Cosmic Ray Spectrum and Composition from PeV to EeV from the IceCube Neutrino Observatory

Karen Andeen; Matthias Plum (for the IceCube Collaboration)

REVIEW 3 major objections 5 minor 25 references

Cosmic Ray Spectrum and Composition from PeV to EeV from the IceCube Neutrino Observatory

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Cosmic rays harden near 20 PeV and soften above 100 PeV.

desk verdict An honest IceCube proceedings summary: the all-particle spectrum is the reliable part, while the composition trend is plausible but leans on companion papers and an incomplete template basis. read the letter →

arxiv 1908.08139 v1 pith:MQHJHFF4 submitted 2019-08-21 astro-ph.HE

Karen Andeen , Matthias Plum (for the IceCube Collaboration) This is my paper · ORCID

classification astro-ph.HE

keywords cosmicrayspectrumcompositionIceTopCubePeV-EeVairshowersmuonbundlesmachinelearning

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

The paper argues that the IceCube Neutrino Observatory, using the surface array IceTop together with the deep in-ice muon detector, can measure the cosmic-ray energy spectrum from roughly 300 TeV to 2 EeV and simultaneously resolve how much of the flux comes from protons, helium, oxygen, and iron. The key results are a spectral hardening near 20 PeV, a softening just above 100 PeV, and a composition that gets heavier up to about 100 PeV, after which the trend may flatten or reverse. A sympathetic reader should care because this energy range is thought to mark the transition between galactic and extragalactic cosmic-ray sources, and separating elemental spectra is one of the few direct handles on where and how cosmic rays are accelerated. The authors present this as a consistent picture across two independent analyses: an IceTop-only spectrum and an IceTop-plus-IceCube coincidence measurement.

What carries the argument

The analysis rests on two complementary observables. IceTop's shower-size parameter, $S_{125}$, is the fitted signal at 125 m from the shower axis in vertical equivalent muons and serves as a nearly composition-independent energy proxy; the in-ice array adds the muon-bundle energy loss, $dE_\mu/dX_{1500}$, plus two stochastic-loss selections that are sensitive to the primary mass. A neural network maps these five inputs to a primary energy and a mass proxy, and an unbinned kernel density estimate turns simulated proton, helium, oxygen, and iron distributions into templates that are fit to the data in energy slices to extract elemental fractions. The argument is carried by the fact that the surface signal pins down energy while the muon-bundle information pins down mass, so no composition assumption is needed for the coincident spectrum.

What would settle it

Re-analyse the same three years of data with simulations that add intermediate nuclei such as magnesium and silicon and use a post-LHC hadronic model (for example, EPOS-LHC or QGSJet-II-04). If the extracted iron flux at 100 PeV changes by more than the quoted detector systematics, or the measured mass ordering is altered, the claim that heavier elements retain a harder spectrum would be falsified. An independent cross-check would be measuring the all-particle spectrum in the same energy range with a calorimetric or radio technique and seeing whether the 20 PeV hardening and 100 PeV softening occur at the same energies within systematic errors.

Watch

Extended reading notes

Core claim

The central claim is that, with three years of data (2010-2013), IceCube measures the all-particle cosmic-ray flux and the spectra of four mass groups from about 300 TeV to 2 EeV, and that these spectra show a clear break structure: the all-particle spectrum hardens around 20 PeV and softens just above 100 PeV. The average mass increases with energy up to roughly 100 PeV, and above that energy it is consistent with either a flat or a lightening composition. The authors also claim that higher-mass elements keep a harder spectrum to higher energies than lighter elements, and that the resulting elemental spectra are consistent with the H3a and H4a galactic-propagation models, and not inconsistent with the GST and GSF phenomenological models. The IceTop-only and the coincident analyses agree with each other within uncertainties.

Load-bearing premise

The load-bearing premise is that air showers from cosmic rays can be described by only four simulated primary nuclei (proton, helium, oxygen, and iron) using the Sibyll 2.1 hadronic interaction model; if real primaries include other abundant nuclei or the interaction physics is wrong, the energy scale and the elemental fractions shift even though the qualitative spectral shape may survive.

Editorial extensions

If this is right

The spectrum is not a single power law: it hardens near 20 PeV and softens just above 100 PeV, so the knee region has substructure.
Higher-mass primaries carry the flux at the highest measured energies, meaning the transition to extragalactic sources must produce or preserve a harder heavy-nuclei component.
Because the IceTop-only and coincident spectra agree, the composition assumption used to unfold the IceTop-only spectrum does not dominate the result.
The resolved proton, helium, oxygen, and iron spectra are concrete targets for galactic acceleration and propagation models, and the agreement with H3a/H4a supports models of a galactic origin through the PeV-EeV range.

