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REVIEW 2 major objections 5 minor 31 references

Current constraints from cosmogenic neutrinos on the fraction of protons in UHECRs

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Cosmogenic neutrinos at 1 EeV already place an 11% cap on UHECR protons.

desk verdict Useful parameter-scan application of the authors' own sweet-spot method; the qualitative constraint is solid, but the f<0.11 number is rougher than it looks. read the letter →

arxiv 1909.01932 v1 pith:3WTJCNOK submitted 2019-09-04 astro-ph.HE

Arjen van Vliet , Rafael Alves Batista , Jörg R. Hörandel This is my paper · ORCID
classification astro-ph.HE
keywords cosmogenicneutrinosultra-high-energycosmicraysprotonfractionsourceevolutionparameterEeVneutrinofluxUHECRcompositionupperlimits
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that cosmogenic neutrinos—the ones produced when ultra-high-energy cosmic rays (UHECRs) pass through extragalactic photon fields—can already be used as an interaction-model-independent probe of UHECR composition. At a neutrino energy near $E_\nu \approx 1$ EeV, the expected flux is a 'sweet spot': it depends mainly on two unknowns, the fraction $f$ of protons in UHECRs at Earth at $10^{1.55}$ EeV and the source-evolution parameter $m$, with only mild dependence on spectral index, maximum energy, and extragalactic background light. Given that current neutrino observatory upper limits sit roughly at the flux level this paper uses, the authors conclude that the combination of a large proton fraction and a strong source evolution is already excluded, specifically $f \lesssim 0.11$ for $m \gtrsim 7.1$. If correct, this gives an independent, hadronic-model-free way to bound the proton content of UHECRs and to discriminate among source classes.

What carries the argument

The load-bearing object is the 'sweet spot' at $E_\nu \approx 1$ EeV: a neutrino energy at which the predicted cosmogenic flux is nearly insensitive to the spectral index $\alpha$, the maximum source energy $E_{\max}$, and the extragalactic background light, so the flux level is effectively set by the two parameters $f$ and $m$ alone. The argument is carried by a map of constant neutrino flux contours in the $(f,m)$ plane, generated by propagating simulated proton spectra—with injection spectrum $dN/dE \propto E^{-\alpha}\exp(-E/E_{\max})$ and a broken power-law source evolution $\mathrm{SE}(z) = (1+z)^m$ for $z<1.5$, flattening above—and normalizing to the measured UHECR flux at $E_0$. Shifting to smaller $f$ scales both the cosmic-ray and neutrino spectra linearly, so each fixed flux level becomes one curve; the current upper limits then carve out the excluded side of that curve.

What would settle it

Recompute the constant-flux contours with the two extreme parameter sets (e.g. $\alpha=1.0,\ \log(E_{\max}/\mathrm{eV})=19.6$ and $\alpha=3.0,\ \log(E_{\max}/\mathrm{eV})=23$) plus an extragalactic magnetic-field model that boosts the 1 EeV flux by the maximal factor; if a non-negligible part of the region $f>0.11,\ m>7.1$ then falls below the current upper limits, the claimed exclusion is not robust. Conversely, a detected flux above the assumed reference level at 1 EeV for a model with $f\lesssim 0.11$ and $m\gtrsim 7.1$ would disprove the mapping.

Watch

Extended reading notes

Core claim

The central claim is that the existing upper limits on the cosmogenic neutrino flux at $E_\nu \approx 1$ EeV already constrain the two parameters that jointly control that flux: the fraction $f$ of protons in UHECRs at Earth at $E_0 = 10^{1.55}$ EeV and the redshift evolution $m$ of the sources. Using the sweet-spot approximation from the authors' companion work, the paper computes fixed-flux contours—for example the single-flavor level $E^2_\nu\,dN/dE_\nu = 10^{-8}$ GeV cm$^{-2}$ s$^{-1}$ sr$^{-1}$, which tracks current sensitivity—through the $(f,m)$ plane for realistic ranges of spectral index and maximum energy. Overlaying the current EeV-range neutrino upper limits, the region of strong source evolution combined with a large proton fraction is ruled out; concretely, for $m \gtrsim 7.1$ the allowed proton fraction must satisfy $f \lesssim 0.11$. That number corresponds to the source evolution of high-luminosity active galactic nuclei, so the paper reads this as: if such sources dominate UHECRs, at most about 11% of the detected cosmic rays at $E_0$ can be protons.

