Modeling the Effect of the Heliospheric Magnetic Field on Cosmic Ray Muon Shadows

A. Aurisano; A. Blake; A. Habig; A. Holin; A. Kreymer; A. Perch; A. Radovic; A. Schreckenberger; A. Sousa; A. Timmons

REVIEW 2 major objections 1 minor 14 references

Modeling the Effect of the Heliospheric Magnetic Field on Cosmic Ray Muon Shadows

T0 review · 2 major / 1 minor · reviewed 2026-06-29 · grok-4.3

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Pith's one-line read The Parker spiral model of the heliospheric magnetic field matches cosmic ray muon shadows best near solar minimum.

desk verdict MINOS 13-year muon data gives a differential solar-cycle test of Parker spiral HMF shadows, but the simulation omits turbulence and the abstract supplies no quantitative fit metrics. read the letter →

arxiv 2605.29306 v1 pith:6UM6QULE submitted 2026-05-28 astro-ph.SR astro-ph.HE

MINOS+ Collaboration: P. Adamson , I. Anghel , A. Aurisano , G. Barr , A. Blake , S. V. Cao , T. J. Carroll , C. M. Castromonte

show 68 more authors

R. Chen S. Childress J. A. B. Coelho S. De Rijck J. J. Evans G. J. Feldman W. Flanagan S. Fogarty M. Gabrielyan H. R. Gallagher S. Germani R. A. Gomes M. C. Goodman P. Gouffon N. Graf N. Grossman K. Grzelak A. Habig S. R. Hahn J. Hartnell R. Hatcher A. Holin J. Huang L. W. Koerner M. Kordosky A. Kreymer J. Krueger K. Lang P. Lucas W. A. Mann M. L. Marshak N. Mayer R. Mehdiyev J. Meier W. H. Miller G. Mills D. Naples J. K. Nelson R. Nichol J. OConnor R. B. Pahlka Ž. Pavlović G. Pawloski A. Perch M. M. Pfützner D. D. Phan R. K. Plunkett N. Poonthottathil X. Qiu A. Radovic P. Sail M. C. Sanchez A. Schreckenberger R. Sharma N. Skuza A. Sousa N. Tagg J. Thomas M. A. Thomson A. Timmons J. Todd S. C. Tognini R. Toner D. Torretta P. Vahle A. Weber L. H. Whitehead S. G. Wojcicki

This is my paper

classification astro-ph.SRastro-ph.HE

keywords cosmicraymuonshadowsParkerspiralheliosphericmagneticfieldsolarminimummaximumMINOSdetectorgeomagneticspectrum

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 locates shadows in the cosmic ray muon sky cast by the Sun using data from the MINOS far detector across solar minimum, solar maximum, and the full 13-year period. Particle motions are simulated with the Parker spiral heliospheric magnetic field and a dipole geomagnetic field to produce distributions for comparison to the observed shadow positions. The model proves most consistent with the solar minimum shadow and least with the solar maximum shadow. It aligns better with a harder cosmic ray spectrum than the one observed, which signals that a more detailed heliospheric magnetic field model is needed.

What carries the argument

The Parker spiral model of the Heliospheric Magnetic Field combined with a dipole model of the Geomagnetic Field, used to simulate cosmic ray particle distributions near the Sun and compare to observed muon shadow positions.

What would settle it

A measurement showing the solar maximum shadow position matches the Parker spiral simulation when using the actual observed softer cosmic ray spectrum would indicate the simple model suffices and contradict the need for a more detailed HMF model.

Watch

Extended reading notes

Core claim

Shadows cast in the cosmic ray muon sky by the Sun were located using muon data from the MINOS far detector in Northern Minnesota. The shadows were observed independently across three time periods; near solar minimum, near solar maximum, and over the entire 13 year span of the data. A distribution of muon positions for each shadow was then sampled to simulate CR motions near the Sun using the Parker spiral model of the Heliospheric Magnetic Field and a dipole model of the Geomagnetic Field. The resulting particle distributions were then compared to their position with respect to the Sun. Results show that the Parker spiral model is most consistent with the solar minimum shadow and least cons

Load-bearing premise

The Parker spiral plus dipole GMF simulation without additional turbulence or time-varying structures is sufficient to produce particle distributions whose comparison to observed shadows can validate or invalidate the model.

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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.

Desk Editor's Note

read the letter

The main thing to know is that this paper takes 13 years of MINOS far-detector muon data, splits it into solar-minimum, solar-maximum, and full-span periods, and finds the Parker spiral plus dipole GMF simulation matches the observed shadow positions best at minimum and worst at maximum, while also preferring a harder cosmic-ray spectrum than the one actually measured.

The work does one thing cleanly: it applies a long, independent surface-muon dataset to the shadow problem and performs the obvious differential check across solar activity levels. That comparison is a legitimate extension of earlier shadow studies and the data themselves are real.

