Advertisement

Fundamentals of collisionless shocks for astrophysical application, 2. Relativistic shocks

  • A. M. Bykov
  • R. A. TreumannEmail author
Article

Abstract

In this concise review of the recent developments in relativistic shock theory in the Universe we restrict ourselves to shocks that do not exhibit quantum effects. On the other hand, emphasis is given to the formation of shocks under both non-magnetised and magnetised conditions. We only briefly discuss particle acceleration in relativistic shocks where much of the results are still preliminary. Analytical theory is rather limited in predicting the real shock structure. Kinetic instability theory is briefed including its predictions and limitations. A recent self-similar relativistic shock theory is described which predicts the average long-term shock behaviour to be magnetised and to cause reasonable power-law distributions for energetic particles. The main focus in this review is on numerical experiments on highly relativistic shocks in (i) pair and (ii) electron-nucleon plasmas and their limitations. These simulations do not validate all predictions of analytic and self-similar theory and so far they do not solve the injection problem and the self-modification by self-generated cosmic rays. The main results of the numerical experiments discussed in this review are: (i) a confirmation of shock evolution in non-magnetised relativistic plasma in 3D due to either the lepton-Weibel instability (in pair plasmas) or to the ion-Weibel instability; (ii) the sensitive dependence of shock formation on upstream magnetisation which causes suppression of Weibel modes for large upstream magnetisation ratios σ>10−3; (iii) the sensitive dependence of particle dynamics on the upstream magnetic inclination angle θ Bn , where particles of θ Bn >34° cannot escape upstream, leading to the distinction between ‘subluminal’ and ‘superluminal’ shocks; (iv) particles in ultra-relativistic shocks can hardly overturn the shock and escape to upstream; they may oscillate around the shock ramp for a long time, so to speak ‘surfing it’ and thereby becoming accelerated by a kind of SDA; (v) these particles form a power-law tail on the downstream distribution; their limitations are pointed out; (vi) recently developed methods permit the calculation of the radiation spectra emitted by the downstream high-energy particles; (vii) the Weibel-generated downstream magnetic fields form large-amplitude vortices which could be advected by the downstream flow to large distances from the shock and possibly contribute to an extended strong field region; (viii) if cosmic rays are included, Bell-like modes can generate upstream magnetic turbulence at short and, by diffusive re-coupling, also long wavelengths in nearly parallel magnetic field shocks; (ix) advection of such large-amplitude waves should cause periodic reformation of the quasi-parallel shock and eject large-amplitude magnetic field vortices downstream where they contribute to turbulence and to maintaining an extended region of large magnetic fields.

Keywords

Collisionless shocks Relativistic shocks Generation of magnetic fields Weibel modes Bell modes Gamma ray bursts Pulsar Wind Nebulae termination shocks External shocks Internal shocks Particle acceleration Shock radiation Downstream turbulence 

References

  1. Acciari VA et al. (2009) radio imaging of the very-high-energy γ-ray emission region in the central engine of a radio galaxy. Science 325:444–448. doi: 10.1126/science.1175406, 0908.0511 ADSGoogle Scholar
  2. Acero F et al. (2009) detection of gamma rays from a Starburst galaxy. Science 326:1080–1082. doi: 10.1126/science.1178826, 0909.4651 ADSGoogle Scholar
  3. Achterberg A (1983) Modification of scattering waves and its importance for shock acceleration. Astron Astrophys 119:274–278 zbMATHADSGoogle Scholar
  4. Achterberg A, Wiersma J (2007) The Weibel instability in relativistic plasmas. I. Linear theory. Astron Astrophys 475:1–18. doi: 10.1051/0004-6361:20065365 zbMATHADSGoogle Scholar
  5. Achterberg A, Wiersma J, Norman CA (2007) The Weibel instability in relativistic plasmas. II. Nonlinear theory and stabilization mechanism. Astron Astrophys 475:19–36. doi: 10.1051/0004-6361:20065366 zbMATHADSGoogle Scholar
  6. Aharonian F et al. (2002) An unidentified TeV source in the vicinity of Cygnus OB2. Astron Astrophys 393:L37–L40. doi: 10.1051/0004-6361:20021171, arXiv:astro-ph/0207528 ADSGoogle Scholar
