Seasonal variation of atmospheric muons in IceCube

Dennis Soldin; Paolo Desiati (for the IceCube Collaboration); Serap Tilav; Thomas K. Gaisser

REVIEW 3 major objections 4 minor 2 cited by

Seasonal variation of atmospheric muons in IceCube

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read IceCube data reveal, for the first time, that the seasonal muon rate is nonlinear in atmospheric temperature, forming a hysteresis loop with measured correlation coefficient 0.75 in 2012.

desk verdict A credible long-baseline measurement of seasonal muon-rate variation with honest model caveats, but the advertised 'first observation' of hysteresis is not quantified and therefore not established. read the letter →

arxiv 1909.01406 v1 pith:VOI5IBYB submitted 2019-09-03 astro-ph.HE

Serap Tilav , Thomas K. Gaisser , Dennis Soldin , Paolo Desiati (for the IceCube Collaboration) This is my paper · ORCID

classification astro-ph.HE

keywords seasonalvariationatmosphericmuonseffectivetemperaturehysteresisIceCubepiondecaykaonprimarycosmic-rayspectrum

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

Seven years of full IceCube data, more than half a trillion muon events at an average trigger rate of 2.15 kHz, show that the seasonal variation of the atmospheric muon rate is not a single straight-line response to atmospheric temperature. The paper reports the first observation of a nonlinear, hysteresis-like relation between the measured muon rate and a model-weighted effective temperature, with a measured correlation coefficient $\alpha_T = 0.75$ for 2012. A calculation using the same effective-temperature weighting reproduces the hysteresis qualitatively, with $\alpha_T \simeq 0.84$, and also matches sudden short-term rate jumps such as the 5.4% increase in five days in October 2012. The result matters because it indicates that the atmospheric response to temperature carries information about the vertical temperature profile, not just a single slope, and it connects directly to seasonal variations of atmospheric neutrinos in the same energy range.

What carries the argument

The load-bearing object is the model-weighted effective temperature $T_\mathrm{eff}$ of Eq. (1.2), which weights each atmospheric temperature $T(X)$ by the muon production spectrum $P_\mu(E_\mu,\theta,X)$ along the muon trajectory and by the detector effective area. Temperature enters the physics only through the critical energies $\varepsilon_\pi \simeq 115$ GeV and $\varepsilon_K \simeq 857$ GeV at $T=220$ K, Eq. (1.3), which control the competition between decay and re-interaction of charged pions and kaons. The production spectrum combines a low-energy pion and kaon decay form with a high-energy form, using the Sibyll 2.3c hadronic interaction model and the H3a nucleon flux model, and the correlation coefficient $\alpha_T$ is defined as the slope of $\delta R/\langle R\rangle$ versus $\delta T_\mathrm{eff}/\langle T_\mathrm{eff}\rangle$. That weighting is what turns a one-dimensional temperature into a prediction for the muon rate, and it is the quantity whose nonlinearity the data reveal.

What would settle it

Recompute the 2012 daily effective temperatures with a substantially different hadronic interaction model, or with pion and kaon production moments varied within their uncertainties, and re-plot $\delta R/\langle R\rangle$ against $\delta T_\mathrm{eff}/\langle T_\mathrm{eff}\rangle$. If the hysteresis loop disappears, changes orientation, or changes size by more than the statistical precision of the IceCube rate, the claimed nonlinearity is an artifact of the production-spectrum weighting; if the loop persists in roughly the same shape, the atmospheric temperature profile is the cause.

Watch

Extended reading notes

Core claim

The central discovery is that the fractional variation of the IceCube muon rate, plotted against the fractional variation of the model-weighted effective temperature for 2012, does not scatter around a straight line. It forms a loop, or hysteresis, with a fitted correlation coefficient $\alpha_T = 0.75$, close to the value expected for the roughly TeV muons that dominate the InIce-SMT8 trigger. A forward calculation using the analytic production spectrum and the same daily temperature profiles reproduces a similar but slightly smaller loop, with $\alpha_T \simeq 0.84$, and the paper attributes the loop to the austral spring: the upper atmosphere warms quickly while deeper air remains cold, so the same $T_\mathrm{eff}$ can correspond to different rates. The paper also notes that the calculated absolute rate is a factor of two higher than observed, which it attributes to the normalization of the primary nucleon spectrum, and that the calculated annual amplitude is about 2% larger than measured.

