🔭 astrophysics

Evidence for Sympathetic Flaring in TESS Data

This study presents the first statistically robust detection of sympathetic flaring on other stars by applying a new algorithm to TESS data, revealing that 4% to 9% of flares on approximately 16,000 M-dwarfs are triggered by preceding events, a rate consistent with observations on the Sun.

Original authors: Veronica Pratt, Jason R. Reeves, David V. Martin, Andy B. Zhang, Andrew Korkus, S. Edelman

Published 2026-02-25

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Veronica Pratt, Jason R. Reeves, David V. Martin, Andy B. Zhang, Andrew Korkus, S. Edelman

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

Imagine the surface of a star as a busy, chaotic city. Sometimes, the city has "storms" called flares—sudden, massive bursts of energy that light up the sky. For a long time, scientists thought these storms happened completely randomly, like raindrops hitting a sidewalk. If you saw one raindrop, it didn't mean another was about to hit right next to it.

But on our own Sun, scientists noticed something weird: sometimes, one storm triggers another nearby storm almost immediately. They call this "sympathetic flaring." It's like if you sneezed, and your friend immediately sneezed back, not because they were sick, but because your sneeze startled them.

Until now, we had no proof that this "sneeze-back" phenomenon happened on other stars. We couldn't see the surface of distant stars clearly enough to know where the storms were happening, only when.

This paper is the first time scientists have successfully proven that other stars also have sympathetic flares. Here is how they did it, explained simply:

1. The Problem: Missing the "Double-Click"

Imagine you are trying to count how many times people clap in a room. If two people clap at the exact same time, or one claps right after the other, a slow camera might miss the second clap entirely. It just looks like one long, messy clap.

Previous tools used to study stars were like that slow camera. They were great at spotting big, loud flares, but if a second, smaller flare happened just seconds after a big one, the tools would miss it. They would think, "Oh, that's just part of the first flare," and ignore the second one. This made it impossible to study "sympathetic" flares because those are the ones that happen very close together in time.

2. The Solution: A New "Super-Scanner"

The team built a new computer program called TOFFEE (TESS Overlapping Flare Finder and Energy Evaluator). Think of TOFFEE as a high-speed, super-sensitive microphone that can hear every single clap, even if two people clap almost at the exact same time.

They used data from the TESS space telescope, which takes pictures of the sky every 2 minutes. TOFFEE scanned through data from 16,000 different stars (mostly small, red stars called M-dwarfs) and found 220,000 flares. That's a lot of storms!

3. The Detective Work: Waiting for the Next Sneeze

To prove sympathetic flaring exists, the scientists looked at the Wait Time Distribution. This is just a fancy way of asking: "How long do we usually have to wait between flares?"

If flares are random: The time between them should follow a smooth curve, like rolling dice. You might wait 1 hour, then 10 hours, then 2 hours. It's all mixed up.
If flares are sympathetic: You should see a huge spike in the data where flares happen very, very close together (like within an hour of each other).

When they looked at their data, they found exactly that spike. There were way more "double-flares" happening close together than random chance would allow.

4. The Results: The Universe is Connected

Here is what they discovered:

The Rate: About 4% to 9% of all flares on these stars are "sympathetic." One flare triggers another.
The Timing: These triggered flares usually happen within 30 minutes to 1.5 hours of the first one.
The Connection: This matches the rate we see on our own Sun perfectly.

This is a big deal because it means the physics of our Sun isn't unique. The same "contagious" behavior of magnetic storms happens on distant, tiny red stars too. It suggests that the laws of magnetism work the same way across the galaxy.

5. Why This Matters

Before this study, we were like people watching a movie with the sound turned off. We could see the explosions (flares), but we couldn't hear the chain reaction.

By building TOFFEE, the team turned the sound back on. They proved that stars, just like our Sun, have a "social" side where one event can trigger another nearby. It's a reminder that even in the vast, cold emptiness of space, stars are connected by invisible magnetic threads, reacting to each other just like we do.

In a nutshell: Scientists built a better tool to listen to distant stars, found that they "sneeze" in pairs just like our Sun, and proved that the universe is full of connected, sympathetic storms.

1. Problem Statement

Sympathetic flaring is a phenomenon where a flare in one active region on a star triggers a subsequent flare in a nearby, distinct active region. While well-documented on the Sun (occurring at a rate of ~5% with a lag of ~1 hour), there has been no widespread, statistically robust confirmation of this phenomenon on other stars.

The primary challenge in detecting sympathetic flares on other stars is the lack of spatial resolution; astronomers cannot observe the stellar surface to see if two flares originate from different active regions. Consequently, researchers must rely on Wait Time Distributions (WTD). If flares are purely random (a stationary Poisson process), the WTD follows an exponential distribution. An excess of very short wait times relative to an exponential distribution suggests sympathetic triggering.

However, previous studies using large photometric surveys (like Kepler and TESS) have struggled with detection incompleteness. Standard flare detection algorithms often fail to identify flares that are closely separated in time or overlap with larger events, leading to a false scarcity of short wait times and masking potential sympathetic signals.

