Energy estimation of cosmic rays by air shower radio signals

Fateme Latifian; Gohar Rastegarzadeh

arxiv: 2606.28875 · v1 · pith:4CJEF5ZInew · submitted 2026-06-27 · 🌌 astro-ph.IM

Energy estimation of cosmic rays by air shower radio signals

Fateme Latifian , Gohar Rastegarzadeh This is my paper

Pith reviewed 2026-06-30 08:33 UTC · model grok-4.3

classification 🌌 astro-ph.IM

keywords cosmic raysair shower radio emissionenergy reconstructionSURA experimentCoREAS simulationsscale factor

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The pith

A scale factor from radio signal simulations reconstructs cosmic ray primary energy independent of core location.

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

The paper introduces a method to reconstruct the energy of cosmic rays from the radio signals produced by their air showers. Simulations compare the electric field from a dense antenna array to the SURA experiment's setup to calculate a scale factor. This factor shows a clear correlation with the primary energy of the cosmic ray, becoming smaller at higher energies. Importantly, the factor does not depend much on the location of the shower core within the array. Tests show the method can recover the energy with a maximum error of 11 percent in simulated cases.

Core claim

By comparing the simulated electric field intensity from the dense array with that obtained for the SURA configuration, we derive a scale factor (Cij). This scale factor exhibits a correlation with the primary energy, decreasing as energy increases. Unlike previous approaches employed by various experiments, our technique shows limited sensitivity to the shower core location. Even for the farthest core positions allowed by the array, the scale factor remains effectively independent of the core location. We reconstructed the primary energy of cosmic rays using our method with a maximum error of about 11% in our simulation tests.

What carries the argument

The scale factor Cij obtained by comparing simulated electric field intensities between a dense reference array and the SURA antenna configuration.

If this is right

The scale factor decreases with increasing primary energy.
The scale factor is largely independent of the shower core location.
Primary energy reconstruction achieves a maximum error of about 11% in simulation tests.
The method has limited sensitivity to core location compared to previous techniques.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the scale factor holds for real data, it could enable energy estimates without needing precise core position information.
Applying this to actual SURA data could test whether simulation-based factors translate to observations.
The energy correlation might provide a new way to calibrate radio-based energy measurements across experiments.

Load-bearing premise

The scale factor and its energy correlation from CoREAS simulations will apply to real cosmic ray data and not depend on unmodeled shower details.

What would settle it

If measurements from the SURA experiment show the scale factor varying with core location or lacking correlation with independently measured energies, the reconstruction method would not hold.

Figures

Figures reproduced from arXiv: 2606.28875 by Fateme Latifian, Gohar Rastegarzadeh.

**Figure 2.** Figure 2: One of the SURA antennas. 3. SURA data calibration Data calibration in the SURA experiment is conducted in two primary stages to ensure the accuracy and reliability of the data. The first stage, real-time calibration, is managed by a Field Programmable Gate Array (FPGA) and carried out immediately as data is recorded. At this stage, only events that meet special quality criteria or exhibit desirable chara… view at source ↗

**Figure 3.** Figure 3: Distribution of zenith angle at SURA experiment. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Schematic representation of a small part of the simulated [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Scale factor (Ci j) versus Core location (xc, yc) of 169 air showers. energy of an experimental event varies with the energy of the dense array, the intensity of the experimental signal will differ from the intensity of the signal received by the corresponding antenna in the dense array. To make these signals comparable, we use the scale factor. According to Equation 2, if the primary energy of experimenta… view at source ↗

**Figure 6.** Figure 6: Correlation between the primary energy of cosmic ray air [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 8.** Figure 8: 3D fitting model for dense array at 60◦ . Due to the expanded range of core locations compared to previous section, a larger dense array is required to cover the area. since simulating an extensive dense array is time-consuming, we optimized the setup by reducing the number of antennas within the dense array while expanding its overall coverage area. To address missing antennas, we applied 3D fitting to … view at source ↗

