⚛️ phenomenology

Earth rotation turns event timing into a geometric probe of UHE neutrino origin

This paper introduces a time-resolved statistical framework that leverages Earth's rotation and detector visibility to efficiently distinguish between dark matter decay and isotropic origins for ultra-high-energy neutrinos, demonstrating that incorporating temporal information significantly reduces the number of events required to exclude the dark matter hypothesis.

Original authors: Andrew Cheek, João Paulo Pinheiro, Jordi Salvado

Published 2026-07-24

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Andrew Cheek, João Paulo Pinheiro, Jordi Salvado

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 universe as a giant, dark ocean, and we are trying to figure out where the fish are swimming. For a long time, scientists have been listening for "neutrinos"—tiny, ghostly particles that zip through everything without bumping into much. Usually, these particles come from violent cosmic events like exploding stars or black holes eating matter. But recently, a super-powerful neutrino detector named KM3NeT, sitting deep in the Mediterranean Sea, caught a very special, super-energetic neutrino. It was so energetic it made headlines.

The big mystery is: where did it come from? One exciting idea is that it came from "Dark Matter" decaying. Dark Matter is the invisible stuff that holds galaxies together, and some theories say it might slowly fall apart, releasing these ghost particles. If this were true, the neutrinos should mostly come from the center of our galaxy, the Milky Way, because that's where the Dark Matter is thickest. But here's the twist: the neutrino that was caught was coming from the exact opposite direction. It's like finding a fish swimming away from the school instead of toward it. This makes the "Dark Matter" idea seem very unlikely, but is it impossible? That's the question this paper tackles.

The authors of this paper decided to play a game of "cosmic detective" using a clever trick involving time and the spinning Earth. They realized that because the Earth is round and opaque (you can't see through it), a detector underwater can only "see" neutrinos coming from a very specific, narrow strip of the sky right near the horizon. As the Earth spins, this strip of visible sky sweeps around like a lighthouse beam. This means the exact time a neutrino arrives tells you exactly which part of the sky was visible at that moment.

The team built a new way to test the Dark Matter theory. Instead of just looking at where the neutrino came from (its direction), they added when it arrived. They ran computer simulations to see how many more neutrinos KM3NeT would need to catch to prove whether the Dark Matter idea is right or wrong.

Here is what they found:

The Single Event: For that one specific neutrino they caught (called KM3-230213A), the Dark Matter idea is still possible, but it's not the favorite. The math says there's about a 13% to 15% chance that this event could happen even if Dark Matter is the source. It's not a "no," but it's a "maybe, probably not."
The Power of Time: The most important discovery is that using the time of arrival makes the test much sharper. If they only looked at direction, they would need to catch about 33 to 43 more neutrinos to be sure. If they looked at direction and the average visibility, they'd need about 22 to 27. But by using the exact arrival time for every single event, they found they would only need about 14 to 16 events to confirm or rule out the Dark Matter theory.
The Verdict: The paper doesn't say Dark Matter is definitely the answer, nor does it say it's definitely wrong. It says that with just a handful more of these super-energetic neutrinos, we will finally know for sure. The "time" of the event is the secret key that turns a blurry picture into a clear one.

So, the next time you hear about a cosmic mystery, remember: sometimes, knowing when something happened is just as important as knowing where it happened. The Earth's spin is giving us a free, rotating spotlight, and this paper shows us how to use it to catch the truth about the universe's darkest secrets.

Technical Summary: Earth Rotation Turns Event Timing into a Geometric Probe of UHE Neutrino Origin

Problem Statement
The neutrino telescope KM3NeT detected an ultra-high-energy (UHE) event, KM3-230213A, with a reconstructed energy of $\sim 220$ PeV. While the event's energy is consistent with decaying super-heavy dark matter (DM), its arrival direction ( $RA, Dec \approx 94.3^\circ, -7.8^\circ$ ) is nearly opposite to the Galactic Centre (GC). Since the flux from Galactic DM decay is expected to peak strongly toward the GC, this anti-centre direction initially appears to disfavor the DM hypothesis. However, a purely spatial analysis is insufficient at these energies because the Earth becomes opaque to UHE neutrinos. Consequently, the detector is only sensitive to a narrow band of directions near the local horizon. The authors aim to quantitatively assess the DM decay hypothesis by determining if the event's direction is statistically incompatible with the DM model and forecasting how many future events are required to exclude or confirm this origin.

