Particle acceleration in interstellar shocks

  • Dejan UroševićEmail author
  • Bojan Arbutina
  • Dušan Onić
Review Article
Part of the following topical collections:
  1. Plasma, Particles, and Photons: ISM Physics Revisited


This review presents the fundamentals of the particle acceleration processes active in interstellar medium (ISM), which are essentially based on the so-called Fermi mechanism theory. More specifically, the review presents here in more details the first order Fermi acceleration process—also known as diffusive shock acceleration (DSA) mechanism. In this case, acceleration is induced by the interstellar (IS) shock waves. These IS shocks are mainly associated with emission nebulae (H ii regions, planetary nebulae and supernova remnants). Among all types of emission nebulae, the strongest shocks are associated with supernova remnants (SNRs). Due to this fact they also provide the most efficient manner to accelerate ISM particles to become high energy particles, i.e. cosmic-rays (CRs). The review therefore focuses on the particle acceleration at the strong shock waves of supernova remnants.


Acceleration mechanisms Supernova remnants 



We thank the anonymous referee for useful comments and suggestions that greatly improved the quality of this paper. We acknowledge the financial support of the Ministry of Education, Science, and Technological Development of the Republic of Serbia through the project No. 176005 “Emission Nebulae: Structure and Evolution”. The authors thank Dragana Momic for careful reading and correction of the manuscript.


  1. Acero, F., Ackermann, M., Ajello, M., Baldini, L., Ballet, J., Barbiellini, G., Bastieri, D., Bellazzini, R., Bissaldi, E., Blandford, R.D., et al.: The first Fermi LAT supernova remnant catalog. Astrophys. J. Suppl. 224, 8–58 (2016) CrossRefADSGoogle Scholar
  2. Allen, G.E., Houck, J.C., Sturner, S.J.: Evidence of a curved synchrotron spectrum in the supernova remnant SN 1006. Astrophys. J. 683, 773–785 (2008) CrossRefADSGoogle Scholar
  3. Amato, E., Blasi, P.: A general solution to non-linear particle acceleration at non-relativistic shock waves. Mon. Not. R. Astron. Soc. 364, L76–L80 (2005) CrossRefADSGoogle Scholar
  4. Arbutina, B.: Evolution of supernova remnants. Publ. Obs. Astron. Belgr. 97, 1–92 (2017) ADSGoogle Scholar
  5. Axford, W.I., Leer, E., Skadron, G.: The acceleration of cosmic-rays by shock waves. In: International Cosmic Ray Conference, vol. 11, pp. 132–137 (1977) Google Scholar
  6. Bell, A.R.: The acceleration of cosmic-rays in shock fronts. I. Mon. Not. R. Astron. Soc. 182, 147–156 (1978a) CrossRefADSGoogle Scholar
  7. Bell, A.R.: The acceleration of cosmic-rays in shock fronts. II. Mon. Not. R. Astron. Soc. 182, 443–455 (1978b) CrossRefADSGoogle Scholar
  8. Bell, A.R.: Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic-rays. Mon. Not. R. Astron. Soc. 353, 550–558 (2004) CrossRefADSGoogle Scholar
  9. Bell, A.R., Schure, K.M., Reville, B.: Cosmic ray acceleration at oblique shocks. Mon. Not. R. Astron. Soc. 418, 1208–1216 (2011) CrossRefADSGoogle Scholar
  10. Bell, A.R., Schure, K.M., Reville, B., Giacinti, G.: Cosmic-ray acceleration and escape from supernova remnants. Mon. Not. R. Astron. Soc. 431, 415–429 (2013) CrossRefADSGoogle Scholar
  11. Bell, A.R., Matthews, J.H., Blundell, K.M.: Cosmic ray acceleration by shocks: spectral steepening due to turbulent magnetic field amplification. Mon. Not. R. Astron. Soc. 488, 2466–2472 (2019) CrossRefADSGoogle Scholar
