Skip to main content
Log in

Non-Classical Diffusion of the Cosmic Rays in the Galaxy: Retrieval of Primary Nuclei Spectra in Sources

  • Elementary Particles and Fields/Experiment
  • Published:
Physics of Atomic Nuclei Aims and scope Submit manuscript

Abstract

This study investigates the use of results from new-generation balloon-borne and satellite instruments and earthbound observatories for quantifying primary nuclei spectra in the Galactic sources. The unique data of these experiments allowed to establish new features in cosmic ray spectra in the GV–sub-PV rigidity region, make it possible to formulate an inverse approach of retrieval the spectra of primary nuclei in cosmic ray sources. We use the non-classical diffusion model of cosmic rays in the inhomogeneous Galaxy as the forward model in the inversion. The main parameters of diffusion model are self-consistently determined from experimental data. The inversion is based on the key element of the forward model solution—the presence of knee in the cosmic ray spectrum. We demonstrate that the average value of the injection index \(\gamma\) of primary nuclei spectra in sources equals \(\gamma\sim 2.8{-}2.9\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

REFERENCES

  1. V. L. Ginzburg and S. I. Syrovatskii, The Origin of Cosmic Rays (Pergamon, 1964).

    Book  Google Scholar 

  2. V. S. Berezinskii, S. V. Bulanov, V. A. Dogiel, and V. S. Ptuskin, Astrophysics of Cosmic Rays (Amsterdam, North-Holland, 1990).

    Google Scholar 

  3. E. G. Berezhko and L. G. Ksenofontov, J. Exp. Theor. Phys. 89, 391 (1999).

    Article  ADS  Google Scholar 

  4. A. A. Lagutin, V. V. Makarov, and A. G. Tyumentsev, in Proceedings of the 27th International Cosmic Ray Conference, Hamburg, 2001, Vol. 5, p. 1889.

  5. M. Aguilar et al. (AMS Collab.), Phys. Rev. Lett. 120, 021101 (2018).

    Article  ADS  Google Scholar 

  6. B. G. Elmegreen and E. Falgarone, Astrophys. J. 471, 816 (1996).

    Article  ADS  Google Scholar 

  7. M. H. Heyer, C. Brunt, R. L. Snell, J. E. Howe, F. P. Schloerb, and J. M. Carpenter, Astrophys. J. Suppl. 115, 241 (1998).