Methodology
The authors develop a per-event test statistic that incorporates three layers of information:

Geometric Model: They model the differential neutrino flux from DM decay as a sum of a Galactic component (dependent on the DM halo density profile, $\rho_{DM}$ ) and an isotropic extragalactic component. They utilize the Navarro–Frenk–White (NFW) profile and account for uncertainties by testing "restrictive" (centrally concentrated) and "permissive" (shallower core) halo profiles derived from hydrodynamic simulations.
Detector Visibility: Unlike previous analyses that assume an all-sky view, this work explicitly models the Earth's opacity. The visibility function $V(E, \hat{n}, t)$ is defined as the probability that a neutrino of energy $E$ arriving from direction $\hat{n}$ at time $t$ produces a detectable up-going lepton. This depends on the chord length through the Earth, the muon range, and the neutrino-nucleon cross-sections.
Time-Resolved Analysis: The core innovation is treating the arrival time of an event as an independent observable. Because KM3NeT is located near the equator, the Earth's rotation causes the visible horizon band to sweep across the sky. The arrival time $t_i$ of an event selects a specific strip of Right Ascension (RA) that was observable at that instant.

Test Statistic Definition
For a given event $i$ with arrival time $t_i$ and coordinates $(\delta_i, \alpha_i)$ , the authors define a test statistic:
$TS_i = -\log P_{DM}(t_i, \delta_i, \alpha_i) \times \psi_{GC}(\delta_i, \alpha_i)$
where $P_{DM}$ is the normalized, time-dependent probability density of the DM flux, and $\psi_{GC}$ is the angular distance to the Galactic Centre. The total statistic for $N$ events is the sum $TS_{tot} = \sum TS_i$ .
To determine significance, they generate Monte Carlo realizations under the null hypothesis (DM decay) and the alternative hypothesis (isotropic signal). The $p$ -value is calculated as the fraction of simulated DM experiments yielding a $TS_{tot}$ greater than or equal to the observed value.

Key Contributions

Time-Resolved Discrimination: The paper demonstrates that for equatorial detectors, the arrival time of an event provides crucial geometric information that is discarded in time-averaged or all-sky analyses. The daily modulation of the visible band relative to the Galactic Centre allows for stronger discrimination between anisotropic (DM) and isotropic signals.
Quantitative Exclusion Forecast: The authors provide a rigorous forecast for the number of future events required to exclude the DM hypothesis at a $p$ -value $< 0.05$ , comparing three scenarios: geometry-only, time-averaged exposure, and fully time-resolved exposure.
Robustness Analysis: The framework is shown to be robust against variations in DM halo profiles (restrictive vs. permissive) and decay channels ( $\nu\bar{\nu}$ , $\tau^+\tau^-$ , $b\bar{b}$ ).

Results

Single Event Status: For the single observed event KM3-230213A, the DM decay hypothesis is disfavoured but not excluded. The $p$ -values range from $0.065$ (geometry-only, restrictive profile) to $0.149$ (time-resolved, permissive profile). Notably, including time-resolved visibility actually increases the $p$ -value (making the event slightly more compatible with DM) compared to the geometry-only case. This is because restricting the analysis to the instantaneously visible band removes the high-density GC region from the normalization denominator, increasing the relative probability of an anti-centre arrival.
Exclusion Reach: The number of events required to exclude the DM hypothesis ( $p < 0.05$ $p < 0.05$ ) decreases significantly as more information is utilized:
- Geometry Only: $\sim 33$ (restrictive) to $43$ (permissive) events.
- Time-Averaged Exposure: $\sim 22$ to $27$ events.
- Time-Resolved Exposure: $\sim 14$ to $16$ events.
  The time-resolved approach reduces the required sample size by approximately 40% compared to the time-averaged approach.
Channel Dependence: Harder decay spectra (e.g., $b\bar{b}$ ) require fewer events for exclusion because higher energies increase Earth opacity, narrowing the visible band and amplifying the daily modulation signal.

Significance and Claims
The authors claim that their framework transforms event timing into a geometric probe of signal origin, a method generic to any UHE equatorial neutrino telescope. They argue that time information is decisive and potentially more important than spectral information for determining the origin of these neutrinos.

Immediate Impact: The current single event cannot rule out DM decay, but the statistical framework is established.
Future Outlook: A modest sample of $\sim 10$ additional UHE neutrinos would allow KM3NeT to confirm or rule out decaying DM as the common origin.
Broader Application: The methodology is applicable to other anisotropic flux hypotheses (e.g., Galactic vs. extragalactic, point sources vs. diffuse) and should be adopted by next-generation equatorial telescopes (such as TRIDENT, P-ONE, and Baikal-GVD) to separate Galactic dark matter from astrophysical backgrounds.

The paper concludes that while the specific event KM3-230213A is not a "smoking gun" for DM, the inclusion of time-resolved data significantly enhances the statistical power to test such hypotheses with future data.

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