The soft spots are more substantial. The abstract asserts consistency ordering but reports none of the usual numbers—no chi-squared values, no error bars on the shadow centroids, no spectrum binning details—so the strength of the claim cannot be judged from what is written. More critically, the trajectory sampling uses only the steady Parker spiral without added turbulence or time-varying structures. Turbulence is known to deflect GeV–TeV particles by angles comparable to the reported shadow shifts, which means the reported ordering could be an artifact of the idealized field rather than evidence about the actual HMF. The spectrum-mismatch remark is interesting but likewise lacks the quantitative backing needed to evaluate it.

This is for people who work on cosmic-ray modulation and heliospheric field modeling and who want an additional observational handle beyond spacecraft measurements. A reader in that niche would get some incremental value from the dataset length and the solar-cycle split, but would still need the missing numbers and a more realistic simulation before treating the result as a firm constraint.

It deserves peer review. The dataset and the basic question are worth referee time even if the current analysis needs tightening on both the statistics and the field model.

Referee Report

2 major / 1 minor

Summary. The manuscript analyzes cosmic-ray muon shadows observed in MINOS far-detector data across three intervals (solar minimum, solar maximum, and the full 13-year span). Muon position distributions are sampled and propagated through a steady Parker-spiral HMF plus dipole GMF; the resulting simulated shadows are compared with the observed positions. The central claim is that the Parker spiral reproduces the solar-minimum shadow best and the solar-maximum shadow worst, and that the model is more consistent with a harder CR spectrum than the one actually present, implying that a more detailed HMF model is required.

Significance. If the quantitative comparison holds, the work supplies an independent observational test of the Parker spiral that highlights its inadequacy during high solar activity and motivates inclusion of turbulence or time-dependent structures. The direct use of real MINOS muon data rather than purely synthetic benchmarks is a methodological strength.

major comments (2)

[Simulation method] Simulation method (abstract and methods): the model employs only the steady Parker spiral without turbulence or time-dependent structures. Because modest HMF turbulence is known to deflect GeV–TeV particles by angles comparable to the reported shadow shifts, the ordering of consistency across solar epochs could be an artifact of the idealized field rather than evidence about the real HMF.
[Abstract] Abstract: the statements that the Parker spiral is “most consistent” with the solar-minimum shadow and “least consistent” with the solar-maximum shadow are presented without any quantitative metric (χ², Kolmogorov–Smirnov distance, error bars on the position distributions, or exclusion criteria), making it impossible to assess whether the data actually support the ordering.

minor comments (1)

The CR spectrum hardness parameter used in the simulations is mentioned only qualitatively; the specific spectral index or range should be stated explicitly together with the quantitative comparison results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We respond point-by-point to the major comments below, indicating where revisions will be incorporated.

read point-by-point responses

Referee: [Simulation method] Simulation method (abstract and methods): the model employs only the steady Parker spiral without turbulence or time-dependent structures. Because modest HMF turbulence is known to deflect GeV–TeV particles by angles comparable to the reported shadow shifts, the ordering of consistency across solar epochs could be an artifact of the idealized field rather than evidence about the real HMF.

Authors: The steady Parker spiral is deliberately adopted as the baseline HMF model to test its consistency with the MINOS observations across solar epochs, as stated in the abstract and methods. The manuscript already concludes that this simple model performs best at solar minimum and discusses plausible modifications that would affect shadow shifts. We agree turbulence can contribute deflections of comparable magnitude; we will add a clarifying sentence in the discussion section noting that turbulence (or time dependence) may modulate the absolute shifts while the relative epoch ordering still indicates the idealized model is least adequate at solar maximum. This directly supports the paper's call for more detailed HMF models. revision: partial
Referee: [Abstract] Abstract: the statements that the Parker spiral is “most consistent” with the solar-minimum shadow and “least consistent” with the solar-maximum shadow are presented without any quantitative metric (χ², Kolmogorov–Smirnov distance, error bars on the position distributions, or exclusion criteria), making it impossible to assess whether the data actually support the ordering.

Authors: We agree the abstract would benefit from explicit reference to the comparison approach. The full manuscript quantifies consistency via the displacement between observed and simulated shadow centroids together with the degree of overlap in the position distributions. We will revise the abstract to include a concise statement referencing these centroid shifts and distribution comparisons as the basis for the reported ordering of consistency. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; forward simulation compared to independent MINOS data

full rationale

The paper records muon shadow positions from independent MINOS far-detector data in three epochs, then applies the standard (unfitted) Parker spiral HMF plus dipole GMF to sample and propagate particle trajectories. The simulated position distributions are compared directly to the observed shadows. This is an external benchmark, not a self-referential fit or derivation. No parameters are adjusted to the target shadows, no self-citation supplies a uniqueness theorem or ansatz that the central claim rests upon, and the spectrum-hardness remark references an independently measured CR spectrum. The derivation chain therefore remains self-contained against external data.

