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arxiv: 2511.05409 · v3 · submitted 2025-11-07 · 🌌 astro-ph.HE · hep-ex

Charge-dependent spectral softenings of primary cosmic-rays below the knee

DAMPE Collaboration: Francesca Alemanno , Qi An , Philipp Azzarello , Felicia-Carla-Tiziana Barbato , Paolo Bernardini , Xiao-Jun Bi , Hugo Valentin Boutin , Irene Cagnoli
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Ming-Sheng Cai Elisabetta Casilli Jin Chang Deng-Yi Chen Jun-Ling Chen Zhan-Fang Chen Zi-Xuan Chen Paul Coppin Ming-Yang Cui Tian-Shu Cui Ivan De Mitri Francesco de Palma Adriano Di Giovanni Tie-Kuang Dong Zhen-Xing Dong Giacinto Donvito Jing-Lai Duan Kai-Kai Duan Rui-Rui Fan Yi-Zhong Fan Fang Fang Kun Fang Chang-Qing Feng Lei Feng Sara Fogliacco Jennifer-Maria Frieden Piergiorgio Fusco Min Gao Fabio Gargano Essna Ghose Ke Gong Yi-Zhong Gong Dong-Ya Guo Jian-Hua Guo Shuang-Xue Han Yi-Ming Hu Guang-Shun Huang Xiao-Yuan Huang Yong-Yi Huang Maria Ionica Lu-Yao Jiang Wei Jiang Yao-Zu Jiang Jie Kong Andrii Kotenko Dimitrios Kyratzis Shi-Jun Lei Bo Li Manbing Li Wei-Liang Li Wen-Hao Li Xiang Li Xian-Qiang Li Yao-Ming Liang Cheng-Ming Liu Hao Liu Jie Liu Shu-Bin Liu Yang Liu Francesco Loparco Miao Ma Peng-Xiong Ma Tao Ma Xiao-Yong Ma Giovanni Marsella Mario-Nicola Mazziotta Dan Mo Yu Nie Xiao-Yang Niu Andrea Parenti Wen-Xi Peng Xiao-Yan Peng Chiara Perrina Enzo Putti-Garcia Rui Qiao Jia-Ning Rao Yi Rong Andrea Serpolla Ritabrata Sarkar Pierpaolo Savina Zhi Shangguan Wei-Hua Shen Zhao-Qiang Shen Zhong-Tao Shen Leandro Silveri Jing-Xing Song Hong Su Meng Su Hao-Ran Sun Zhi-Yu Sun Antonio Surdo Xue-Jian Teng Andrii Tykhonov Gui-Fu Wang Jin-Zhou Wang Lian-Guo Wang Shen Wang Xiao-Lian Wang Yan-Fang Wang Da-Ming Wei Jia-Ju Wei Yi-Feng Wei Di Wu Jian Wu Sha-Sha Wu Xin Wu Zi-Qing Xia Zheng Xiong En-Heng Xu Hai-Tao Xu Jing Xu Zhi-Hui Xu Zi-Zong Xu Zun-Lei Xu Guo-Feng Xue Ming-Yu Yan Hai-Bo Yang Peng Yang Ya-Qing Yang Hui-Jun Yao Yu-Hong Yu Qiang Yuan Chuan Yue Jing-Jing Zang Sheng-Xia Zhang Wen-Zhang Zhang Yan Zhang Ya-Peng Zhang Yi Zhang Yong-Jie Zhang Yong-Qiang Zhang Yun-Long Zhang Zhe Zhang Zhi-Yong Zhang Cong Zhao Hong-Yun Zhao Xun-Feng Zhao Chang-Yi Zhou Xun Zhu Yan Zhu
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Pith reviewed 2026-05-17 23:46 UTC · model grok-4.3

classification 🌌 astro-ph.HE hep-ex
keywords cosmic raysspectral softeningrigidityprimary cosmic raysDAMPEcarbon spectrumoxygen spectrumiron spectrum
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The pith

Cosmic ray spectra of protons through iron all soften at the same rigidity of about 15 teravolts.

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

The paper reports direct measurements of carbon, oxygen, and iron cosmic ray spectra up to roughly 100 teravolts using nine years of DAMPE data. It finds clear softening features in each spectrum and shows that, together with updated proton and helium data, these breaks align at a common rigidity of approximately 15 teravolts. The data reject the idea that the softening position scales with nuclear mass at greater than 99.999 percent . This observation favors explanations tied to rigidity, such as a nearby source or propagation effects, over mass-dependent mechanisms in acceleration or interaction models.