  7. Aharonian F et al. (2005a) Discovery of extended VHE gamma-ray emission from the asymmetric pulsar wind nebula in MSH 15-52 with HESS. Astron Astrophys 435:L17–L20. doi: 10.1051/0004-6361:200500105, arXiv:astro-ph/0504120 ADSGoogle Scholar
  8. Aharonian F et al. (2005b) Observations of Mkn 421 in 2004 with HESS at large zenith angles. Astron Astrophys 437:95–99. doi: 10.1051/0004-6361:20053050, arXiv:astro-ph/0506319 ADSGoogle Scholar
  9. Aharonian F et al. (2006a) A detailed spectral and morphological study of the gamma-ray supernova remnant RX J1713.7-3946 with HESS. Astron Astrophys 449:223–242. doi: 10.1051/0004-6361:20054279, arXiv:astro-ph/0511678 ADSGoogle Scholar
  10. Aharonian F et al. (2006b) Discovery of the two “wings” of the Kookaburra complex in VHE γ-rays with HESS. Astron Astrophys 456:245–251. doi: 10.1051/0004-6361:20065511, arXiv:astro-ph/0606311 ADSGoogle Scholar
  11. Aharonian F et al. (2006c) Discovery of very-high-energy γ-rays from the Galactic centre ridge. Nature 439:695–698. doi: 10.1038/nature04467, arXiv:astro-ph/0603021 ADSGoogle Scholar
  12. Aharonian F et al. (2006d) Energy dependent γ-ray morphology in the pulsar wind nebula HESS J1825-137. Astron Astrophys 460:365–374. doi: 10.1051/0004-6361:20065546, arXiv:astro-ph/0607548 ADSGoogle Scholar
  13. Aharonian F et al. (2006e) First detection of a VHE gamma-ray spectral maximum from a cosmic source: HESS discovery of the Vela X nebula. Astron Astrophys 448:L43–L47. doi: 10.1051/0004-6361:200600014, arXiv:astro-ph/0601575 ADSGoogle Scholar
  14. Aharonian F et al. (2009a) Constraints on the multi-TeV particle population in the Coma galaxy cluster with HESS observations. Astron Astrophys 502:437–443. doi: 10.1051/0004-6361/200912086, 0907.0727 ADSGoogle Scholar
  15. Aharonian F et al. (2009b) Very high energy γ-ray observations of the binary PSR B1259-63/SS2883 around the 2007 Periastron. Astron Astrophys 507:389–396. doi: 10.1051/0004-6361/200912339 ADSGoogle Scholar
  16. Aharonian F et al. (2009c) Very high energy gamma-ray observations of the galaxy clusters Abell 496 and Abell 85 with HESS. Astron Astrophys 495:27–35. doi: 10.1051/0004-6361:200811372, 0812.1638 ADSGoogle Scholar
  17. Aharonian F, Neronov A (2005a) High-energy gamma rays from the massive black hole in the galactic center. Astrophys J 619:306–313. doi: 10.1086/426426, arXiv:astro-ph/0408303 ADSGoogle Scholar
  18. Aharonian F, Neronov A (2005b) TeV gamma rays from the galactic center direct and indirect links to the massive black hole in SGR A. Astrophys Space Sci 300:255–265. doi: 10.1007/s10509-005-1209-4 ADSGoogle Scholar
  19. Akhiezer AI, Akhiezer IA, Polovin RV, Sitenko AG, Stepanov KN (1975) Plasma electrodynamics. Volume 1—Linear theory. Volume 2—Non-linear theory and fluctuations. Oxford Pergamon Press International Series on Natural Philosophy 1 Google Scholar
  20. Albert J et al. (2006) Variable very-high-energy gamma-ray emission from the microquasar LSI + 61303. Science 312:1771–1773. doi: 10.1126/science.1128177, arXiv:astro-ph/0605549 ADSGoogle Scholar
  21. Albert J et al. (2007) Variable very high energy γ-ray emission from Markarian 501. Astrophys J 669:862–883. doi: 10.1086/521382, arXiv:astro-ph/0702008 ADSGoogle Scholar
  22. Amato E, Arons J (2006) Heating and nonthermal particle acceleration in relativistic, transverse magnetosonic shock waves in proton–electron–positron plasmas. Astrophys J 653:325–338. doi: 10.1086/508050, arXiv:astro-ph/0609034 ADSGoogle Scholar
  23. Amato E, Blasi P (2009) A kinetic approach to cosmic-ray-induced streaming instability at supernova shocks. Mon Not R Astron Soc 392:1591–1600. doi: 10.1111/j.1365-2966.2008.14200.x, 0806.1223 ADSGoogle Scholar
  24. Amato E, Blasi P, Gabici S (2008) Kinetic approaches to particle acceleration at cosmic ray modified shocks. Mon Not R Astron Soc 385:1946–1958. doi: 10.1111/j.1365-2966.2008.12876.x, 0705.3723 ADSGoogle Scholar
  25. Balogh A, Treumann RA (2011) Physics of collisionless shocks—the space plasma shock waves. ISSI Scientific Report Series, vol 10. Springer, Berlin Google Scholar
  26. Bamba A, Yamazaki R, Ueno M, Koyama K (2003) Small-scale structure of the SN 1006 shock with Chandra observations. Astrophys J 589:827–837. doi: 10.1086/374687, arXiv:astro-ph/0302174 ADSGoogle Scholar
  27. Bell AR (2004) Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays. Mon Not R Astron Soc 353:550–558. doi: 10.1111/j.1365-2966.2004.08097.x ADSGoogle Scholar
