Search for Diffuse Galactic Neutrinos with the Full ANTARES Telescope Dataset

Using 15 years of data from the ANTARES neutrino telescope, this study analyzes the full all-flavor dataset to test Galactic cosmic ray emission models, ultimately deriving upper limits on the diffuse neutrino flux that are consistent with results from other experiments but do not provide stringent constraints on the tested models.

The Gist

The Great Galactic Ghost Hunt: How ANTARES Listened to the Milky Way

Imagine the Milky Way galaxy not as a quiet, starry night sky, but as a bustling, chaotic construction site. Giant cosmic cranes (supernovae) are constantly dropping heavy beams of high-energy particles called cosmic rays. These particles zoom through space, crashing into clouds of gas and dust.

When these cosmic rays hit the gas, they create a tiny, invisible explosion that produces two things:

1. Gamma rays (high-energy light).
2. Neutrinos (ghostly, tiny particles that can pass through entire planets without stopping).

For years, scientists have been trying to catch these "ghosts" to understand how the construction site works. This paper is the final report from the ANTARES telescope, a giant underwater detector located off the coast of France, which spent 15 years (2007–2022) listening for these neutrino ghosts.

Here is the story of their hunt, explained simply.

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1. The Detective's Toolkit: The Underwater Telescope

Think of the ANTARES telescope as a giant, deep-sea fishing net made of light sensors. It sits in the Mediterranean Sea, looking up through the water.

• Why underwater? The ocean is dark and quiet. When a neutrino (the ghost) finally hits a water molecule, it creates a tiny flash of blue light (Cherenkov radiation). The sensors catch this flash.
• The Two Types of Catches:
  • Tracks: Sometimes the neutrino hits a particle that shoots a long, straight line through the water (like a bullet). This is easy to trace.
  • Showers: Sometimes the neutrino hits and creates a messy, expanding burst of particles (like a firework). These are harder to spot but happen at lower energies.

ANTARES is special because it is in the Northern Hemisphere, giving it a perfect view of the center of our galaxy, where the "construction site" is busiest.

2. The Theory: What Are We Looking For?

Before looking at the data, the scientists had to guess what the "ghosts" should look like. They built several digital maps (templates) based on different theories:

• The "Smooth Sausage" Theory (Fermi-LAT/π0): This model assumes cosmic rays spread out evenly everywhere, like butter on toast. It predicts a steady, boring stream of neutrinos.
• The "Crowded City Center" Theory (KRA models): This model suggests that near the center of the galaxy, the magnetic fields are wilder and more turbulent. It predicts that the neutrino "traffic" should be much heavier and more intense right in the middle of the galaxy.
• The "Hidden Sources" Theory (DiffUSE/CRINGE): This theory suggests that some neutrinos come from invisible, tiny factories (unresolved sources) scattered around the galaxy, not just from the general gas clouds.

3. The Investigation: Comparing the Map to the Reality

The scientists took their 15 years of real data (thousands of neutrino events) and compared it against their digital maps.

They used a statistical method called Maximum Likelihood. Imagine you are trying to find a specific song in a noisy room. You have a recording of what the song should sound like (the template). You play your recording of the room (the data) and ask: "Does the noise in the room match the song, or is it just random static?"

• The Result: They checked every theory.
  • Did the data look like the "Smooth Sausage"? No.
  • Did it look like the "Crowded City Center"? No.
  • Did it look like the "Hidden Sources"? No.

In fact, the data didn't match any of the theories strongly enough to say, "Yes, this is definitely it!" The signal was too faint.

4. The "Almost" Moment: The Galactic Ridge

While they couldn't confirm a specific theory, they did find a hint.

They focused on a specific strip of the sky called the Galactic Ridge (the central spine of the galaxy). When they counted the neutrinos in this specific area, they found 1.9 times more than they expected from random background noise.

• The Analogy: Imagine you are counting cars in a parking lot. You expect 10 cars based on the time of day. You count 19. Is it a new event? Maybe. But it's not definitely a parade yet. It's a "hint" that something interesting is happening there.
• Significance: In science, a "1.9 sigma" result is like a "maybe." It's not a discovery (which usually requires 5 sigma), but it's a strong whisper that says, "Keep looking here."