Load-bearing premise

The result assumes that the particle-physics model of how cosmic-ray nuclei produce pions and kaons in the atmosphere — implemented here with the Sibyll 2.3c interaction model and the H3a nucleon flux — is accurate enough that the effective-temperature weighting reflects the real atmosphere rather than imposing the observed curvature on the rate-temperature relation.

Editorial extensions

If this is right

The seasonal response of atmospheric muons cannot be summarized by a single $\alpha_T$; the rate versus effective temperature relation has a loop structure that encodes the vertical temperature profile.
Short-term rate jumps of several percent on day-to-week time scales are reproduced by the same effective-temperature calculation, so the production-spectrum formalism can be used to predict daily muon rates from satellite temperature profiles.
The factor-two discrepancy between calculated and observed absolute rate, together with the 0.75 versus 0.84 difference in $\alpha_T$, points to the normalization of the primary cosmic-ray nucleon spectrum as the main missing ingredient, not the temperature weighting.
Because the same formalism applies to atmospheric muon neutrinos, with kaon decay becoming the dominant neutrino source above roughly 100 GeV, simultaneous seasonal measurements of muons and neutrinos should be sensitive to the kaon-to-pion ratio.

Reading between the lines

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

If the hysteresis is truly atmospheric, replacing the Sibyll 2.3c production moments with a different hadronic model should move the curve in Fig. 3 slightly but should not erase the loop; erasure would identify the nonlinearity as an artifact of the weighting scheme rather than a property of the atmosphere.
Because the austral-spring profile drives the loop, the same analysis applied to other years should show a loop of similar shape only in years whose October temperature profiles share the same upper-stratosphere warming; a year with a different profile would be a natural test of the mechanism.
The factor-two normalization offset suggests that absolute atmospheric-muon rate measurements at IceCube could serve as a check on primary cosmic-ray flux models, provided the detector effective area and the contribution of coincident or multiple muons are known to comparable precision.

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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

Colleague,

The thing to know: this is a solid IceCube measurement of seasonal muon-rate variation, with half a trillion events over seven years, and the authors are candid about where their model fails. But the advertised novelty—the "first observation" of a hysteresis in rate vs effective temperature—is not actually established, because the paper never quantifies the loop. That is the difference between a useful progress report and a finished result.

The genuinely good parts: the daily rate data, the effective-temperature weighting built on Sibyll 2.3c and H3a, the measured alpha_T = 0.75 for 2012, the reproduction of the sharp October rate jump (5.4% measured vs 5.9% calculated), and the angular comparison of muon vs neutrino correlation as a handle on the kaon-to-pion ratio. The paper also sits honestly in the literature, citing MINOS and earlier IceCube work. The factor-of-two absolute normalization offset is admitted up front, and the authors say the seasonal amplitude is overpredicted by about 2%; that is the kind of limitation you want to see stated.

The soft spots are real but specific. First, the hysteresis figure has no error bars, no loop-area metric, and no test against a linear null. The claim that statistical fluctuations are at the 10^-4 level does not by itself prove the loop is significant; daily rates are correlated with weather, and systematic effects could mimic the pattern. Second, Fig. 3(b) is calculated with the same model-derived Teff, so it does not independently validate the nonlinearity. Third, there is no systematic uncertainty budget, so alpha_T = 0.75 floats without a sigma. These are all fixable, but they are not cosmetic; they are exactly what a referee would need before the "first time" claim can stand.