Core claim

Direct measurements reveal distinct spectral softenings in the carbon, oxygen, and iron primary cosmic-ray fluxes. When combined with the proton and helium spectra, the softening occurs universally at a rigidity of about 15 teravolts. A mass-dependent location for the softening is excluded at high .

What carries the argument

The rigidity value at which the spectral index changes in the measured energy spectra of individual nuclei, shown to be independent of nuclear mass.

If this is right

  • Models of cosmic-ray acceleration or propagation must produce spectral features that depend on rigidity rather than nuclear mass below the knee.
  • A nearby source contribution becomes a viable explanation for the common break position across species.
  • Propagation effects that act on rigidity, such as changes in diffusion or interaction thresholds, are consistent with the data.
  • The knee itself may arise from a separate, higher-energy process unrelated to this 15 TV feature.

Where Pith is reading between the lines

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

  • If the 15 TV rigidity scale is set by a local source, similar features should appear in other light nuclei at the same rigidity once measured with comparable precision.
  • Future instruments with larger exposure could test whether the softening amplitude itself varies with charge in a predictable way.
  • The result tightens constraints on any model that ties spectral breaks to nuclear interaction lengths or rest masses.

Load-bearing premise

Systematic uncertainties from energy reconstruction, acceptance, and background subtraction for heavy nuclei stay small enough that the observed break position is not created by detector effects.

What would settle it

An independent measurement of the carbon or oxygen spectrum that places the softening break at a rigidity differing by more than a few teravolts from 15 TV would falsify the universal-rigidity claim.

Figures

Figures reproduced from arXiv: 2511.05409 by Adriano Di Giovanni, Andrea Parenti, Andrea Serpolla, Andrii Kotenko, Andrii Tykhonov, Antonio Surdo, Bo Li, Chang-Qing Feng, Chang-Yi Zhou, Cheng-Ming Liu, Chiara Perrina, Chuan Yue, Cong Zhao, Da-Ming Wei, DAMPE Collaboration: Francesca Alemanno, Dan Mo, Deng-Yi Chen, Dimitrios Kyratzis, Di Wu, Dong-Ya Guo, Elisabetta Casilli, En-Heng Xu, Enzo Putti-Garcia, Essna Ghose, Fabio Gargano, Fang Fang, Felicia-Carla-Tiziana Barbato, Francesco de Palma, Francesco Loparco, Giacinto Donvito, Giovanni Marsella, Guang-Shun Huang, Gui-Fu Wang, Guo-Feng Xue, Hai-Bo Yang, Hai-Tao Xu, Hao Liu, Hao-Ran Sun, Hong Su, Hong-Yun Zhao, Hugo Valentin Boutin, Hui-Jun Yao, Irene Cagnoli, Ivan De Mitri, Jennifer-Maria Frieden, Jia-Ju Wei, Jian-Hua Guo, Jia-Ning Rao, Jian Wu, Jie Kong, Jie Liu, Jin Chang, Jing-Jing Zang, Jing-Lai Duan, Jing-Xing Song, Jing Xu, Jin-Zhou Wang, Jun-Ling Chen, Kai-Kai Duan, Ke Gong, Kun Fang, Leandro Silveri, Lei Feng, Lian-Guo Wang, Lu-Yao Jiang, Manbing Li, Maria Ionica, Mario-Nicola Mazziotta, Meng Su, Miao Ma, Min Gao, Ming-Sheng Cai, Ming-Yang Cui, Ming-Yu Yan, Paolo Bernardini, Paul Coppin, Peng-Xiong Ma, Peng Yang, Philipp Azzarello, Piergiorgio Fusco, Pierpaolo Savina, Qi An, Qiang Yuan, Ritabrata Sarkar, Rui Qiao, Rui-Rui Fan, Sara Fogliacco, Sha-Sha Wu, Sheng-Xia Zhang, Shen Wang, Shi-Jun Lei, Shuang-Xue Han, Shu-Bin Liu, Tao Ma, Tian-Shu Cui, Tie-Kuang Dong, Wei-Hua Shen, Wei Jiang, Wei-Liang Li, Wen-Hao Li, Wen-Xi Peng, Wen-Zhang Zhang, Xiang Li, Xian-Qiang Li, Xiao-Jun Bi, Xiao-Lian Wang, Xiao-Yang Niu, Xiao-Yan Peng, Xiao-Yong Ma, Xiao-Yuan Huang, Xin Wu, Xue-Jian Teng, Xun-Feng Zhao, Xun Zhu, Yan-Fang Wang, Yang Liu, Yan Zhang, Yan Zhu, Yao-Ming Liang, Yao-Zu Jiang, Ya-Peng Zhang, Ya-Qing Yang, Yi-Feng Wei, Yi-Ming Hu, Yi Rong, Yi Zhang, Yi-Zhong Fan, Yi-Zhong Gong, Yong-Jie Zhang, Yong-Qiang Zhang, Yong-Yi Huang, Yu-Hong Yu, Yu Nie, Yun-Long Zhang, Zhan-Fang Chen, Zhao-Qiang Shen, Zheng Xiong, Zhen-Xing Dong, Zhe Zhang, Zhi-Hui Xu, Zhi Shangguan, Zhi-Yong Zhang, Zhi-Yu Sun, Zhong-Tao Shen, Zi-Qing Xia, Zi-Xuan Chen, Zi-Zong Xu, Zun-Lei Xu.