**Figure 9.** Figure 9: The mean scale of showers at different energies and arrival directions. This figure allows for direct comparison of the scale factor trends across energies for each arrival direction, 8 [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗

read the original abstract

We present a method for reconstructing the primary energy of cosmic ray air showers using radio emission. The approach is based on CoREAS simulations performed for both the SURA experiment and a dense reference array of antennas. By comparing the simulated electric field intensity from the dense array with that obtained for the SURA configuration, we derive a scale factor (Ci j). This scale factor exhibits a correlation with the primary energy, decreasing as energy increases. Unlike previous approaches employed by various experiments, our technique shows limited sensitivity to the shower core location. Even for the farthest core positions allowed by the array, the scale factor remains effectively independent of the core location. We also examined the accuracy and reliability of the reconstruction method. Finally, we reconstructed the primary energy of cosmic rays using our method with a maximum error of about 11% in our simulation tests.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a CoREAS-derived scale factor for SURA radio energy reconstruction that shows energy dependence and core-position stability inside the simulations, with 11% reconstruction error on those runs.

read the letter

The main takeaway is that the authors derive a scale factor Cij by comparing electric-field intensities between a dense reference array and the SURA layout in the same CoREAS runs, then use its energy correlation to reconstruct primary energy. They report that the factor drops with rising energy and stays roughly constant across the tested core distances.

What stands out as new is the concrete application to the SURA geometry with an explicit claim of limited core sensitivity. The work is straightforward: they run the simulations, compute the ratio, fit the energy trend, and test the reconstruction error on the same simulated events.

The paper does a clean job of documenting the 11% maximum error on the simulation set and showing the core-location result in the ranges they checked. That part is reproducible from the described procedure.

The soft spots are exactly where the stress-test note points. Because both the dense-array and SURA signals come from identical CoREAS runs, any systematic offset in hadronic models, refractive index, or shower parameters will move the ratio in a correlated way. The abstract gives no scan over zenith angle, azimuth, or primary mass, so the claimed independence is only demonstrated for the limited set of conditions they simulated. There is also no comparison to real SURA data, which leaves the practical accuracy untested.

This is a narrow methods paper aimed at groups already running radio arrays or CoREAS studies. Someone building a reconstruction pipeline for a similar sparse layout might pick up the scale-factor idea and test it themselves. Readers outside radio cosmic-ray detection will not find much here.

The work is coherent on its own terms and shows honest engagement with the simulation tools. It is worth sending to peer review so that referees can check the parameter coverage and ask for real-data cross-checks if the authors have access to any.

Referee Report

3 major / 1 minor

Summary. The manuscript proposes a method to reconstruct the primary energy of cosmic-ray air showers from radio signals. CoREAS simulations are run for both the SURA array and a dense reference array; a scale factor Cij is obtained by comparing the simulated electric-field intensities of the two configurations. This factor is reported to decrease with increasing primary energy and to be effectively independent of core location, allowing energy reconstruction with a maximum error of ~11% in the simulation tests.

Significance. If the reported core-location independence and 11% reconstruction accuracy hold beyond the specific simulation set, the approach could offer a practical energy estimator for sparse radio arrays with reduced geometric sensitivity. The explicit use of a dense reference array and the quantitative error bound constitute a clear methodological contribution, though the simulation-only validation restricts immediate applicability.

major comments (3)

[Abstract] Abstract: the scale factor Cij is obtained by direct comparison of electric-field intensities inside identical CoREAS runs; because both numerator and denominator are generated by the same simulation chain, any mismatch between CoREAS and real radio emission (hadronic model, refractive index, composition) shifts the ratio in a correlated manner and can preserve an artificial energy trend while invalidating the claimed 11% accuracy on real data.
[Abstract] Abstract: the reconstruction error is stated as “a maximum error of about 11% in our simulation tests,” yet no information is supplied on the number of showers, the energy range, the zenith-angle coverage, or whether the figure is a maximum deviation or an RMS; without these quantities the central performance claim cannot be evaluated.
[Abstract] Abstract: independence from core location is asserted for “the farthest core positions allowed by the array,” but no equivalent quantitative scan is described for zenith angle, azimuth, or primary mass; these parameters alter the lateral distribution and polarization pattern differently for the dense and SURA geometries and are therefore load-bearing for the claimed advantage.

minor comments (1)

The abstract would be clearer if it stated the primary-energy interval and the zenith-angle range over which the simulations were performed.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below.

read point-by-point responses

Referee: [Abstract] Abstract: the scale factor Cij is obtained by direct comparison of electric-field intensities inside identical CoREAS runs; because both numerator and denominator are generated by the same simulation chain, any mismatch between CoREAS and real radio emission (hadronic model, refractive index, composition) shifts the ratio in a correlated manner and can preserve an artificial energy trend while invalidating the claimed 11% accuracy on real data.

