# Does or did the supernova remnant Cassiopeia A operate as a PeVatron?

Zhen Cao  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  F. Aharonian  Dublin Institute for Advanced Studies, 31
Fitzwilliam Place, 2 Dublin, Ireland  Max-Planck-Institut for Nuclear Physics,
P.O. Box 103980, 69029 Heidelberg, Germany  Q. An  State Key Laboratory of
Particle Detection and Electronics, China  University of Science and
Technology of China, 230026 Hefei, Anhui, China  Axikegu  School of Physical
Science and Technology & School of Information Science and Technology,
Southwest Jiaotong University, 610031 Chengdu, Sichuan, China  Y.X. Bai  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  Y.W. Bao  School of Astronomy and Space Science,
Nanjing University, 210023 Nanjing, Jiangsu, China  D. Bastieri  Center for
Astrophysics, Guangzhou University, 510006 Guangzhou, Guangdong, China  X.J.
Bi  Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  Y.J. Bi  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  J.T. Cai  Center for
Astrophysics, Guangzhou University, 510006 Guangzhou, Guangdong, China  Q. Cao
Hebei Normal University, 050024 Shijiazhuang, Hebei, China  W.Y. Cao
University of Science and Technology of China, 230026 Hefei, Anhui, China  Zhe
Cao  State Key Laboratory of Particle Detection and Electronics, China
University of Science and Technology of China, 230026 Hefei, Anhui, China  J.
Chang  Key Laboratory of Dark Matter and Space Astronomy & Key Laboratory of
Radio Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences,
210023 Nanjing, Jiangsu, China  J.F. Chang  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  State Key
Laboratory of Particle Detection and Electronics, China  A.M. Chen  Tsung-Dao
Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong
University, 200240 Shanghai, China  E.S. Chen  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
University of Chinese Academy of Sciences, 100049 Beijing, China  Tianfu
Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Liang Chen  Key
Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical
Observatory, Chinese Academy of Sciences, 200030 Shanghai, China  Lin Chen
School of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
Long Chen  School of Physical Science and Technology & School of Information
Science and Technology, Southwest Jiaotong University, 610031 Chengdu,
Sichuan, China  M.J. Chen  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  M.L. Chen  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China
State Key Laboratory of Particle Detection and Electronics, China  Q.H. Chen
School of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
S.H. Chen  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  S.Z. Chen Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  T.L. Chen  Key Laboratory of
Cosmic Rays (Tibet University), Ministry of Education, 850000 Lhasa, Tibet,
China  Y. Chen  School of Astronomy and Space Science, Nanjing University,
210023 Nanjing, Jiangsu, China  N. Cheng  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Y.D. Cheng
Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  M.Y. Cui  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  S.W. Cui  Hebei
Normal University, 050024 Shijiazhuang, Hebei, China  X.H. Cui  National
Astronomical Observatories, Chinese Academy of Sciences, 100101 Beijing, China
Y.D. Cui  School of Physics and Astronomy (Zhuhai) & School of Physics
(Guangzhou) & Sino-French Institute of Nuclear Engineering and Technology
(Zhuhai), Sun Yat-sen University, 519000 Zhuhai & 510275 Guangzhou, Guangdong,
China  B.Z. Dai  School of Physics and Astronomy, Yunnan University, 650091
Kunming, Yunnan, China  H.L. Dai  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  State Key Laboratory of
Particle Detection and Electronics, China  Z.G. Dai  University of Science and
Technology of China, 230026 Hefei, Anhui, China  Danzengluobu  Key Laboratory
of Cosmic Rays (Tibet University), Ministry of Education, 850000 Lhasa, Tibet,
China  D. della Volpe  Département de Physique Nucléaire et Corpusculaire,
Faculté de Sciences, Université de Genève, 24 Quai Ernest Ansermet, 1211
Geneva, Switzerland  X.Q. Dong  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  University of
Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research
Center, 610000 Chengdu, Sichuan, China  K.K. Duan  Key Laboratory of Dark
Matter and Space Astronomy & Key Laboratory of Radio Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu,
China  J.H. Fan  Center for Astrophysics, Guangzhou University, 510006
Guangzhou, Guangdong, China  Y.Z. Fan  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  J. Fang  School
of Physics and Astronomy, Yunnan University, 650091 Kunming, Yunnan, China  K.
Fang  Key Laboratory of Particle Astrophysics & Experimental Physics Division
& Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  C.F. Feng  Institute of Frontier and
Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong,
China  L. Feng  Key Laboratory of Dark Matter and Space Astronomy & Key
Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese Academy of
Sciences, 210023 Nanjing, Jiangsu, China  S.H. Feng  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  X.T.
Feng  Institute of Frontier and Interdisciplinary Science, Shandong
University, 266237 Qingdao, Shandong, China  Y.L. Feng  Key Laboratory of
Cosmic Rays (Tibet University), Ministry of Education, 850000 Lhasa, Tibet,
China  S. Gabici  APC, Université Paris Cité, CNRS/IN2P3, CEA/IRFU,
Observatoire de Paris, 119 75205 Paris, France  B. Gao  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  C.D.
Gao  Institute of Frontier and Interdisciplinary Science, Shandong University,
266237 Qingdao, Shandong, China  L.Q. Gao  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
University of Chinese Academy of Sciences, 100049 Beijing, China  Tianfu
Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Q. Gao  Key
Laboratory of Cosmic Rays (Tibet University), Ministry of Education, 850000
Lhasa, Tibet, China  W. Gao  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  W.K. Gao  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  University of Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  M.M. Ge
School of Physics and Astronomy, Yunnan University, 650091 Kunming, Yunnan,
China  L.S. Geng  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  G. Giacinti  Tsung-Dao Lee Institute & School
of Physics and Astronomy, Shanghai Jiao Tong University, 200240 Shanghai,
China  G.H. Gong  Department of Engineering Physics, Tsinghua University,
100084 Beijing, China  Q.B. Gou  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  M.H. Gu  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China
State Key Laboratory of Particle Detection and Electronics, China  F.L. Guo
Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical
Observatory, Chinese Academy of Sciences, 200030 Shanghai, China  X.L. Guo
School of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
Y.Q. Guo  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  Y.Y. Guo  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  Y.A. Han  School
of Physics and Microelectronics, Zhengzhou University, 450001 Zhengzhou,
Henan, China  H.H. He  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  University of Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  H.N. He  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  J.Y. He  Key
Laboratory of Dark Matter and Space Astronomy & Key Laboratory of Radio
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, 210023
Nanjing, Jiangsu, China  X.B. He  School of Physics and Astronomy (Zhuhai) &
School of Physics (Guangzhou) & Sino-French Institute of Nuclear Engineering
and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai & 510275
Guangzhou, Guangdong, China  Y. He  School of Physical Science and Technology
& School of Information Science and Technology, Southwest Jiaotong University,
610031 Chengdu, Sichuan, China  M. Heller  Département de Physique Nucléaire