  28. Bell AR (2005) The interaction of cosmic rays and magnetized plasma. Mon Not R Astron Soc 358:181–187. doi: 10.1111/j.1365-2966.2005.08774.x ADSGoogle Scholar
  29. Berezinsky V (2008) Propagation and origin of ultra high-energy cosmic rays. Adv Space Res 41:2071–2078. doi: 10.1016/j.asr.2007.02.065 ADSGoogle Scholar
  30. Blandford R, Eichler D (1987) Particle acceleration at astrophysical shocks: a theory of cosmic ray origin. Phys Rep 154:1–75. doi: 10.1016/0370-1573(87)90134-7 ADSGoogle Scholar
  31. Blandford RD, McKee CF (1976) Fluid dynamics of relativistic blast waves. Phys Fluids 19:1130–1138. doi: 10.1063/1.861619 zbMATHADSGoogle Scholar
  32. Blandford RD, McKee CF (1977) Radiation from relativistic blast waves in quasars and active galactic nuclei. Mon Not R Astron Soc Lett 180:343–371 ADSGoogle Scholar
  33. Blandford RD, Ostriker JP (1980) Supernova shock acceleration of cosmic rays in the Galaxy. Astrophys J 237:793–808. doi: 10.1086/157926 ADSGoogle Scholar
  34. Blasi P, Amato E (2008) A kinetic approach to non resonant modes and growth rates of streaming instability: consequences for shock acceleration. In: International cosmic ray conference, vol 2, pp 235–238. 0706.1722 Google Scholar
  35. Bret A (2009) Weibel, two-stream, filamentation, oblique, bell, buneman. Which one grows faster? Astrophys J 699:990–1003. doi: 10.1088/0004-637X/699/2/990, 0903.2658 ADSGoogle Scholar
  36. Bret A, Gremillet L, Dieckmann ME (2010) Multidimensional electron beam-plasma instabilities in the relativistic regime. Phys Plasmas 17(12):12501–12537. doi: 10.1063/1.3514586 Google Scholar
  37. Bucciantini N, Arons J, Amato E (2011) Modelling spectral evolution of pulsar wind nebulae inside supernova remnants. Mon Not R Astron Soc Lett 410:381–398. doi: 10.1111/j.1365-2966.2010.17449.x Google Scholar
  38. Budnik R, Katz B, Sagiv A, Waxman E (2010) Relativistic radiation mediated shocks. Astrophys J 725:63–90. doi: 10.1088/0004-637X/725/1/63, 1005.0141 ADSGoogle Scholar
  39. Bykov AM, Toptygin IN (1985) Shock generation of turbulence and cosmic-ray diffusion in the interstellar medium. Sov Astron Lett 11:75–77 ADSGoogle Scholar
  40. Bykov AM, Uvarov YA (1999) Electron kinetics in collisionless shock waves. Sov Phys JETP 88:465–475. doi: 10.1134/1.558817 ADSGoogle Scholar
  41. Bykov AM, Paerels FBS, Petrosian V (2008) Equilibration processes in the warm–hot intergalactic medium. Space Sci Rev 134:141–153. doi: 10.1007/s11214-008-9309-4, 0801.1008 ADSGoogle Scholar
  42. Bykov AM, Osipov SM, Toptygin IN (2009) Long-wavelength MHD instability in the prefront of collisionless shocks with accelerated particles. Astron Lett 35:555–563. doi: 10.1134/S1063773709080052 ADSGoogle Scholar
  43. Bykov AM, Ellision DC, Reynaud M (2011a) Magnetic fields in cosmic particle acceleration sources. Space Sci Rev 160, in press Google Scholar
  44. Bykov AM, Osipov SM, Ellison DC (2011b) Cosmic ray current driven turbulence in shocks with efficient particle acceleration: the oblique, long-wavelength mode instability. Mon Not R Astron Soc 410:39–52. doi: 10.1111/j.1365-2966.2010.17421.x, 1010.0408 ADSGoogle Scholar
  45. Califano F, Pegoraro F, Bulanov SV (1997) Spatial structure and time evolution of the Weibel instability in collisionless inhomogeneous plasmas. Phys Rev E 56:963–969. doi: 10.1103/PhysRevE.56.963 ADSGoogle Scholar
  46. Califano F, Pegoraro F, Bulanov SV, Mangeney A (1998a) Kinetic saturation of the Weibel instability in a collisionless plasma. Phys Rev E 57:7048–7059. doi: 10.1103/PhysRevE.57.7048 ADSGoogle Scholar
  47. Califano F, Prandi R, Pegoraro F, Bulanov SV (1998b) Magnetic-field generation and wave-breaking in collisionless plasmas. J Plasma Phys 60:331–339. doi: 10.1017/S0022377898006862 ADSGoogle Scholar
  48. Chandra P et al. (2010) Discovery of radio afterglow from the most distant cosmic explosion. Astrophys J Lett 712:L31–L35. doi: 10.1088/2041-8205/712/1/L31, 0910.4367 ADSGoogle Scholar
  49. Dermer CD (2006) External shocks, UHECRs, and the early afterglow of GRBs. Nuovo Cimento B 121:1331–1336. doi: 10.1393/ncb/i2007-10254-5, arXiv:astro-ph/0611194 ADSGoogle Scholar
  50. Dermer CD, Atoyan A (2006) Ultra-high energy cosmic rays, cascade gamma rays, and high-energy neutrinos from gamma-ray bursts. New J Phys 8:122. doi: 10.1088/1367-2630/8/7/122, arXiv:astro-ph/0606629 Google Scholar
