More than a decade after IceCube's discovery of a diffuse flux of high-energy astrophysical neutrinos, the sources producing that flux remain unidentified, the neutrino spectrum above 1 PeV is essentially unmeasured, the most energetic neutrino ever observed — the KM3NeT event KM3-230213A, with a parent-neutrino energy most likely of order 100–1000 PeV (median about 220 PeV) — has no confirmed origin, and cosmogenic neutrinos from ultra-high-energy cosmic rays have never been detected. This problem, posed in the TAMBO observatory literature, asks for the identification of the neutrino sky's sources (individual point sources and the populations behind the diffuse flux), the determination of the supra-PeV spectral shape, and the origin of the KM3NeT ultra-high-energy event.

Background

Neutrino astronomy began in 2013, when the IceCube Neutrino Observatory — a cubic-kilometer array of photomultipliers buried in Antarctic ice that detects the Cherenkov light (the bluish flash emitted by charged particles moving faster than light travels in ice) from neutrino-induced particle cascades and muon tracks — reported a diffuse flux of extraterrestrial neutrinos with energies from about 10 TeV to several PeV (TeV = 101210^{12} eV, PeV = 101510^{15} eV). Because neutrinos are electrically neutral and interact only weakly, they reach Earth essentially undeflected and unabsorbed, so they are unique tracers of hadronic accelerators: sites where protons or nuclei are boosted to extreme energies and collide with ambient gas or radiation, producing pions whose decays yield both neutrinos and gamma rays. The discovery paper's hope was that these neutrinos would reveal the cosmic-ray accelerators; instead, the flux has remained a diffuse, approximately isotropic glow whose individual sources have resisted identification.

A neutrino point source is a direction on the sky showing a statistically significant excess of neutrino events above the atmospheric background — neutrinos and muons created by cosmic-ray interactions in Earth's atmosphere, which dominate the event rate below roughly 100 TeV. Point-source searches must also correct for the look-elsewhere effect: scanning many sky positions and source catalogs inflates the probability of a random fluctuation mimicking a signal, so the significance of any excess must be reduced by a trials factor. Under this discipline only a few associations have survived: the flaring blazar TXS 0506+056 (a jetted active galactic nucleus, AGN, whose relativistic jet points toward Earth), coincident with the neutrino IceCube-170922A in 2018; the nearby Seyfert galaxy NGC 1068 in 2022 — Seyferts are a class of active galactic nuclei — whose neutrino emission appears to originate in the hot, magnetized plasma corona surrounding its central supermassive black hole rather than in a jet, and whose neutrino flux exceeds its gamma-ray output by orders of magnitude; and emission from the Milky Way's Galactic plane. Meanwhile, stacking and population analyses using gamma-ray catalogs have constrained GeV-bright blazars to a minority contribution, leaving the bulk of the diffuse flux attributed to source classes that are gamma-ray dim or individually too faint to resolve — candidates include AGN coronae, star-forming galaxies, and energetic transient classes.

The second open strand is spectral. At TeV–PeV energies the diffuse flux is described by a falling power law, dΦ/dE∝E−γd\Phi/dE \propto E^{-\gamma} with spectral index γ≈2.9\gamma \approx 2.9 in IceCube's cascade sample; above about 1 PeV only a handful of events exist in the world's data, so whether the spectrum continues as a single power law, softens, or cuts off is simply not measured. In February 2025 the KM3NeT collaboration — which operates Cherenkov telescopes in the Mediterranean Sea — reported an extraordinary event: a near-horizontal muon with an estimated energy of about 120 PeV, implying a parent neutrino with a median energy of about 220 PeV (68% range 110–790 PeV; 90% range 72 PeV–2.6 EeV; an independent analysis reports a most-likely range of roughly 23–2400 PeV), by far the most energetic neutrino ever observed. Its designation is KM3-230213A (initially announced as KM3-230201A). Its energy is so far above the rest of the sample that it may indicate a different class of accelerator, a rare transient, or the first cosmogenic neutrino — a neutrino produced when an ultra-high-energy cosmic ray (UHECR, above roughly 1 EeV = 101810^{18} eV) scatters on cosmic microwave background photons while propagating through intergalactic space. Cosmogenic neutrinos are a robust prediction of UHECR astrophysics but have never been detected; existing extremely-high-energy (EHE) searches have set only upper limits, already strong enough to constrain the proton fraction of UHECRs.