et Corpusculaire, Faculté de Sciences, Université de Genève, 24 Quai Ernest
Ansermet, 1211 Geneva, Switzerland  Y.K. Hor  School of Physics and Astronomy
(Zhuhai) & School of Physics (Guangzhou) & Sino-French Institute of Nuclear
Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai &
510275 Guangzhou, Guangdong, China  B.W. Hou  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
University of Chinese Academy of Sciences, 100049 Beijing, China  Tianfu
Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  C. Hou  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  X. Hou  Yunnan Observatories, Chinese Academy of
Sciences, 650216 Kunming, Yunnan, China  H.B. Hu  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
University of Chinese Academy of Sciences, 100049 Beijing, China  Tianfu
Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Q. Hu  University
of Science and Technology of China, 230026 Hefei, Anhui, China  Key Laboratory
of Dark Matter and Space Astronomy & Key Laboratory of Radio Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu,
China  S.C. Hu  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  D.H. Huang  School of Physical Science and Technology & School
of Information Science and Technology, Southwest Jiaotong University, 610031
Chengdu, Sichuan, China  T.Q. Huang  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  W.J. Huang  School of Physics
and Astronomy (Zhuhai) & School of Physics (Guangzhou) & Sino-French Institute
of Nuclear Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000
Zhuhai & 510275 Guangzhou, Guangdong, China  X.T. Huang  Institute of Frontier
and Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong,
China  X.Y. Huang  Key Laboratory of Dark Matter and Space Astronomy & Key
Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese Academy of
Sciences, 210023 Nanjing, Jiangsu, China  Y. Huang  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
University of Chinese Academy of Sciences, 100049 Beijing, China  Tianfu
Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Z.C. Huang  School
of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
X.L. Ji  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  State Key Laboratory of Particle Detection and
Electronics, China  H.Y. Jia  School of Physical Science and Technology &
School of Information Science and Technology, Southwest Jiaotong University,
610031 Chengdu, Sichuan, China  K. Jia  Institute of Frontier and
Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong,
China  K. Jiang  State Key Laboratory of Particle Detection and Electronics,
China  University of Science and Technology of China, 230026 Hefei, Anhui,
China  X.W. Jiang  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  Z.J. Jiang  School of Physics and Astronomy,
Yunnan University, 650091 Kunming, Yunnan, China  M. Jin  School of Physical
Science and Technology & School of Information Science and Technology,
Southwest Jiaotong University, 610031 Chengdu, Sichuan, China  M.M. Kang
College of Physics, Sichuan University, 610065 Chengdu, Sichuan, China  T. Ke
Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  D. Kuleshov  Institute for Nuclear Research of
Russian Academy of Sciences, 117312 Moscow, Russia  K. Kurinov  Institute for
Nuclear Research of Russian Academy of Sciences, 117312 Moscow, Russia  B.B.
Li  Hebei Normal University, 050024 Shijiazhuang, Hebei, China  Cheng Li
State Key Laboratory of Particle Detection and Electronics, China  University
of Science and Technology of China, 230026 Hefei, Anhui, China  Cong Li  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  D. Li  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  University of
Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research
Center, 610000 Chengdu, Sichuan, China  F. Li  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  State Key
Laboratory of Particle Detection and Electronics, China  H.B. Li  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  H.C. Li  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  H.Y. Li  University of
Science and Technology of China, 230026 Hefei, Anhui, China  Key Laboratory of
Dark Matter and Space Astronomy & Key Laboratory of Radio Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu,
China  J. Li  University of Science and Technology of China, 230026 Hefei,
Anhui, China  Key Laboratory of Dark Matter and Space Astronomy & Key
Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese Academy of
Sciences, 210023 Nanjing, Jiangsu, China  Jian Li  University of Science and
Technology of China, 230026 Hefei, Anhui, China  Jie Li  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China
State Key Laboratory of Particle Detection and Electronics, China  K. Li  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  W.L. Li  Institute of Frontier and Interdisciplinary
Science, Shandong University, 266237 Qingdao, Shandong, China  W.L. Li  Tsung-
Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong
University, 200240 Shanghai, China  X.R. Li  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Xin Li
State Key Laboratory of Particle Detection and Electronics, China  University
of Science and Technology of China, 230026 Hefei, Anhui, China  Y.Z. Li  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  Zhe Li  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  Zhuo Li  School of Physics, Peking University,
100871 Beijing, China  E.W. Liang  School of Physical Science and Technology,
Guangxi University, 530004 Nanning, Guangxi, China  Y.F. Liang  School of
Physical Science and Technology, Guangxi University, 530004 Nanning, Guangxi,
China  S.J. Lin  School of Physics and Astronomy (Zhuhai) & School of Physics
(Guangzhou) & Sino-French Institute of Nuclear Engineering and Technology
(Zhuhai), Sun Yat-sen University, 519000 Zhuhai & 510275 Guangzhou, Guangdong,
China  B. Liu  University of Science and Technology of China, 230026 Hefei,
Anhui, China  C. Liu  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  D. Liu  Institute of Frontier and
Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong,
China  H. Liu  School of Physical Science and Technology & School of
Information Science and Technology, Southwest Jiaotong University, 610031
Chengdu, Sichuan, China  H.D. Liu  School of Physics and Microelectronics,
Zhengzhou University, 450001 Zhengzhou, Henan, China  J. Liu  Key Laboratory
of Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  J.L.
Liu  Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  J.Y. Liu  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  M.Y. Liu  Key Laboratory of
Cosmic Rays (Tibet University), Ministry of Education, 850000 Lhasa, Tibet,
China  R.Y. Liu  School of Astronomy and Space Science, Nanjing University,
210023 Nanjing, Jiangsu, China  S.M. Liu  School of Physical Science and
Technology & School of Information Science and Technology, Southwest Jiaotong
University, 610031 Chengdu, Sichuan, China  W. Liu  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Y. Liu
Center for Astrophysics, Guangzhou University, 510006 Guangzhou, Guangdong,
China  Y.N. Liu  Department of Engineering Physics, Tsinghua University,
100084 Beijing, China  R. Lu  School of Physics and Astronomy, Yunnan
University, 650091 Kunming, Yunnan, China  Q. Luo  School of Physics and
Astronomy (Zhuhai) & School of Physics (Guangzhou) & Sino-French Institute of
Nuclear Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000
Zhuhai & 510275 Guangzhou, Guangdong, China  H.K. Lv  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  B.Q.
Ma  School of Physics, Peking University, 100871 Beijing, China  L.L. Ma  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  X.H. Ma  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  J.R. Mao  Yunnan
Observatories, Chinese Academy of Sciences, 650216 Kunming, Yunnan, China  Z.
Min  Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  W. Mitthumsiri  Department of Physics, Faculty of
