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Singular Templates of Imaging Cherenkov Shower distribution (STOICS): A background estimation method for Very-High-Energy $\gamma$ -ray observations

This paper introduces Singular Templates of Imaging Cherenkov Shower distribution (STOICS), a novel background estimation method for Very-High-Energy $\gamma$ -ray observations that utilizes Singular Value Decomposition to model cosmic-ray backgrounds in extended sources where traditional field-of-view regions are insufficient, demonstrating its reliability using VERITAS archival data.

Original authors: Ruo-Yu Shang, Karl Kosack, Brian Humensky

Published 2026-03-18

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CC BY 4.0

Original authors: Ruo-Yu Shang, Karl Kosack, Brian Humensky

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 you are trying to listen to a single, quiet violin playing in the middle of a massive, roaring stadium full of people.

In the world of astronomy, that "violin" is a gamma-ray source (like a dying star or a black hole) sending out high-energy light. The "roaring stadium" is the Earth's atmosphere, which is constantly bombarded by cosmic rays (particles from space that crash into the air and create a chaotic shower of secondary particles).

Telescopes called Imaging Atmospheric Cherenkov Telescopes (IACTs) are like super-sensitive ears trying to hear that violin. They can tell the difference between the "violin" (gamma rays) and the "crowd noise" (cosmic rays) because they look at the shape of the sound waves. Gamma rays make a neat, oval shape; cosmic rays make a messy, jagged shape.

The Problem: The Source is Too Big

Usually, astronomers look for small, point-like stars. They can easily find a quiet spot in the stadium (a patch of sky with no stars) to measure the background noise and subtract it from the signal.

But what if the "violin" isn't a single instrument, but a giant choir spreading out across the entire stadium?

The Issue: When the source is huge (like a "TeV halo" or a supernova remnant), it fills up the entire telescope's view. There is no "quiet spot" left in the image to measure the background noise.
The Consequence: If you can't measure the noise, you can't be sure if the signal you see is real or just a trick of the light. It's like trying to hear a choir when the whole stadium is filled with them; you can't tell where the music ends and the noise begins.

The Solution: STOICS (The "Shadow Puppet" Method)

The paper introduces a new method called STOICS (Singular Templates of Imaging Cherenkov Shower distribution). Think of it as a clever way to predict the noise without needing a quiet spot.

Here is how it works, using a creative analogy:

1. The "Bad" and the "Good"

The telescope sorts every event it sees into two piles:

The "Good" Pile (Gamma-like): Events that look like the violin (the signal we want).
The "Bad" Pile (Cosmic-ray-like): Events that look like the crowd noise (the background we need to subtract).

Usually, we throw away the "Bad" pile. But STOICS says, "Wait! The 'Bad' pile actually knows the secrets of the noise!"

2. The Pattern Recognition (The "Shadow")

Even though the "Bad" events are messy, they aren't random. They follow patterns based on the weather, the angle of the telescope, and the time of night.

The Analogy: Imagine you are trying to guess the shape of a cloud (the noise) by looking at the shadow it casts on the ground (the "Bad" events). Even if you can't see the cloud directly in the center of your view, the shadow on the edges tells you exactly what the cloud looks like.

3. The "Magic Mirror" (Singular Value Decomposition)

The scientists use a mathematical trick called Singular Value Decomposition (SVD).

The Analogy: Think of this as a magic mirror that breaks down the complex "Bad" events into simple, fundamental building blocks (like primary colors).
- One block might represent "noise that is brighter in the center."
- Another block might represent "noise that gets wiggly at the edges."
- Another might represent "noise that changes with the temperature."

By looking at the "Bad" events in the current observation, the method figures out which "building blocks" are active right now.

4. Reconstructing the Noise

Once the method knows which "building blocks" are active, it uses them to reconstruct a map of what the noise should look like in the "Good" pile (where the signal is).

It's like saying: "Based on the messy shadows on the floor, I can mathematically draw a perfect picture of the cloud in the sky, even though the cloud is hiding behind the choir."

Why This Matters

Before this method, if a source was too big, astronomers had to give up or make wild guesses.

With STOICS: They can now study giant, diffuse objects (like the "TeV halos" around pulsars) with high precision.
The Result: They can finally measure the true shape and energy of these cosmic choirs, helping us understand how particles are accelerated to incredible speeds in the universe.

In a Nutshell

STOICS is a smart detective that realizes the "clues" (the messy cosmic rays) are hiding in plain sight. By using advanced math to find the patterns in the "clues," it can predict exactly what the background noise looks like, even when the source of interest covers the entire view. This allows astronomers to finally hear the "music" of the universe, even when the "stadium" is completely full.

1. Problem Statement

Imaging Atmospheric Cherenkov Telescopes (IACTs), such as VERITAS, are designed to detect Very-High-Energy (VHE) $\gamma$ -rays. However, a significant challenge arises when observing extended sources (e.g., evolved pulsar wind nebulae, supernova remnants, or TeV halos) whose angular size exceeds or occupies a substantial portion of the telescope's Field of View (FoV).

The Limitation of Conventional Methods: Standard background estimation techniques (e.g., Ring Background, Reflected Region, Template Background) rely on identifying "OFF" regions within the FoV that are free of $\gamma$ -ray emission to normalize the background. When a source fills the FoV, these off-source regions are unavailable or statistically insufficient.
The Consequence: Without reliable background modeling, systematic uncertainties increase, making it difficult to distinguish true $\gamma$ -ray signals from the irreducible background of cosmic-ray (CR)-induced air showers misclassified as $\gamma$ -like events.
The Goal: Develop a method to estimate the background distribution in the $\gamma$ -like signal region using only data from the same observation run, specifically leveraging the correlations between CR-like events and background $\gamma$ -like events.