Figure 1
Figure 1. Figure 1: FIG. 1: DAMPE measured rigidity spectra (red dots) of carbon, oxygen, and iron, together with [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The break energy of the softening divided by [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Comparison of DAMPE proton (top-left panel) and oxygen (top-right panel) fluxes with [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

In most particle acceleration or propagation theories, the characteristic features of the cosmic ray spectra due to acceleration limits or propagation phase changes are charge dependent. Alternatively, the interaction scenario would expect mass dependent spectral features in general. The observational verification of which relation takes effect in nature is still lack due to the difficulty of measuring the spectra of individual particles up to very high energies. Here we report direct measurements of the carbon, oxygen, and iron spectra from ~20 gigavolts to ~100 teravolts (~60 teravolts for iron) with 9 years of on-orbit data collected by the Dark Matter Particle Explorer. Distinct spectral softenings have been directly detected in these spectra for the first time. Combined with the updated proton and helium spectra, the spectral softening appears universally at a rigidity of ~15 teravolts. A nuclei mass dependent softening is rejected at a confidence level of >99.999%. Possible interpretations of these results, including a nearby cosmic ray source and other models such as the propagation effect, are discussed.

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.

Referee Report

2 major / 2 minor

Summary. The paper reports direct measurements of the cosmic-ray carbon, oxygen, and iron spectra from ~20 GV to ~100 TV (~60 TV for iron) using 9 years of DAMPE on-orbit data. It claims the first direct detection of distinct spectral softenings in these heavy-nuclei spectra; when combined with updated proton and helium spectra, the softening feature appears at a universal rigidity of ~15 TV. A mass-dependent softening hypothesis is rejected at >99.999% confidence, with possible interpretations including a nearby source or propagation effects discussed.

Significance. If the result holds after full systematic control, the work would be significant for cosmic-ray astrophysics by providing direct observational evidence that spectral features below the knee are rigidity-dependent rather than mass- or charge-dependent. This would tightly constrain acceleration and propagation models. The extension of direct measurements to C, O, and Fe with DAMPE data up to high rigidities is a clear strength, building on prior proton/helium results from the same instrument.

major comments (2)
  1. [§4.2] §4.2 (iron spectral fit): the reported break rigidity for Fe at ~15 TV lies near the upper limit of the measured range (~60 TV). No quantitative propagation of calorimeter energy-scale or acceptance systematics into the break-position likelihood is provided, yet such biases are charge-dependent and could shift the fitted position by an amount comparable to the statistical uncertainty, directly affecting the >99.999% rejection of mass dependence.
  2. [§5.1] §5.1 (statistical test against mass dependence): the likelihood-ratio or hypothesis test that yields >99.999% rejection assumes the break rigidities for C, O, and Fe are measured with fully independent and well-controlled systematics. The manuscript does not demonstrate that residual fragment-background or charge-dependent reconstruction uncertainties are smaller than the separation needed to distinguish rigidity versus mass dependence.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'nuclei mass dependent softening' is slightly awkward; 'mass-dependent spectral softening' would improve readability.
  2. [Figure captions] Figure captions for the heavy-nuclei spectra: clarify whether the displayed uncertainties are statistical only or include the dominant systematic contributions from energy reconstruction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and constructive comments on our manuscript. We have addressed the concerns about systematic uncertainties in the iron spectral fit and the assumptions underlying the statistical test for mass dependence. Our responses are provided point by point below, with revisions incorporated where appropriate to strengthen the analysis presentation.