Science, Mahidol University, Bangkok 10400, Thailand  H.J. Mu  School of
Physics and Microelectronics, Zhengzhou University, 450001 Zhengzhou, Henan,
China  Y.C. Nan  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  A. Neronov  APC, Université Paris Cité,
CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, 119 75205 Paris, France  Z.W. Ou
School of Physics and Astronomy (Zhuhai) & School of Physics (Guangzhou) &
Sino-French Institute of Nuclear Engineering and Technology (Zhuhai), Sun Yat-
sen University, 519000 Zhuhai & 510275 Guangzhou, Guangdong, China  B.Y. Pang
School of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China  P.
Pattarakijwanich  Department of Physics, Faculty of Science, Mahidol
University, Bangkok 10400, Thailand  Z.Y. Pei  Center for Astrophysics,
Guangzhou University, 510006 Guangzhou, Guangdong, China  M.Y. Qi  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  Y.Q. Qi  Hebei Normal University, 050024
Shijiazhuang, Hebei, China  B.Q. Qiao  Key Laboratory of Particle Astrophysics
& Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  J.J. Qin  University of
Science and Technology of China, 230026 Hefei, Anhui, China  D. Ruffolo
Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400,
Thailand  A. Sáiz  Department of Physics, Faculty of Science, Mahidol
University, Bangkok 10400, Thailand  D. Semikoz  APC, Université Paris Cité,
CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, 119 75205 Paris, France  C.Y.
Shao  School of Physics and Astronomy (Zhuhai) & School of Physics (Guangzhou)
& Sino-French Institute of Nuclear Engineering and Technology (Zhuhai), Sun
Yat-sen University, 519000 Zhuhai & 510275 Guangzhou, Guangdong, China  L.
Shao  Hebei Normal University, 050024 Shijiazhuang, Hebei, China  O.
Shchegolev  Institute for Nuclear Research of Russian Academy of Sciences,
117312 Moscow, Russia  Moscow Institute of Physics and Technology, 141700
Moscow, Russia  X.D. Sheng  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  F.W. Shu  Center for
Relativistic Astrophysics and High Energy Physics, School of Physics and
Materials Science & Institute of Space Science and Technology, Nanchang
University, 330031 Nanchang, Jiangxi, China  H.C. Song  School of Physics,
Peking University, 100871 Beijing, China  Yu.V. Stenkin  Institute for Nuclear
Research of Russian Academy of Sciences, 117312 Moscow, Russia  Moscow
Institute of Physics and Technology, 141700 Moscow, Russia  V. Stepanov
Institute for Nuclear Research of Russian Academy of Sciences, 117312 Moscow,
Russia  Y. Su  Key Laboratory of Dark Matter and Space Astronomy & Key
Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese Academy of
Sciences, 210023 Nanjing, Jiangsu, China  Q.N. Sun  School of Physical Science
and Technology & School of Information Science and Technology, Southwest
Jiaotong University, 610031 Chengdu, Sichuan, China  X.N. Sun  School of
Physical Science and Technology, Guangxi University, 530004 Nanning, Guangxi,
China  Z.B. Sun  National Space Science Center, Chinese Academy of Sciences,
100190 Beijing, China  P.H.T. Tam  School of Physics and Astronomy (Zhuhai) &
School of Physics (Guangzhou) & Sino-French Institute of Nuclear Engineering
and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai & 510275
Guangzhou, Guangdong, China  Q.W. Tang  Center for Relativistic Astrophysics
and High Energy Physics, School of Physics and Materials Science & Institute
of Space Science and Technology, Nanchang University, 330031 Nanchang,
Jiangxi, China  Z.B. Tang  State Key Laboratory of Particle Detection and
Electronics, China  University of Science and Technology of China, 230026
Hefei, Anhui, China  W.W. Tian  University of Chinese Academy of Sciences,
100049 Beijing, China  National Astronomical Observatories, Chinese Academy of
Sciences, 100101 Beijing, China  C. Wang  National Space Science Center,
Chinese Academy of Sciences, 100190 Beijing, China  C.B. Wang  School of
Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
G.W. Wang  University of Science and Technology of China, 230026 Hefei, Anhui,
China  H.G. Wang  Center for Astrophysics, Guangzhou University, 510006
Guangzhou, Guangdong, China  H.H. Wang  School of Physics and Astronomy
(Zhuhai) & School of Physics (Guangzhou) & Sino-French Institute of Nuclear
Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai &
510275 Guangzhou, Guangdong, China  J.C. Wang  Yunnan Observatories, Chinese
Academy of Sciences, 650216 Kunming, Yunnan, China  K. Wang  School of
Astronomy and Space Science, Nanjing University, 210023 Nanjing, Jiangsu,
China  L.P. Wang  Institute of Frontier and Interdisciplinary Science,
Shandong University, 266237 Qingdao, Shandong, China  L.Y. Wang  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  P.H. Wang  School of Physical Science and Technology
& School of Information Science and Technology, Southwest Jiaotong University,
610031 Chengdu, Sichuan, China  R. Wang  Institute of Frontier and
Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong,
China  W. Wang  School of Physics and Astronomy (Zhuhai) & School of Physics
(Guangzhou) & Sino-French Institute of Nuclear Engineering and Technology
(Zhuhai), Sun Yat-sen University, 519000 Zhuhai & 510275 Guangzhou, Guangdong,
China  X.G. Wang  School of Physical Science and Technology, Guangxi
University, 530004 Nanning, Guangxi, China  X.Y. Wang  School of Astronomy and
Space Science, Nanjing University, 210023 Nanjing, Jiangsu, China  Y. Wang
School of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
Y.D. Wang  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  Y.J. Wang  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  Z.H. Wang  College of
Physics, Sichuan University, 610065 Chengdu, Sichuan, China  Z.X. Wang  School
of Physics and Astronomy, Yunnan University, 650091 Kunming, Yunnan, China
Zhen Wang  Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai
Jiao Tong University, 200240 Shanghai, China  Zheng Wang  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China
State Key Laboratory of Particle Detection and Electronics, China  D.M. Wei
Key Laboratory of Dark Matter and Space Astronomy & Key Laboratory of Radio
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, 210023
Nanjing, Jiangsu, China  J.J. Wei  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  Y.J. Wei  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  T. Wen  School of Physics and Astronomy, Yunnan University,
650091 Kunming, Yunnan, China  C.Y. Wu  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  H.R. Wu
Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  S. Wu  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  X.F. Wu  Key Laboratory of
Dark Matter and Space Astronomy & Key Laboratory of Radio Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu,
China  Y.S. Wu  University of Science and Technology of China, 230026 Hefei,
Anhui, China  S.Q. Xi  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  J. Xia  University of Science and Technology
of China, 230026 Hefei, Anhui, China  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  J.J. Xia  School
of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
G.M. Xiang  University of Chinese Academy of Sciences, 100049 Beijing, China
Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical
Observatory, Chinese Academy of Sciences, 200030 Shanghai, China  D.X. Xiao
Hebei Normal University, 050024 Shijiazhuang, Hebei, China  G. Xiao  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  G.G. Xin  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  Y.L. Xin  School of Physical
Science and Technology & School of Information Science and Technology,
Southwest Jiaotong University, 610031 Chengdu, Sichuan, China  Y. Xing  Key
Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical
Observatory, Chinese Academy of Sciences, 200030 Shanghai, China  Z. Xiong
Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  D.L. Xu  Tsung-Dao Lee Institute & School of Physics and