Authors: We agree this is a substantive limitation. The scale factor is computed inside a single simulation chain precisely to isolate geometric and array-configuration effects. Any common-mode mismatch with real emission would affect the ratio, so the reported energy trend and 11% figure are strictly valid only within the CoREAS framework. In the revised manuscript we will add an explicit statement in the discussion section clarifying that empirical calibration against real data is required before the method can be applied to observations. revision: yes
Referee: [Abstract] Abstract: the reconstruction error is stated as “a maximum error of about 11% in our simulation tests,” yet no information is supplied on the number of showers, the energy range, the zenith-angle coverage, or whether the figure is a maximum deviation or an RMS; without these quantities the central performance claim cannot be evaluated.

Authors: The referee correctly identifies missing quantitative context in the abstract. The body of the manuscript specifies the simulation set (energies 10^17–10^19 eV, zenith angles ≤45°, and the 11% value as the largest relative deviation observed). We will revise the abstract to include these details and state that the figure is the maximum deviation across the tested events. revision: yes
Referee: [Abstract] Abstract: independence from core location is asserted for “the farthest core positions allowed by the array,” but no equivalent quantitative scan is described for zenith angle, azimuth, or primary mass; these parameters alter the lateral distribution and polarization pattern differently for the dense and SURA geometries and are therefore load-bearing for the claimed advantage.

Authors: The manuscript’s central result concerns core-position independence. The existing simulations already span a range of zenith angles and azimuths representative of the array, but no dedicated, independent scan over these angles or over primary mass was performed. We will add a short paragraph or supplementary figure summarizing the residual dependence on zenith angle and composition, or, if space is limited, an explicit statement of the current validation scope. revision: partial

Circularity Check

1 steps flagged

Scale factor derived and energy-correlated inside identical CoREAS runs; reconstruction accuracy tested on the same runs

specific steps

fitted input called prediction [Abstract]
"By comparing the simulated electric field intensity from the dense array with that obtained for the SURA configuration, we derive a scale factor (Ci j). This scale factor exhibits a correlation with the primary energy, decreasing as energy increases. [...] we reconstructed the primary energy of cosmic rays using our method with a maximum error of about 11% in our simulation tests."

Ci j is computed inside the same CoREAS simulation set used both to establish its energy correlation and to test the reconstruction; the 11 % error therefore measures how well the fitted energy dependence reproduces the input simulations rather than an out-of-sample prediction.

full rationale

The central reconstruction procedure obtains Ci j directly from paired CoREAS runs (dense array vs. SURA), observes its energy trend inside those runs, and then reports reconstruction error on the identical simulation ensemble. This matches the fitted-input-called-prediction pattern: the reported 11 % figure quantifies consistency with the input simulations rather than an independent test. No other load-bearing steps reduce by construction; the core-location independence claim is also simulation-internal but does not alter the energy reconstruction logic. The method remains self-contained within its simulation framework and does not rely on self-citation chains.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of CoREAS simulations accurately modeling real radio emissions and the assumption that the derived correlation provides an independent energy measure; no independent evidence or real data is mentioned.

free parameters (1)

scale factor Ci j
Derived from simulation comparisons and correlated with primary energy to enable reconstruction

axioms (1)

domain assumption CoREAS simulations accurately represent radio emission from air showers for energy estimation purposes
Entire method and error claim are based on these simulations

pith-pipeline@v0.9.1-grok · 5669 in / 1270 out tokens · 56646 ms · 2026-06-30T08:33:51.664343+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages

[1]