2. Methodology

A. Stellar Samples

The authors analyzed data from the TESS (Transiting Exoplanet Survey Satellite) mission, specifically utilizing 120-second cadence data. They aggregated three previously compiled samples of flaring stars:

Feinstein et al. (2024): ~3,160 stars.
Seli et al. (2025): ~14,408 stars.
Yudovich et al. (2025): ~234 stars.
Total: 16,305 unique stars (mostly M-dwarfs) and 62,450 unique light curves.

B. The `toffee` Algorithm

To overcome detection incompleteness, the authors developed a novel, open-source algorithm called toffee (TESS Overlapping Flare Finder and Energy Evaluator). Key features include:

Detrending: Uses a combination of quadratic trend fitting (per TESS orbit) and Tukey's biweight filters (via the Wotan package) to remove instrumental trends and spot modulation without attenuating flare signals.
Primary Detection: A threshold-based method (3 $\sigma$ above the global spread) that identifies flare candidates. It requires at least 3 out of 4 flux points to be above the threshold to mitigate cosmic ray false positives.
Secondary (Overlapping) Detection: This is the algorithm's core innovation. After modeling a primary flare (Gaussian rise + double exponential decay), toffee analyzes the residuals. If three consecutive points in the residuals exceed a 2 $\sigma$ $σ$ threshold, a secondary flare is identified.
- It handles flares occurring during the rise or decay of a primary flare.
- It includes a "refit" mechanism: if a secondary flare distorts the primary's decay fit, the algorithm removes the secondary points, refits the primary, and re-evaluates the residuals to recover low-amplitude secondaries.
Flags: The code tracks detection flags (primary, secondary, refitted) to assess completeness and bias.

C. Statistical Analysis

Wait Time Distribution (WTD): The authors calculated the time intervals between consecutive flares for each star.
Normalization: To account for non-stationary flare rates (e.g., activity cycles), data was normalized in year-long bins.
Modeling: The WTDs were fitted with:
1. Exponential Distribution: Represents a stationary Poisson process (random flaring).
2. Weibull Distribution: $f(t) = \lambda k (\lambda t)^{k-1} e^{-(\lambda t)^k}$ $f (t) = λk (λ t)^{k - 1} e^{- (λ t)^{k}}$ .
  - $k = 1$ : Exponential (random).
  - $k < 1$ : Excess of short wait times (sympathetic flaring).
  - $k > 1$ : Dearth of short wait times (detection incompleteness).
Bootstrapping: 1,000 resampled datasets were used to calculate uncertainties and robustness.

3. Key Contributions

Development of toffee: A publicly available algorithm specifically designed to detect closely-separated and overlapping flares, addressing a major gap in previous literature.
Massive Flare Catalog: Discovery of ~220,000 flares on ~16,000 stars, the majority of which are M-dwarfs.
First Robust Detection: The first statistically robust evidence of sympathetic flaring on stars other than the Sun.
Comparative Analysis: Demonstrated that previous flare catalogs (Seli and Yudovich) were incomplete at short wait times (yielding $k > 1$ ), whereas toffee recovered the missing short-interval events.

4. Results

A. Evidence for Sympathetic Flaring

The Wait Time Distributions for all three toffee-analyzed catalogs showed a significant excess of short wait times compared to a pure Poisson process.
Weibull Shape Parameter ( $k$ ):
- Seli (toffee): $k = 0.910 \pm 0.006$
- Yudovich (toffee): $k = 0.902 \pm 0.009$
- Feinstein (toffee): $k = 0.894 \pm 0.009$
- Note: All values are statistically significantly less than 1, confirming an excess of short wait times.
Sympathetic Rate:
- Between 4% and 9% of all flares are identified as sympathetic.
- Among the shortest wait time bin, 18% to 30% of flares are sympathetic (depending on the calculation method).
- This rate is consistent with the ~5% rate observed on the Sun.

B. Temporal Characteristics

The median wait time for sympathetic flares in the sample ranges from 0.5 to 1.5 hours.
This timing aligns closely with solar sympathetic flaring events, which typically occur within an hour of the triggering event.

C. Validation

When the authors removed secondary flare detection from toffee, the $k$ values shifted to $>1$ (e.g., $k=1.06$ ), confirming that the detection of overlapping events is essential for observing the sympathetic signal.
Comparison with the stella algorithm (used in the original Feinstein paper) showed toffee found significantly more flares, particularly in the short wait-time regime.

5. Significance

Universal Phenomenon: The study establishes that sympathetic flaring is not unique to the Sun but is a common mechanism across low-mass stars (M-dwarfs) and potentially other spectral types.
Physical Implications: While the exact physical trigger (shockwaves vs. magnetic coupling) remains unknown, the similarity in rates and timing between the Sun and other stars suggests a universal underlying physics governing stellar magnetic activity.
Methodological Advancement: The paper highlights that previous non-detections of sympathetic flaring were likely due to algorithmic limitations rather than their absence. The toffee code provides a new standard for analyzing high-cadence photometric data where overlapping events are common.
Data Availability: The authors have made the toffee code and the three flare catalogs publicly available via GitHub, facilitating future research into stellar flare statistics.