Overall, the central seasonal correlation is robust; the nonlinearity, as presented, is not. This paper is for atmospheric-muon specialists and people using IceCube neutrino seasonal corrections. It deserves peer review—serious review, not a desk reject—but with the expectation that the hysteresis claim gets a quantitative treatment and the systematics get written down.

Recommendation: send it to review, and tell the authors their strongest result is the long-baseline rate–temperature correlation, not the loop.

Referee Report

3 major / 4 minor

Summary. The paper reports a seven-year (IC86, 2011-2018) measurement of the seasonal variation of the downgoing muon rate in IceCube, using roughly half a trillion muon events. The measured daily rate is correlated with an effective atmospheric temperature computed from AIRS temperature profiles and a muon production spectrum based on Sibyll 2.3c and the H3a nucleon flux model. The central claims are: (1) a linear correlation coefficient alpha_T = 0.75 for 2012, consistent with expectations for approximately TeV muons; (2) the first observation of a nonlinear, hysteresis-like relation between muon rate and effective temperature, most pronounced during the austral spring; and (3) a model calculation using Eqs. (3.1)-(3.5) that reproduces the short-term rate features and exhibits qualitatively similar but smaller hysteresis. The paper also discusses implications for atmospheric neutrino seasonal variations and the kaon-to-pion ratio.

Significance. If the central claim holds, this is the first high-precision demonstration that the seasonal response of atmospheric muons is not a single linear function of effective temperature, which would be an important constraint on atmospheric cascade models and on the interpretation of seasonal variations of atmospheric neutrinos. The paper's strengths include a very large data set (2.15 kHz trigger rate, half a trillion events) that reduces statistical errors to the 10^-4 level, and a transparent, physically motivated calculation of the effective temperature from first-principles production spectra. The analysis is also honest about known shortcomings: it explicitly states the absolute calculated rate is off by a factor of two and that the calculated seasonal amplitude is about 2% larger than observed. However, the headline novelty, the claimed hysteresis, is not quantified or tested for statistical significance, and the measured alpha_T is quoted without an uncertainty. Because the effective-temperature definition itself depends on the production model, the nonlinearity claim needs a direct statistical test against a linear null hypothesis before it can be considered established.

major comments (3)

[Section 4, Fig. 3] The claim that the hysteresis is observed 'for the first time' is the paper's central novelty, yet the paper provides no quantitative significance test of the nonlinearity. Fig. 3(a) shows daily points without error bars, the slope is quoted as alpha_T = 0.75 with no uncertainty, and no metric such as loop area or spring-versus-autumn rate difference at equal Teff is defined or compared with the null hypothesis of a purely linear relation. Since the statistical fluctuations are stated to be at the 10^-4 level, the authors should be able to provide a straightforward chi-square or likelihood test; without it, the apparent loop could be due to correlated atmospheric or detector effects.
[Section 4, Fig. 3(b) and Eqs. (1.2), (3.1)-(3.5)] The claimed hysteresis is model-dependent because both the measured and calculated rates are plotted against the same model-derived Teff from Eq. (1.2), weighted by the Sibyll 2.3c/H3a production spectrum. If the production spectrum is wrong, the Teff weights are wrong and the loop could be an artifact of the weighting rather than a physical property of the atmospheric response. The authors state the model comparison is 'qualitatively similar, though slightly smaller,' but this is not a quantitative comparison. The factor-of-two absolute rate offset and the 2% seasonal-amplitude discrepancy reported in Section 4 further indicate that the model is not fully validated, which strengthens the need for a model-robustness test of the nonlinearity, e.g., by recomputing Teff with alternative hadronic interaction models or by checking whether the loop survives when using a purely empirical temperature weighting.
[Eq. (1.1) and Section 4, Fig. 3(a)] The correlation coefficient alpha_T is defined by a straight-line fit in Eq. (1.1), but the same section claims the relation is nonlinear. The paper should clarify whether alpha_T is a linear fit performed over the full-year data (including the hysteresis loop) or over a restricted period, and should report the fit uncertainty and the residuals from the linear fit. Without this, the reader cannot assess whether alpha_T = 0.75 is consistent with the model prediction alpha_T ~ 0.84, especially given the stated 2% discrepancy in seasonal amplitude.