Load-bearing premise

The argument assumes that at $E_\nu \approx 1$ EeV the spread in predicted cosmogenic flux from the unknown spectral index, maximum energy, and extragalactic background is small compared with the distance between the contours, and that extragalactic magnetic fields change the flux by no more than a factor of a few.

Editorial extensions

If this is right

  • If a source class has strong evolution $m \gtrsim 7$, its contribution of protons at $E_0$ must stay below roughly 11%, and this bound tightens if future limits go below the current sensitivity.
  • A detection of cosmogenic neutrinos near 1 EeV would pin down the combination $(f,m)$, with the degeneracy broken by assuming a source evolution or by combining with proton-fraction estimates from other measurements.
  • Because the constraining argument does not rely on hadronic interaction models, it can be cross-checked against composition inferred from air-shower depth, where such models are required.
  • The same contours, evaluated at lower flux levels, become a forecast: next-generation radio-array neutrino detectors with roughly one or two orders of magnitude better sensitivity would constrain the proton fraction for essentially any realistic source evolution.
  • Current limits are most restrictive for large $m$; for moderate evolution, such as star-formation-like $m\sim 3$, the same flux level allows larger $f$, so the discriminating power of the sweet spot grows as limits improve.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same two-parameter degeneracy could be tested against independent composition probes at the same energy: if air-shower measurements later put a strict upper bound on protons at $E_0$ tighter than $f \lesssim 0.11$, the neutrino result would not be needed; if they disagree, it would point to a flaw in the sweet-spot assumption.
  • The normalization to the measured cosmic-ray flux at one energy ($E_0$) makes the derived $f$ sensitive to the choice of that reference energy and to the assumed proton spectral shape; recomputing the contours at a different reference energy would show how robust the 11% number is.
  • If a fraction of the highest-energy protons originates from rare sources with very high maximum energies rather than from the dominant source population, the same neutrino limits may effectively become a constraint on the luminosity of that subpopulation, not on the overall UHECR composition.
  • A null detection at 1 EeV at the next sensitivity level would push the allowed $f$ downward for all $m$, effectively excluding source classes whose evolution is strong even if their proton contribution is small.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper argues that the cosmogenic neutrino flux at a 'sweet spot' energy of Eν ≈ 1 EeV depends primarily on the fraction of protons f in UHECRs at Earth at E0 = 10^1.55 EeV and on the source evolution parameter m. Using CRPropa 3 simulations of an additional proton component, with α ∈ [1, 3] and log(Emax/EeV) ∈ [1.6, 5], the authors compute the (f, m) combinations that give a single-flavor neutrino flux of 10^-8 GeV cm^-2 s^-1 sr^-1 at 1 EeV, which they identify 'roughly' with the current sensitivity of IceCube and Auger. They conclude that the region of large f and large m is already excluded, quoting f ≲ 0.11 for m ≳ 7.1, and that this constraint is independent of hadronic interaction models. The paper is a short proceedings contribution that builds on the companion paper Ref. [1] for the 'sweet spot' property.

Significance. If the 'sweet spot' approximation holds, the paper offers a valuable, hadronic-model-independent way to constrain UHECR composition and source evolution from existing neutrino limits. The use of the public CRPropa 3 code, the explicit enumeration of the parameter ranges scanned, and the candid discussion of neglected EGMF effects are strengths. The qualitative result that a large proton fraction combined with strong source evolution is disfavored by current data is plausible and interesting. The main weakness is that the quantitative bound is tied to an unquantified 'rough' identification of the experimental limits with a single flux level, which is the load-bearing point.