  51. Dewar RL (1977) Energy–momentum tensors for dispersive electromagnetic waves. Aust J Phys 30:533 ADSMathSciNetGoogle Scholar
  52. Dieckmann ME (2009) The filamentation instability driven by warm electron beams: statistics and electric field generation. Plasma Phys Control Fusion 51(12):124. doi: 10.1088/0741-3335/51/12/124042, 0910.0228 Google Scholar
  53. Dieckmann ME, Lerche I, Shukla PK, Drury LOC (2007) Aspects of self-similar current distributions resulting from the plasma filamentation instability. New J Phys 9:10. doi: 10.1088/1367-2630/9/1/010 Google Scholar
  54. Dieckmann ME, Murphy GC, Meli A, Drury LOC (2010) Particle-in-cell simulation of a mildly relativistic collision of an electron-ion plasma carrying a quasi-parallel magnetic field. Electron acceleration and magnetic field amplification at supernova shocks. Astron Astrophys 509:A89. doi: 10.1051/0004-6361/200912643 ADSGoogle Scholar
  55. Drury LO (1983) An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas. Rep Prog Phys 46:973–1027. doi: 10.1088/0034-4885/46/8/002 ADSGoogle Scholar
  56. Drury LO, Ellison DE, Aharonian FA, Berezhko E, Bykov A, Decourchelle A, Diehl R, Meynet G, Parizot E, Raymond J, Reynolds S, Spangler S (2001) Test of galactic cosmic-ray source models—Working Group Report. Space Sci Rev 99:329–352 ADSGoogle Scholar
  57. Dunkel J, Talkner P, Hänggi P (2007) Relative entropy, Haar measures and relativistic canonical velocity distributions. New J Phys 9:144. doi: 10.1088/1367-2630/9/5/144, arXiv:cond-mat/0610045 Google Scholar
  58. Emmering RT, Chevalier RA (1987) Shocked relativistic magnetohydrodynamic flows with application to pulsar winds. Astrophys J 321:334–348. doi: 10.1086/165632 ADSGoogle Scholar
  59. Fox DB, Mészáros P (2006) GRB fireball physics: prompt and early emission. New J Phys 8:199–218. doi: 10.1088/1367-2630/8/9/199, arXiv:astro-ph/0609173 Google Scholar
  60. Frail DA, Kulkarni SR, Nicastro L, Feroci M, Taylor GB (1997) The radio afterglow from the γ-ray burst of 8 May 1997. Nature 389:261–263. doi: 10.1038/38451 ADSGoogle Scholar
  61. Frederiksen JT, Hededal CB, Haugbølle T, Nordlund Å (2004) Magnetic field generation in collisionless shocks: pattern growth and transport. Astrophys J Lett 608:L13–L16. doi: 10.1086/421262, arXiv:astro-ph/0308104 ADSGoogle Scholar
  62. Frederiksen JT, Haugbølle T, Medvedev MV, Nordlund Å(2010) Radiation spectral synthesis of relativistic filamentation. Astrophys J Lett 722:L114–L119. doi: 10.1088/2041-8205/722/1/L114, 1003.1140 ADSGoogle Scholar
  63. Fried BD (1959) Mechanism for instability of transverse plasma waves. Phys Fluids 2:337. doi: 10.1063/1.1705933 ADSMathSciNetGoogle Scholar
  64. Gallant YA, van der Swaluw E, Kirk JG, Achterberg A (2002) Modeling plerion spectra and their evolution. In: Slane PO, Gaensler BM (eds) Neutron stars in supernova remnants, astronomical society of the pacific conference series, vol 271, p 99. arXiv:astro-ph/0112354 Google Scholar
  65. Ginzburg VL, Syrovatskii SI (1969) Developments in the theory of synchrotron radiation and its reabsorption. Annu Rev Astron Astrophys 7:375. doi: 10.1146/annurev.aa.07.090169.002111 ADSGoogle Scholar
  66. Gruzinov A (2001) Gamma-ray burst phenomenology, shock dynamo, and the first magnetic fields. Astrophys J Lett 563:L15–L18. doi: 10.1086/324223, arXiv:astro-ph/0107106 ADSGoogle Scholar
  67. Gruzinov A, Waxman E (1999a) Gamma-ray burst afterglow: polarization and analytic light curves. Astrophys J 511:852–861. doi: 10.1086/306720, arXiv:astro-ph/9807111 ADSGoogle Scholar
  68. Gruzinov A, Waxman E (1999b) Gamma-ray burst afterglow: polarization and analytic light curves. Astrophys J 511:852–861. doi: 10.1086/306720, arXiv:astro-ph/9807111 ADSGoogle Scholar
  69. Harrison FA, Bloom JS, Frail DA, Kulkarni SR, Sari R, Djorgovski SG, Axelrod T, Mould J, Schmidt BP, Wieringa MH, Wark RM, Subrahmanyan R, McConnell D, McCarthy PJ, Schaefer BE, McMahon RG, Markze RO, Firth E, Soffitta P, Amati L (1999) Optical and radio observations of the afterglow from grb 990510: evidence for a jet. Astrophys J Lett 523:L121–L124. doi: 10.1086/312282, arXiv:astro-ph/9905306 ADSGoogle Scholar
  70. Hededal C (2005) Gamma-ray bursts, collisionless shocks and synthetic spectra. PhD thesis, The Niels Bohr Institute, Faculty of Science, University of Copenhagen, Denmark Google Scholar
  71. Hededal CB, Nishikawa K (2005) The influence of an ambient magnetic field on relativistic collisionless plasma shocks. Astrophys J Lett 623:L89–L92. doi: 10.1086/430253, arXiv:astro-ph/0412317 ADSGoogle Scholar
