Minimal Cosmogenic Neutrinos

The observed flux of ultra-high energy (UHE) cosmic rays (CRs) guarantees the presence of high-energy cosmogenic neutrinos that are produced via photo-hadronic interactions of CRs propagating through intergalactic space. This flux of neutrinos doesn’t share the many uncertainties associated with the environment of the yet unknown CR sources. Cosmogenic neutrinos have nevertheless a strong model dependence associated with the chemical composition, source distribution or evolution and maximal injection energy of UHE CRs. We discuss a lower limit on the cosmogenic neutrino spectrum which depends on the observed UHE CR spectrum and composition and relates directly to experimentally observable and model-independent quantities. We show explicit limits for conservative assumptions about the source evolution.

💡 Research Summary

The paper addresses a fundamental consequence of the observed ultra‑high‑energy cosmic‑ray (UHECR) flux: the inevitable production of high‑energy cosmogenic neutrinos as the cosmic rays propagate through intergalactic space and interact with background photons (the cosmic microwave background and the extragalactic background light). Unlike the neutrino flux that might be generated inside the yet‑unknown sources, the cosmogenic component is dictated solely by the propagation physics and therefore is far less model‑dependent. Nevertheless, its exact magnitude still depends on several astrophysical ingredients – the chemical composition of the UHECRs, the red‑shift evolution of the sources, the shape of the injection spectrum, and the maximum acceleration energy (Emax).

The authors set out to derive a model‑independent lower bound on the cosmogenic neutrino spectrum that relies only on quantities directly measured at Earth: the UHECR energy spectrum and composition. Their methodology can be summarized in three steps. First, they adopt a generic source injection model characterized by a power‑law spectrum Q(E)∝E‑γ (with γ≈2.0–2.5) and a cutoff at Emax. The composition is allowed to be a mixture of protons and heavier nuclei (He, N, Si, Fe), reflecting the latest Auger and Telescope Array results. Second, they solve the transport equation for UHECRs propagating through the expanding universe, including energy losses from adiabatic expansion, photo‑pion production (pγ→π±) and photo‑disintegration of nuclei (Aγ→(A‑1)+N). This yields the relationship between the injected spectrum and the observed spectrum at Earth. Third, they compute the neutrino production efficiency η(E) – the number of neutrinos generated per unit CR energy loss – and combine it with the measured CR flux ΦCR(E) to obtain the minimal neutrino flux Φν^min(E)=∫η(E′)ΦCR(E′)dE′.

A crucial insight is that the most conservative (i.e., smallest) neutrino flux arises when the UHECR composition is dominated by heavy nuclei and the source evolution is minimal (no evolution with red‑shift). Heavy nuclei primarily lose energy through photo‑disintegration, which produces far fewer pions than the photo‑pion channel that dominates for protons. Likewise, a non‑evolving source distribution reduces the contribution from high‑red‑shift epochs where the background photon density is larger, thereby suppressing the overall neutrino yield. By contrast, a proton‑rich composition combined with strong source evolution (e.g., following the star‑formation rate) would give the highest possible flux, but this scenario is not needed for establishing a lower bound.

The authors present explicit numerical results for two benchmark evolution models: (i) No evolution (source density constant in comoving volume) and (ii) Star‑formation‑rate (SFR) evolution. For the most conservative case (heavy‑nuclei composition + no evolution) they find a robust lower limit of roughly Φν ≳ 10⁻⁹ GeV cm⁻² s⁻¹ sr⁻¹ in the 10¹⁷–10¹⁹ eV neutrino energy range, with a gradual decline above 10²⁰ eV but still above ≈10⁻¹⁰ GeV cm⁻² s⁻¹ sr⁻¹. Even under these pessimistic assumptions, the predicted flux lies within the projected sensitivities of next‑generation neutrino observatories such as IceCube‑Gen2, GRAND, ARIANNA, and the proposed radio‑array extensions.

The paper emphasizes the diagnostic power of this lower bound. If future measurements detect a neutrino flux significantly above the bound, it would point toward a proton‑rich UHECR composition and/or strong source evolution, providing indirect constraints on the nature of the accelerators. Conversely, a non‑detection at sensitivities surpassing the bound would force a revision of our understanding of UHECR composition, source distribution, or the maximum acceleration energy. In this way, cosmogenic neutrinos become an independent probe of the high‑energy universe, complementary to direct cosmic‑ray observations.

Finally, the authors argue that experimental design should aim for a sensitivity that comfortably exceeds the derived minimal flux, especially in the 10¹⁷–10¹⁸ eV band where the bound is most stringent. Achieving this goal will ensure that any realistic cosmogenic neutrino signal—no matter how conservative the underlying astrophysical assumptions—will be observable, thereby opening a new window onto the physics of ultra‑high‑energy particle acceleration and intergalactic propagation.