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REVIEW 1 major objections 2 minor 27 references

Longitudinal Development Analysis of Extensive Air Showers Using CORSIKA Simulations

T0 review · 1 major / 2 minor · reviewed 2026-06-28 · grok-4.3

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Pith's one-line read Simulations confirm that Xmax in extensive air showers increases logarithmically with energy and decreases with primary mass.

desk verdict Routine CORSIKA runs confirm standard EAS scalings without adding new results. read the letter →

arxiv 2606.03882 v1 pith:ZPU6Z32S submitted 2026-06-02 astro-ph.HE

Ali A. Shihab , A. A. Al-Rubaiee This is my paper · ORCID
classification astro-ph.HE
keywords extensiveairshowersCORSIKAXmaxcosmicraysGaisser-Hillasfunctionlongitudinalprofileprimarycomposition
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 uses CORSIKA to simulate extensive air showers from proton, helium, and iron primaries at energies from 10^15 to 10^17 eV and zenith angles up to 45 degrees. For each of 450 showers, the Gaisser-Hillas function is fitted to the longitudinal profile to determine the depth of shower maximum Xmax and the particle number at maximum Nmax. The results reproduce the expected increase of Xmax by about 10 g/cm² per decade of energy and a mass-dependent shift of around 160 g/cm² between iron and proton at 10^17 eV, along with the sec(theta) angular scaling. These benchmarks support the use of such simulations for inferring cosmic ray composition from observations.

What carries the argument

Fitting the Gaisser-Hillas function to the simulated longitudinal particle-number profiles to extract Xmax and Nmax.

What would settle it

A measurement of Xmax in real air showers that fails to show an increase of roughly 10 g/cm² per decade of energy or a mass difference of about 160 g/cm² between proton and iron primaries at 10^17 eV would contradict the simulation results.

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Extended reading notes

Core claim

The longitudinal development of extensive air showers simulated with CORSIKA for different primaries shows a logarithmic rise in the depth of maximum Xmax with increasing primary energy at a rate of approximately 10 g/cm² per decade, with heavier primaries exhibiting systematically smaller Xmax values, differing by about 160 g/cm² between iron and protons at 10^17 eV, while also following the expected sec(theta) dependence on zenith angle.

Load-bearing premise

The Gaisser-Hillas function accurately parametrizes the longitudinal development of all simulated air showers regardless of primary type, energy, or angle.

Editorial extensions

If this is right

  • Heavier cosmic ray primaries produce air showers that reach maximum earlier than lighter ones.
  • Xmax measurements can help determine the composition of cosmic rays.
  • The CORSIKA code reliably models the multi-component development of electromagnetic, muonic, and hadronic particles in the shower.
  • These simulations serve as references for analyzing real data from air shower observatories.

Reading between the lines

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

  • If the Gaisser-Hillas parametrization holds in nature, then Xmax data from experiments should align with these simulation trends to within the reported differences.
  • Further simulations at higher energies could test whether the logarithmic trend continues or deviates.
  • Analyzing the separate components might allow for more precise primary mass estimation than using Xmax alone.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 2 minor

Summary. The manuscript presents CORSIKA 7.7500 simulations of 450 extensive air showers initiated by proton, helium, and iron primaries at 10^15–10^17 eV for zenith angles 0°, 30°, and 45°. For each primary/energy/angle combination, 50 showers are generated; the Gaisser-Hillas function is fitted to the longitudinal profiles to extract Xmax and Nmax. The reported results confirm the expected logarithmic increase of Xmax with energy (~10 g cm^{-2} per decade), a ~160 g cm^{-2} difference between proton and iron at 10^17 eV, sec(θ) scaling, and distinct electromagnetic/muonic/hadronic component behaviors, positioning the work as benchmark simulations for cosmic-ray composition studies.

Significance. If the simulation settings and fitting procedures are standard and correctly implemented, the paper supplies a controlled set of reference showers that can be useful for validating analysis pipelines in EAS studies. However, because the reported scalings are already well-established in the literature and the exercise is confirmatory rather than predictive or comparative, the overall significance remains modest unless the full shower libraries or detailed fit outputs are released for community reuse.

major comments (1)
  1. The central extraction of Xmax and Nmax (and therefore all reported trends) rests on the assumption that the Gaisser-Hillas parametrization accurately describes the longitudinal particle-number profiles for every primary, energy, and zenith angle; no fit-quality metrics (χ², residuals, or bias estimates) or comparison to alternative parametrizations are mentioned, leaving the robustness of the extracted parameters unquantified.
minor comments (2)
  1. The abstract contains minor typographic inconsistencies (e.g., “Gaisser - Hillas” with extraneous space, “sec (theta)” with space) that should be standardized.
  2. No uncertainties, standard deviations, or number of degrees of freedom are quoted for the quoted slopes or ΔXmax values, making it impossible to judge the statistical significance of the reproduced trends.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the review and the specific comment on fit-quality metrics. We address the point below and will revise the manuscript accordingly to strengthen the presentation of the Xmax and Nmax extraction.

