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Particle acceleration at relativistic shock waves - cont.

Lecture 4. Particle acceleration at relativistic shock waves - cont. Ultra-relativistic shock waves. superluminal (perpendicular) shocks, u B,1 > c. Considered objects: - mechanism of GRB generation - pulsar wind terminal shock - shocks in AGN sub-parsec scale jets.

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Particle acceleration at relativistic shock waves - cont.

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  1. Lecture 4 Particle acceleration at relativistic shock waves- cont.

  2. Ultra-relativistic shock waves superluminal (perpendicular) shocks, uB,1 > c Considered objects: - mechanism of GRB generation - pulsar wind terminal shock - shocks in AGN sub-parsec scale jets

  3. Crab Nebula (Chandra + Hubble)

  4. Crab Nebula : :wide range spectrum in over 20 decades in frequency  photons detected in 9 decades ! 100 keV – 100 TeV IC: syn, opt, IR, micro, CMB COMPTEL EGRET SYN HEGRA CELESTE B=160 G Ee ~1015 eV

  5. Spectral index for particles accelerated at ultrarelativistic shocks (Bednarz & Ostrowski 1998)  2.2 

  6. Due to high anisotropy of interacting particles the mean energy gain at anindividual interaction <E> ~ E u u

  7. Reflections – first interactions of upstream CR particles u High energy upstream particles reflections lead toE/E ~ 2 . Only for highly turbulent conditions downstream of the shock reflection efficiency can reach ~10% for the original isotropic distribution.In weakly perturbed conditions the numbers are ~10-5, or less.

  8. Does there exist an universal spectral index for  >> 1 ? As analysed by O.&Bednarz (2002), the same value of •  2.2 derived for ultra-relativistic shocks by Gallant, Achterberg, Kirk, Guthmann, Vietri, Pelletier, et al. always requires a strongturbulence downstream of the shock, if one neglects possibility of strictly parallel shocks. Do such conditions exist in real shocks ?

  9. A role of realistic background conditions in CR acceleration at relativistic and ultra-relativistic shocks was discussed in a series of our ApJ papers: Niemiec & O. (2004, 2006, & Pohl 2006). • In the Monte Carlo simulations we considered : • shock Lorentz factors between 2 and 30 • different inclinations of B0 • different spectra of the background long wave • MHD (static – no Fermi II accel.) turbulence • possibility of generation of highly nonlinear • turbulence at the shock (like in PIC simulations)

  10. At figures below we use the "wavevector – particle energy" resonance relation to characterise the considered structure of the particle distribution function relative to the introduced turbulence. In our units this relation reads: E = 2p/k .

  11. Mildly relativistic shocks oblique subluminal shock: hard component before the cut off "flat" kolmogorov in red – the wave power spectrum F(k)

  12. flat kolmogorov Oblique superluminal shocks 1.93c a short power law with a cut off within the resonance range 1.27c Note: a role of long waves and reflections at locally subluminal configurations 3.48c

  13. Oblique parallel shocks spectral index varies with turbulence ampli- tude and spectrum

  14. Ultrarelativistic shock waves 1 = 5 , u1 = 0.98c , uB,1 = 1.4c flat (wave spectrum) kolmogorov

  15. 1 = 5, 10, 30 , u1 = 0.98c, 0.995c, 0.9994c uB,1  1.4c

  16. Parallel shock flat kolmogorov 1 = 10 1 = 30

  17. Conditions downstream of the shock in the model Components of the spatial diffusion tensor downstream of the shock

  18. Ultrarelativistic shock waves with "shock generated" downstream short-wave turbulence 1 = 10 short wave MHD turbulence

  19. Short wave turbulence perturbs particle trajectory (pitch angle) sh  E-1/2 in a time interval given in the simulations as t  E , while the regular and long wave B-components in such time interval lead to reg  const. Thus the role of short wave turbulence in perturbing particle trajectories decreases with growing particle energy.

  20. Parallel shock universal spectral index

  21. !!! The opinion saying that spectra of particles accelerated at relativistic shocks are the power-laws(+ a cut off) with the spectral index close to 2.2 was (and it is still) prevailing in the astrophysical literature. This erroneous opinion comes from misinterpretation of existing papers discussing the Fermi I acceleration at relativistic shock waves.

  22. Some proposals ofnon-standard or non-Fermirelativistic shock acceleration processes

  23. „Microscoping” studies of relativistic shock structure For example: • Hoshino et al., 1992, „Relativistic magnetosonic shock waves in synchrotron sources - Shock structure and nonthermal acceleration of positrons”, ApJ, 390, 454 PIC modelling of the perpendicular wind terminal shock in Crab • Pohl at al., 2002, „Channeled blast wave behavior based on longitudinal instabilities”, A&A, 383, 309 Analytic modelling of macroscopic instabilities and wave generation • Medvedev & Loeb, 1999, „Generation of Magnetic Fields in the Relativistic Shock of Gamma-Ray Burst Sources”, ApJ, 526, 697 Instability in the shocked magnetized plasma for generation of short wave magnetic field perturbations Hededal, Nishikava, .... – a series of relativistic shock models applying PIC simulations

  24. Derishev et al., 2003, „Particle Acceleration through Multiple Conversions from Charged into Neutral State and Back”, Phys.Rev. D 68, 043003 • Boris Stern, 2003, „Electromagnetic Catastrophe in Ultrarelativistic Shocks and the • Prompt Emission of Gamma-Ray Bursts”, MNRAS 345, 590 • Pisin Chen et al., 2002, „Plasma Wakefield Acceleration for Ultrahigh Energy • Cosmic Rays”, Phys.Rev.Lett. 89, 1101and others • Interaction of a relativistic particle beam with plasma Jonathan Arons, 2003, „Surf-riding acceleration in relativistic winds”, in Proc. „PARTICLE ACCELERATION IN ASTROPHYSICAL OBJECTS” (cf. ApJ, 589, 871) Acceleration at long waves in the relativistic pulsar wind

  25. Works of Derishev et al. and Stern forultrarelativistic shock waves -  >> 1 charged particle neutral particle upstream shock downstream NUCLEONS n +   p + - p +   n +  (or decay of n) PAIRS (e+, e-)  +   e+ + e- e +   e + 

  26. Conclusions theory of cosmic ray acceleration at relativistic shocks is not sufficiently developed to enable realistic modelling of astrophysical sources • wide range of the studied physical conditions at relativistic shocks do not allow for generation of the accelerated particle spectra which are wide range power-laws and/with the universal spectral index  2.2 • cosmic ray spectra generated at ultrarelativistic shock waves are not expected to extend to very high energies – thus postulating such shocks to be sources of UHE CR particles is doubtful

  27. A few more remarks - observational results and numerical simulations still play an essential role in developing the theory of relativistic shock acceleration - in our opinion the full picture requires consideration of the second order Fermi acceleration acting in the relativistic MHD turbulence near (downstream) the shock - PIC simulations are unable to study higher CR energies - interesting non-standard proposals by Derishev et al. , Stern

  28. Final warning: Observed radio and IC X-rays are from 103 (E  1 GeV) electrons. At relativistic shocks propagating in ordinary (e, nuclei) plasma such electrons are below the energy limit required for the I order Fermi acceleration: rg,e shock „thickness”  rg,nuclei(th) Analogous remark can be true for electrons generating -rays in GRB sources

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