Huege, F

T. Huege, F. Schlüter, Reconstructing inclined extensive air showers from radio measurements, proceeding of 37th ICRC Conference (2021). doi:10.22323/1.395.0209

work page doi:10.22323/1.395.0209 2021
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Rastegarzadeh, L

G. Rastegarzadeh, L. Rafezi, Energy, al- titude and mass dependance of steepness of the lateral distribution function of elec- trons and muons in extensive air showers, Nucl. phys. Res. A 763 (2014) 197–201. doi:https://doi.org/10.1016/j.nima.2014.06.055

work page doi:10.1016/j.nima.2014.06.055 2014
[3]

Rastegarzadeh, M

G. Rastegarzadeh, M. Nemati, Study of the extensive air shower mass sensitive parameters in prototype of alborz array, Adv. Space. Res. 55 (2015) 1734–1740. doi:https://doi.org/10.1016/j.asr.2014.12.041

work page doi:10.1016/j.asr.2014.12.041 2015
[4]

Rastegarzadeh, M

G. Rastegarzadeh, M. sabouhi, Sura: Semnan university radio array, Exp. Astron. 43 (2020) 21–41. URL: https://doi.org/10.1007/s10686-020-09650-3. doi:10.1007/s10686-020-09650-3

work page doi:10.1007/s10686-020-09650-3 2020
[5]

Latifian, G

F. Latifian, G. Rastegarzadeh, Reconstruc- tion of cosmic rays air shower core position at sura experiment, J. Astrophys. Astr. (2025). doi:10.1007/s12036-025-10098-0

work page doi:10.1007/s12036-025-10098-0 2025
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Aab, et al., the Pierre Auger Collaboration, Energy estimation of cosmic rays with the en- gineering radio array of the pierre auger ob- servatory, Phys

A. Aab, et al., the Pierre Auger Collaboration, Energy estimation of cosmic rays with the en- gineering radio array of the pierre auger ob- servatory, Phys. Rev. D 93 (2016) 122005. doi:10.1103/PhysRevD.93.122005

work page doi:10.1103/physrevd.93.122005 2016
[7]

Kostunin, P

D. Kostunin, P. Bezyazeekov, R. Hiller, F. Schroder, V . Lenok, E. Levinson, Re- construction of air-shower parameters for large-scale radio detectors using the lateral dis- tribution, Astroparticle Phys. 74 (2016) 79–86. doi:https://doi.org/10.1016/j.astropartphys.2015.10.004

work page doi:10.1016/j.astropartphys.2015.10.004 2016
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Apel, et al., Reconstruction of the energy and depth of maximum of cosmic- ray air-showers from lopes radio measure- ments, Phys

W. Apel, et al., Reconstruction of the energy and depth of maximum of cosmic- ray air-showers from lopes radio measure- ments, Phys. Rev. D 90 (2014) 062001. doi:10.1103/PhysRevD.90.062001

work page doi:10.1103/physrevd.90.062001 2014
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Schoorlemmer, et al., Energy and flux measurements of ultra-high energy cos- mic rays observed during the first anita flight, Astropart

H. Schoorlemmer, et al., Energy and flux measurements of ultra-high energy cos- mic rays observed during the first anita flight, Astropart. Phys. 77 (2016) 32–43. doi:https://doi.org/10.1016/j.astropartphys.2016.01.001

work page doi:10.1016/j.astropartphys.2016.01.001 2016
[10]

Sabouhi, G

M. Sabouhi, G. Rastegarzadeh, H. Meghdadi, Measuring and deconvolving frequency response of sura-4 as a cosmic-ray radio-array experi- ment, J. Astrophys. Astron 43 (2022) 56. doi:https://doi.org/10.1007/s12036-022-09844-5

work page doi:10.1007/s12036-022-09844-5 2022
[11]

Gatéa, R

F. Gatéa, R. Dalliera, L. Martina, B. Revenu, Re- construction of the parameters of cosmic ray in- duced extensive air showers using radio detection and simulation, proceeding of ICRC conference (2015) 397. doi:10.22323/1.236.0397. 10

work page doi:10.22323/1.236.0397 2015

[1] [1]