    Article  Google Scholar 

  8. B. G. Elmegreen and J. Scalo, Ann. Rev. Astron. Astrophys. 42, 211 (2004).

    Article  ADS  Google Scholar 

  9. E. A. Bergin and M. Tafalla, Ann. Rev. Astron. Astrophys. 45, 339 (2007).

    Article  ADS  Google Scholar 

  10. N. Sánchez and E. J. Alfaro, Astrophys. J. Suppl. Ser. 178, 1 (2008).

    Article  ADS  Google Scholar 

  11. Y. N. Efremov and A. D. Chernin, Phys. Usp. 46(1), 1 (2003).

    Article  ADS  Google Scholar 

  12. R. de la Fuente Marcos and C. de la Fuente Marcos, Astrophys. J. 700, 436 (2009).

    Article  ADS  Google Scholar 

  13. N. Sánchez, N. Añez, E. J. Alfaro, and M. Crone Odekon, Astrophys. J. 720, 541 (2010).

    Article  ADS  Google Scholar 

  14. Ya. B. Zeldovich, A. A. Ruzmaikin, and D. D. Sokoloff, The Almighty Chance (World Scientific, Singapore, 1990).

  15. S. L. Wilkin, C. F. Barenghi, and A. Shukurov, Phys. Rev. Lett. 99, 134501 (2007).

    Article  ADS  Google Scholar 

  16. A. M. Bykov and I. N. Toptygin, Astrophys. Space Sci. 138, 341 (1987).

    Article  ADS  Google Scholar 

  17. A. Shukurov, A. P. Snodin, A. Seta, P. J. Bushby, and T. S. Wood, Astrophys. J. Lett. 839, L16 (2017).

    Article  ADS  Google Scholar 

  18. A. A. Lagutin, Yu. A. Nikulin, and V. V. Uchaikin, Preprint ASU, No. 4 (Barnaul, 2000).

  19. A. A. Lagutin, Yu. A. Nikulin, and V. V. Uchaikin, Nucl. Phys. B Proc. Suppl. 97, 267 (2001).

    Article  ADS  Google Scholar 

  20. A. A. Lagutin and V. V. Uchaikin, in Proceedings of the 27th International Cosmic Ray Conference, Hamburg, 2001, Vol. 5, p. 1900.

  21. A. A. Lagutin and V. V. Uchaikin, Nucl. Instrum. Methods Phys. Res., Sect. B 201, 212 (2003).

    Google Scholar 

  22. A. D. Erlykin, A. A. Lagutin, and A. W. Wolfendale, Astropart. Phys. 19, 351 (2003).

    Article  ADS  Google Scholar 

  23. A. A. Lagutin and A. G. Tyumentsev, Izv. Altaisk. Univ. 5, 4 (2004).

    Google Scholar 

  24. A. A. Lagutin, A. V. Yushkov, and A. G. Tyumentsev, Int. J. Mod. Phys. A 20, 6834 (2005).

    Article  ADS  Google Scholar 

  25. A. A. Lagutin, N. V. Volkov, A. S. Kuzmin, and A. G. Tyumentsev, Bull. Russ. Acad. Sci.: Phys. 73, 581 (2009).

    Article  Google Scholar 

  26. N. V. Volkov, A. A. Lagutin, and A. G. Tyumentsev, J. Phys.: Conf. Ser. 632, 012027 (2015).

    Google Scholar 

  27. S. G. Samco, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives — Theory and Applications (Gordon and Breach, New York, 1993).

    Google Scholar 

  28. V. V. Uchaikin and V. M. Zolotarev, Chance and Stability. Stable Distributions and Their Applications (VSP, Utrecht, 1999).

    Book  MATH  Google Scholar 

  29. V. M. Zolotarev, V. V. Uchaikin, and V. V. Saenko, J. Exp. Theor. Phys. 88, 780 (1999).

    Article  ADS  Google Scholar 

  30. B. Bartoli et al. (ARGO-YBJ Collab.), Phys. Rev. D 92, 092005 (2015).

    Article  ADS  Google Scholar 

  31. A. A. Lagutin, D. V. Strelnikov and A. G. Tyumentsev, in Proceedings of the 27th International Cosmic Ray Conference, Hamburg, 2001, Vol. 5, p. 1896.

  32. B. Bartoli et al. (ARGO-YBJ Collab.), Phys. Rev. D 91, 112017 (2015).

    Article  ADS  Google Scholar 

  33. L. J. Gleeson and W. I. Axford, Astrophys. J. 154, 1011 (1968).

    Article  ADS  Google Scholar 

  34. A. D. Panov, J. H. Adams, H. S. Ahn, G. L. Bashinzhagyan, J. W. Watts, J. P. Wefel, J. Wu, O. Ganel, T. G. Guzik, V. I. Zatsepin, I. Isbert, K. C. Kim, M. Christl, E. N. Kouznetsov, M. I. Panasyuk, E. S. Seo, et al., Bull. Russ. Acad. Sci.: Phys. 73, 564 (2009).

    Article  Google Scholar 

  35. O. Adriani, G. C. Barbarino, G. A. Bazilevskaya, M. Boezio, E. A. Bogomolov, L. Bonechi, M. Bongi, V. Bonvicini, S. V. Borisov, S. Bottai, A. Bruno, F. Cafagna, D. Campana, R. Carbone, P. Carlson, M. Casolino, et al., Adv. Space Res. 51, 219 (2013).