Astronomy, Shanghai Jiao Tong University, 200240 Shanghai, China  R.F. Xu  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  R.X. Xu  School of Physics, Peking University, 100871 Beijing,
China  W.L. Xu  College of Physics, Sichuan University, 610065 Chengdu,
Sichuan, China  L. Xue  Institute of Frontier and Interdisciplinary Science,
Shandong University, 266237 Qingdao, Shandong, China  D.H. Yan  School of
Physics and Astronomy, Yunnan University, 650091 Kunming, Yunnan, China  J.Z.
Yan  Key Laboratory of Dark Matter and Space Astronomy & Key Laboratory of
Radio Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences,
210023 Nanjing, Jiangsu, China  T. Yan  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  C.W. Yang
College of Physics, Sichuan University, 610065 Chengdu, Sichuan, China  F.
Yang  Hebei Normal University, 050024 Shijiazhuang, Hebei, China  F.F. Yang
Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  State Key Laboratory of Particle Detection and
Electronics, China  H.W. Yang  School of Physics and Astronomy (Zhuhai) &
School of Physics (Guangzhou) & Sino-French Institute of Nuclear Engineering
and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai & 510275
Guangzhou, Guangdong, China  J.Y. Yang  School of Physics and Astronomy
(Zhuhai) & School of Physics (Guangzhou) & Sino-French Institute of Nuclear
Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai &
510275 Guangzhou, Guangdong, China  L.L. Yang  School of Physics and Astronomy
(Zhuhai) & School of Physics (Guangzhou) & Sino-French Institute of Nuclear
Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai &
510275 Guangzhou, Guangdong, China  M.J. Yang  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  R.Z. Yang
University of Science and Technology of China, 230026 Hefei, Anhui, China
S.B. Yang  School of Physics and Astronomy, Yunnan University, 650091 Kunming,
Yunnan, China  Y.H. Yao  College of Physics, Sichuan University, 610065
Chengdu, Sichuan, China  Z.G. Yao  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  Y.M. Ye  Department of
Engineering Physics, Tsinghua University, 100084 Beijing, China  L.Q. Yin  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  N. Yin  Institute of Frontier and Interdisciplinary
Science, Shandong University, 266237 Qingdao, Shandong, China  X.H. You  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  Z.Y. You  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  Y.H. Yu  University of
Science and Technology of China, 230026 Hefei, Anhui, China  Q. Yuan  Key
Laboratory of Dark Matter and Space Astronomy & Key Laboratory of Radio
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, 210023
Nanjing, Jiangsu, China  H. Yue  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  University of
Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research
Center, 610000 Chengdu, Sichuan, China  H.D. Zeng  Key Laboratory of Dark
Matter and Space Astronomy & Key Laboratory of Radio Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu,
China  T.X. Zeng  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  State Key Laboratory of Particle Detection and
Electronics, China  W. Zeng  School of Physics and Astronomy, Yunnan
University, 650091 Kunming, Yunnan, China  M. Zha  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  B.B. Zhang
School of Astronomy and Space Science, Nanjing University, 210023 Nanjing,
Jiangsu, China  F. Zhang  School of Physical Science and Technology & School
of Information Science and Technology, Southwest Jiaotong University, 610031
Chengdu, Sichuan, China  H.M. Zhang  School of Astronomy and Space Science,
Nanjing University, 210023 Nanjing, Jiangsu, China  H.Y. Zhang  Key Laboratory
of Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  J.L.
Zhang  National Astronomical Observatories, Chinese Academy of Sciences,
100101 Beijing, China  L.X. Zhang  Center for Astrophysics, Guangzhou
University, 510006 Guangzhou, Guangdong, China  Li Zhang  School of Physics
and Astronomy, Yunnan University, 650091 Kunming, Yunnan, China  P.F. Zhang
School of Physics and Astronomy, Yunnan University, 650091 Kunming, Yunnan,
China  P.P. Zhang  University of Science and Technology of China, 230026
Hefei, Anhui, China  Key Laboratory of Dark Matter and Space Astronomy & Key
Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese Academy of
Sciences, 210023 Nanjing, Jiangsu, China  R. Zhang  University of Science and
Technology of China, 230026 Hefei, Anhui, China  Key Laboratory of Dark Matter
and Space Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain
Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  S.B.
Zhang  University of Chinese Academy of Sciences, 100049 Beijing, China
National Astronomical Observatories, Chinese Academy of Sciences, 100101
Beijing, China  S.R. Zhang  Hebei Normal University, 050024 Shijiazhuang,
Hebei, China  S.S. Zhang  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  X. Zhang  School of Astronomy
and Space Science, Nanjing University, 210023 Nanjing, Jiangsu, China  X.P.
Zhang  Key Laboratory of Particle Astrophysics & Experimental Physics Division
& Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  Y.F. Zhang  School of Physical Science and Technology
& School of Information Science and Technology, Southwest Jiaotong University,
610031 Chengdu, Sichuan, China  Yi Zhang  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China  Key
Laboratory of Dark Matter and Space Astronomy & Key Laboratory of Radio
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, 210023
Nanjing, Jiangsu, China  Yong Zhang  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  B. Zhao  School of Physical
Science and Technology & School of Information Science and Technology,
Southwest Jiaotong University, 610031 Chengdu, Sichuan, China  J. Zhao  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  L. Zhao  State Key Laboratory of Particle Detection
and Electronics, China  University of Science and Technology of China, 230026
Hefei, Anhui, China  L.Z. Zhao  Hebei Normal University, 050024 Shijiazhuang,
Hebei, China  S.P. Zhao  Key Laboratory of Dark Matter and Space Astronomy &
Key Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese
Academy of Sciences, 210023 Nanjing, Jiangsu, China  Institute of Frontier and
Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong,
China  F. Zheng  National Space Science Center, Chinese Academy of Sciences,
100190 Beijing, China  B. Zhou  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  H. Zhou  Tsung-Dao Lee
Institute & School of Physics and Astronomy, Shanghai Jiao Tong University,
200240 Shanghai, China  J.N. Zhou  Key Laboratory for Research in Galaxies and
Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences,
200030 Shanghai, China  M. Zhou  Center for Relativistic Astrophysics and High
Energy Physics, School of Physics and Materials Science & Institute of Space
Science and Technology, Nanchang University, 330031 Nanchang, Jiangxi, China
P. Zhou  School of Astronomy and Space Science, Nanjing University, 210023
Nanjing, Jiangsu, China  R. Zhou  College of Physics, Sichuan University,
610065 Chengdu, Sichuan, China  X.X. Zhou  School of Physical Science and
Technology & School of Information Science and Technology, Southwest Jiaotong
University, 610031 Chengdu, Sichuan, China  C.G. Zhu  Institute of Frontier
and Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong,
China  F.R. Zhu  School of Physical Science and Technology & School of
Information Science and Technology, Southwest Jiaotong University, 610031
Chengdu, Sichuan, China  H. Zhu  National Astronomical Observatories, Chinese
Academy of Sciences, 100101 Beijing, China  K.J. Zhu  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  University of Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  State Key
Laboratory of Particle Detection and Electronics, China  X. Zuo  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China F. Aharonian, R.Z. Yang, Y.H. Yu felix.aharonian@mpi-
hd.mpg.de<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