5. The Verdict: What Did They Learn?

The paper concludes with a few key takeaways:

1. No Smoking Gun: They couldn't prove which specific theory about how cosmic rays travel is correct. The data is still too quiet to distinguish between the "Smooth Sausage" and the "Crowded City Center."
2. Setting the Limits: Even though they didn't find the signal, they set a "speed limit." They can now say, "If the neutrino flux were this high, we would have seen it. Since we didn't, it must be lower than this." This helps other scientists refine their theories.
3. The Future: The ANTARES telescope is now retired, but this analysis is its final gift. The scientists are passing the torch to KM3NeT, a new, even bigger detector that will be able to catch these ghosts with much higher precision.

Summary in a Nutshell

The ANTARES team spent 15 years listening to the center of our galaxy for invisible particles. They compared their listening logs to several different theories about how the galaxy works. While they didn't find a definitive answer, they found a suspicious "clue" (a slight excess of particles in the center) that suggests the galaxy is indeed producing neutrinos, just not as loudly or in the specific pattern the current theories predicted. It's a "not yet" victory, paving the way for the next generation of detectors to solve the mystery.

Technical Summary

1. Problem Statement and Scientific Context

The paper addresses the challenge of identifying the origin and propagation mechanisms of cosmic rays (CRs) within the Milky Way. While the IceCube collaboration recently identified a diffuse neutrino flux from the Milky Way, the absolute flux, spectral shape, and spatial distribution remain poorly constrained.

• The Core Issue: High-energy cosmic rays interact with interstellar gas to produce pions, which decay into gamma-rays and neutrinos. However, current models struggle to explain the observed "hardening" (flattening) of the cosmic ray spectrum toward the Galactic Center, as seen in gamma-ray data (Fermi-LAT, H.E.S.S.).
• The Gap: There is a lack of stringent constraints on phenomenological models that attempt to explain this anomaly through:
  1. Space-dependent CR transport: Assuming diffusion coefficients vary with galactocentric radius (e.g., due to magnetic field turbulence).
  2. Unresolved sources: Assuming a component of the flux comes from undetected point sources (e.g., pulsars, supernova remnants) rather than purely diffuse interactions.
• Objective: To test these competing models against the full 15-year dataset (2007–2022) from the ANTARES neutrino telescope to determine which physical scenarios best describe the observed Galactic neutrino emission.

2. Methodology

The study employs a sophisticated unbinned maximum likelihood analysis using the complete ANTARES dataset.

A. Data Samples

The analysis utilizes the final 15-year dataset, categorized into three mutually exclusive topologies to maximize sensitivity across different energy ranges:

1. Track-like events (3,392 events): Primarily muon neutrinos ($\nu_\mu$) interacting via Charged Current (CC). These offer superior angular resolution ($<0.4^\circ$).
2. Shower-high events (187 events): Cascade events at higher energies.
3. Shower-low events (219 events): Cascade events at lower energies (down to a few hundred GeV), extending the energy reach below IceCube's typical threshold.

• Background Rejection: Rigorous cuts were applied, including zenith angle constraints for tracks and Random Decision Forest (RDF) / Boosted Decision Tree (BDT) classifiers for showers to reject atmospheric muons and neutrinos.

B. Statistical Framework

• Likelihood Ratio Test: The authors compare a background-only hypothesis ($H_b$) against a signal-plus-background hypothesis ($H_s$).
• Flux Ratio ($r$): A scaling factor is fitted to the model's predicted flux. The test statistic (TS) is derived from the difference in log-likelihoods.
• Probability Density Functions (PDFs):
  • Spatial-Energy Correlation: Unlike traditional factorized approaches, the PDFs preserve the correlation between spatial position and energy.
  • Healpix Maps: Signal PDFs are constructed using Healpix sky-maps ($N_{side}=512$ for tracks, $256$ for showers) convolved with the detector response for specific energy bins.
  • Bootstrap Method: To overcome limited Monte Carlo (MC) statistics, a resampling technique is used. MC events are randomized in right ascension and declination bands to generate smooth, high-statistics PDFs without introducing artificial fluctuations.
  • Overlapping Energy Bins: To ensure stability in the energy distribution of the PDFs, events from neighboring energy bins are merged, creating a smooth spectrum that avoids shape mismatches between data and templates.

