Spatial dependent diffusion of cosmic rays and the excess of primary electrons derived from high precision measurements by AMS-02

  • The precise spectra of Cosmic Ray (CR) electrons and positrons have been published by the measurement of AMS-02. It is reasonable to regard the difference between the electron and positron spectra (ΔΦ= Φe--Φe+) as being dominated by primary electrons. The resulting electron spectrum shows no sign of spectral softening above 20 GeV, which is in contrast with the prediction of the standard model of CR propagation. In this work, we generalize the analytic one-dimensional two-halo model of diffusion to a three-dimensional realistic calculation by implementing spatial variant diffusion coefficients in the DRAGON package. As a result, we can reproduce the spectral hardening of protons observed by several experiments, and predict an excess of high energy primary electrons which agrees with the measurement reasonably well. Unlike the break spectrum obtained for protons, the model calculation predicts a smooth electron excess and thus slightly over-predicts the flux from tens of GeV to 100 GeV. To understand this issue, further experimental and theoretical studies are necessary.
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    [5] D. Hooper, P. Blasi, and P. Dario Serpico. JCAP, 1: 25 (2009)
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    [7] P. Blasi, Phy. Rev. Lett., 103: 051104 (2009)
    [8] M. Ahlers, P. Mertsch, and S. Sarkar, Phy. Rev. D, 80: 123017 (2009)
    [9] H. B. Hu, Q. Yuan, B. Wang et al, ApJ, 700: L170-L173 (2009)
    [10] B. Wang, Q. Yuan, C. Fan et al, Science China Physics, Mechanics, and Astronomy, 53: 842 (2010)
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    [13] S. J. Lin, Q. Yuan, and X. J. Bi, Phys. Rev. D, 91: 063508 (2015)
    [14] A. D. Panov, J. H. Adams, H. S. Ahn et al, Bulletin of the Russian Academy of Science, Phys., 73: 564-567 (2009)
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    [16] O. Adriani, G. C. Barbarino, G. A. Bazilevskaya et al, Science, 332: 69 (2011)
    [17] N. Tomassetti, ApJ, 752: L13 (2012)
    [18] D. Gaggero, D. Grasso, A. Marinelli et al, arXiv:1504.00227
    [19] P. L. Biermann, J. K. Becker, J. Dreyer et al, ApJ, 725: 184-187 (2010)
    [20] D. C. Ellison, E. G. Berezhko, and M. G. Baring, ApJ, 540: 292 (2000)
    [21] S. Thoudam and J. R. Hrandel, MNRAS, 421: 1209-1214 (2012)
    [22] S. Thoudam and J. R. Hrandel, AA, 567: A33 (2014)
    [23] A. D. Erlykin and A. W. Wolfendale, J. Phys. G: Nucl. Part. Phys., 28: 2329-2348 (2002)
    [24] C. Evoli, D. Gaggero, D. Grasso et al, JCAP, 10: 18 (2008)
    [25] E. S. Seo and V. S. Ptuskin, ApJ, 431: 705 (1994)
    [26] K. M. Ferrire, Reviews of Modern Physics, 73: 1031-1066 (2001)
    [27] C. Consolandi et al (AMS-02 Collaboration), arXiv:1402.0467
    [28] A. D. Panov, J. H. Adams, H. S. Ahn et al, arXiv:0612377
    [29] H. S. Ahn, P. Allison, M. G. Bagliesi et al, ApJ, 714: L89-L93 (2010)
    [30] T. Antoni, W. D. Apel, and A. F. Badea, Astroparticle Physics, 24: 1-25 (2005)
    [31] L. J. Gleeson and W. I. Axford, ApJ, 154: 1011 (1968)
    [32] L. Accardo, M. Aguilar, D. Aisa et al, Phys. Rev. Lett., 113: 121101 (2014)
    [33] M. Aguilar, D. Aisa, B. Alpat et al, Phys. Rev. Lett., 113: 221102 (2014)
    [34] C. S. Shen, ApJ, 162: L181 (1970)
    [35] T. Kobayashi, Y. Komori, K. Yoshida et al, ApJ, 601: 340-351 (2004)
    [36] N. J. Shaviv, E. Nakar, and T. Piran, Phy. Rev. Lett., 103: 111302 (2009)
    [37] Y. Q. Guo, H. B. Hu, and Z. Tian, arXiv:1412.8590
  • [1] M. Aguilar, G. Alberti, B. Alpat et al, Phys. Rev. Lett., 110: 141102 (2013)
    [2] O. Adriani, G. C. Barbarino, G. A. Bazilevskaya et al, Nature, 458: 607-609 (2009)
    [3] L. Bergstrm, T. Bringmann, and J. Edsj, Phys. Rev. D, 78: 103520 (2008)
    [4] V. Barger, W. Y. Keung, D. Marfatia et al, Phy. Lett. B, 672: 141-146 (2009)
    [5] D. Hooper, P. Blasi, and P. Dario Serpico. JCAP, 1: 25 (2009)
    [6] H. Yksel, M. D. Kistler, and T. Stanev, Phy. Rev. Lett., 103: 051101 (2009)
    [7] P. Blasi, Phy. Rev. Lett., 103: 051104 (2009)
    [8] M. Ahlers, P. Mertsch, and S. Sarkar, Phy. Rev. D, 80: 123017 (2009)
    [9] H. B. Hu, Q. Yuan, B. Wang et al, ApJ, 700: L170-L173 (2009)
    [10] B. Wang, Q. Yuan, C. Fan et al, Science China Physics, Mechanics, and Astronomy, 53: 842 (2010)