For decades, supernova remnants (SNRs) have been considered the prime sources
of Galactic Cosmic rays (CRs). But whether SNRs can accelerate CR protons to
PeV energies and thus dominate CR flux up to the knee is currently under
intensive theoretical and phenomenological debate. The direct test of the
ability of SNRs to operate as CR PeVatrons can be provided by ultrahigh-energy
(UHE; $E_{\gamma}\geq 100$ TeV) $\gamma$-rays. In this context, the historical
SNR Cassiopeia A (Cas A) is considered one of the most promising target for
UHE observations. This paper presents the observation of Cas A and its
vicinity by the LHAASO KM2A detector. The exceptional sensitivity of LHAASO
KM2A in the UHE band, combined with the young age of Cas A, enabled us to
derive stringent model-independent limits on the energy budget of UHE protons
and nuclei accelerated by Cas A at any epoch after the explosion. The results
challenge the prevailing paradigm that Cas A-type SNRs are major suppliers of
PeV CRs in the Milky Way.

supernova remnants, cosmic rays, gamma rays

††journal: ApJL

##  1 Introduction

Within the current Galactic CR paradigm, SNRs are considered the major
contributors to the observed CR flux. For decades, this conviction has been
based on phenomenological arguments and supported by the Diffusive Shock
Acceleration (DSA) theory (for a review, see Malkov & Drury (2001)). The
dominance of SNRs’ contribution up to the ”knee”, a distinct break in the CR
spectrum around 3-4 PeV, would imply that at certain epochs of their
evolution, SNRs should operate as PeVatrons. However, as has been recognised
long ago (Lagage & Cesarsky, 1983), within the framework of the standard DSA
applied to young SNRs, the energy of accelerated protons could hardly exceed
100 TeV. A possible solution was proposed by Bell (2004) by amplifying the
magnetic field upstream of the shock through the instabilities driven by CRs.
Combined with two other critical conditions, (1) shock speed of thousands of
km/s, and (2) particle diffusion in the extreme (Bohm) regime, enhancing the
magnetic field to $B\geq 100\mu\rm G$ allows acceleration of protons and
nuclei to 1 PeV/nuc.

The interactions of the shock accelerated protons and nuclei with the ambient
gas make young SNRs potentially detectable sources of $\gamma$-rays and
neutrinos. Therefore, the detection of TeV $\gamma$-rays from more than a
dozen young SNRs 111see the online catalogue for TeV $\gamma$-ray sources,
http://tevcat.uchicago.edu/ is a direct proof of effective acceleration of
protons and/or electrons to very high energies. In general, the available data
do not allow us to distinguish between the hadronic (“$\pi^{0}$-decay”) and
leptonic (“inverse Compton”) origin of TeV $\gamma$-rays. Even ignoring this
ambiguity, i.e., assuming that $\gamma$-rays are produced by accelerated
protons, we face a problem with the explanation of TeV $\gamma$-ray
measurements. The reported steep $\gamma$-ray spectra with a differential
power-law index $\Gamma\sim 2.4-2.7$ (e.g., as summerised in the supplementary
of Aharonian et al., 2019) do not readily agree with predictions of the
standard DSA theory for strong shocks of young SNRs. This result can be
interpreted in three different ways:

(1) A steep power-law proton spectrum is mimicked by the result of the
combination of a hard ($E^{-2}$ type) power-law spectrum and an ”early”
exponential cutoff, $E_{0}\ll 100$ TeV. This simple explanation supports the
predictions of the standard DSA and the conclusion of Lagage & Cesarsky (1983)
for the case of a non-amplified magnetic field. This mathematical trick works
in a relatively narrow (one decade or so) energy interval around and below the
cutoff energy. If this explanation is correct, at higher energies the
measurements should reveal a gradual spectral steepening in the deep
exponential cutoff region.

(2) The claim that strong shock acceleration results in a hard acceleration
spectrum is not always correct. Indeed, steep power-law proton spectra can be
formed over a wide energy interval in certain realistic environments and
scenarios (see, e.g., Bell et al., 2011, 2019; Malkov & Aharonian, 2019;
Hanusch et al., 2019; Caprioli et al., 2020; Xu & Lazarian, 2022). The steep
power-law spectra can extend over a wide energy interval, formally up to 1
PeV, assuming that such energetic protons are effectively confined in the
shell. Correspondingly, the resulting steep power-law $\gamma$-ray spectra
could continue up to 100 TeV. The detection of steep multi-TeV $\gamma$-ray
spectra in both above scenarios is a rather difficult but feasible task for
detectors like CTA and LHAASO.

(3) Acceleration of protons to PeV energies at the very early ($\ll 100$ yr)
epoch of the SNR evolution is preferable (Bell et al., 2013; Zirakashvili et
al., 2014), in particular, because of the shock speed exceeding 10,000 km/s
and the high density of the progenitor wind. However, the CRs with highest
energy have already escaped from the shock upstream and thus the remnant is
currently emptied of multi-TeV CRs. This can naturally explain the steep
spectra of $\gamma$-rays from SNRs, including from very young ones, in
particular from SNR Cassiopeia A (Aharonian et al., 2001; Ahnen et al., 2017;
Acciari et al., 2010) and Tycho (Acciari et al., 2011).

The $\gamma$-ray spectrum in scenario (2) is predicted to have a steeper power
law shape without cutoff, which is significantly different from the other two
scenarios. The $\gamma$-ray spectra from the remnants in scenarios (1) and (3)
could be similar, although for different reasons. On the other hand, scenario
(3) differs principally from scenario (1) by the $\gamma$-radiation outside
the remnant. While in scenario (1), PeV particles are not produced at all,
scenario (3) allows proton acceleration up to 1 PeV, but assumes that
presently the highest energy particles already left the remnant and presently
occupy regions beyond the shell. Any outcome of $\gamma$-ray measurements at
tens to hundreds TeV performed with detectors of adequate sensitivity - either
detection of positive signals or upper limits - would provide definite answers
to whether specific SNRs could accelerate protons 1 PeV at any epoch of their
evolution.

The detection or upper limits from SNRs of different types and ages could
finally establish whether SNRs, as a source population, can be responsible for
the CR fluxes up to the ”knee”. The results would be relevant to both
scenarios (2) and (3).

The historical SNR Cas A represents a key target for such studies. It has a
well-defined age and distance. It also belongs to a class of core-collapse
supernova that explodes in a dense red supergiant wind. Such systems are
believed to be able to accelerate ions to the highest energy due to the
efficient amplification of magnetic fields by CR streaming in dense
environments.

In this paper, using LHAASO KM2A data, we derive $\gamma$-ray flux upper
limits towards Cas A and test its ability to act as a PeVatron. In Sec.2, we
discuss the status of previous gamma-ray observations of Cas A and the
theoretical challenges of acceleration of protons to ultrahigh energies at
different epochs of its evolution. In Sec.3, we review the physical properties
of Cas A, including the gas distribution in proximity to the remnant. In
Sec.4, we describe the procedure of extraction of flux upper limits based on
the LHAASO KM2A data. In Sec.5, we discuss the astrophysical implications of
the obtained results.

##  2 Basic facts about Cas A

Cassiopeia A (Cas A, SNR G111.7-02.1) is one of the youngest SNRs in our
Galaxy. This $\approx 340$ year old (Reed et al., 1995) structure is the
remnant of a type IIb supernova (Krause et al., 2008) located at a distance of
3.4 kpc. It is one of the brightest galactic radio sources with a shell
structure of angular radius 2.5’ corresponding to the physical size of 2.5 pc
(Kassim et al., 1995). The synchrotron radiation extends from radio (Tuffs et
al., 1997) to hard X-rays of about $100\leavevmode\nobreak\ \rm keV$
(Grefenstette et al., 2015). Fermi LAT observations reveal a hint of a
hadronic origin of the $\gamma$-ray emissions (Yuan et al., 2013; Zirakashvili
et al., 2014). TeV $\gamma$-ray emission from Cas A has been discovered by the
HEGRA IACT array (Aharonian et al., 2001), and later confirmed by the MAGIC
(Ahnen et al., 2017) and VERITAS (Acciari et al., 2010) collaborations.