C. Models Tested

The study tests several phenomenological models predicting the diffuse Galactic neutrino flux:

1. $\pi^0$ (SSZ4R20T150C5): A standard model assuming a single power law ($\gamma = -2.7$) and homogeneous CR transport.
2. KRA$\gamma$ Models (KRA$^{5\text{PeV}}_\gamma$, KRA$^{\text{max}}_\gamma$, KRA$^{\text{min}}_\gamma$): Models incorporating space-dependent diffusion coefficients (using DRAGON/DRAGON2/HERMES codes) to explain the Galactic Center hardening.
3. DiffUSE Model: Combines a diffuse component with an "Unresolved Source Emission" (USE) component, assuming 20% of the flux comes from unresolved hadronic sources.
4. CRINGE Model: Similar to DiffUSE but uses different uncertainty sources and rigidity breaks in the diffusion coefficient.

3. Key Contributions

• Full Dataset Analysis: This is the first analysis of the entire 15-year ANTARES dataset, significantly increasing statistics compared to previous partial analyses.
• Advanced Template Method: The development of a template-based likelihood analysis that preserves the intricate spatial-energy correlations of the models and convolves them directly with the detector response, avoiding simplified parametrizations.
• Low-Energy Sensitivity: By including "shower-low" events, the analysis probes the sub-TeV to few-TeV range, a region where ANTARES has superior sensitivity compared to IceCube due to the optical properties of water and lower atmospheric background.
• Model-Independent Ridge Search: An update to the "Galactic Ridge" analysis (a model-independent search for an excess in the Galactic Center region) using the full dataset.

4. Results

• No Significant Discovery: No statistically significant signal was detected for any of the tested models. The maximum significance reached was 1.28$\sigma$ for the KRA$^{5\text{PeV}}_\gamma$ model.
• Flux Ratios:
  • The $\pi^0$ model yielded a fitted flux ratio of $\hat{r} \approx 2.7$ (implying the data prefers a higher flux than the model, but with low significance).
  • KRA$\gamma$ and DiffUSE models yielded fitted ratios around $\hat{r} \approx 0.3 - 0.6$.
• Upper Limits: 90% Confidence Level (CL) upper limits were derived.
  • The sensitivity is best for the KRA$\gamma$ models (sensitivity $\approx 0.7$ flux ratio).
  • However, the derived upper limits (ranging from 1.2 to 2.1 flux ratios) are not stringent enough to rule out any of the tested models.
• Galactic Ridge Analysis:
  • A model-independent "on-off" counting analysis of the Galactic Ridge ($|l| < 30^\circ, |b| < 2^\circ$) revealed an excess of 1.9$\sigma$ in the track channel.
  • This confirms a previous hint of a Galactic signal found in earlier ANTARES data, providing the first model-independent indication of Galactic neutrinos in this dataset.
• Comparison with IceCube: The results are compatible with IceCube's best-fit models for the Galactic Plane. The upper limits derived by ANTARES are consistent with IceCube's findings, though ANTARES provides complementary constraints in the lower energy range.

5. Significance and Conclusion

• Validation of Methods: The study demonstrates that the unbinned maximum likelihood approach with complex, spatially-dependent templates is a robust method for testing Galactic emission models.
• Physics Implications: While no definitive discovery was made, the results suggest that the "hardening" of the cosmic ray spectrum toward the Galactic Center (observed in gamma-rays) is not yet conclusively explained by neutrino data alone. The current data cannot distinguish between homogeneous transport and space-dependent diffusion models.
• Future Prospects: The analysis highlights the potential of larger datasets. The authors note that the method is highly promising for future detectors like KM3NeT, which will offer significantly higher statistics and better angular resolution, potentially allowing for the definitive identification of the physical origins of Galactic diffuse neutrino emission.
• Complementarity: The study reinforces the importance of combining data from different detectors (IceCube and ANTARES) and different energy ranges to fully characterize the Galactic neutrino sky.