Reading between the lines

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

A direct test not performed here is to add intermediate-mass nuclei (e.g., magnesium, silicon) to the simulation; this would reveal whether the four-species assumption biases the extracted proton and iron fluxes.
Because the paper states the hadronic interaction model changes the composition scale dramatically, the robust statement is the qualitative ordering (heavier stays harder), not the absolute elemental fluxes; reweighting to post-LHC models would show how much quantitative weight can be placed on the current spectra.
A cross-calibration with an independent detector with different systematics, such as a radio or Cherenkov air-shower array, could confirm whether the 20 PeV and 100 PeV features are astrophysical breaks or artifacts of the IceTop energy scale.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

This is a short conference proceedings, not a standalone methods paper, and it should be read that way. What the paper does well is present two independent IceCube analyses of the all-particle spectrum — IceTop-alone and IceTop plus in-ice coincident — and show that they agree across three years of data. That cross-check is real, and the quoted spectral features (hardening near 20 PeV, softening above 100 PeV) are consistent with other measurements in the field. The authors also name the dominant systematic, the hadronic interaction model, and they are transparent that the absolute composition scale shifts dramatically with that choice. For a proceedings, that level of honesty is better than usual.

Where the paper is soft is in the composition extraction. The KDE templates are built from only four primaries — proton, helium, oxygen, iron — and the paper itself says in Section 8 that simulations with more intermediate elements are needed future work. That is a genuine limitation, not a manufactured one. The mass-proxy templates overlap, so unmodeled intermediate nuclei can be absorbed into the oxygen and iron components. Without a closure test that injects intermediate primaries, the specific ordering "higher mass elements retain a harder spectrum to higher energies" is not established by this paper alone. The paper does not hide this; it points to companion paper [23] for the detailed treatment, and the qualitative trend may well survive a fuller analysis. But the claim is underdetermined here.

The reader's conditional verdict is fair, and the stress-test concern about intermediate nuclei is on target. I would add that this is not a circular argument: the H4a composition prior is used in the IceTop-alone energy unfolding and is explicitly treated as a systematic, so the circularity burden is small. The all-particle spectrum is the robust deliverable; the elemental spectra are a preview.

Who is this for? Someone who wants the IceCube collaboration's official summary of the PeV–EeV spectrum and a first look at the composition trend. As a proceedings, it deserves to exist. If it were submitted as a self-contained research article, it would not be sufficient — the unfolding details and validation live in the companion papers. But as a snapshot of an important experimental result, it is worth a serious referee, provided the referee also looks at [6] and [23].

Referee Report

3 major / 5 minor

Summary. This proceedings paper reports two IceCube cosmic-ray analyses using three years of 2010-2013 data. The IceTop-alone analysis unfolds the reconstructed shower-size parameter S125 into an all-particle energy spectrum from about 300 TeV to 2 EeV, using the H4a composition model as a prior and treating the residual zenith-angle dependence as a systematic uncertainty. The IceTop/IceCube coincident analysis trains a neural network on simulated proton, helium, oxygen, and iron showers to reconstruct the primary energy and a mass proxy, then uses kernel-density-estimate templates in energy slices to extract elemental spectra for these four groups. The two all-particle spectra agree, and both show a hardening around 20 PeV and a softening just above 100 PeV. The paper further claims that higher-mass elements retain a harder spectrum to higher energies than lighter elements, with results compared to H3a, H4a, GST, and GSF models.

Significance. If the central claims hold, the paper provides an important cross-check of the cosmic-ray spectrum and composition across the galactic-to-extragalactic transition region, using two quasi-independent experimental methods with consistent results. The strength of the paper is its explicit separation of the detector-related systematic band from the hadronic-model uncertainty, and its honest admission that the composition scale is model-dependent. The all-particle spectral features are relatively robust because they are confirmed by two analyses with different systematics. The elemental composition trend, however, is the least supported part of the paper: it depends on a four-species template fit, an unquantified hadronic-model scale shift, and results that are largely deferred to a companion paper. The proceedings format makes the paper a useful status report, but the composition conclusion would need a closure test and quantitative uncertainty treatment to be fully load-bearing.

major comments (3)