    Article  ADS  Google Scholar 

  36. M. Aguilar et al. (AMS Collab.), Phys. Rev. Lett. 114, 171103 (2015).

    Article  ADS  Google Scholar 

  37. K. Abe, H. Fuke, S. Haino, T. Hams, M. Hasegawa, A. Horikoshi, A. Itazaki, K. C. Kim, T. Kumazawa, A. Kusumoto, M. H. Lee, Y. Makida, S. Matsuda, Y. Matsukawa, K. Matsumoto, J. W. Mitchell, et al., Astrophys. J. 822, 65 (2016).

    Article  ADS  Google Scholar 

  38. Y. S. Yoon, T. Anderson, A. Barrau, N. B. Conklin, S. Coutu, L. Derome, J. H. Han, J. A. Jeon, K. C. Kim, M. H. Kim, H. Y. Lee, J. Lee, M. H. Lee, S. E. Lee, J. T. Link, A. Menchaca-Rocha, et al., Astrophys. J. 839, 5 (2017).

    Article  ADS  Google Scholar 

  39. V. Grebenyuk, D. Karmanov, I. Kovalev, I. Kudryashov, A. Kurganov, A. Panov, D. Podorozhny, A. Tkachenko, L. Tkachev, A. Turundaevskiy, O. Vasiliev, and A. Voronin, Adv. Space Res. 64, 2546 (2019).

    Article  ADS  Google Scholar 

  40. Q. An et al. (DAMPE Collab.), Sci. Adv. 5, eaax3793 (2019).

  41. O. Adriani et al. (CALET Collab.), Phys. Rev. Lett. 112, 181102 (2019).

    Article  ADS  Google Scholar 

  42. T. Antoni et al. (KASKADE Collab.), Astropart. Phys. 24, 1 (2005).

    Article  ADS  Google Scholar 

  43. W. D. Apel, J. C. Arteaga-Velazquez, K. Bekk, M. Bertaina, J. Blümer, H. Bozdog, I. M. Brancus, E. Cantoni, A. Chiavassa, F. Cossavella, K. Daumiller, V. de Souza, F. Di Pierro, P. Doll, R. Engel, J. Engler, et al., Astropart. Phys. 47, 54 (2013).

    Article  ADS  Google Scholar 

  44. M. G. Aartsen et al. (IceCube Collab.), Phys. Rev. D 100, 082002 (2019).

    Article  ADS  Google Scholar 

  45. M. Aguilar et al. (AMS Collab.), Phys. Rev. Lett. 115, 211101 (2015).

    Article  ADS  Google Scholar 

  46. J. J. Engelmann, P. Ferrando, A. Soutoul, P. Goret, E. Juliusson, L. Koch-Miramond, N. Lund, P. Masse, B. Peters, N. Petrou, and I. L. Rasmussen, Astron. Astrophys. 233, 96 (1990).

    ADS  Google Scholar 

  47. H. S. Ahn, P. Allison, M. G. Bagliesi, L. Barbier, J. J. Beatty, G. Bigongiari, T. J. Brandt, J. T. Childers, N. B. Conklin, S. Coutu, M. A. Du Vernois, O. Ganel, J. H. Han, J. A. Jeon, K. C. Kim, M. H. Lee, et al., Astrophys. J. 707, 593 (2009).

    Article  ADS  Google Scholar 

  48. O. Adriani, G. C. Barbarino, G. A. Bazilevskaya, R. Bellotti, M. Boezio, E. A. Bogomolov, M. Bongi, V. Bonvicini, S. Bottai, A. Bruno, F. Cafagna, D. Campana, R. Carbone, P. Carlson, M. Casolino, G. Castellini, et al., Astrophys. J. 791, 93 (2014).

    Article  ADS  Google Scholar 

  49. M. Aguilar et al. (AMS Collab.), Phys. Rev. Lett. 119, 251101 (2017).

    Article  ADS  Google Scholar 

  50. E. Juliusson, Astrophys. J. 191, 331 (1974).

    Article  ADS  Google Scholar 

  51. C. D. Orth, A. Buffington, G. F. Smoot, and T. S. Mast, Astrophys. J. 226, 1147 (1978).

    Article  ADS  Google Scholar 

  52. M. Simon, H. Spiegelhauer, W. K. H. Schmidt, F. Siohan, J. F. Ormes, V. K. Balasubrahmanyan, and J. F. Arens, Astrophys. J. 239, 712 (1980).