The hadronic models of GeV-to-TeV radiation require a very high, but still
acceptable, acceleration efficiency of about 25% (Zirakashvili et al., 2014),
while in the two-zone models the acceleration efficiency required can be lower
(Liu et al., 2022). The significant steepening or a cutoff in the spectrum
reported around a few TeV by Ahnen et al. (2017) and Abeysekara et al. (2020)
implies a corresponding steepening in the spectrum of parent protons at
energies of tens of TeV. This constrains but does not exclude the presence of
PeV protons in the nebula or outside the shell. Due to the limited age of Cas
A, even if PeV protons have been accelerated at the early ($\ll 100$ years)
epoch of the SNR, they could not propagate too far from the SNR. Thus, for
robust conclusions, one should probe both the SNR itself and the $\approx 100$
pc environment surrounding Cas A, for $\gamma$-rays of energy exceeding 100
TeV.

##  3 Gas and CRs in the vicinity of Cas A

Since we are searching for $\gamma$-rays produced by PeV CR protons through
interactions with the ambient gas, the information about the gas is crucial
for our studies. Cas A is located within a dense gas environment. Zhou et al.
(2018) have detected molecular clouds of total mass $200\leavevmode\nobreak\
\rm M_{\rm\odot}$ in front of Cas A. Within 200 pc around Cas A, Kim et al.
(2008) has derived the average gas density of about $3\leavevmode\nobreak\ \rm
cm^{-3}$ by investigating the infrared emission. In this region, compact
molecular clumps with a density as high as $10^{5}\leavevmode\nobreak\ \rm
cm^{-3}$ have also been detected (Reynoso & Goss, 2002). Ma et al. (2019) have
performed a detailed J = 1-0 survey of CO in a large field near Cas A using
the Purple Mountain Observatory (PMO) 13.7 m millimetre telescope. The total
mass of molecular gas was $\approx 9.5\times 10^{5}\leavevmode\nobreak\ \rm
M_{\odot}$, which corresponds to an average density of $10\leavevmode\nobreak\
\rm cm^{-3}$ within 100 pc proximity of Cas A. The line profiles have
asymmetric or broadened shapes, which indicates a possible interaction between
the SNR and the molecular clouds. In this work, we used the J = 1-0
${}^{12}\rm CO$ data as described in Ma et al. (2019). The derived molecular
gas column densities are shown in Figure.1 by assuming $2.0\times
10^{20}\leavevmode\nobreak\ \rm(K\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1})^{-1}$ for the $\rm CO-to-H_{2}$ conversion factor (Bolatto et al.,
2013).

Figure 1: left panel: The LHAASO-KM2A TS map above $25\leavevmode\nobreak\ \rm
TeV$ in the $4^{\circ}\times 4^{\circ}$ region around Cas A, the colorbar
shows the TS value. right panel:The gas column density near Cas A derived from
${}^{12}CO$ line observations (Ma et al., 2019). The green circle labels the
position of Cas A.

As mentioned above, the average gas density is estimated as
$10\leavevmode\nobreak\ \rm cm^{-3}$ in the vicinity, so to estimate the gas
mass we need to calculate the volume that is occupied by CRs. The latter
depends on the CR propagation in the vicinity of Cas A. Since we deal with
relatively small spatial scales and ultra-high energies, we cannot a priori
assume that the propagation proceeds in the diffusive regime. One cannot
exclude that close to the accelerator, highest energy CRs propagate
ballistically near the source and enter the diffusive regime when $r>D/c$,
where $r$ is the distance from the source, $D$ is the diffusion coefficient
and $c$ is the speed of light. The diffusion coefficient in the Interstellar
Medium (ISM) is estimated as $D(E)\sim 2\times
10^{28}(\frac{E}{1\leavevmode\nobreak\ \rm GeV})^{0.5}\leavevmode\nobreak\ \rm
cm^{2}/s$ (Yuan et al., 2017). Its extrapolation to $E=1\leavevmode\nobreak\
\rm PeV$ gives $D\sim 2\times 10^{31}\leavevmode\nobreak\ \rm cm^{2}/s$. This
implies $r\gtrsim D/c\simeq$ 200 pc. For comparison, rectilinear propagation
length of protons over 340 years is $\simeq$ 110 pc. Thus, even in the case of
acceleration of PeV protons at the early epochs of the SNR, they would still
continue to move ballistically. Due to the beaming effects, only the protons
propagating towards us can produce visible $\gamma$-rays. Then the
$\gamma$-ray source should have a similar angular size as the accelerator,
i.e., the SNR shell. This is about $2.5^{\prime}$, so it can be detected by
LHAASO-KM2A as a point-like source.

The diffusion of CRs in the vicinity of the accelerators could be strongly
suppressed due to enhanced turbulence introduced, e.g., by the streaming
instability of injected CRs (see e.g. (Malkov et al., 2013)). The interaction
of the cosmic ray precursor and dense clumps can also drive turbulence. By
either following the turbulent tangling field lines or mirror diffusion in
compressible magnetic fluctuations (Lazarian & Xu, 2021), high-energy CR
protons might undergo very slow diffusion. In this case, PeV CRs could
propagate in the diffusive regime and the region occupied by VHE CRs would be
of the order $r\sim\sqrt{2DT}\sim 20\leavevmode\nobreak\ \rm
pc(\frac{\chi}{10^{-2}})^{0.5}$, where $\chi$ is the suppression factor of the
diffusion coefficient near the source compared with the Galactic diffusion
coefficient, $D_{source}(E)=\chi D(E)$. The angular size of the $\gamma$-ray
emission is estimated as $r/d\sim 0.33^{\circ}(\frac{\chi}{10^{-2}})^{0.5}$.
The maximum diffusion length, in any case, should be smaller than 110 pc, the
ballistic propagation length over 340 years. And the maximum angular extension
of the $\gamma$-ray emission when CRs are in the diffusive regime should be
smaller than $1.8^{\circ}$. To estimate the total CR energy budget from the
$\gamma$-ray luminosity, only the average density matters. As estimated in Ma
et al. (2019), the average density in the nearby 100 pc of Cas A is
$10\leavevmode\nobreak\ \rm cm^{-3}$. In this case, due to the lower average
density and larger integration area in deriving the $\gamma$-ray flux, the
derived CR energy budget would be more conservative than the ballistic
propagation case we considered above. To derive the robust and model
independent estimations we consider only the diffusive regime in the following
discussion.

##  4 KM2A data analysis

The data used in this analysis were collected from December 2019 to September
2022 by the half KM2A, three quarters KM2A and full KM2A. Quality selections
have been applied to ensure a reliable data quality. We select the periods
when at least 95$\%$ of working sub-detectors were in good condition. The
total effective observation time is 932.74 days after data quality selection.
To achieve a better performance of the array, several event cuts are also
implemented. The cuts on data and event selections are the same as listed in
the KM2A performance paper (Aharonian et al., 2021).