  12. Berezhko, E.G., Ellison, D.C.: A simple model of nonlinear diffusive shock acceleration. Astrophys. J. 526, 385–399 (1999) CrossRefADSGoogle Scholar
  13. Berezhko, E.G., Völk, H.J.: The theory of synchrotron emission from supernova remnants. Astron. Astrophys. 427, 525–536 (2004) CrossRefADSGoogle Scholar
  14. Blandford, R.D., Eichler, D.: Particle acceleration at astrophysical shocks: a theory of cosmic-ray origin. Phys. Rep. 154(1), 1–75 (1987) CrossRefADSGoogle Scholar
  15. Blandford, R.D., Ostriker, J.P.: Particle acceleration by astrophysical shocks. Astrophys. J. 221, L29–L32 (1978) CrossRefADSGoogle Scholar
  16. Blasi, P.: A novel approach to non linear shock acceleration. Nucl. Phys. B, Proc. Suppl. 110, 475–477 (2002a) CrossRefADSGoogle Scholar
  17. Blasi, P.: A semi-analytical approach to non-linear shock acceleration. Astropart. Phys. 16, 429–439 (2002b) CrossRefADSGoogle Scholar
  18. Blasi, P.: Nonlinear shock acceleration in the presence of seed particles. Astropart. Phys. 21, 45–57 (2004) CrossRefADSGoogle Scholar
  19. Blasi, P.: Shock acceleration of electrons in the presence of synchrotron losses—I. Test-particle theory. Mon. Not. R. Astron. Soc. 402, 2807–2816 (2010) CrossRefADSGoogle Scholar
  20. Blasi, P., Gabici, S., Vannoni, G.: On the role of injection in kinetic approaches to non-linear particle acceleration at non-relativistic shock waves. Mon. Not. R. Astron. Soc. 361, 907–918 (2005) CrossRefADSGoogle Scholar
  21. Blasi, P., Amato, E., Caprioli, D.: The maximum momentum of particles accelerated at cosmic-ray modified shocks. Mon. Not. R. Astron. Soc. 375, 1471–1478 (2007) CrossRefADSGoogle Scholar
  22. Caprioli, D.: Understanding hadronic gamma-ray emission from supernova remnants. J. Cosmol. Astropart. Phys. 5, 26 (2011) ADSGoogle Scholar
  23. Caprioli, D., Spitkovsky, A.: Simulations of ion acceleration at non-relativistic shocks. I. Acceleration efficiency. Astrophys. J. 783, 91–107 (2014) CrossRefADSGoogle Scholar
  24. Caprioli, D., Blasi, P., Amato, E., Vietri, M.: Dynamical effects of self-generated magnetic fields in cosmic-ray-modified shocks. Astrophys. J. Lett. 679, L139–L142 (2008) CrossRefADSGoogle Scholar
  25. Caprioli, D., Blasi, P., Amato, E., Vietri, M.: Dynamical feedback of self-generated magnetic fields in cosmic-ray modified shocks. Mon. Not. R. Astron. Soc. 395, 895–906 (2009) CrossRefADSGoogle Scholar
  26. Caprioli, D., Amato, E., Blasi, P.: Non-linear diffusive shock acceleration with free-escape boundary. Astropart. Phys. 33, 307–311 (2010) CrossRefADSGoogle Scholar
  27. Caprioli, D., Pop, A., Spitkovsky, A.: Simulations and theory of ion injection at non-relativistic collisionless shocks. Astrophys. J. Lett. 798, L28 (2015) CrossRefADSGoogle Scholar
  28. Caprioli, D., Zhang, H., Spitkovsky, A.: Diffusive shock re-acceleration. J. Plasma Phys. 84, 715840301 (2018) CrossRefGoogle Scholar
  29. de Looze, I., Barlow, M.J., Swinyard, B.M., Rho, J., Gomez, H.L., Matsuura, M., Wesson, R.: The dust mass in Cassiopeia A from a spatially resolved Herschel analysis. Mon. Not. R. Astron. Soc. 465, 3309–3342 (2017) CrossRefADSGoogle Scholar
  30. Drury, L.OC.: An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas. Rep. Prog. Phys. 46, 973–1027 (1983) CrossRefADSGoogle Scholar
  31. Drury, L.O’C., Downes, T.P.: Turbulent magnetic field amplification driven by cosmic ray pressure gradients. Mon. Not. R. Astron. Soc. 427, 2308–2313 (2012) CrossRefADSGoogle Scholar
  32. Drury, L.O’C., Strong, A.W.: Cosmic-ray diffusive reacceleration: a critical look. In: The 34th International Cosmic Ray Conference (2015). arXiv:1508.02675v1 Google Scholar