major comments (2)
  1. [Sec. 4, Fig. 2] The quoted bound f ≲ 0.11 for m ≳ 7.1 is obtained by equating the current Auger and IceCube upper limits to a single flux level of 10^-8 GeV cm^-2 s^-1 sr^-1 at Eν = 1 EeV. The actual experimental limits are binned, energy-dependent upper limits with different systematics; the paper does not report the limit values at 1 EeV or overlay the differential limit curves on the predicted fluxes. Because the cosmogenic neutrino flux at fixed m scales approximately linearly with f, a factor-of-two difference between the assumed and actual sensitivity would change the f bound by a factor of two (e.g., a 90% C.L. limit of 2×10^-8 GeV cm^-2 s^-1 sr^-1 would loosen the bound to f ≲ 0.22). Since the paper itself labels the correspondence as 'roughly', the numerical headline is not supported with a stated accuracy. The authors should either compute the exclusion directly from the differential limit curves or propagate the uncertainty of the flux-level mapping into the quoted f bound.
  2. [Sec. 3, Fig. 2] The 'sweet spot' approximation from Ref. [1] is load-bearing: it justifies neglecting the dependence on α, Emax and the EBL at Eν ≈ 1 EeV. The shaded bands in Fig. 2 illustrate the spread across the scanned parameter ranges, but the paper does not quantify the width of these bands in terms of f at fixed m, nor does it compare this spread with the experimental uncertainty in the flux level. A quantitative statement (e.g., the range of f spanned by the lightest band at m = 7) is needed to assess whether the f ≲ 0.11 limit is robust against the sweet-spot approximation. In addition, the normalization to the Auger spectrum at E0 = 10^1.55 EeV carries an experimental uncertainty that is not propagated into the (f, m) contours; quoting this uncertainty would help the reader judge the significance of the constraint.
minor comments (5)
  1. [Sec. 2] After noting that EGMF effects could enhance the expected flux by up to a factor of a few, the paper states that the predictions 'can be considered as lower bounds' but does not spell out the consequence for the direction of the derived constraint; it would be helpful to state explicitly that the exclusion region in Fig. 2 is therefore conservative.
  2. [Fig. 1 caption] The caption says the TA spectrum is shown 'for comparison' but does not indicate that it appears in the left panel; please make the panel reference explicit.
  3. [Sec. 2] The phrase 'as long as f & 0.01' is imprecise; 'for f ≳ 0.01' or 'if f ≳ 0.01' would be clearer.
  4. [Sec. 2 / Fig. 2 caption] The paper switches between log(Emax/EeV) in the text and log(Emax/eV) in the Fig. 2 caption; please use one convention consistently.
  5. [Eq. (2.1)] The first and second branches of SE(z) both read (1+z)^m; although the conditions m ≤ 0 and m > 0, z < 1.5 are distinct, a brief explanatory note would avoid confusing readers into thinking this is a typo.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the f–m constraint is a forward-model comparison to external limits, not a fit disguised as a prediction.

full rationale

The derivation chain is not circular. The paper defines f as the fraction of protons in UHECRs at Earth at E0 = 10^1.55 EeV, normalizes the simulated proton spectrum to the externally measured Auger cosmic-ray spectrum, computes the corresponding cosmogenic neutrino flux with CRPropa 3, and then compares that flux to external IceCube and Auger neutrino upper limits. The target combination (f, m) is therefore not fitted to the neutrino data; it is excluded by forward-modeling. The reliance on the authors' earlier Ref. [1] for the 'sweet spot' at E_nu ~ 1 EeV is a self-citation, but it is not circular: that result is independently published and the present paper explicitly scans the alpha and Emax ranges in Fig. 2, showing the residual parameter dependence as shaded bands. The quantitative bound f <~ 0.11 for m >~ 7.1 follows algebraically from fixing a single-flavor flux level of 10^-8 GeV cm^-2 s^-1 sr^-1 at 1 EeV, which the paper labels as only 'roughly' the current sensitivity; any discrepancy between that assumed level and the detailed experimental limits is a calibration or correctness concern, not a definitional equivalence. No equation is defined in terms of the target result, and no fitted parameter is renamed as a prediction. The paper is self-contained in its use of external benchmarks, and the self-citation does not carry the central argument by itself.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The analysis introduces no new particles or interactions; it relies on a set of modeling assumptions about the proton component, the source distribution, and the correspondence between current limits and a single flux level.