Considering the energy resolution and statistics, one decade of energy is
divided into 5 bins with a bin width of $log_{10}E=0.2$. The sky in celestial
coordinates (right ascension and declination) is divided into cells of size
$0.1^{\circ}\times 0.1^{\circ}$ and filled with detected events according to
their reconstructed arrival directions for each energy bin. To extract the
excess of $\gamma$-rays from each cell, the “direct integration method”
(Fleysher et al., 2004) is adopted to estimate the number of cosmic ray
background events. The test statistic (TS) used to evaluate the significance
of the source in this work is ${\rm TS}=2\log(\lambda)$, where
$\lambda={\mathcal{L}_{1}/\mathcal{L}_{0}}$, $\mathcal{L}_{1}$ is the maximum
likelihood value for the alternative hypothesis, and ${\mathcal{L}_{0}}$ is
the maximum likelihood value of the null hypothesis. The TS map of the ROI is
shown in the left panel of Fig.1. We found that there is no significant excess
in the vicinity of Cas A.

As mentioned in the last section, we consider both the ballistic propagation
and diffusive regime. In the former case, the expected $\gamma$-ray emission
produced by CRs escaping from Cas A is point-like. In KM2A analysis, taking
into account the point spread function (PSF), we integrate all photons in the
90% contamination radius from a point source. For diffusive regime, the
intrinsic size of the source varies with the diffusion coefficient; however,
the maximum angular radius is 1.8∘ as estimated in the previous section.
Taking into account of the angular resolution of the detector, we use an
integration radius of 2.2∘ for the lower energy bin and 1.85∘ for energies
higher than 100 TeV, to estimate the upper limits. No significant excess has
been detected. We derived an upper limit for each energy bin at the 95%
confidence level using the method proposed by Helene (1983). For a more
conservative estimate of the upper limit, we use the CERN ROOT tools following
Feldman & Cousins (1998) to calculate the 95% upper limit of the signal when
the background count is less than 20. The results are shown in Fig.2 and
Fig.3. The main uncertainties come from the uncertainty in the differential
spectral index of the $\gamma$-ray emission, which we assume to derive the
upper limit. In order to estimate such systematic uncertainties, the analysis
is separately performed for the $\gamma$-ray spectral index of -2 or -3. The
uncertainties found from this test are small: about 10% and 3% for the first
two energy bins, and less than 1% at higher energies.

The systematic uncertainties affecting the flux upper limits are similar to
those studied in Aharonian et al. (2021). The number of operating units varied
with time due to debugging a few percent of detector units. The variable
layout of the array, affecting the $\gamma$-ray/background separation, has a
slight effect on the flux. The systematic uncertainty also comes from the
atmospheric model used in the simulation, which affects the detection
efficiency. The overall systematic uncertainty affecting the flux is estimated
to be $\sim$7$\%$.

In principle, the diffuse galactic $\gamma$-ray emission (DGE) should be
subtracted before we derive the upper limit for sources. But the inclusion of
such a component in deriving the upper limit only has a marginal (10%) impact
on the final results. Thus to avoid further systematic errors, we do not
subtract the DGE in this work and use the most conservative upper limits.

Figure 2: The UHE $\gamma$-ray flux upper limits assuming Cas A is a point
source. The data points are from MAGIC and VERITAS obervations. The grey curve
is the power law function with the index of 2.8. A harder spectrum would
violate the LHAASO upper limit.  Figure 3: The UHE $\gamma$-ray flux upper
limits within 1.8 degree from Cas A. The black, red and blue curves correspond
to the predicted pion-decay $\gamma$-ray fluxes for the proton index of 2.0,
2.4 and 2.7, respectively. The total energies of CR protons within
$100-1000\leavevmode\nobreak\ \rm TeV$ are $5\times 10^{49}\rm erg$, $3\times
10^{48}\rm erg$ and $1\times 10^{47}\rm erg$, respectively, which are the CR
energy budgets expected if Cas A type SNR produce all the PeV CRs in our
Galaxy.

##  5 Discussion

###  5.1 Point source scenario

The recent MAGIC and VERITAS observations reveal a significant steepening in
the $\gamma$-ray spectrum at TeV energies (Ahnen et al., 2017; Abeysekara et
al., 2020). This can be interpreted as a break or a cutoff in the spectrum.
The latter would imply that Cas A accelerates particles only up to tens of
TeV. However, recent studies (see e.g. Malkov & Aharonian (2019)) show that
taking into account realistic geometry and magnetic field configurations, one
can expect a significant deviation from the standard DSA predictions, namely
very steep, power-law type spectra. This option does not need a cutoff to
describe the TeV data; a broken power law can fit the GeV-TeV SEDs well, with
a spectral index of about 2.7 above the break (Abeysekara et al., 2020).

To explore whether this scenario is compatible with the KM2A observations, we
extrapolate the data points measured by IACTs with a power law. It should be
noted that in this scenario Cas A can still be in the PeVatron phase, and thus
the gamma-ray observations cannot set a limit on the total CR energy budget
above $100\leavevmode\nobreak\ \rm TeV$. But information regarding the
acceleration spectrum can be obtained from the observed $\gamma$-ray spectrum.
We found that a spectral index smaller than 2.8 already violates the KM2A
upper limit. The $\gamma$-ray spectral index of 2.8 corresponds to the index
of $\simeq 2.9$ for CR protons. Such an injection spectrum is softer than the
CR spectrum measured in this energy range, even ignoring the further
steepening of the spectrum of particles during their propagation in the
galactic plane and halo. Such a soft injection spectrum can hardly be
accommodated in the current CR propagation concept; thus, their contribution
to the locally measured CR flux can not be significant.

###  5.2  Extended source scenario

One should note that, in general, independent of the question of its
contribution to the local CR flux, the very steep proton spectrum does not
exclude acceleration of PeV protons by Cas A. Therefore, to probe the amount
of PeV protons accelerated at the early epochs of Cas A, we assume an
integrated spectrum of these CRs in the form $N(E)\sim
E^{-\gamma}{e^{-E/E_{c}}}$. Since we are considering the possibility of Cas A
as a PeVatron, we fix $E_{c}$ =2$\leavevmode\nobreak\ \rm PeV$, and choose the
index $\gamma=$2.0, 2.4, or 2.7 (see the discussion below) . As long as we are
investigating CRs released between $100\leavevmode\nobreak\ \rm TeV$ and
$1\leavevmode\nobreak\ \rm PeV$, the exact value of the cutoff energy does not
have a strong impact on the total energy budget. The $\gamma$-ray flux is
proportional to the product of CR total energy and gas density. Thus from the
observed upper limit of $\gamma$-ray flux and the derived gas density, one can
derive an upper limit for the CR total energy. By using the $\gamma$-ray
production cross-section parametrised in Kafexhiu et al. (2014), we calculated
the predicted $\gamma$-ray flux for $\gamma=$ 2.0, 2.4, or 2.7. Taking into
account the average gas density of about $10\leavevmode\nobreak\ \rm cm^{-3}$,
we derived the upper limit of total energy of CRs in the energy range 100 -
1000 $\leavevmode\nobreak\ \rm TeV$ as 3.6/3.0/4.0$\times 10^{47}$ (10
cm-3/$n$) $\leavevmode\nobreak\ \rm erg$, assuming all the molecular gas has
been illuminated by the escaped CRs, with an index of 2.0/2.4/2.7. The derived
upper limit of total CR energy only slightly depends on the spectral index.