  33. Fermi, E.: On the origin of the cosmic radiation. Phys. Rev. 75, 1169–1174 (1949) CrossRefADSzbMATHGoogle Scholar
  34. Ferrand, G.: Blasi’s semi-analytical kinetic model of non-linear diffusive shock acceleration (2010). Personal notes Google Scholar
  35. Ferrand, G., Danos, R.J., Shalchi, A., Safi-Harb, S., Edmon, P., Mendygral, P.: Cosmic ray acceleration at perpendicular shocks in supernova remnants. Astrophys. J. 792, 133–145 (2014) CrossRefADSGoogle Scholar
  36. Gaggero, D., Zandanel, F., Cristofari, P., Gabici, S.: Time evolution of gamma rays from supernova remnants. Mon. Not. R. Astron. Soc. 475, 5237–5245 (2018) CrossRefADSGoogle Scholar
  37. Ginzburg, V.L., Syrovatskii, S.I.: Cosmic rays in the galaxy (introductory report). In: van Woerden, H. (ed.) Radio Astronomy and the Galactic System. IAU Symposium, vol. 31, p. 411 (1967) Google Scholar
  38. Green, D.A.: A Catalogue of Galactic Supernova Remnants (2017 June Version). Cavendish Laboratory, Cambridge (2017). Available at Google Scholar
  39. Hussein, M., Shalchi, A.: Detailed numerical investigation of the Bohm limit in cosmic ray diffusion theory. Astrophys. J. 785, 31–37 (2014) CrossRefADSGoogle Scholar
  40. Inoue, T.: Bell-instability-mediated spectral modulation of hadronic gamma-rays from a supernova remnant interacting with a molecular cloud. Astrophys. J. 872, 46–54 (2019) CrossRefADSGoogle Scholar
  41. Jones, T.J., Rudnick, L., DeLaney, T., Bowden, J.: The identification of infrared synchrotron radiation from Cassiopeia A. Astrophys. J. 587, 227–234 (2003) CrossRefADSGoogle Scholar
  42. Koyama, K., Petre, R., Gotthelf, E.V., Hwang, U., Matsuura, M., Ozaki, M., Holt, S.S.: Evidence for shock acceleration of high-energy electrons in the supernova remnant SN 1006. Nature 378, 255–258 (1995) CrossRefADSGoogle Scholar
  43. Krymsky, G.F.: A regular mechanism for the acceleration of charged particles on the front of a shock wave. Dokl. Akad. Nauk SSSR 234, 1306–1308 (1977) ADSGoogle Scholar
  44. Lequeux, J.: The Interstellar Medium, with the Collaboration of E Falgarone and C Ryter. Springer, Berlin (2005) CrossRefGoogle Scholar
  45. Longair, M.S.: High Energy Astrophysics. Volume 2. Stars, the Galaxy and the Interstellar Medium. Cambridge University Press, Cambridge (2011) Google Scholar
  46. Malkov, M.A., Drury, LO’C: Nonlinear theory of diffusive acceleration of particles by shock waves. Rep. Prog. Phys. 64, 429–481 (2001) CrossRefADSGoogle Scholar
  47. Onić, D.: On the supernova remnants with flat radio spectra. Astrophys. Space Sci. 346, 3–13 (2013) CrossRefADSGoogle Scholar
  48. Onić, D., Urošević, D.: On the continuum radio spectrum of Cas A: possible evidence of non-linear particle acceleration. Astrophys. J. 805, 119–125 (2015) CrossRefADSGoogle Scholar
  49. Ostrowski, M.: Supernova remnants in molecular clouds: on cosmic-ray electron spectra. Astron. Astrophys. 345, 256–258 (1999) ADSGoogle Scholar
  50. Parker, E.: The passage of energetic charged particles through interplanetary space. Planet. Space Sci. 13, 9–49 (1965) CrossRefADSGoogle Scholar
  51. Pavlović, M.Z.: Hydrodynamical and radio evolution of young supernova remnant G1.9+0.3 based on the model of diffusive shock acceleration. Mon. Not. R. Astron. Soc. 468, 1616–1630 (2017) ADSGoogle Scholar
  52. Pavlović, M.Z.: Modeling the radio-evolution of supernova remnants by using hydrodynamic simulations and non-linear diffusive shock acceleration. PhD thesis, University of Belgrade (2018) Google Scholar