read point-by-point responses

  1. Referee: The central extraction of Xmax and Nmax (and therefore all reported trends) rests on the assumption that the Gaisser-Hillas parametrization accurately describes the longitudinal particle-number profiles for every primary, energy, and zenith angle; no fit-quality metrics (χ², residuals, or bias estimates) or comparison to alternative parametrizations are mentioned, leaving the robustness of the extracted parameters unquantified.

    Authors: We agree that the manuscript does not report quantitative fit-quality metrics, which would better substantiate the robustness of the extracted parameters. The Gaisser-Hillas function is the conventional choice for EAS longitudinal profiles in the literature, and the trends we report align with well-established expectations. To address the concern directly, the revised manuscript will include average χ²/dof values (and their dispersion) for the fits across all primary/energy/zenith combinations, together with a short discussion of typical residuals. This addition will allow readers to evaluate the parametrization's accuracy under the simulated conditions without altering the core results. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity

full rationale

The paper reports standard CORSIKA 7.7500 Monte Carlo runs (50 showers per bin) followed by conventional Gaisser-Hillas fits to extract Xmax and Nmax. All reported scalings (logarithmic rise of Xmax with energy, mass dependence, sec(theta) behavior) are direct outputs of the simulation code and the fit; no derivation chain is presented that reduces a claimed prediction to a fitted parameter or to a self-citation. The work is a confirmatory exercise whose validity rests on the external, independently validated CORSIKA framework and the well-known Gaisser-Hillas parametrization, making the central claims self-contained against external benchmarks.

Assumptions & free parameters 1 free parameters · 1 assumptions · 0 invented entities

The analysis depends on the domain assumption that CORSIKA version 7.7500 and the Gaisser-Hillas parametrization are adequate for the energies and primaries considered; no new entities are postulated.

free parameters (1)
  • Gaisser-Hillas fit parameters per shower
    Xmax and Nmax are obtained by fitting the function to each individual simulated profile.
assumptions (1)
  • domain assumption CORSIKA 7.7500 and its hadronic interaction models correctly describe EAS development at 10^15-10^17 eV
    All reported Xmax values rest on the validity of this simulation package.

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Cite this review

Pith. "Pith review of Longitudinal Development Analysis of Extensive Air Showers Using CORSIKA Simulations." pith.science (2026). https://pith.science/paper/ZPU6Z32S

@misc{pith2026260603882,
  author       = {Pith},
  title        = {Pith review of: Longitudinal Development Analysis of Extensive Air Showers Using CORSIKA Simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZPU6Z32S}},
  note         = {Machine review of arXiv:2606.03882}
}
read the original abstract

We present a comprehensive analysis of the longitudinal development of Extensive Air Showers (EAS) simulated with CORSIKA version 7.7500 for proton, helium, and iron primaries at energies of 10^15, 10^16, and 10^17 eV across zenith angles of 0, 30, and 45 degrees. For each combination of primary type, energy, and zenith angle, 50 independent showers were simulated, resulting in a total of 450 simulated showers. The Gaisser - Hillas function was fitted to extract the depth of shower maximum (Xmax) and the number of particles at maximum (Nmax). Our results confirm the expected logarithmic increase of Xmax with energy (about 10 g/cm^2 per decade), as well as systematically shallower Xmax for heavier primaries (iron vs. proton: Delta (Xmax) equal to about 160 g/cm^2 at 10^17 eV).The simulations also reproduce the expected sec (theta) scaling behavior. Multi-component analysis reveals distinct evolutionary patterns for electromagnetic, muonic, and hadronic components. These findings provide benchmark-level simulations for cosmic-ray composition studies and validate the CORSIKA framework for multi-parameter analyses of air-shower development.

Figures

Figures reproduced from arXiv: 2606.03882 by the authors.

Figure 1
Figure 1. Comparison of longitudinal profiles for proton, helium, and iron primaries across [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Zenith angle dependence (θ = 0◦ , 30◦ , 45◦ ) for different primary types and energy selections. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Energy dependence of normalized longitudinal profiles, shown as [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Multi-component longitudinal profiles for different primaries at selected energies and [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Comparison of simulated Xmax with Pierre Auger Observatory [6] and Telescope Array [7] measurements across zenith angles, along with the theoretical 1/ cos θ prediction. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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