A structural difficulty is instrumental: optical Cherenkov telescopes lose effective area above a few PeV, while proposed radio-detection arrays (sensitive to the radio pulse emitted by neutrino-induced particle showers in dense media) only become effective above about 1 EeV, leaving a sensitivity gap between 1 PeV and 1 EeV — precisely where the KM3-230213A event lies. The Tau Air-shower Mountain-Based Observatory (TAMBO) is a proposed telescope designed to bridge this gap: it would place on one face of a deep valley an array of about 5,000 detector units covering roughly 50 square kilometers, facing the opposite cliff wall to detect air showers from tau leptons produced by Earth-skimming tau neutrinos — neutrinos that traverse the planet, interact near the surface, and spawn a tau that emerges and decays in the atmosphere above the valley. This geometry suppresses the atmospheric background and is projected to yield an exceptionally pure sample of 1–1000 PeV neutrinos with sub-degree angular resolution. The TAMBO proposal literature poses two questions: where are all the neutrino point sources, and how does the neutrino energy spectrum behave above 1 PeV — with the origin of the KM3NeT very-high-energy event as a concrete instance of both.

Problem Statement

Determine the origins and the supra-PeV spectral behavior of the high-energy astrophysical neutrino flux. Concretely: (1) identify, at statistically defensible significance corrected for trials factors, the astrophysical population(s) — and where possible the individual sources — responsible for the diffuse neutrino flux observed by IceCube, among candidates including blazars, the X-ray-bright cores (coronae) of Seyfert galaxies, star-forming galaxies, Galactic emitters, energetic transient classes, and more exotic objects; (2) establish whether the all-flavor (summed over the three neutrino flavors) astrophysical neutrino spectrum continues as a single power law above 1 PeV or softens or cuts off, and whether a second, harder component emerges toward 100 PeV; and (3) establish the origin of the KM3NeT ultra-high-energy event KM3-230213A — membership in the diffuse astrophysical flux, a steady or transient point source, or the cosmogenic component. The three requests are jointly required; a definitive result on any one of them advances the objective without by itself resolving it, and the objective is resolved only when all three are addressed. They serve one objective — characterizing where the highest-energy neutrinos come from and how their spectrum behaves — and are mutually diagnostic: the supra-PeV spectral shape and the nature of the KM3NeT event discriminate among the candidate source populations, including the cosmogenic hypothesis that would tie the neutrino flux to the ultra-high-energy cosmic-ray origin problem.