If the appearance of the Cas A-like SNRs events has a rate of 1 per century,
as suggested by Schure & Bell (2013), the CR injection rate in our Galaxy in
the energy interval $100-1000\leavevmode\nobreak\ \rm TeV$ would be
$1.2/1.0/1.3\times 10^{38}\leavevmode\nobreak\ \rm erg/s$ for an injection
index of 2.0/2.4/2.7, respectively. The total CR injection rate is estimated
as $1-3\times 10^{41}\leavevmode\nobreak\ \rm erg/s$ in our Galaxy (Drury,
2012), which corresponds to an injection rate in the energy interval
$100-1000\leavevmode\nobreak\ \rm TeV$ as $1.6-5.0\times
10^{40}\leavevmode\nobreak\ \rm erg/s$ for $\gamma=2.0$, $1.0-3.0\times
10^{39}\leavevmode\nobreak\ \rm erg/s$ for $\gamma=2.4$ and $3.0-9.0\times
10^{37}\leavevmode\nobreak\ \rm erg/s$ for $\gamma=2.7$. For the acceleration
spectral index of 2.0, which is predicted in the standard DSA theory, the Cas
A upper limits are more than two orders of magnitude smaller than that
required for the total CR energy budget in our Galaxy. For a softer injection
spectral index of 2.4, the $100-1000\leavevmode\nobreak\ \rm TeV$ CR injection
power from Cas A type SNRs derived here is still one order of magnitude
smaller than the requirement for the whole Galaxy. And in the case of the
injection spectral index of 2.7, we cannot rule out the possibility that all
CRs above $100\leavevmode\nobreak\ \rm TeV$ in our Galaxy are injected from
Cas A type objects. As an alternative way to express this result, we plotted
the predicted $\gamma$-ray flux in Figure 3 assuming the CRs injected by Cas A
type SNRs dominated the PeV CRs in our Galaxy. We again see that the limits
from LHAASO KM2A rule out that Cas A type SNRs produce all PeV CRs in the
Galaxy for $\gamma=$ 2.0 or 2.4,but do not rule out if $\gamma=$ 2.7.

Indeed, as shown in the last paragraph, the upper limit of the rate of CR
above $100\leavevmode\nobreak\ \rm TeV$ injected by Cas A only slightly
depends on the injection spectrum and is estimated as $\sim 1.3\times
10^{38}(10\leavevmode\nobreak\ \rm cm^{-3}/n)\leavevmode\nobreak\ \rm erg/s$.
On the other hand, the total energy budget required for CRs above
$100\leavevmode\nobreak\ \rm TeV$ depends only on the injection spectrum. If
we assume a pure power law, the injection energy budget above
$100\leavevmode\nobreak\ \rm TeV$ is $W(E>100\leavevmode\nobreak\ \rm
TeV)=(1-3)\times 10^{(41-5(\Gamma-2))}\leavevmode\nobreak\ \rm erg/s$ for
$\Gamma>2.0$, where $\Gamma$ is the injection spectral index. By comparing
with the limit set by KM2A observations on Cas A, we found that for $n\simeq
10\leavevmode\nobreak\ \rm cm^{-3}$ as estimated from CO observations, our
results can rule out the hypothesis that Cas A type SNRs are the only
PeVatrons contributing to CRs above $100\leavevmode\nobreak\ \rm TeV$ for a CR
injection spectrum index less than $2.5$. A smaller gas density would relax
the constraints. But note that an average gas density well below
$10\leavevmode\nobreak\ \rm cm^{3}$ seems unrealistic in this region. In the
most conservative case, assuming a gas density of $1\leavevmode\nobreak\ \rm
cm^{-3}$, the lower limit for the injection spectral index is $2.4$.

In scenario (3), the highest energy CRs have already escaped from the shock
upstream. Cas A still lies in its progenitor’s wind bubble (Weil et al.,
2020), which has a size of about $10\leavevmode\nobreak\ \rm pc$ and a much
lower density compared with the ISM. In the most extreme case, it is possible
that CRs escaped from the shell and confined in the bubble. The angular size
of the bubble is about 5 arcminutes, which is much smaller than the PSF of
KM2A. As a result, the bubble is also a point source in KM2A, and the upper
limit derived from a point source is about 1/5 of the extended source scenario
considered above. If we assume an average density of $0.1\leavevmode\nobreak\
\rm cm^{-3}$ in the wind bubble, the constraints on the total CR energy budget
can be 20 times larger than our estimation above.

In the derivation of the $\gamma$-ray upper limit, the Galactic diffuse
$\gamma$-ray emission is not considered, which would make the upper limit even
lower and the constraint more stringent. Thus we argue that our calculation
implies that the Cas A-type SNRs cannot be the only sources for CRs up to PeV
in the regime of standard DSA (hard injection spectrum). If we assume a softer
injection spectrum, Cas A type SNRs can still be major PeVatrons in our
Galaxy. But such a softer injection spectrum would be in tension with most CR
propagation models, in which a strong energy dependence of the CR diffusion
coefficient is used, and the CR injection spectrum should be hard to fit the
locally observed CR spectrum.

We also note that a more complex spectral shape, such as a broken power law,
is possible for the total CR flux injected by Cas A. But in this work our
constraints mainly come from a rather narrow energy band, and the constraints
on the exact spectral shape are limited. To avoid uncertainties and
degeneracy, we used a single power law spectra in this study.

In conclusion, based on the LHAASO KM2A measurements, we set stringent upper
limits on the total energy budget of UHE protons accelerated by Cas A. Our
constraints here are nearly model independent, unless in the hypothetical, and
in our view, not very realistic situation, when cosmic rays are confined in a
compact low density wind bubble after escaping from the shell. Although we
cannot formally rule out the possibility that the Cas A type SNRs are the
Galactic PeVatrons, the stringent limits on the accelerated (injection)
spectrum have important implications. Further UHE observations will
investigate more parameter spaces. We note that the most stringent limits come
from the $\gamma$-ray fluxes above $100\leavevmode\nobreak\ \rm TeV$, for
which the sensitivity of LHAASO KM2A will remain unrivalled in the foreseeable
future. We anticipate that the accumulation of LHAASO KM2A data for another 5
to 10 years will improve the upper limit substantially and would finally rule
out or confirm Cas A type SNRs as a PeVatron population.

We would like to thank all staff members who work at the LHAASO site above
4400 meters above sea level year-round to maintain the detector and keep the
water recycling system, electricity power supply and other components of the
experiment operating smoothly. We are grateful to Chengdu Management Committee
of Tianfu New Area for the constant financial support for research with LHAASO
data. We deeply appreciate the computing and data service support provided by
the National High Energy Physics Data Center for the data analysis in this
paper. This research work is also supported by the following grants: The
National Key R&D program of China under grants 2018YFA0404201, 2018YFA0404202,
2018YFA0404203, and 2018YFA0404204, by the National Natural Science Foundation
of China NSFC No.12022502, No.12205314, No. 12105301, No. 12261160362,
No.12105294, No.U1931201. In Thailand, support was provided by the National
Science and Technology Development Agency (NSTDA) and the National Research
Council of Thailand (NRCT) under the High-Potential Research Team Grant
Program (N42A650868).

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