Charge-dependent spectral softenings of primary cosmic rays below the knee (original) (raw)

Data availability

The raw data of DAMPE are not made publicly accessible, as they are highly complicated and heavy in volume. The processed data of the fluxes are presented in tables in the Supplementary Information. The other data that support the plots within this paper are available from the Code Ocean platform (https://codeocean.com/signup/nature?token=83bb272cf81f4beda9577162a6362039). Source data are provided with this paper.

Code availability

Part of the codes used to analyse the results are available from the Code Ocean platform (https://codeocean.com/signup/nature?token=83bb272cf81f4beda9577162a6362039).

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Acknowledgements

The DAMPE mission was funded by the strategic priority science and technology projects in space science of Chinese Academy of Sciences (CAS). In China, the data analysis was mainly supported by the National Natural Science Foundation of China (no. 12588101) and the National Key Research and Development Program of China (no. 2022YFF0503302). Additional supports were from the CAS Project for Young Scientists in Basic Research (nos. YSBR-061 and YSBR-092), the NSFC (nos. 12220101003 and 12503107), the Strategic Priority Program on Space Science of CAS (no. E02212A02S), the Youth Innovation Promotion Association of CAS, the Young Elite Scientists Sponsorship Program by CAST (no. YESS20220197), the Natural Science Foundation of Jiangsu Province (no. SBK20250300783) and the Program for Innovative Talents and Entrepreneur in Jiangsu. Y.-Z.F. thanks the support of New Cornerstone Science Foundation through the XPLORER PRIZE. In Europe, the activities and data analysis were supported by the Swiss National Science Foundation (SNSF), Switzerland, the National Institute for Nuclear Physics (INFN), Italy, and the European Research Council (ERC) under the Horizon 2020 research and innovation programme of the European Union (no. 851103) and the Swiss State Secretariat for Education, Research and Innovation (SERI).

Author information

Author notes

  1. Jennifer-Maria Frieden & Chiara Perrina
    Present address: Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
  2. Yao-Zu Jiang
    Present address: Dipartimento di Fisica e Geologia, Università degli Studi di Perugia, Perugia, Italy
  3. Giovanni Marsella
    Present address: Dipartimento di Fisica e Chimica ‘E. Segrè’, Università degli Studi di Palermo, Palermo, Italy
  4. Andrea Parenti
    Present address: Interuniversity Institute for High Energies, Universitè Libre de Bruxelles, Brussels, Belgium
  5. Leandro Silveri
    Present address: New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
  6. Jing-Jing Zang
    Present address: School of Physics and Electronic Engineering, Linyi University, Linyi, China
  7. Xun Zhu
    Present address: School of Computing, Nanjing University of Posts and Telecommunications, Nanjing, China
  8. Deceased: Qi An, Jian Wu