References

  1. P. Zhelnin, J. Dacpano, C. Argüelles (on behalf of the TAMBO collaboration), TAMBO: A Novel Neutrino Telescope for High-Energy Astrophysical Neutrino Detection, arXiv:2606.11230 (2026), https://arxiv.org/abs/2606.11230
  2. TAMBO Collaboration (C. A. Argüelles et al.), TAMBO: A Deep-Valley Neutrino Observatory, arXiv:2507.08070 (2025), https://arxiv.org/abs/2507.08070
  3. KM3NeT Collaboration (S. Aiello et al.), Observation of an ultra-high-energy cosmic neutrino with KM3NeT, Nature 638, 376-382 (2025), DOI:10.1038/s41586-024-08543-1, https://doi.org/10.1038/s41586-024-08543-1
  4. IceCube Collaboration, Evidence for High-Energy Extraterrestrial Neutrinos at the IceCube Detector, Science 342 (2013), DOI:10.1126/science.1242856, https://doi.org/10.1126/science.1242856
  5. IceCube Collaboration and partners, Multimessenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A, Science 361 (2018), DOI:10.1126/science.aat1378, https://doi.org/10.1126/science.aat1378
  6. IceCube Collaboration (R. Abbasi et al.), Evidence for neutrino emission from the nearby active galaxy NGC 1068, Science 378 (2022), DOI:10.1126/science.abg3395, https://doi.org/10.1126/science.abg3395
  7. IceCube Collaboration (R. Abbasi et al.), All-sky neutrino point-source search with IceCube combined track and cascade data, arXiv:2507.07275 (2025), https://arxiv.org/abs/2507.07275
  8. IceCube Collaboration (R. Abbasi et al.), Evidence for Neutrino Emission from X-Ray-bright Active Galactic Nuclei with IceCube, arXiv:2510.13403 (2025), https://arxiv.org/abs/2510.13403
  9. S. Hori, A. Desai, J. Vandenbroucke (for the IceCube Collaboration), IceCube population constraints on neutrino emission by Fermi-LAT detected active galactic nuclei, arXiv:2507.07098 (2025), https://arxiv.org/abs/2507.07098
  10. L. Saurenhaus, F. Capel, F. Oikonomou, J. Buchner, Constraining the contribution of Seyfert galaxies to the diffuse neutrino flux in light of point source observations, arXiv:2507.06110 (2025), https://arxiv.org/abs/2507.06110
  11. K. M. Groth, M. Ahlers, Deciphering the Sources of Cosmic Neutrinos, arXiv:2503.07718 (2025), https://arxiv.org/abs/2503.07718
  12. S. W. Li, P. Machado, D. Naredo-Tuero, T. Schwemberger, Clash of the Titans: ultra-high energy KM3NeT event versus IceCube data, arXiv:2502.04508 (2025), https://arxiv.org/abs/2502.04508
  13. M. S. Muzio, T. Yuan, L. Lu, Emergence of a neutrino flux above 5 PeV and implications for ultrahigh energy cosmic rays, arXiv:2502.06944 (2025), https://arxiv.org/abs/2502.06944
  14. D. S. Chattopadhyay, C. A. Argüelles, V. Brdar, Four, One, and None: Quantifying the Ultra-High-Energy Neutrino Anomaly across ANITA-IV, KM3NeT, and IceCube, arXiv:2607.19487 (2026), https://arxiv.org/abs/2607.19487
  15. T. A. Dzhatdoev, The blazar PKS 0605-085 as the origin of the KM3-230213A ultra high energy neutrino event, arXiv:2502.11434 (2025), https://arxiv.org/abs/2502.11434
  16. D. Allard, B. Baret, N. Globus, E. Parizot, Cosmogenic neutrinos from FRII galaxies as potential origin of the ultra-high-energy KM3-230213A event, arXiv:2608.16540 (2026), https://arxiv.org/abs/2608.16540
  17. M. Yu. Kuznetsov, N. A. Petrov, Y. S. Savchenko, Ultra-high energy event KM3-230213A as a cosmogenic neutrino in light of minimal UHECR flux models, arXiv:2509.09590 (2025), https://arxiv.org/abs/2509.09590
  18. M. Mukhopadhyay, S. S. Kimura, High energy neutrinos from pulsar-powered optical transients: LFBOTs as potential origin of the KM3NeT event KM3-230213A, arXiv:2601.22266 (2026), https://arxiv.org/abs/2601.22266
  19. M. Meier, B. A. Clark (for the IceCube Collaboration), A search for extremely-high-energy neutrinos with IceCube and implications for the ultra-high-energy cosmic-ray proton fraction, arXiv:2507.07497 (2025), https://arxiv.org/abs/2507.07497
  20. KM3NeT Collaboration, Search for an all-sky and a Galactic Ridge diffuse neutrino emission with the first 2 years of KM3NeT/ARCA data, arXiv:2608.06163 (2026), https://arxiv.org/abs/2608.06163