    [11] X. Li, Z. Q. Shen, B. Q. Lu et al, arXiv:1412.1550
    [12] Q. Yuan and X. J. Bi, Phys. Lett. B, 727: 1-7 (2013)
    [13] S. J. Lin, Q. Yuan, and X. J. Bi, Phys. Rev. D, 91: 063508 (2015)
    [14] A. D. Panov, J. H. Adams, H. S. Ahn et al, Bulletin of the Russian Academy of Science, Phys., 73: 564-567 (2009)
    [15] H. S. Ahn, P. S. Allison, M. G. Bagliesi et al, ApJ, 715: 1400-1407 (2010)
    [16] O. Adriani, G. C. Barbarino, G. A. Bazilevskaya et al, Science, 332: 69 (2011)
    [17] N. Tomassetti, ApJ, 752: L13 (2012)
    [18] D. Gaggero, D. Grasso, A. Marinelli et al, arXiv:1504.00227
    [19] P. L. Biermann, J. K. Becker, J. Dreyer et al, ApJ, 725: 184-187 (2010)
    [20] D. C. Ellison, E. G. Berezhko, and M. G. Baring, ApJ, 540: 292 (2000)
    [21] S. Thoudam and J. R. Hrandel, MNRAS, 421: 1209-1214 (2012)
    [22] S. Thoudam and J. R. Hrandel, AA, 567: A33 (2014)
    [23] A. D. Erlykin and A. W. Wolfendale, J. Phys. G: Nucl. Part. Phys., 28: 2329-2348 (2002)
    [24] C. Evoli, D. Gaggero, D. Grasso et al, JCAP, 10: 18 (2008)
    [25] E. S. Seo and V. S. Ptuskin, ApJ, 431: 705 (1994)
    [26] K. M. Ferrire, Reviews of Modern Physics, 73: 1031-1066 (2001)
    [27] C. Consolandi et al (AMS-02 Collaboration), arXiv:1402.0467
    [28] A. D. Panov, J. H. Adams, H. S. Ahn et al, arXiv:0612377
    [29] H. S. Ahn, P. Allison, M. G. Bagliesi et al, ApJ, 714: L89-L93 (2010)
    [30] T. Antoni, W. D. Apel, and A. F. Badea, Astroparticle Physics, 24: 1-25 (2005)
    [31] L. J. Gleeson and W. I. Axford, ApJ, 154: 1011 (1968)
    [32] L. Accardo, M. Aguilar, D. Aisa et al, Phys. Rev. Lett., 113: 121101 (2014)
    [33] M. Aguilar, D. Aisa, B. Alpat et al, Phys. Rev. Lett., 113: 221102 (2014)
    [34] C. S. Shen, ApJ, 162: L181 (1970)
    [35] T. Kobayashi, Y. Komori, K. Yoshida et al, ApJ, 601: 340-351 (2004)
    [36] N. J. Shaviv, E. Nakar, and T. Piran, Phy. Rev. Lett., 103: 111302 (2009)
    [37] Y. Q. Guo, H. B. Hu, and Z. Tian, arXiv:1412.8590
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Chao Jin, Yi-Qing Guo and Hong-Bo Hu. Spatial dependent diffusion of cosmic rays and the excess of primary electrons derived from high precision measurements by AMS-02[J]. Chinese Physics C, 2016, 40(1): 015101. doi: 10.1088/1674-1137/40/1/015101
Chao Jin, Yi-Qing Guo and Hong-Bo Hu. Spatial dependent diffusion of cosmic rays and the excess of primary electrons derived from high precision measurements by AMS-02[J]. Chinese Physics C, 2016, 40(1): 015101.  doi: 10.1088/1674-1137/40/1/015101 shu
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Received: 2015-04-30
Revised: 2015-09-02
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    Supported by Natural Sciences Foundation of China (11135010)

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Spatial dependent diffusion of cosmic rays and the excess of primary electrons derived from high precision measurements by AMS-02

    Corresponding author: Chao Jin,
  • 1. School of Physical Engineering, Zhengzhou University, Zhengzhou 450001, China
  • 2. Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
  • 3.  Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
Fund Project:  Supported by Natural Sciences Foundation of China (11135010)

Abstract: The precise spectra of Cosmic Ray (CR) electrons and positrons have been published by the measurement of AMS-02. It is reasonable to regard the difference between the electron and positron spectra (ΔΦ= Φe--Φe+) as being dominated by primary electrons. The resulting electron spectrum shows no sign of spectral softening above 20 GeV, which is in contrast with the prediction of the standard model of CR propagation. In this work, we generalize the analytic one-dimensional two-halo model of diffusion to a three-dimensional realistic calculation by implementing spatial variant diffusion coefficients in the DRAGON package. As a result, we can reproduce the spectral hardening of protons observed by several experiments, and predict an excess of high energy primary electrons which agrees with the measurement reasonably well. Unlike the break spectrum obtained for protons, the model calculation predicts a smooth electron excess and thus slightly over-predicts the flux from tens of GeV to 100 GeV. To understand this issue, further experimental and theoretical studies are necessary.

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