minor comments (4)

[Section 1, Eq. (1.3)] The text states 'For T = 220° K, επ = 115 GeV and εK = 857 GeV,' but the equation uses a temperature-dependent epsilon; it would be helpful to state explicitly that these values are computed at that reference temperature and to give the numerical values of the other constants used.
[Section 4, Fig. 2 caption] The caption 'Comparison of measured muon rate with calculated rate for 2012' does not state that the calculated rate is normalized to the observed rate; this is mentioned in the text but should be in the caption to avoid misinterpretation.
[Section 5, last paragraph] The sentence 'The important region for downward muons is near the vertical cosθ≥ 0.5' contains a minor grammar issue; it should read 'is at cosθ ≥ 0.5' or 'is the region cosθ ≥ 0.5.'
[References] Reference [9] is formatted as 'PoS(ICRC2017)301 (2018). [35,301(2017)]'; the journal reference appears incomplete. Please provide the full arXiv identifier or published DOI for the Sibyll 2.3c paper.

Circularity Check

0 steps flagged · score 1.0 of 10

No material circularity: the effective-temperature weighting uses external hadronic and flux models, the measured alpha_T is a slope fitted to data, and the calculated alpha_T is an independent prediction; self-citations are contextual, not load-bearing.

full rationale

The paper's derivation is not circular in any load-bearing sense. The effective temperature Teff (Eq. 1.2) is defined by weighting observed atmospheric temperature profiles with a muon production spectrum P_mu taken from the external Sibyll 2.3c and H3a models (Eqs. 3.1-3.5; refs [9,10]), not from the IceCube muon-rate data being analyzed. The measured correlation coefficient alpha_T = 0.75 is obtained by fitting Eq. 1.1 to the measured daily rate versus this independently computed Teff; the calculated coefficient in Fig. 3(b) is derived from the same production formalism via Eqs. 4.1-4.5 without adjusting parameters to the 2012 rate data. The only numerical adjustment to data is an overall normalization of the calculated rate to the observed rate (Sec. 4), which cannot manufacture the slope or the hysteresis because it is a global multiplicative constant. The claimed nonlinearity is an empirical pattern in the plotted data; the paper's failure to provide a significance test for the hysteresis is a statistical-correctness concern, not a circularity. Citations to earlier IceCube seasonal-variation papers [4,5,6] are contextual references to prior analyses and do not supply any premise on which the present measurement depends. The openly stated factor-of-two rate offset and 2% amplitude discrepancy (Sec. 4) further show that the model is not fitted to the target result.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The analysis uses standard atmospheric cascade theory and prior hadronic interaction and flux models; no new entities are introduced. The only parameter fitted to the data is the overall normalization of the rate model.

free parameters (1)

Overall normalization of calculated rate = normalized to observed rate
In Sec. 4 the calculated rate is normalized to the observed rate because the primary spectrum normalization leads to a factor-of-two offset. This scale factor is data-fitted but cancels in the correlation coefficient.

assumptions (5)

domain assumption Atmospheric cascade formalism for inclusive muon fluxes (Eqs. 3.1-3.5)
The production spectrum is taken from Gaisser et al. (ref [8]) and is the basis for the effective temperature weighting.
domain assumption Sibyll 2.3c hadronic interaction model
Used for spectrum-weighted moments Z_Npi, Z_NK; validity is assumed.
domain assumption H3a nucleon flux model
Used for primary spectrum; this is a prior model by one of the authors.
domain assumption AIRS temperature profiles are accurate at 21 pressure levels
All effective temperature calculations depend on these profiles.
standard math Ideal gas law relation between density, pressure, and temperature (Eq. 1.3)
Used to define the temperature-dependent critical energies.