  72. Hededal CB, Haugbølle T, Frederiksen JT, Nordlund Å (2004) Non-Fermi power-law acceleration in astrophysical plasma shocks. Astrophys J Lett 617:L107–L110. doi: 10.1086/427387, arXiv:astro-ph/0408558 ADSGoogle Scholar
  73. Hededal CB, Haugbølle T, Frederiksen JT, Nordlund Å (2005) In situ particle acceleration in collisionless shocks. Nuovo Cimento C Geophysics Space. Physics C 28:411. doi: 10.1393/ncc/i2005-10071-y, arXiv:astro-ph/0502372 Google Scholar
  74. Jaroschek CH, Lesch H, Treumann RA (2004) Self-consistent diffusive lifetimes of weibel magnetic fields in gamma-ray bursts. Astrophys J 616:1065–1071. doi: 10.1086/424923 ADSGoogle Scholar
  75. Jaroschek CH, Lesch H, Treumann RA (2005) Ultrarelativistic plasma shell collisions in γ-ray burst sources: dimensional effects on the final steady state magnetic field. Astrophys J 618:822–831. doi: 10.1086/426066 ADSGoogle Scholar
  76. Kuramitsu Y et al. (2011) Time evolution of collisionless shock in counterstreaming laser-produced plasmas. Phys Rev Lett 106:175002. doi: 10.1103/PhysRevLett.106.175002 ADSGoogle Scholar
  77. Katz B, Keshet U, Waxman E (2007) Self-similar collisionless shocks. Astrophys J 655:375–390. doi: 10.1086/509115, arXiv:astro-ph/0607345 ADSGoogle Scholar
  78. Katz B, Mészáros P, Waxman E (2010) The spectrum of cosmic rays escaping from relativistic shocks. J Cosmol Astropart Phys 10:12. doi: 10.1088/1475-7516/2010/10/012, 1001.0134 ADSGoogle Scholar
  79. Kazimura Y, Califano F, Sakai J, Neubert T, Pegoraro F, Bulanov S (1998) Magnetic field generation during the collision of electron–ion plasma clouds. J Phys Soc Jpn 67:1079–1082. doi: 10.1143/JPSJ.67.1079 ADSGoogle Scholar
  80. Kennel CF, Coroniti FV (1984a) Confinement of the Crab pulsar’s wind by its supernova remnant. Astrophys J 283:694–709. doi: 10.1086/162356 ADSGoogle Scholar
  81. Kennel CF, Coroniti FV (1984b) Magnetohydrodynamic model of Crab nebula radiation. Astrophys J 283:710–730. doi: 10.1086/162357 ADSGoogle Scholar
  82. Keppens R, Meliani Z (2008) Linear wave propagation in relativistic magnetohydrodynamics. Phys Plasmas 15(10):102. doi: 10.1063/1.2991408, 0810.2416 Google Scholar
  83. Keshet U, Katz B, Spitkovsky A, Waxman E (2009) Magnetic field evolution in relativistic unmagnetized collisionless shocks. Astrophys J Lett 693:L127–L130. doi: 10.1088/0004-637X/693/2/L127, 0802.3217 ADSGoogle Scholar
  84. Komissarov SS (1999) A Godunov-type scheme for relativistic magnetohydrodynamics. Mon Not R Astron Soc 303:343–366. doi: 10.1046/j.1365-8711.1999.02244.x ADSGoogle Scholar
  85. Lagage PO, Cesarsky CJ (1983) Cosmic-ray shock acceleration in the presence of self-excited waves. Astron Astrophys 118:223–228. http://adsabs.harvard.edu/abs/1983A%26A...118..223L zbMATHADSGoogle Scholar
  86. Landau LD, Lifshitz EM (1975) The classical theory of fields, vol 2. Pergamon, Oxford Google Scholar
  87. Lemoine M, Pelletier G (2010) On electromagnetic instabilities at ultra-relativistic shock waves. Mon Not R Astron Soc 402:321–334. doi: 10.1111/j.1365-2966.2009.15869.x, 0904.2657 ADSGoogle Scholar
  88. Lemoine M, Pelletier G (2011) The role of electromagnetic instabilities in the precursor of collisionless relativistic shock waves. ArXiv:1102.1308
  89. Lucek SG, Bell AR (2000) Non-linear amplification of a magnetic field driven by cosmic ray streaming. Mon Not R Astron Soc 314:65–74. doi: 10.1046/j.1365-8711.2000.03363.x ADSGoogle Scholar
  90. Lyubarsky Y, Eichler D (2006) Are gamma-ray burst shocks mediated by the weibel instability? Astrophys J 647:1250–1254. doi: 10.1086/505523, arXiv:astro-ph/0512579 ADSGoogle Scholar
  91. Malkov MA, Drury LO (2001) Nonlinear theory of diffusive acceleration of particles by shock waves. Rep Prog Phys 64:429–481. doi: 10.1088/0034-4885/64/4/201 ADSGoogle Scholar
  92. Malkov MA, Diamond PH, Sagdeev RZ (2005) On the gamma-ray spectra radiated by protons accelerated in supernova remnant shocks near molecular clouds: the case of Supernova remnant RX j1713.7-3946. Astrophys J Lett 624:L37–L40. doi: 10.1086/430344, arXiv:astro-ph/0503403 ADSGoogle Scholar
  93. Martins JL, Martins SF, Fonseca RA, Silva LO (2009a) Radiation post-processing in PIC codes. In: Society of photo-optical instrumentation engineers (SPIE) conference series, presented at the society of photo-optical instrumentation engineers (SPIE) conference. vol 7359. doi: 10.1117/12.820736 Google Scholar
