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 \(\gamma\sim 2.8{-}2.9\).
Similar content being viewed by others
REFERENCES
V. L. Ginzburg and S. I. Syrovatskii, The Origin of Cosmic Rays (Pergamon, 1964).
V. S. Berezinskii, S. V. Bulanov, V. A. Dogiel, and V. S. Ptuskin, Astrophysics of Cosmic Rays (Amsterdam, North-Holland, 1990).
E. G. Berezhko and L. G. Ksenofontov, J. Exp. Theor. Phys. 89, 391 (1999).
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.
M. Aguilar et al. (AMS Collab.), Phys. Rev. Lett. 120, 021101 (2018).
B. G. Elmegreen and E. Falgarone, Astrophys. J. 471, 816 (1996).
M. H. Heyer, C. Brunt, R. L. Snell, J. E. Howe, F. P. Schloerb, and J. M. Carpenter, Astrophys. J. Suppl. 115, 241 (1998).
B. G. Elmegreen and J. Scalo, Ann. Rev. Astron. Astrophys. 42, 211 (2004).
E. A. Bergin and M. Tafalla, Ann. Rev. Astron. Astrophys. 45, 339 (2007).
N. Sánchez and E. J. Alfaro, Astrophys. J. Suppl. Ser. 178, 1 (2008).
Y. N. Efremov and A. D. Chernin, Phys. Usp. 46(1), 1 (2003).
R. de la Fuente Marcos and C. de la Fuente Marcos, Astrophys. J. 700, 436 (2009).
N. Sánchez, N. Añez, E. J. Alfaro, and M. Crone Odekon, Astrophys. J. 720, 541 (2010).
Ya. B. Zeldovich, A. A. Ruzmaikin, and D. D. Sokoloff, The Almighty Chance (World Scientific, Singapore, 1990).
S. L. Wilkin, C. F. Barenghi, and A. Shukurov, Phys. Rev. Lett. 99, 134501 (2007).
A. M. Bykov and I. N. Toptygin, Astrophys. Space Sci. 138, 341 (1987).
A. Shukurov, A. P. Snodin, A. Seta, P. J. Bushby, and T. S. Wood, Astrophys. J. Lett. 839, L16 (2017).
A. A. Lagutin, Yu. A. Nikulin, and V. V. Uchaikin, Preprint ASU, No. 4 (Barnaul, 2000).
A. A. Lagutin, Yu. A. Nikulin, and V. V. Uchaikin, Nucl. Phys. B Proc. Suppl. 97, 267 (2001).
A. A. Lagutin and V. V. Uchaikin, in Proceedings of the 27th International Cosmic Ray Conference, Hamburg, 2001, Vol. 5, p. 1900.
A. A. Lagutin and V. V. Uchaikin, Nucl. Instrum. Methods Phys. Res., Sect. B 201, 212 (2003).
A. D. Erlykin, A. A. Lagutin, and A. W. Wolfendale, Astropart. Phys. 19, 351 (2003).
A. A. Lagutin and A. G. Tyumentsev, Izv. Altaisk. Univ. 5, 4 (2004).
A. A. Lagutin, A. V. Yushkov, and A. G. Tyumentsev, Int. J. Mod. Phys. A 20, 6834 (2005).
A. A. Lagutin, N. V. Volkov, A. S. Kuzmin, and A. G. Tyumentsev, Bull. Russ. Acad. Sci.: Phys. 73, 581 (2009).
N. V. Volkov, A. A. Lagutin, and A. G. Tyumentsev, J. Phys.: Conf. Ser. 632, 012027 (2015).
S. G. Samco, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives — Theory and Applications (Gordon and Breach, New York, 1993).
V. V. Uchaikin and V. M. Zolotarev, Chance and Stability. Stable Distributions and Their Applications (VSP, Utrecht, 1999).
V. M. Zolotarev, V. V. Uchaikin, and V. V. Saenko, J. Exp. Theor. Phys. 88, 780 (1999).
B. Bartoli et al. (ARGO-YBJ Collab.), Phys. Rev. D 92, 092005 (2015).
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.
B. Bartoli et al. (ARGO-YBJ Collab.), Phys. Rev. D 91, 112017 (2015).
L. J. Gleeson and W. I. Axford, Astrophys. J. 154, 1011 (1968).
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).
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).
M. Aguilar et al. (AMS Collab.), Phys. Rev. Lett. 114, 171103 (2015).
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).
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).
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).
Q. An et al. (DAMPE Collab.), Sci. Adv. 5, eaax3793 (2019).
O. Adriani et al. (CALET Collab.), Phys. Rev. Lett. 112, 181102 (2019).
T. Antoni et al. (KASKADE Collab.), Astropart. Phys. 24, 1 (2005).
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).
M. G. Aartsen et al. (IceCube Collab.), Phys. Rev. D 100, 082002 (2019).
M. Aguilar et al. (AMS Collab.), Phys. Rev. Lett. 115, 211101 (2015).
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).
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).
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).
M. Aguilar et al. (AMS Collab.), Phys. Rev. Lett. 119, 251101 (2017).
E. Juliusson, Astrophys. J. 191, 331 (1974).
C. D. Orth, A. Buffington, G. F. Smoot, and T. S. Mast, Astrophys. J. 226, 1147 (1978).
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).
D. Mueller, S. P. Swordy, P. Meyer, J. L’Heureux, and J. M. Grunsfeld, Astrophys. J. 374, 356 (1991).
A. A. Lagutin, N. V. Volkov, R. I. Raikin, and A. G. Tyumentsev, J. Phys.: Conf. Ser. 1181, 012023 (2019).
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).
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).
H. Abdalla et al. (H.E.S.S. Collab.), Astron. Astrophys. 612, A5 (2018).
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).
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).
M. Amenomori et al. (The Tibet AS\(\gamma\) Collab.), Nat. Astron. 5, 460 (2021).
M. A. Malkov and F. A. Aharonian, Astrophys. J. 881, 2 (2019).
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).
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
Corresponding authors
Rights and permissions
About this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063778821130184