[Sec. 6 and Sec. 8] The composition extraction fits KDE templates built from only four simulated primaries (proton, helium, oxygen, iron) to the neural-network mass proxy. As the paper itself notes in Sec. 8, 'updated simulations from more intermediate elements' are needed. If the real flux contains nitrogen, magnesium, silicon, or other intermediate nuclei, their mass-proxy distributions are absent from the template basis, and because the KDE templates overlap, such events can be absorbed into the oxygen and iron components. This could bias the individual elemental spectra and manufacture the claimed ordering that 'higher mass elements retain a harder spectrum to higher energies.' No closure test injecting intermediate primaries into the template fit is shown. The authors should either provide such a test or explicitly restrict the claim to the four analyzed species.
[Sec. 7 and Fig. 5] The paper states that the hadronic interaction model choice 'affects the absolute scale dramatically, particularly in the case of the composition,' but the systematic band labeled 'Total detector syst.' in Fig. 5 excludes this effect and only the detector-related systematics are shown. Consequently, the comparison of the individual elemental spectra with H3a, H4a, GST, and GSF models, and the statement that GST 'seems to deviate outside the systematic uncertainty,' do not include the dominant systematic. The hadronic-model uncertainty should be quantified and either propagated into the plotted band or clearly separated in the figure, and the model-comparison claims should be limited accordingly.
[Sec. 8 and Fig. 5] The composition trend is asserted qualitatively but the elemental spectra in Fig. 5 are not accompanied by numerical values, statistical errors, or a significance estimate. The text refers to companion paper [23] for the trend 'above 100 PeV,' and the statistical errors in that regime are acknowledged to be significant. As written, the composition claim is not quantitatively assessable from this manuscript alone. The authors should provide the numerical results or explicitly label the composition trend as a preliminary observation supported by the companion paper.

minor comments (5)

[Sec. 2] The high-energy hadronic interaction model is written as 'SYBILL 2.1'; the standard spelling is 'SIBYLL 2.1'.
[Figs. 2, 4, 5] The vertical-axis labels such as 'E3.0 dN/dEdAd dt [GeV2.0m2s1sr1]' are rendered in a way that obscures the intended exponents; using LaTeX-style superscripts would make the units and the E^3 weighting much clearer.
[Throughout] The notation for the IceTop shower-size parameter is inconsistent: the text uses S125, S_{125}, and 'S 125' interchangeably. Please standardize, preferably as S_{125}.
[Sec. 6] The kernel density estimate method is cited, but the bandwidth or smoothing choice is not described, even though the KDE templates are the basis of the composition fit. A sentence on the smoothing procedure would improve reproducibility.
[Sec. 7] The phrase 'post-LHC hadronic interaction models' is slightly ambiguous; it presumably means models tuned to LHC data. Consider rewording for clarity.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the spectrum and composition are extracted by MC-calibrated unfolding and template fits, not by returning the models used as inputs.

full rationale

The paper's derivation chain is an experimental measurement, not a closed-form derivation. The IceTop-alone spectrum is obtained by unfolding S125 using a composition assumption (H4a) that is explicitly labeled as a systematic uncertainty, and the coincident analysis trains a neural network on four simulated primaries and then fits KDE templates to the observed mass-proxy distributions. In neither case is the measured quantity defined in terms of the target result: the H4a prior affects the energy scale but is treated as a systematic, and the template fit assigns free per-species weights determined by data. The self-citations ([6], [7], [8], [18], [23]) document methods, prior IceCube analyses, or companion results; they are not used as an unverified uniqueness or existence argument. The paper itself flags the main limitation: the hadronic interaction model choice "affects the absolute scale dramatically, particularly in the case of the composition," and the outlook requests "updated simulations from more intermediate elements." These are model-dependence caveats indicating that the inferred composition may be biased if the four-species template basis is incomplete, but that is an accuracy and coverage concern, not circularity. No quoted equation or fitted parameter reduces to the paper's own inputs by construction, so the circularity score is low.

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

The central claims rest on simulation-based calibration and model assumptions, not on new free parameters or invented entities. No numerical free parameters are reported in the text. The main dependencies are the hadronic interaction model, the composition prior for IceTop-alone, the four-primary training set, and the assumption of zenith-angle independence, all counted as domain assumptions.