  53. Pavlović, M.Z., Urošević, D., Arbutina, B., Orlando, S., Maxted, N., Filipović, M.: Radio evolution of supernova remnants including nonlinear particle acceleration: insights from hydrodynamic simulations. Astrophys. J. 858, 84 (2018) CrossRefADSGoogle Scholar
  54. Reber, G.: Cosmic static. Astrophys. J. 100, 279–287 (1944) CrossRefADSGoogle Scholar
  55. Reynolds, S.P.: Supernova remnants at high energy. Annu. Rev. Astron. Astrophys. 46, 89–126 (2008) CrossRefADSGoogle Scholar
  56. Reynolds, S.P., Ellison, D.C.: Electron acceleration in Tycho’s and Kepler’s supernova remnants—spectral evidence of Fermi shock acceleration. Astrophys. J. 399, L75–L78 (1992) CrossRefADSGoogle Scholar
  57. Sano, H., Rowell, G., Reynoso, E.M., Jung-Richardt, J., Yamane, Y., Nagaya, T., Yoshiike, S., Hayashi, K., Torii, K., Maxted, N., Mitsuishi, I., Inoue, T., Inutsuka, S., Yamamoto, H., Tachihara, K., Fukui, Y.: Possible Evidence for cosmic-ray acceleration in the Type Ia supernova remnant RCW 86: spatial correlation between TeV gamma rays and interstellar atomic protons. Astrophys. J. 876, 37 (2019). CrossRefADSGoogle Scholar
  58. Schlickeiser, R., Fürst, E.: The origin of flat radio spectra in shell-type supernova remnants. Astron. Astrophys. 219, 192–194 (1989) ADSGoogle Scholar
  59. Shalchi, A.: Diffusive shock acceleration in supernova remnants: on the validity of the Bohm limit. Astropart. Phys. 31, 237–242 (2009) CrossRefADSGoogle Scholar
  60. Shalchi, A., Skoda, T., Tautz, R.C., Schlickeiser, R.: Analytical description of nonlinear cosmic ray scattering: isotropic and quasilinear regimes of pitch-angle diffusion. Astron. Astrophys. 507, 589–597 (2009) CrossRefADSzbMATHGoogle Scholar
  61. Skilling, J.: Cosmic rays in the Galaxy: convection or diffusion. Astrophys. J. 170, 265–273 (1971) CrossRefADSGoogle Scholar
  62. Skilling, J.: Cosmic ray streaming. I—Effect of Alfven waves on particles. Mon. Not. R. Astron. Soc. 172, 557–566 (1975) CrossRefADSGoogle Scholar
  63. Uchiyama, Y., Aharonian, F.A., Tanaka, T., Takahashi, T., Maeda, Y.: Extremely fast acceleration of cosmic rays in a supernova remnant. Nature 449, 576–578 (2007) CrossRefADSGoogle Scholar
  64. Uchiyama, Y., Blandford, R.D., Funk, S., Tajima, H., Tanaka, T.: Gamma-ray emission from crushed clouds in supernova remnants. Astrophys. J. 723, L122–L126 (2010) CrossRefADSGoogle Scholar
  65. Urošević, D.: On the radio spectra of supernova remnants. Astrophys. Space Sci. 354, 541–552 (2014) CrossRefADSGoogle Scholar
  66. Vainio, R., Schlickeiser, R.: Self-consistent Alfven-wave transmission and test-particle acceleration at parallel shocks. Astron. Astrophys. 343, 303–311 (1999) ADSGoogle Scholar
  67. Vink, J.: Supernova remnants: the X-ray perspective. Astron. Astrophys. Rev. 20, 49 (2012) CrossRefADSGoogle Scholar
  68. Vink, J., Bleeker, J., van der Heyden, K., Bykov, A., Bamba, A., Yamazak, R.: The X-ray synchrotron emission of RCW 86 and the implications for its age. Astrophys. J. 648, L33–L37 (2006) CrossRefADSGoogle Scholar
  69. Zeković, V.: Resonant micro-instabilities at quasi-parallel collisionless shocks: cause or consequence of shock (re)formation. Phys. Plasmas 26, 032106 (2019) CrossRefADSGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Dejan Urošević
    • 1
    Email author
  • Bojan Arbutina
    • 1
  • Dušan Onić
    • 1
  1. 1.Department of Astronomy, Faculty of MathematicsUniversity of BelgradeBelgradeSerbia

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