  94. Martins SF, Fonseca RA, Silva LO, Mori WB (2009b) Ion dynamics and acceleration in relativistic shocks. Astrophys J Lett 695:L189–L193. doi: 10.1088/0004-637X/695/2/L189, 0903.3573 ADSGoogle Scholar
  95. McKee CF, Ostriker JP (1977) A theory of the interstellar medium—three components regulated by supernova explosions in an inhomogeneous substrate. Astrophys J 218:148–169. doi: 10.1086/155667 ADSGoogle Scholar
  96. Medvedev MV (2009a) Physics of relativistic shocks. In: Ao X, Burrows GZR (eds) American institute of physics conference series, vol 1183, pp 189–200. doi: 10.1063/1.3266775 Google Scholar
  97. Medvedev MV (2009b) Radiation of electrons in Weibel-generated fields: a general case. Astrophys Space Sci 322:147–150. doi: 10.1007/s10509-008-9927-z, 0906.1090 zbMATHADSGoogle Scholar
  98. Medvedev MV, Loeb A (1999) Generation of magnetic fields in the relativistic shock of gamma-ray burst sources. Astrophys J 526:697–706. doi: 10.1086/308038, arXiv:astro-ph/9904363 ADSGoogle Scholar
  99. Medvedev MV, Spitkovsky A (2009a) Radiative cooling in relativistic collisionless shocks: can simulations and experiments probe relevant gamma-ray burst physics? Astrophys J 700:956–964. doi: 10.1088/0004-637X/700/2/956, 0810.4014 ADSGoogle Scholar
  100. Medvedev MV, Spitkovsky A (2009b) Whence particle acceleration. arXiv:0906.1087
  101. Medvedev MV, Trier Frederiksen J, Haugboelle T, Nordlund A (2010) Radiation from sub-Larmor scale magnetic fields. arXiv:1003.0063
  102. Meli A, Biermann PL (2006) Cosmic rays X. The cosmic ray knee and beyond: diffusive acceleration at oblique shocks. Astron Astrophys 454:687–694. doi: 10.1051/0004-6361:20064964, arXiv:astro-ph/0602308 ADSGoogle Scholar
  103. Mészáros P (2002) Theories of gamma-ray bursts. Annu Rev Astron Astrophys 40:137–169. doi: 10.1146/annurev.astro.40.060401.093821, arXiv:astro-ph/0111170 Google Scholar
  104. Mészáros P (2006) Gamma-ray bursts. Rep Prog Phys 69:2259–2321. doi: 10.1088/0034-4885/69/8/R01, arXiv:astro-ph/0605208 Google Scholar
  105. Mészáros P, Rees MJ (2010) Population III gamma-ray bursts. Astrophys J 715:967–971. doi: 10.1088/0004-637X/715/2/967, 1004.2056 ADSGoogle Scholar
  106. Mirabel IF, Rodríguez LF (1994) A superluminal source in the Galaxy. Nature 371:46–48. doi: 10.1038/371046a0 ADSGoogle Scholar
  107. Nakar E (2007) Short-hard gamma-ray bursts. Phys Rep 442:166–236. doi: 10.1016/j.physrep.2007.02.005, arXiv:astro-ph/0701748 ADSGoogle Scholar
  108. Nakar E (2010) What do we know about gamma-ray bursts? arXiv:1009.4648
  109. Niemiec J, Pohl M, Stroman T, Nishikawa K (2008) Production of magnetic turbulence by Cosmic Rays drifting upstream of Supernova Remnant Shocks. Astrophys J 684:1174–1189. doi: 10.1086/590054, 0802.2185 ADSGoogle Scholar
  110. Niemiec J, Pohl M, Bret A, Stroman T (2010) Aperiodic magnetic turbulence produced by relativistic ion beams. Astrophys J 709:1148–1156. doi: 10.1088/0004-637X/709/2/1148, 0912.0101 ADSGoogle Scholar
  111. Nishikawa K et al. (2010a) Radiation from relativistic shocks with turbulent magnetic fields. Int J Mod Phys D 19:715–721. doi: 10.1142/S0218271810016865, 0906.5018 ADSGoogle Scholar
  112. Nishikawa K et al. (2010b) Simulation of relativistic shocks and associated self-consistent radiation. In: Kawai N, Nagataki S (eds) Deciphering the Ancient universe with gamma-ray bursts. AIP Conference Series, vol 1279, pp 261–264. doi: 10.1063/1.3509279, 0912.1583 Google Scholar
  113. Nishikawa K, Zhao J, Sakai J, Neubert T (1997) Study of nonlinear Alfvén waves in an electron–positron plasma with a 3D EM particle code. Adv Space Res 19:117–120. doi: 10.1016/S0273-1177(97)00046-X ADSGoogle Scholar
  114. Nishikawa K, Hardee P, Richardson G, Preece R, Sol H, Fishman GJ (2003) Particle acceleration in relativistic jets due to Weibel instability. Astrophys J 595:555–563. doi: 10.1086/377260, arXiv:astro-ph/0305091 ADSGoogle Scholar
  115. Nishikawa K, Hardee P, Richardson G, Preece R, Sol H, Fishman GJ (2005) Particle acceleration and magnetic field generation in electron–positron relativistic shocks. Astrophys J 622:927–937. doi: 10.1086/428394, arXiv:astro-ph/0410266 ADSGoogle Scholar
  116. Nishikawa K, Hardee PE, Hededal CB, Fishman GJ (2006) Acceleration mechanics in relativistic shocks by the weibel instability. Astrophys J 642:1267–1274. doi: 10.1086/501426, arXiv:astro-ph/0510590 ADSGoogle Scholar