    Article  ADS  Google Scholar 

  53. D. Mueller, S. P. Swordy, P. Meyer, J. L’Heureux, and J. M. Grunsfeld, Astrophys. J. 374, 356 (1991).

    Article  ADS  Google Scholar 

  54. A. A. Lagutin, N. V. Volkov, R. I. Raikin, and A. G. Tyumentsev, J. Phys.: Conf. Ser. 1181, 012023 (2019).

    Google Scholar 

  55. A. A. Abdo, M. Ackermann, M. Ajello, L. Baldini, J. Ballet, G. Barbiellini, M. G. Baring, D. Bastieri, B. M. Baughman, K. Bechtol, R. Bellazzini, B. Berenji, R. D. Blandford, E. D. Bloom, E. Bonamente, A. W. Borgland, et al., Science (Washington, DC, U. S.) 327, 1103 (2010).

    Article  ADS  Google Scholar 

  56. A. A. Abdo, M. Ackermann, M. Ajello, L. Baldini, J. Ballet, G. Barbiellini, D. Bastieri, B. M. Baughman, K. Bechtol, R. Bellazzini, B. Berenji, R. D. Blandford, E. D. Bloom, E. Bonamente, A. W. Borgland, J. Bregeon, et al., Astrophys. J. 712, 459 (2010).

    Article  ADS  Google Scholar 

  57. H. Abdalla et al. (H.E.S.S. Collab.), Astron. Astrophys. 612, A5 (2018).

    Google Scholar 

  58. T. Tanaka, Y. Uchiyama, F. A. Aharonian, T. Takahashi, A. Bamba, J. S. Hiraga, J. Kataoka, T. Kishishita, M. Kokubun, K. Mori, K. Nakazawa, R. Petre, H. Tajima, and S. Watanabe, Astrophys. J. 685, 988 (2008).

    Article  ADS  Google Scholar 

  59. S. Archambault, A. Archer, W. Benbow, R. Bird, E. Bourbeau, M. Buchovecky, J. H. Buckley, V. Bugaev, M. Cerruti, M. P. Connolly, W. Cui, V. V. Dwarkadas, M. Errando, A. Falcone, Q. Feng, J. P. Finley, et al., Astrophys. J. 836, 23 (2017).

    Article  ADS  Google Scholar 

  60. M. Amenomori et al. (The Tibet AS\(\gamma\) Collab.), Nat. Astron. 5, 460 (2021).

    ADS  Google Scholar 

  61. M. A. Malkov and F. A. Aharonian, Astrophys. J. 881, 2 (2019).

    Article  ADS  Google Scholar 

  62. S. Gabici, C. Evoli, D. Gaggero, P. Lipari, P. Mertsch, E. Orlando, A. Strong, and A. Vittino, Int. J. Mod. Phys. D 28, 1930022 (2019).

    Article  ADS  Google Scholar 

Download references

ACKNOWLEDGMENTS

The authors are deeply grateful to the anonymous referee for valuable comments and suggestions, which helped to improve the paper.

Funding

The work was performed at the UNU ‘‘Astrophysical Complex of MSU-ISU’’ (agreement 13.UNU.21.0007). The work is supported by the Russian Foundation for Basic Research (grants nos. 19-52-44002, 19-32-60003), the Russian Science Foundation (grants nos. 19-72-20067, 19-72-00010), the Russian Federation Ministry of Science and High Education (projects FZZE-2020-0017, FZZE-2020-0024).

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to A. A. Lagutin or N. V. Volkov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lagutin, A.A., Volkov, N.V. Non-Classical Diffusion of the Cosmic Rays in the Galaxy: Retrieval of Primary Nuclei Spectra in Sources. Phys. Atom. Nuclei 84, 975–984 (2021). https://doi.org/10.1134/S1063778821130184

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063778821130184

Navigation