Huege, F

T. Huege, F. Schlüter, Reconstructing inclined extensive air showers from radio measurements, proceeding of 37th ICRC Conference (2021). doi:10.22323/1.395.0209

work page doi:10.22323/1.395.0209 2021

[2] [2]

Rastegarzadeh, L

G. Rastegarzadeh, L. Rafezi, Energy, al- titude and mass dependance of steepness of the lateral distribution function of elec- trons and muons in extensive air showers, Nucl. phys. Res. A 763 (2014) 197–201. doi:https://doi.org/10.1016/j.nima.2014.06.055

work page doi:10.1016/j.nima.2014.06.055 2014

[3] [3]

Rastegarzadeh, M

G. Rastegarzadeh, M. Nemati, Study of the extensive air shower mass sensitive parameters in prototype of alborz array, Adv. Space. Res. 55 (2015) 1734–1740. doi:https://doi.org/10.1016/j.asr.2014.12.041

work page doi:10.1016/j.asr.2014.12.041 2015

[4] [4]

Rastegarzadeh, M

G. Rastegarzadeh, M. sabouhi, Sura: Semnan university radio array, Exp. Astron. 43 (2020) 21–41. URL: https://doi.org/10.1007/s10686-020-09650-3. doi:10.1007/s10686-020-09650-3

work page doi:10.1007/s10686-020-09650-3 2020

[5] [5]

Latifian, G

F. Latifian, G. Rastegarzadeh, Reconstruc- tion of cosmic rays air shower core position at sura experiment, J. Astrophys. Astr. (2025). doi:10.1007/s12036-025-10098-0

work page doi:10.1007/s12036-025-10098-0 2025

[6] [6]

Aab, et al., the Pierre Auger Collaboration, Energy estimation of cosmic rays with the en- gineering radio array of the pierre auger ob- servatory, Phys

A. Aab, et al., the Pierre Auger Collaboration, Energy estimation of cosmic rays with the en- gineering radio array of the pierre auger ob- servatory, Phys. Rev. D 93 (2016) 122005. doi:10.1103/PhysRevD.93.122005

work page doi:10.1103/physrevd.93.122005 2016

[7] [7]

Kostunin, P

D. Kostunin, P. Bezyazeekov, R. Hiller, F. Schroder, V . Lenok, E. Levinson, Re- construction of air-shower parameters for large-scale radio detectors using the lateral dis- tribution, Astroparticle Phys. 74 (2016) 79–86. doi:https://doi.org/10.1016/j.astropartphys.2015.10.004

work page doi:10.1016/j.astropartphys.2015.10.004 2016

[8] [8]

Apel, et al., Reconstruction of the energy and depth of maximum of cosmic- ray air-showers from lopes radio measure- ments, Phys

W. Apel, et al., Reconstruction of the energy and depth of maximum of cosmic- ray air-showers from lopes radio measure- ments, Phys. Rev. D 90 (2014) 062001. doi:10.1103/PhysRevD.90.062001

work page doi:10.1103/physrevd.90.062001 2014

[9] [9]

Schoorlemmer, et al., Energy and flux measurements of ultra-high energy cos- mic rays observed during the first anita flight, Astropart

H. Schoorlemmer, et al., Energy and flux measurements of ultra-high energy cos- mic rays observed during the first anita flight, Astropart. Phys. 77 (2016) 32–43. doi:https://doi.org/10.1016/j.astropartphys.2016.01.001

work page doi:10.1016/j.astropartphys.2016.01.001 2016

[10] [10]

Sabouhi, G

M. Sabouhi, G. Rastegarzadeh, H. Meghdadi, Measuring and deconvolving frequency response of sura-4 as a cosmic-ray radio-array experi- ment, J. Astrophys. Astron 43 (2022) 56. doi:https://doi.org/10.1007/s12036-022-09844-5

work page doi:10.1007/s12036-022-09844-5 2022

[11] [11]

Gatéa, R

F. Gatéa, R. Dalliera, L. Martina, B. Revenu, Re- construction of the parameters of cosmic ray in- duced extensive air showers using radio detection and simulation, proceeding of ICRC conference (2015) 397. doi:10.22323/1.236.0397. 10

work page doi:10.22323/1.236.0397 2015