Authors and Affiliations

  1. Dipartimento di Matematica e Fisica ‘Ennio De Giorgi’, Università del Salento, Lecce, Italy
    Francesca Alemanno, Paolo Bernardini, Francesco de Palma, Essna Ghose & Giovanni Marsella
  2. Istituto Nazionale di Fisica Nucleare (INFN) Sezione di Lecce, Lecce, Italy
    Francesca Alemanno, Paolo Bernardini, Francesco de Palma, Essna Ghose, Giovanni Marsella & Antonio Surdo
  3. State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China
    Qi An, Chang-Qing Feng, Guang-Shun Huang, Shu-Bin Liu, Yu Nie, Yi Rong, Zhong-Tao Shen, Hao-Ran Sun, Gui-Fu Wang, Xiao-Lian Wang, Yan-Fang Wang, Yi-Feng Wei, En-Heng Xu, Zi-Zong Xu, Ming-Yu Yan, Yun-Long Zhang, Zhi-Yong Zhang & Cong Zhao
  4. Department of Modern Physics, University of Science and Technology of China, Hefei, China
    Qi An, Chang-Qing Feng, Guang-Shun Huang, Shu-Bin Liu, Yu Nie, Yi Rong, Zhong-Tao Shen, Hao-Ran Sun, Gui-Fu Wang, Xiao-Lian Wang, Yan-Fang Wang, Yi-Feng Wei, En-Heng Xu, Zi-Zong Xu, Ming-Yu Yan, Yun-Long Zhang, Zhi-Yong Zhang & Cong Zhao
  5. Department of Nuclear and Particle Physics, University of Geneva, Geneva, Switzerland
    Philipp Azzarello, Hugo Boutin, Paul Coppin, Jennifer-Maria Frieden, Andrii Kotenko, Manbing Li, Chiara Perrina, Enzo Putti-Garcia, Andrea Serpolla, Andrii Tykhonov & Xin Wu
  6. Gran Sasso Science Institute (GSSI), L’Aquila, Italy
    Felicia-Carla-Tiziana Barbato, Irene Cagnoli, Elisabetta Casilli, Ivan De Mitri, Adriano Di Giovanni, Sara Fogliacco, Dimitrios Kyratzis, Andrea Parenti, Ritabrata Sarkar, Pierpaolo Savina, Leandro Silveri & Zheng Xiong
  7. Istituto Nazionale di Fisica Nucleare (INFN), Laboratori Nazionali del Gran Sasso, L’Aquila, Italy
    Felicia-Carla-Tiziana Barbato, Irene Cagnoli, Elisabetta Casilli, Ivan De Mitri, Adriano Di Giovanni, Sara Fogliacco, Dimitrios Kyratzis, Andrea Parenti, Ritabrata Sarkar, Pierpaolo Savina, Leandro Silveri & Zheng Xiong
  8. University of Chinese Academy of Sciences, Beijing, China
    Xiao-Jun Bi & Zi-Xuan Chen
  9. Particle Astrophysics Division, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China
    Xiao-Jun Bi, Rui-Rui Fan, Kun Fang, Min Gao, Ke Gong, Dong-Ya Guo, Wen-Xi Peng, Rui Qiao, Jin-Zhou Wang & Di Wu
  10. Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, China
    Ming-Sheng Cai, Jin Chang, Deng-Yi Chen, Ming-Yang Cui, Tie-Kuang Dong, Kai-Kai Duan, Yi-Zhong Fan, Lei Feng, Yi-Zhong Gong, Jian-Hua Guo, Yi-Ming Hu, Xiao-Yuan Huang, Yong-Yi Huang, Lu-Yao Jiang, Wei Jiang, Shi-Jun Lei, Bo Li, Wen-Hao Li, Xiang Li, Hao Liu, Yang Liu, Peng-Xiong Ma, Tao Ma, Xiao-Yan Peng, Zhao-Qiang Shen, Shen Wang, Da-Ming Wei, Jia-Ju Wei, Jian Wu, Zi-Qing Xia, Jing Xu, Zun-Lei Xu, Qiang Yuan, Chuan Yue, Jing-Jing Zang, Yan Zhang, Yi Zhang, Yong-Qiang Zhang, Zhe Zhang & Xun Zhu
  11. School of Astronomy and Space Science, University of Science and Technology of China, Hefei, China
    Ming-Sheng Cai, Jin Chang, Yi-Zhong Fan, Jian-Hua Guo, Xiao-Yuan Huang, Bo Li, Xiang Li, Da-Ming Wei, Jian Wu, Qiang Yuan & Yi Zhang
  12. State Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, China
    Jun-Ling Chen, Zhan-Fang Chen, Zi-Xuan Chen, Jing-Lai Duan, Fang Fang, Jie Kong, Jie Liu, Dan Mo, Xiao-Yang Niu, Hong Su, Zhi-Yu Sun, Zhi-Hui Xu, Hai-Bo Yang, Peng Yang, Ya-Qing Yang, Hui-Jun Yao, Yu-Hong Yu, Sheng-Xia Zhang, Ya-Peng Zhang, Yong-Jie Zhang & Hong-Yun Zhao
  13. National Space Science Center, Chinese Academy of Sciences, Beijing, China
    Tian-Shu Cui, Zhen-Xing Dong, Shuang-Xue Han, Wei-Liang Li, Xian-Qiang Li, Yao-Ming Liang, Miao Ma, Xiao-Yong Ma, Jia-Ning Rao, Zhi Shangguan, Wei-Hua Shen, Jing-Xing Song, Xue-Jian Teng, Lian-Guo Wang, Sha-Sha Wu, Hai-Tao Xu, Guo-Feng Xue, Wen-Zhang Zhang, Xun-Feng Zhao, Chang-Yi Zhou & Yan Zhu
  14. Istituto Nazionale di Fisica Nucleare, Sezione di Bari, Bari, Italy
    Giacinto Donvito, Piergiorgio Fusco, Fabio Gargano, Francesco Loparco & Mario-Nicola Mazziotta
  15. Dipartimento di Fisica ‘M. Merlin’, Università e del Politecnico di Bari, Bari, Italy
    Piergiorgio Fusco & Francesco Loparco
  16. Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di Perugia, Perugia, Italy
    Maria Ionica, Yao-Zu Jiang & Cheng-Ming Liu
  17. Department of Physics and Laboratory for Space Research, The University of Hong Kong, Hong Kong, Hong Kong SAR, China
    Meng Su