assumptions (5)

domain assumption CORSIKA with FLUKA and Sibyll 2.1 accurately simulates air showers and detector response in the PeV to EeV range.
Section 2: all S125-to-energy conversions and composition templates are generated from these simulations. The paper itself says in Section 7 that the hadronic interaction model choice affects the absolute scale dramatically, especially composition.
domain assumption The four simulated primaries (proton, helium, oxygen, iron) span the true cosmic ray composition.
Section 2 and Section 8: only four elemental groups are simulated, and the paper forecasts updated simulations from more intermediate elements, indicating this is a known approximation.
domain assumption The H4a composition model is a valid prior for weighting simulations in the IceTop-alone unfolding.
Section 4: H4a was chosen because it gives the most consistent results across zenith bins, and the paper acknowledges the composition assumption is one of the main systematics in the IceTop-alone energy spectrum.
domain assumption The true cosmic ray energy spectrum is independent of zenith angle.
Section 4 uses zenith-angle consistency to select the H4a composition model, so the unfolding procedure depends on this physical invariance.
domain assumption The neural network trained on simulated events generalizes to real data without additional correction.
Section 6: the network is trained on simulated air showers of the four primary types, and no cross-validation on independent data is reported in this text.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Cosmic Ray Spectrum and Composition from PeV to EeV from the IceCube Neutrino Observatory." pith.science (2026). https://pith.science/paper/MQHJHFF4

@misc{pith2026190808139,
  author       = {Pith},
  title        = {Pith review of: Cosmic Ray Spectrum and Composition from PeV to EeV from the IceCube Neutrino Observatory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MQHJHFF4}},
  note         = {Machine review of arXiv:1908.08139}
}

abstract

The IceCube Neutrino Observatory at the South Pole is a multi-component detector capable of measuring the cosmic ray energy spectrum and composition from PeV to EeV, the energy region typically thought to cover the transition from galactic to extragalactic sources of cosmic rays. The IceTop array at the surface is sensitive to the electromagnetic part of the air shower while the deep in-ice array detects the high-energy (TeV) muonic component of air showers. IceTop's reconstructed shower size parameter, S$_{125}$, is unfolded into a high statistics all-particle energy spectrum. Furthermore, for air showers that pass through both arrays, the in-ice reconstructed muon energy loss information is combined with S$_{125}$ in a machine learning algorithm to simultaneously extract both the all-particle energy spectrum and individual spectra for elemental groups. The all-particle spectra as well as spectra for individual elemental groups are presented.

Figures

Figures reproduced from arXiv: 1908.08139 by the authors.

**Figure 1.** Left: A top view of the IceTop surface array. Colors indicate the construction periods for the strings and tanks. This work will focus on IceTop-73 (IT-73) and IceCube-79 (IC-79), bordered in black [7]. Right: Relationship between S125 and primary energy in IceTop for primary protons at high (cos(θ) ≥ 0.95) zenith angles [6]. helium, oxygen and iron) are also generated to an E −1 spectrum using the IT-73/IC-79 detec… view at source ↗

**Figure 2.** All-particle energy spectrum from the IceTopalone analysis from each of the three years individually (colors), and all three years together (black) [6]. Systematic uncertainties are shown as the gray band. After event quality selections (also detailed in [8]), the uncertainty in the direction of events is ∼ 0.2◦ at 30 PeV, and the energy resolution for protons at 30 PeV is ∼ 0.05 in log10(E/GeV) [2]. This very go… view at source ↗

**Figure 3.** Left: Example of the energy loss reconstruction of a large event, where the solid red line demonstrates the average energy loss fit, the dashed red line represents the standard stochastics selection, and the dotted red line indicates the strong stochastics selection. The gray band is the approximate location of the dust layer for the slant depth of this particular event. (After [7, 17].) Right: Composition sensitivi… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Left: A comparison of the combined three-year spectra from the two analyses in these proceedings [6]: the IceTop-alone analysis (blue), and the coincident analysis (black). The gray band represents the total systematic uncertainty of the IceTop detector from the IceTop…

**Figure 5.** Figure 5: Individual spectra for the four mass groups (protons in red, helium in yellow, oxygen in green, and iron in blue) including total detector systematic compared with various predictions of cosmic ray composition (H3a, H4a, GST, and GSF [15, 24, 25]), as shown in [6]. T…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

25 extracted references · 23 canonical work pages

[23]

IceCube Collaboration, arXiv:1906.04317

arXiv 1906
[6]

Andeen and M

K. Andeen and M. Plum, EPJ Web Conf. 210 (2019) 03005

work page 2019
[1]

Aartsen et al., J

IceCube Collaboration, M. Aartsen et al., J. Inst. 12 (2017) P03012

work page 2017
[2]

Abbasi et al., Nucl

IceCube Collaboration, R. Abbasi et al., Nucl. Instr . and Meth. A 700 (2013) 188–220

work page 2013
[3]