Assumptions & free parameters 1 free parameters · 2 assumptions · 0 invented entities

The claim rests on the domain assumption that the Parker spiral is an adequate base model and on the choice of CR spectrum in the simulation; no new entities are introduced.

free parameters (1)

CR spectrum hardness
The abstract states the model fits better for a harder spectrum than observed, implying spectrum choice affects the result.

assumptions (2)

domain assumption Parker spiral model describes the dominant structure of the HMF for CR deflection
Invoked as the simulation input whose consistency with data is tested.
domain assumption Dipole approximation suffices for GMF in this context
Used alongside Parker spiral without further justification in abstract.

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Cite this review

Pith. "Pith review of Modeling the Effect of the Heliospheric Magnetic Field on Cosmic Ray Muon Shadows." pith.science (2026). https://pith.science/paper/6UM6QULE

@misc{pith2026260529306,
  author       = {Pith},
  title        = {Pith review of: Modeling the Effect of the Heliospheric Magnetic Field on Cosmic Ray Muon Shadows},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6UM6QULE}},
  note         = {Machine review of arXiv:2605.29306}
}

read the original abstract

Shadows cast in the cosmic ray (CR) muon sky by the Sun were located using muon data from the MINOS far detector in Northern Minnesota. The shadows were observed independently across three time periods; near solar minimum, near solar maximum, and over the entire 13 year span of the data. A distribution of muon positions for each shadow was then sampled to simulate CR motions near the Sun using the Parker spiral model of the Heliospheric Magnetic Field (HMF) and a dipole model of the Geomagnetic Field (GMF). The resulting particle distributions were then compared to their position with respect to the Sun. Results show that the Parker spiral model is most consistent with the solar minimum shadow and least consistent with the solar maximum shadow, as expected. The simple Parker spiral is more consistent with the data for a harder CR spectrum than is actually present, indicating the need for a more detailed HMF model. Plausible modifications to the Parker spiral model which would affect the overall shift of the Sun's CR shadow are discussed.

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Reference graph

Works this paper leans on

14 extracted references · 6 canonical work pages

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Pith tools

Reviewed June 29, 2026 · model on record in the stance chip above.

[1] [1]

Petr Travnicek,Detection of high-energy muons in cosmic ray showers,Charles University, CERN-THESIS-2006-032, 2004

2006

[2] [2]

P. Adamson and et al.,Observation in theMINOSfar detector of the shadowing of cosmic rays by the sun and moon,Astroparticle Physics,vol34 (jan 2011) 6, pages 457-466, [10.1016/j.astropartphys.2010.10.010]

work page doi:10.1016/j.astropartphys.2010.10.010 2011

[3] [3]

Gaisser,Cosmic Rays and Particle Physics,Cambridge, Cambridge University Press, (1990) – 24 –

Thomas K. Gaisser,Cosmic Rays and Particle Physics,Cambridge, Cambridge University Press, (1990) – 24 –

1990

[4] [4]

Michael and et al.,The magnetized steel and scintillator calorimeters of theMINOS experiment,Nuclear Instruments and Methods in Physics Research Section A,vol596 (Nov

D.G. Michael and et al.,The magnetized steel and scintillator calorimeters of theMINOS experiment,Nuclear Instruments and Methods in Physics Research Section A,vol596 (Nov

[5] [5]

2, pages 190-228, [10.1016/j.nima.2008.08.003]

work page doi:10.1016/j.nima.2008.08.003 2008

[6] [6]

Fogarty,Observation of the Cosmic Ray Shadows of the Moon and the Sun Using the MINOS Far Detector,University of Minnesota Duluth Digital Conservancy(2019)

S.J. Fogarty,Observation of the Cosmic Ray Shadows of the Moon and the Sun Using the MINOS Far Detector,University of Minnesota Duluth Digital Conservancy(2019)

2019

[7] [7]

Adamson and et al.,Observation of muon intensity variations by season with the MINOS near detector,Physical Review D,vol90 (jul 2014) 1, [10.1103/physrevd.90.012010]

P. Adamson and et al.,Observation of muon intensity variations by season with the MINOS near detector,Physical Review D,vol90 (jul 2014) 1, [10.1103/physrevd.90.012010]

work page doi:10.1103/physrevd.90.012010 2014

[8] [8]

May-Britt Kallenrode,Space Physics: An Introduction to Plasma and Particles in the Heliosphere and Magnetospheres, New York, Springer-Verlag Berlin Heidelberg, (2004) [8]Solar Cycle Progression, [https://www.swpc.noaa.gov/products/solar-cycle-progression], Accessed: 2022-06-15

2004