Consortia

The DAMPE Collaboration

Contributions

This work is the result of the contributions and efforts of all the participating institutes, under the leadership of Purple Mountain Observatory, Chinese Academy of Sciences. The authors contributed to the design, construction and operation of the detector, as well as data taking, detector calibration, software development, data processing and Monte Carlo simulation. The manuscript was reviewed and approved by all authors. In line with the collaboration policy, the authors are listed alphabetically.

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Extended data figures and tables

Extended Data Fig. 1 Charge distributions of events.

The left panels (a,c,e) are for deposited energy bin of 0.5 < _E_dep < 1 TeV, and the right panels (b,d,f) are for deposited energy bin of 10 < _E_dep < 100 TeV. From top to bottom, three charge ranges relevant to protons and helium, carbon and oxygen, and iron nuclei are shown. Black dots depict the flight data. Dashed lines with different colors show the best-fit MC simulated samples. The red solid lines show the sum of MC samples.

Source data

Extended Data Fig. 2 Relative uncertainties versus energy.

Panels a–e correspond to those of proton, helium, carbon, oxygen, and iron, respectively. The systematic uncertainties in analysis, shown in black, are the quadratic sum of all systematic contributions except for those from the hadronic models.

Source data

Extended Data Fig. 3 Rigidity spectra of boron weighted by _R_2.6.

The solid lines show the results from the background plus nearby source model, with individual contributions from the two components being shown by dotted lines (blue for the background and green for the nearby source). The dashed lines show the results from the propagation model. Thin lines correspond to the results in the local interstellar medium and thick lines are modulated fluxes with potential of 650 MV. The measurements of AMS-0213 and DAMPE17 are shown for comparison.

Source data

Extended Data Fig. 4 Dipole anisotropies of CRs.

Panel a shows the amplitudes of the dipole anisotropies, and panel b shows the phases. The solid lines show the predictions from the background plus nearby source model. The measurements are from: ARGO-YBJ77, Baksan78, EAS-TOP79, HAWC80, IceCube81, IceTop81, KASCADE-Grande82, MACRO83, Super-K84, Tibet-AS_γ_85.

Source data

Extended Data Fig. 5 Relative abundances (normalized to oxygen) of the measurements.

Blue triangles show the results at 0.1 TV, red dots show those at 10 TV, and black squares show the solar system abundances76.

Source data

Extended Data Table 1 The SBPL model fitting parameters for the hardening features

Full size table

Extended Data Table 2 The SBPL model fitting parameters for the softening features

Full size table

Extended Data Table 3 Model parameters used to give the results shown in Fig. 3

Full size table

Supplementary information

Source data

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The DAMPE Collaboration. Charge-dependent spectral softenings of primary cosmic rays below the knee.Nature 653, 52–55 (2026). https://doi.org/10.1038/s41586-026-10472-0

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