  117. Ohira Y, Reville B, Kirk JG, Takahara F (2009) Two-dimensional particle-in-cell simulations of the nonresonant, cosmic-ray-driven instability in supernova remnant shocks. Astrophys J 698:445–450. doi: 10.1088/0004-637X/698/1/445, 0812.0901 ADSGoogle Scholar
  118. Piran T (1999a) Gamma-ray bursts and related phenomena. Nucl Phys B, Proc Suppl 70:431–438. doi: 10.1016/S0920-5632(98)00464-2, arXiv:astro-ph/9801001 ADSGoogle Scholar
  119. Piran T (1999b) Gamma-ray bursts and the fireball model. Phys Rep 314:575–667. doi: 10.1016/S0370-1573(98)00127-6, arXiv:astro-ph/9810256 ADSGoogle Scholar
  120. Piran T (2004) The physics of gamma-ray bursts. Rev Mod Phys 76:1143–1210. doi: 10.1103/RevModPhys.76.1143, arXiv:astro-ph/0405503 ADSGoogle Scholar
  121. Piran T (2005) Accretion power in GRBs. In: Burderi L, Antonelli LA, D’Antona F, di Salvo T, Israel GL, Piersanti L, Tornambè A, Straniero O (eds) Interacting binaries: accretion, evolution, and outcomes, American institute of physics conference series, vol 797, pp 123–131. doi: 10.1063/1.2130224 Google Scholar
  122. Rabinak I, Katz B, Waxman E (2010) Long wavelength unstable modes in the far upstream of relativistic collisionless shocks. arXiv:1005.3791
  123. Reville B, Kirk JG, Duffy P (2006) A current-driven instability in parallel, relativistic shocks. Plasma Phys Control Fusion 48:1741–1747. doi: 10.1088/0741-3335/48/12/004, arXiv:astro-ph/0608462 ADSGoogle Scholar
  124. Reville B, Kirk JG, Duffy P, O’Sullivan S (2007) A cosmic ray current-driven instability in partially ionised media. Astron Astrophys 475:435–439. doi: 10.1051/0004-6361:20078336, 0707.3743 zbMATHADSGoogle Scholar
  125. Reville B, O’Sullivan S, Duffy P, Kirk JG (2008) The transport of cosmic rays in self-excited magnetic turbulence. Mon Not R Astron Soc Lett 386:509–515. doi: 10.1111/j.1365-2966.2008.13059.x, 0802.0109 ADSGoogle Scholar
  126. Riquelme MA, Spitkovsky A (2009) Nonlinear study of Bell’s cosmic ray current-driven instability. Astrophys J 694:626–642. doi: 10.1088/0004-637X/694/1/626, 0810.4565 ADSGoogle Scholar
  127. Riquelme MA, Spitkovsky A (2010) Magnetic amplification by magnetized cosmic rays in supernova remnant shocks. Astrophys J 717:1054–1066. doi: 10.1088/0004-637X/717/2/1054, 0912.4990 ADSGoogle Scholar
  128. Sagdeev RZ (1966) Cooperative phenomena and shock waves in collisionless plasmas. Rev Plasma Phys 4:23–91 ADSGoogle Scholar
  129. Sedov LI (1959) Similarity and dimensional methods in mechanics. Academic Press, New York zbMATHGoogle Scholar
  130. Silva LO, Fonseca RA, Tonge JW, Mori WB, Dawson JM (2002) On the role of the purely transverse Weibel instability in fast ignitor scenarios. Phys Plasmas 9:2458–2461. doi: 10.1063/1.1476004 ADSGoogle Scholar
  131. Silva LO, Fonseca RA, Tonge JW, Dawson JM, Mori WB, Medvedev MV (2003) Interpenetrating plasma shells: near-equipartition magnetic field generation and nonthermal particle acceleration. Astrophys J Lett 596:L121–L124. doi: 10.1086/379156, arXiv:astro-ph/0307500 ADSGoogle Scholar
  132. Sironi L, Spitkovsky A (2009a) Particle acceleration in relativistic magnetized collisionless pair shocks: dependence of shock acceleration on magnetic obliquity. Astrophys J 698:1523–1549. doi: 10.1088/0004-637X/698/2/1523, 0901.2578 ADSGoogle Scholar
  133. Sironi L, Spitkovsky A (2009b) Synthetic spectra from particle-in-cell simulations of relativistic collisionless shocks. Astrophys J Lett 707:L92–L96. doi: 10.1088/0004-637X/707/1/L92, 0908.3193 ADSGoogle Scholar
  134. Sironi L, Spitkovsky A (2010) Efficiency of particle acceleration in relativistic magnetized shocks. In: Bulletin of the American astronomical society, vol 42, p 737 Google Scholar
  135. Sironi L, Spitkovsky A (2011) Particle acceleration in relativistic magnetized collisionless electron–ion shocks. Astrophys J 726:75. doi: 10.1088/0004-637X/726/2/75, 1009.0024 ADSGoogle Scholar
  136. Spitkovsky A (2005) Simulations of relativistic collisionless shocks: shock structure and particle acceleration. In: Bulik T, Rudak B, Madejski G (eds) Astrophysical sources of high energy particles and radiation, AIP Conf. series, vol 801, pp 345–350. doi: 10.1063/1.2141897, arXiv:astro-ph/0603211 Google Scholar
  137. Spitkovsky A (2008a) On the structure of relativistic collisionless shocks in electron–ion plasmas. Astrophys J Lett 673:L39–L42. doi: 10.1086/527374, 0706.3126 ADSGoogle Scholar
  138. Spitkovsky A (2008b) Particle acceleration in relativistic collisionless shocks: Fermi process at last? Astrophys J Lett 682:L5–L8. doi: 10.1086/590248, 0802.3216 ADSGoogle Scholar
