" by Boyle, Bouma, and Mann.

1. Problem Statement

Stellar rotation is a critical tracer for stellar magnetic evolution, age (gyrochronology), and activity. While previous surveys (Kepler, K2, ZTF) have measured rotation periods for tens of thousands of stars, they were limited by field-of-view constraints or heterogeneous data products.

• The Gap: No existing study provided a flux- and distance-limited, all-sky catalog of rotation periods using TESS data.
• The Challenge: TESS observes the entire sky but typically in 27-day sectors. This baseline limits sensitivity to periods longer than $\sim$12 days (the Nyquist limit for a single sector) and introduces significant aliasing (specifically half-period aliases, $P_{rot}/2$) due to the window function. Additionally, TESS light curves are contaminated by instrumental systematics (e.g., momentum dumps, scattered light) that mimic periodic signals.

2. Methodology

The authors present the TESS All-Sky Rotation Survey (TARS), a homogeneous catalog derived from TESS Full Frame Images (FFIs).

Target Selection

• Sample: 7,481,412 unique stars observed by TESS (Sectors 1–96) with TESS magnitude $T < 16$ and Gaia DR3 distances $d < 500$ pc.
• Data Processing: Light curves were extracted from FFIs using the unpopular package, which employs a causal pixel model to remove systematics by distinguishing between common instrumental signals and unique astrophysical signals.
• Period Search: A Lomb-Scargle (LS) periodogram was computed for 39 million star-sector combinations.

Classification and Vetting Pipeline

To distinguish true rotation from noise and aliases, the authors employed a two-stage Random Forest (RF) classifier approach:

1. Systematics Classifier:
   • Goal: Distinguish astrophysical rotation signals from instrumental systematics (e.g., momentum dumps).
   • Training: Trained on "positive" examples (consistent periods across $\ge$5 sectors) and "negative" examples (inconsistent periods).
   • Performance: Achieves 99% accuracy (AUC = 0.998).
   • Threshold: A probability $P(\text{signal}) > 0.8$ is required to pass.
2. Alias Classifier:
   • Goal: Identify half-period aliases ($P_{measured} \approx P_{true}/2$) caused by the TESS window function.
   • Training: Trained using the Kepler rotation catalog (McQuillan et al. 2014) as ground truth.
   • Logic: If a period is flagged as an alias ($P(\text{alias}) > 0.8$), the measured period is doubled to recover the true rotation period.
   • Performance: Correctly identifies true periods in 89% of cases and flags aliases in 85% of cases (AUC = 0.951).
   • Threshold: A probability $P(\text{match}) > 0.8$ or $P(\text{alias}) > 0.8$ is used.

Period Adoption Logic

For each star, the pipeline:

1. Filters sector-level periods using the systematics classifier.
2. Flags and doubles periods identified as aliases.
3. Propagates alias corrections to other sectors for the same star if periods are consistent within 15%.
4. Computes a weighted mean of the consistent, corrected periods to derive a single final rotation period ($P_{rot}$) and uncertainty.

3. Key Contributions

• Scale: The largest homogeneous catalog of stellar rotation periods to date, containing 944,056 stars within 500 pc.
• Discovery Rate: Increases the number of known rotation periods for stars with $T < 16$ by a factor of 2.1 (within 100 pc) and 3.7 (within 500 pc).
• Alias Correction: Demonstrates a robust method to recover rotation periods up to 25 days from single-sector TESS data by identifying and correcting half-period aliases.
• Flexibility: Provides a framework allowing users to trade off completeness vs. reliability by adjusting probability thresholds and quality flags (e.g., removing binaries, ensuring multi-sector coverage).
• Data Availability: Light curves, vetting plots, and the full catalog are available via MAST (HLSP) and Zenodo, including code to regenerate the catalog with custom thresholds.

4. Results

• Reliability:
  • Approximately 94% of the cataloged periods correspond to stellar rotation.
  • Validation against Kepler, K2, and ZTF shows that with default thresholds ($P > 0.8$), the match rate is $\sim$85–90%.
  • Applying strict quality flags (multi-sector agreement, no binaries, no contamination) yields a "clean" sample of 202,223 stars with match rates exceeding 90% against literature values.
• Physical Insights:
  • The Intermediate Period Gap: The survey recovers the known "cool star gap" (a deficit of periods between $\sim$10–20 days for $T_{eff} \lesssim 5000$ K) and extends it to hotter, Sun-like stars ($5300-6200$K), revealing a diagonal underdensity in the$P_{rot}$-$T_{eff}$ plane.
  • Kraft Break: A distinct transition in variability amplitude and rotation behavior is observed near $T_{eff} \approx 6600$ K.
  • Binarity: Analysis of the color-magnitude diagram reveals that 45% of the fastest rotators ($P_{rot} < 7$ days) are likely tidally synchronized binaries, compared to only $\sim$5% for slow rotators.
  • Cluster Sequences: The alias-correction method successfully reconstructs coherent rotation sequences for open clusters (Pleiades, Praesepe, Hyades), recovering slow rotators ($P_{rot} > 13$ days) that are typically missed in single-sector analyses.

5. Significance

The TARS catalog represents a paradigm shift in stellar astrophysics by providing a uniform, all-sky dataset that overcomes the temporal limitations of the TESS mission.

• Galactic Archaeology: Enables the mapping of stellar ages and angular momentum evolution across diverse Galactic environments, not just specific fields.
• Exoplanet Science: Provides essential rotation constraints for host stars, aiding in the characterization of exoplanet atmospheres and the mitigation of activity-induced noise in radial velocity and transit surveys.
• Stellar Evolution: Offers a massive sample to study the "stalled" spin-down phase of intermediate-age stars and the transition from convective to radiative envelopes.
• Future Utility: The provided code and data products allow the community to generate custom catalogs tailored to specific scientific needs, ensuring the data remains a foundational resource for years to come.