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Cite this review

Pith. "Pith review of Seasonal variation of atmospheric muons in IceCube." pith.science (2026). https://pith.science/paper/VOI5IBYB

@misc{pith2026190901406,
  author       = {Pith},
  title        = {Pith review of: Seasonal variation of atmospheric muons in IceCube},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VOI5IBYB}},
  note         = {Machine review of arXiv:1909.01406}
}

read the original abstract

After more than seven years of data taking with the full IceCube detector triggering at an average rate of 2.15 kHz, a sample of half a trillion muon events is available for analysis. The extreme temperature variations in the stratosphere together with the high data rate reveal features on both long and short time scales with unprecedented precision. In this paper we report an analysis in terms of the atmospheric profile for production of muons from decay of charged pions and kaons. We comment on the implications for seasonal variations of neutrinos, which are presented in a separate paper at this conference.

Figures

Figures reproduced from arXiv: 1909.01406 by the authors.

**Figure 1.** IceCube Muon Rate (black line) overlaid with the temperature profile of the South Pole atmosphere at different pressure heights. The plot illustrates the behavior of the seasonal cycles as well as the short-term (day to week time scales) variations in rate with respect to the temperature variations in the stratosphere. 2. Measurement of muons in IceCube The IceCube Neutrino Observatory, located at the geographical … view at source ↗

**Figure 2.** [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Correlation coefficient between (a): the measured rate and Teff (b): the calculated rate and Teff for InIce-SMT8 muon events of IceCube 2012 data. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Left: Rate and correlation coefficient for TeV muons at cosθ = 0.85. Right: muon production and temperature profiles for 4 days at the beginning of each quarter of 2012. 5. Discussion Production spectra for νµ +νµ have the same form as for muons. The only difference co…

**Figure 5.** Figure 5: Zenith angle dependence of the calculated correlation coefficient. Work in progress includes updating the primary spectrum and revisiting the calculation of effective area to account for details of the data selection, for accidental coincident events and for the small …

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Using Cosmic Rays to Predict the Weather: Meteorological Data Assimilation of Atmospheric Muon Flux Data
physics.ao-ph 2025-09 conditional novelty 7.0 of 10

Simulated cosmic-ray muon counts, assimilated into an ensemble weather model, improve short-range forecasts of a tropical cyclone beyond what a single surface pressure measurement provides.
Measuring the Cosmic Ray Spectrum with Next Generation Neutrino Detectors
hep-ph 2025-05 conditional novelty 6.0 of 10

A sensitivity study showing Hyper-Kamiokande can use atmospheric neutrinos to reconstruct the primary cosmic ray spectrum, cutting its flux uncertainty from about 20% to 7% and sharpening neutrino oscillation measurements.

Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages · cited by 2 Pith papers

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write newline

" write newline "" before.all 'output.state := FUNCTION blank.sep after.quote 'output.state := FUNCTION fin.entry output.state after.quoted.block = 'skip 'add.period if write newline FUNCTION new.block output.state before.all = 'skip output.state after.quote = after.quoted.block 'output.state := after.block 'output.state := if if FUNCTION new.sentence out...

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Pith tools

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

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write newline

" write newline "" before.all 'output.state := FUNCTION blank.sep after.quote 'output.state := FUNCTION fin.entry output.state after.quoted.block = 'skip 'add.period if write newline FUNCTION new.block output.state before.all = 'skip output.state after.quote = after.quoted.block 'output.state := after.block 'output.state := if if FUNCTION new.sentence out...

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work page 1952

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Adamson et al., Phys

MINOS Collaboration, P. Adamson et al., Phys. Rev. D81 (2010) 012001

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Adamson et al., Phys

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Desiati, K

IceCube Collaboration, P. Desiati, K. Jagielski, A. Schukraft, G. Hill, T. Kuwabara, and T. Gaisser, Seasonal variation of atmospheric neutrinos in IceCube , in Proceedings, 33rd International Cosmic Ray Conference (ICRC2013): Rio de Janeiro, Brazil, July 2-9, 2013 , p. 492

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Desiati, T

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