  139. Taylor G (1950) The formation of a blast wave by a very intense explosion. I theoretical discussion . Proc R Soc Lond Ser A, Math Phys Sci 201:159–174. doi: 10.1098/rspa.1950.0049 zbMATHADSGoogle Scholar
  140. Taylor GB, Frail DA, Berger E, Kulkarni SR, (2004) The angular size and proper motion of the afterglow of GRB 030329. Astrophys J Lett 609:L1–L4. doi: 10.1086/422554, arXiv:astro-ph/0405300 ADSGoogle Scholar
  141. Toma K, Sakamoto T, Meszaros P (2010) Population III GRB afterglows: constraints on stellar masses and external medium densities. arXiv:1008.1269
  142. Treumann RA (2006) The electron-cyclotron maser for astrophysical application. Astron Astrophys Rev 13:229–315. doi: 10.1007/s00159-006-0001-y ADSGoogle Scholar
  143. Treumann RA (2009) Fundamentals of collisionless shocks for astrophysical application 1. Non-relativistic shocks. Astron Astrophys Rev 17:409–535. doi: 10.1007/s00159-009-0024-2 ADSGoogle Scholar
  144. Treumann RA, Terasawa T (2001) Electron acceleration in the heliosphere. Space Sci Rev 99:135–150 ADSGoogle Scholar
  145. Treumann RA, Jaroschek CH, Pottelette R (2009) Auroral evidence for multiple reconnection in the magnetospheric tail plasma sheet. Europhys Lett 85:49001. doi: 10.1209/0295-5075/85/49001, 0811.0096 ADSGoogle Scholar
  146. Treumann RA, Nakamura R, Baumjohann W (2010) Collisionless reconnection: mechanism of self-ignition in thin plane homogeneous current sheets. Ann Geophys 28:1935–1943. doi: 10.5194/angeo-28-1935-2010, 1004.3992 ADSGoogle Scholar
  147. Tsurutani BT, Stone RG (1985) Collisionless shocks in the heliosphere: reviews of current research. In: Washington DC American Geophysical Union Geophysical Monograph Series 35 Google Scholar
  148. van der Swaluw E, Achterberg A, Gallant YA, Downes TP, Keppens R (2003) Interaction of high-velocity pulsars with supernova remnant shells. Astron Astrophys 397:913–920. doi: 10.1051/0004-6361:20021488, arXiv:astro-ph/0202232 ADSGoogle Scholar
  149. van Kampen NG (1968) Relativistic thermodynamics of moving systems. Phys Rev 173:295–301. doi: 10.1103/PhysRev.173.295 ADSGoogle Scholar
  150. van Kampen NG (1969) Lorentz-invariance of the distribution in phase space. Physica 43:244–262. doi: 10.1016/0031-8914(69)90005-6 ADSGoogle Scholar
  151. Vietri M (1995) The acceleration of ultra–high-energy cosmic rays in gamma-ray bursts. Astrophys J 453:883. doi: 10.1086/176448, arXiv:astro-ph/9506081 ADSGoogle Scholar
  152. Waxman E (1995a) Cosmological gamma-ray bursts and the highest energy cosmic rays. Phys Rev Lett 75:386–389. doi: 10.1103/PhysRevLett.75.386, arXiv:astro-ph/9505082 ADSGoogle Scholar
  153. Waxman E (1995b) Cosmological Origin for Cosmic Rays above 1019 eV. Astrophys J Lett 452:L1–L4. doi: 10.1086/309715, arXiv:astro-ph/9508037 ADSGoogle Scholar
  154. Waxman E (2006) Gamma-ray bursts and collisionless shocks. Plasma Phys Control Fusion 48:B137–B151. doi: 10.1088/0741-3335/48/12B/S14, arXiv:astro-ph/0607353 Google Scholar
  155. Weibel ES (1959) Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Phys Rev Lett 2:83–84. doi: 10.1103/PhysRevLett.2.83 ADSGoogle Scholar
  156. Wick SD, Dermer CD, Atoyan A (2004) High-energy cosmic rays from galactic and extragalactic γ-ray bursts. Nucl Phys B, Proc Suppl 134:81–83. doi: 10.1016/j.nuclphysbps.2004.08.013, arXiv:astro-ph/0312213 ADSGoogle Scholar
  157. Wiersma J, Achterberg A (2004) Magnetic field generation in relativistic shocks. An early end of the exponential Weibel instability in electron–proton plasmas. Astron Astrophys 428:365–371. doi: 10.1051/0004-6361:20041882, arXiv:astro-ph/0408550 zbMATHADSGoogle Scholar
  158. Yoon PH, Davidson RC (1987) Exact analytical model of the classical Weibel instability in a relativistic anisotropic plasma. Phys Rev A 35:2718–2721. doi: 10.1103/PhysRevA.35.2718 ADSGoogle Scholar
  159. Zweibel EG (2002) Ambipolar drift in a turbulent medium. Astrophys J 567:962–970 doi: 10.1007/s00159-011-0042-8. arXiv:astro-ph/0107462 ADSGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Ioffe Institute for Physics and TechnologySt. PetersburgRussia
  2. 2.Department of Geophysics and Environmental SciencesGeophysics Section, Ludwig-Maximilians-University MunichMunichGermany
  3. 3.Department of Physics and AstronomyDartmouth CollegeHanoverUSA
  4. 4.International Space Science InstituteBernSwitzerland

Personalised recommendations