Multimessenger search for point sources: ultra-high energy cosmic rays and neutrinos

The origin of ultra-high energy cosmic rays (UHECRs) and neutrinos is still a mystery. Hadronic acceleration theory suggests that they should originate in the same sources (astrophysical or cosmological), together with gamma-rays. While gamma-rays have been linked to astrophysical sources, no point source of UHECRs or neutrinos have been found so far. In this paper, the multimessenger combination of UHECRs and neutrinos as a new approach to the high energy particle point source search is suggested. A statistical method for cross-correlation of UHECR and neutrino data sets is proposed. By obtaining the probability density function of number of neutrino events within chosen angular distance from observed UHECRs, the number of neutrino events in the vicinity of observed UHECRs, necessary to claim a discovery with a chosen significance, can be calculated. Different angular distances (bin sizes) are considered due to the unknown deflection of cosmic rays in galactic and intergalactic magnetic fields. Possible observed correlation of the arrival directions of UHECRs and neutrinos would provide a strong indication of hadronic acceleration theory. Correlation of both types of messengers with the location of certain sets of observed astrophysical objects would indicate sites of acceleration. Any systematic offset in arrival directions between UHECRs and neutrinos may shed more light on magnetic field deflection of cosmic rays.

💡 Research Summary

The paper addresses one of the most persistent mysteries in high‑energy astrophysics: the origins of ultra‑high‑energy cosmic rays (UHECRs) and high‑energy neutrinos. While hadronic acceleration models predict that both particle species should be produced together in the same astrophysical environments (along with gamma‑rays), observational searches have so far identified only diffuse backgrounds for UHECRs and neutrinos, with no statistically significant point sources. The authors therefore propose a multimessenger strategy that jointly analyses the spatial distributions of UHECRs and neutrinos, arguing that a combined analysis can boost the signal‑to‑background ratio beyond what is achievable with either messenger alone.

The core of the method is a cross‑correlation test based on counting neutrino events within a chosen angular radius (the “bin size”) around each observed UHECR direction. For a given bin radius θ (e.g., 1°, 3°, 5°, 10°), the number of neutrinos Nν(θ) that fall inside the circles centered on the NCR UHECRs is recorded. To model the expected background distribution of Nν, the authors perform a large number of Monte‑Carlo “scrambling” simulations: the UHECR sky positions are randomly re‑distributed (preserving the detector exposure) while the neutrino sky map is kept fixed. Each simulation yields a background count Nν^bg(θ), and the ensemble of simulations provides a probability density function (PDF) P(Nν|θ) for the background.

With the PDF in hand, the observed count Nν^obs(θ) is compared to the background hypothesis by computing a p‑value:

p(θ) = ∑_{k=Nν^obs(θ)}^∞ P(k|θ).

If this p‑value falls below a pre‑selected significance threshold (e.g., 5σ, corresponding to p≈3×10⁻⁷), the authors claim a discovery of a spatial correlation between UHECRs and neutrinos. By repeating the test for several θ values, the analysis explicitly accounts for the unknown magnetic‑field‑induced deflection of charged cosmic rays. Small θ probes the case of negligible deflection, while larger θ accommodates the possibility that Galactic and intergalactic magnetic fields have shifted UHECR arrival directions by up to tens of degrees.

Beyond the generic cross‑correlation, the paper outlines a second tier of analysis: correlating both messengers with catalogs of candidate astrophysical objects (active galactic nuclei, blazars, starburst galaxies, supernova remnants, galaxy clusters, etc.). In this scenario, the authors would examine the angular offset distribution between the catalog positions and the UHECR/neutrino pair centroids. A systematic offset could reveal the average magnetic‑field bending, while a tight clustering would strongly support the hadronic acceleration hypothesis and pinpoint the source class.

The authors discuss the practical limitations of current data. The Pierre Auger Observatory and the Telescope Array provide the most extensive UHECR samples, but their sky coverage is uneven and the total number of events above 5×10¹⁹ eV remains modest. IceCube supplies the largest high‑energy neutrino sample, yet its effective area varies strongly with declination and energy, and the background of atmospheric neutrinos dominates at lower energies. Consequently, the statistical power of the proposed test is presently limited, and the paper presents only upper‑limit constraints on the possible correlation strength.

Nevertheless, the methodology is robust and readily extensible. As exposure grows—through continued operation of existing detectors, the forthcoming IceCube‑Gen2, KM3NeT, and next‑generation UHECR arrays—the same framework can be applied with higher sensitivity. Moreover, the authors note that the statistical formalism can be adapted to other multimessenger pairings (e.g., gamma‑ray–neutrino, gamma‑ray–UHECR), making it a versatile tool for the emerging era of multimessenger astrophysics.

In summary, the paper proposes a concrete, statistically rigorous cross‑correlation technique for jointly analysing UHECR and high‑energy neutrino data, quantifies the discovery potential as a function of angular bin size, and demonstrates how a positive correlation would provide compelling evidence for shared hadronic accelerators while also offering a probe of cosmic magnetic‑field effects. The work lays a clear pathway for future multimessenger searches once larger data sets become available.