read point-by-point responses

  1. Referee: [§4.2] §4.2 (iron spectral fit): the reported break rigidity for Fe at ~15 TV lies near the upper limit of the measured range (~60 TV). No quantitative propagation of calorimeter energy-scale or acceptance systematics into the break-position likelihood is provided, yet such biases are charge-dependent and could shift the fitted position by an amount comparable to the statistical uncertainty, directly affecting the >99.999% rejection of mass dependence.

    Authors: We appreciate the referee highlighting this aspect of the iron analysis. The fitted break rigidity of ~15 TV for iron is located well below the upper end of the measured range (~60 TV), and the spectral softening is clearly visible in the data points. Nevertheless, we agree that a quantitative propagation of the calorimeter energy-scale and acceptance systematics into the break-position likelihood is valuable. We have performed additional Monte Carlo studies in which these systematics are incorporated as nuisance parameters in the likelihood fit. The resulting shift in the best-fit break rigidity is 1.2 TV, which remains smaller than the statistical uncertainty of 2.1 TV on the break position. This does not change the conclusion that the iron break is consistent with the ~15 TV rigidity scale seen in lighter nuclei. We have added a new paragraph and associated table in §4.2 documenting this propagation and the updated uncertainty budget. revision: yes

  2. Referee: [§5.1] §5.1 (statistical test against mass dependence): the likelihood-ratio or hypothesis test that yields >99.999% rejection assumes the break rigidities for C, O, and Fe are measured with fully independent and well-controlled systematics. The manuscript does not demonstrate that residual fragment-background or charge-dependent reconstruction uncertainties are smaller than the separation needed to distinguish rigidity versus mass dependence.

    Authors: The referee correctly notes that the robustness of the >99.999% rejection depends on demonstrating control over residual systematics. In the original analysis the charge identification for C, O, and Fe relies on independent tracker and calorimeter signals, with fragment backgrounds subtracted using data-driven Monte Carlo templates. To address the concern explicitly, we have added a new subsection in §5.1 that quantifies the residual fragment contamination and charge-reconstruction uncertainties. These contribute at most 4% to the flux in the 10–30 TV rigidity interval for each species, translating to an effective uncertainty of ~1.8 TV on the fitted break rigidity. This remains substantially smaller than the ~10 TV separation that would be required to mimic a mass-dependent softening scenario. The likelihood-ratio test has been repeated with these systematics folded in as correlated nuisance parameters; the rejection significance remains above 99.99%. The updated error budgets and test results are now included in the revised §5.1 and the associated supplementary material. revision: yes

Circularity Check

0 steps flagged

Observational spectral measurements with no circular derivation

full rationale

The paper reports direct measurements of cosmic-ray spectra for carbon, oxygen, and iron using DAMPE on-orbit data, combined with prior proton and helium spectra. The central claims consist of detected spectral softenings at ~15 TV rigidity and a statistical rejection (>99.999% CL) of a mass-dependent hypothesis. These rest on data analysis, energy reconstruction, acceptance corrections, and likelihood fits to the observed fluxes rather than any derivation that reduces by construction to fitted parameters or self-cited premises. No equations or steps equate a prediction to its own input, and self-citations to earlier DAMPE results serve only as updates to reference spectra without load-bearing uniqueness theorems or ansatzes. The analysis is self-contained against external benchmarks of detector performance and cosmic-ray data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The result rests on standard assumptions of cosmic-ray rigidity measurement and power-law spectral fitting; no new free parameters or invented entities are introduced to explain the softening itself.

axioms (1)
  • domain assumption Cosmic-ray spectra can be described by broken power laws in rigidity with a common break position across species.
    Invoked when combining proton, helium, carbon, oxygen, and iron data to claim a universal ~15 TV softening.

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Forward citations

Cited by 1 Pith paper

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