2. Methodology: STOICS

The authors propose Singular Templates of Imaging Cherenkov Shower distribution (STOICS), a method utilizing Singular Value Decomposition (SVD) to model background distributions.

A. Data Preparation and Regions

Event Classification: Events are separated into $\gamma$ $γ$ -like (Signal Region, SR) and cosmic-ray-like (Control Regions, CR) based on Hillas parameters ($MSCL$ and $MSCW$).
- SR: Passes $\gamma$ /hadron cuts ($MSCL < 0.7, MSCW < 0.6$).
- CR: Fails cuts, divided into seven distinct regions (CR1–CR7) in the parameter space.
Template Construction:
- The method searches the VERITAS archive for "OFF" runs (observations of blank sky or sources far from the target) that match the observing conditions (elevation, azimuth, night-sky brightness) of the target "ON" run.
- Event counts in the camera frame ( $X, Y$ ) are binned into pixels and serialized into profile vectors for each energy bin and region (SR and CRs).
- These vectors form a Template Matrix ( $M$ ), where rows represent different OFF runs and columns represent spatial pixels across energy bins and regions.

B. Singular Value Decomposition (SVD)

The core of STOICS is the factorization of the template matrix $M$ using SVD:
$M = \sum_{k} \sigma_k \vec{u}_k \vec{v}_k^T$
Dimensionality Reduction: The singular values ( $\sigma_k$ ) decrease rapidly. The authors find that the first $\sim 32$ singular vectors capture the significant correlations between CR-like and $\gamma$ -like background distributions, while higher-order vectors represent statistical noise.
Correlation Exploitation: The method assumes that systematic variations in the background (caused by atmospheric conditions, telescope pointing, etc.) affect both the CR-like and $\gamma$ -like regions similarly. The SVD extracts the "basis" shapes of these variations.

C. Background Prediction and Optimization

Likelihood Maximization: To predict the background for a specific ON run, the method approximates the true background profile ( $\vec{\lambda}$ ) in the SR as a linear combination of the singular vectors:
$\vec{\lambda} = \sum_{k=1}^{k_c} a_k \vec{v}_k$
The coefficients ( $a_k$ ) are determined by maximizing a Poisson likelihood function using data only from the CR-like regions. The SR pixels are kept "blind" during this optimization to prevent signal contamination.
Systematic Uncertainty: The accuracy of the model is validated by checking residuals in the CR regions. If the model fits the CR regions well, it is assumed to fit the SR background well. Systematic uncertainties are calculated based on these residuals and incorporated into the final significance calculation to prevent false positives.

3. Key Contributions

Novel Background Estimation: STOICS is the first method to use SVD to learn correlations between CR-like and $\gamma$ -like background events within a single observation, eliminating the need for off-source regions in the FoV.
Handling Extended Sources: It specifically addresses the limitation of current IACT analyses where large sources (filling the $3.5^\circ$ – $5.0^\circ$ FoV) prevent standard background normalization.
Energy-Dependent Modeling: The method naturally incorporates energy dependence, as the template matrix is constructed across multiple energy bins (0.25 TeV to 17.78 TeV), capturing how background shapes change with energy (e.g., center-peaked at low energies vs. edge-peaked at high energies).
Robustness to Systematics: By using a large library of matched OFF runs and SVD, the method effectively models subtle systematic variations (e.g., night-sky brightness, atmospheric transparency) that single-template methods might miss.

4. Results

The authors validated STOICS using archival VERITAS data across various source types:

Blank Sky Validation: Using 135 hours of blank-sky data, they demonstrated that the background model accuracy improves as the number of singular vectors ( $k_c$ ) increases. For exposures $>100$ hours, $k_c \approx 32$ is optimal. Pixel sizes smaller than $0.57^\circ \times 0.57^\circ$ were found necessary to resolve background gradients.
Point-like Sources:
- Extragalactic (1ES 0229+200, H 1426+428): The method successfully modeled backgrounds for deep exposures (up to 220 hours), showing that significance distributions outside the source remained consistent with a normal distribution, indicating no systematic bias.
- Galactic (HESS J1943+213, Cas A): The method worked effectively even for Galactic plane observations with higher night-sky background, using templates derived from extragalactic runs.
Extended Sources:
- MGRO J1908+06 and MGRO J2019+37: The method successfully detected and mapped extended $\gamma$ -ray emission in the Galactic plane. The resulting significance maps aligned with previous findings and reported source extensions, confirming the method's ability to handle sources larger than the FoV.
Systematic Uncertainty: The study showed that the error in the CR region ( $\epsilon_{CR}$ ) is a strong predictor of the error in the SR ( $\epsilon_{SR}$ ), validating the use of CR residuals to estimate systematic uncertainties.

5. Significance and Future Applications

Enabling New Science: STOICS unlocks the ability to perform precise morphological studies of large-scale structures (e.g., TeV halos, supernova remnants, galactic diffuse emission) that were previously difficult to analyze due to background estimation limitations.
CTAO Readiness: The method is highly relevant for the upcoming Cherenkov Telescope Array Observatory (CTAO). CTAO will have a larger FoV and will likely observe sources that fill the entire instrument view. STOICS can provide pre-normalized, 2D spatial background models to users without requiring prior knowledge of all sources in the FoV, significantly reducing systematic errors in future large-scale surveys.
Efficiency: It maximizes observing time by removing the need for dedicated OFF runs of blank sky, allowing all observation time to be dedicated to the target source.

In conclusion, STOICS represents a paradigm shift in IACT data analysis, moving from geometric background subtraction to a data-driven, statistical modeling approach that leverages the intrinsic correlations of air-shower events to solve the background estimation problem for extended VHE sources.