free parameters (5)
  • f (proton fraction at Earth at E0 = 10^1.55 EeV) = constrained to < 0.11 for m > 7.1 (scanned and bounded, not fitted)
    The target parameter; both cosmic-ray and neutrino fluxes are scaled by f, and the paper derives an upper limit on f from the neutrino flux bound.
  • alpha (spectral index) = scanned over 1.0-3.0 (restrictive ranges 1.5-3.0 and 2.0-3.0)
    Injection spectral index for the additional proton component; scanned because the flux at the sweet spot is supposed to depend weakly on it.
  • Emax (maximum source energy) = scanned over log10(Emax/eV) in [19.6, 23]
    Exponential cutoff energy for proton injection; scanned to test sensitivity of the neutrino flux constraint.
  • m (source evolution parameter) = scanned over 2-7; constrained for HL AGN m ~ 7.1
    Power-law index for the source evolution SE(z); constrained together with f by the neutrino limits.
  • E0 = 10^1.55 EeV (normalization energy) = 10^1.55 EeV
    Energy at which the simulated proton spectrum is normalized to the Auger flux and at which f is defined.
assumptions (5)
  • domain assumption The additional proton component is produced by identical sources distributed with source evolution SE(z) of Eq. (2.1), with an injection spectrum dN/dE proportional to E^(-alpha) exp(-E/Emax).
    Introduced in Sec. 2; the constraint applies only to such a subdominant proton component, not to the full UHECR source population.
  • domain assumption At E_nu approximately 1 EeV, the cosmogenic neutrino flux depends mainly on f and m and is minimally affected by alpha, Emax, and the EBL (the 'sweet spot', from Ref [1]).
    Invoked in Sec. 3 to justify reading the constraint from Fig. 2 while marginalizing over alpha and Emax.
  • domain assumption The contribution of heavier nuclei to the cosmogenic neutrino flux at E_nu approximately 1 EeV is negligible as long as f >= 0.01.
    Stated in Sec. 2, citing Refs. [20,3]; underlies the interpretation of f as the parameter controlling the flux.
  • domain assumption Neglecting extragalactic magnetic fields yields a lower bound on the neutrino flux, with the true flux at most a factor of a few higher in the relevant energy range.
    Sec. 2; this makes the derived constraint conservative if EGMFs increase the flux.
  • domain assumption The current differential upper limits of IceCube and Auger at E_nu approximately 1 EeV are approximately at E^2 dN/dE = 10^-8 GeV cm^-2 s^-1 sr^-1.
    Sec. 3 and Sec. 4; the quantitative bound f < 0.11 depends on this approximate correspondence.

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Cite this review

Pith. "Pith review of Current constraints from cosmogenic neutrinos on the fraction of protons in UHECRs." pith.science (2026). https://pith.science/paper/3WTJCNOK

@misc{pith2026190901932,
  author       = {Pith},
  title        = {Pith review of: Current constraints from cosmogenic neutrinos on the fraction of protons in UHECRs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3WTJCNOK}},
  note         = {Machine review of arXiv:1909.01932}
}
abstract

Cosmogenic neutrinos are created when ultra-high-energy cosmic rays (UHECRs) interact with extragalactic photon backgrounds. In general, the expected flux of these cosmogenic neutrinos depends on multiple parameters, describing the sources and propagation of UHECRs. In our recent paper (van Vliet et al. 2019), we show that a `sweet spot` occurs at a neutrino energy of $E_{\nu} \sim 1$ EeV. At that energy the flux mainly depends on two parameters, the source evolution and the fraction of protons in UHECRs at Earth for $E_p \gtrsim 30$ EeV. Therefore, with current upper limits on the cosmogenic neutrino flux at $E_{\nu} \sim 1$ EeV and assuming a certain source class, a constraint on the composition of UHECRs can be obtained. This constraint is independent of hadronic interaction models and indicates that the combination of a large proton fraction and a strong source evolution is disfavored. Upcoming neutrino experiments will be able to constrain the fraction of protons in UHECRs even further, and for any realistic model for the evolution of UHECR sources.

Figures

Figures reproduced from arXiv: 1909.01932 by the authors.

Figure 1
Figure 1. Left Examples of cosmic-ray spectra for additional proton components that can be added to the full cosmic-ray spectra. The models are normalized to the Auger flux [6] (black circles) at E0 = 101.55 EeV and then multiplied by f to get a specific proton fraction at that energy. The red solid line (with α = 1.0, Emax = 103 EeV and m = 5.0) and the dark-blue dashed-dotted line (with α = 2.5, Emax = 101.6 EeV and m = 5.0… view at source ↗
Figure 2
Figure 2. Observable fraction of protons f at ultra-high energies as a function of the source evolution parameter, m. A single-flavor flux level of 10−8 GeV cm−2 s −1 sr−1 at a neutrino energy of Eν = 1 EeV, corresponding roughly to the current sensitivity of IceCube and Auger is assumed. Three shaded areas are shown for different source parameters, from more restrictive (darker) to less restrictive (lighter). 4. Conclusions … view at source ↗

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Reference graph

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