Kampert and M

K.-H. Kampert and M. Unger, Astroparticle Physics 35 (2012) 660 – 678

work page 2012
[4]

Abbasi et al., Nucl

IceCube Collaboration, R. Abbasi et al., Nucl. Instr . and Meth. A 618 (2009) 139

work page 2009
[5]

Abbasi et al., Nucl

IceCube Collaboration, R. Abbasi et al., Nucl. Instr . and Meth. A 601 (2008) 294

work page 2008
[7]

T. Feusels. PhD thesis, Gent Uni., 2014

work page 2014

Show all 25 references

[8]

Aartsen et al., Physical Review D 88 (Aug, 2013) 042004

IceCube Collaboration, M. Aartsen et al., Physical Review D 88 (Aug, 2013) 042004

2013
[9]

Heck et al., CORSIKA: A Monte Carlo code to simulate extensive air showers, Report FZKA 6019, F orschungszentrum Karlsruhe, 1998

D. Heck et al., CORSIKA: A Monte Carlo code to simulate extensive air showers, Report FZKA 6019, F orschungszentrum Karlsruhe, 1998

1998
[10]

Heck and T

D. Heck and T. Pierog, Extensive air shower simulation with CORSIKA: A user’s guide
[11]

Battistoni et al., AIP Conference Proceedings 896 (2007) 31–49

G. Battistoni et al., AIP Conference Proceedings 896 (2007) 31–49

2007
[12]

E. Ahn, R. Engel, T. Gaisser, P. Lipari, and T. Stanev, Physical Review D 80 (2009) 94003

2009
[13]

Agostinelli et al., Nucl

S. Agostinelli et al., Nucl. Instr . and Meth. A 506 (2003) 250–303

2003
[14]

Allison et al., IEEE Transactions on Nuclear Science 53 (2006) 270–278

J. Allison et al., IEEE Transactions on Nuclear Science 53 (2006) 270–278

2006
[15]

T. K. Gaisser, Astroparticle Physics 35 (2012) 801

2012
[16]

IceCube Collaboration, M. G. Aartsen et al., J. Inst. 9 (2014) P03009

2014
[17]

De Ridder

S. De Ridder. PhD thesis, Gent Uni., 2019

2019
[18]

Abbasi et al., Astroparticle Physics 42 (2013) 33

IceCube Collaboration, R. Abbasi et al., Astroparticle Physics 42 (2013) 33

2013
[19]

Cranmer, Computer Physics Communications 136 (2001) 198 – 207

K. Cranmer, Computer Physics Communications 136 (2001) 198 – 207

2001
[20]

Pierog, I

T. Pierog, I. Karpenko, J. M. Katzy, E. Yatsenko, and K. Werner, Phys. Rev. C 92 (Sep, 2015) 034906

2015
[21]

Riehn, R

F. Riehn, R. Engel, A. Fedynitch, T. K. Gaisser, and T. Stanev, PoS(ICRC2015)558 (2016)

2016
[22]

Ostapchenko, Phys

S. Ostapchenko, Phys. Rev. D 83 (Jan, 2011) 014018

2011
[24]

T. K. Gaisser, T. Stanev, and S. Tilav, Front. Phys. (Beijing) 8 (2013) 748–758

2013
[25]

H. P. Dembinski, R. Engel, A. Fedynitch, T. Gaisser, F. Riehn, and T. Stanev,PoS(ICRC2017)533 (2018). 8

2018

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [23]

IceCube Collaboration, arXiv:1906.04317

arXiv 1906

[2] [6]

Andeen and M

K. Andeen and M. Plum, EPJ Web Conf. 210 (2019) 03005

work page 2019

[3] [1]

Aartsen et al., J

IceCube Collaboration, M. Aartsen et al., J. Inst. 12 (2017) P03012

work page 2017

[4] [2]

Abbasi et al., Nucl

IceCube Collaboration, R. Abbasi et al., Nucl. Instr . and Meth. A 700 (2013) 188–220

work page 2013

[5] [3]

Kampert and M

K.-H. Kampert and M. Unger, Astroparticle Physics 35 (2012) 660 – 678

work page 2012

[6] [4]

Abbasi et al., Nucl

IceCube Collaboration, R. Abbasi et al., Nucl. Instr . and Meth. A 618 (2009) 139

work page 2009

[7] [5]

Abbasi et al., Nucl

IceCube Collaboration, R. Abbasi et al., Nucl. Instr . and Meth. A 601 (2008) 294

work page 2008

[8] [7]

T. Feusels. PhD thesis, Gent Uni., 2014

work page 2014