Magnetic fields and cosmic rays in GRBs. A self-similar collisionless foreshock

Abstract

Cosmic rays accelerated by a shock form a streaming distribution of outgoing particles in the foreshock region. If the ambient fields are negligible compared to the shock and cosmic ray energetics, a stronger magnetic field can be generated in the shock upstream via the streaming (Weibel-type) instability. Here we develop a self-similar model of the foreshock region and calculate its structure, e.g., the magnetic field strength, its coherence scale, etc., as a function of the distance from the shock. Our model indicates that the entire foreshock region of thickness $\sim R/(2{\Gamma }_{\mathrm{sh}}^2)$, being comparable to the shock radius in the late afterglow phase when ${\Gamma }_{\mathrm{sh}}\sim 1$, can be populated with large-scale and rather strong magnetic fields (of sub-gauss strengths with the coherence length of order $10^{17}\mathrm{cm}$) compared to the typical interstellar medium magnetic fields. The presence of such fields in the foreshock region is important for high efficiency of Fermi acceleration at the shock. Radiation from accelerated electrons in the foreshock fields can constitute a separate emission region radiating in the UV/optical through radio band, depending on time and shock parameters. We also speculate that these fields being eventually transported into the shock downstream can greatly increase radiative efficiency of a gamma-ray burst afterglow shock.

10 pages, 1 figure. Submitted to ApJ

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• Electron Power-Law Spectra in Solar and Space Plasmas
• Signatures of a Maxwellian Component in Shock-Accelerated Electrons in GRBs
• Physics of Weibel-mediated relativistic collisionless shocks
• Maximum synchrotron frequency for shock-accelerated particles
• PIC methods in astrophysics: Simulations of relativistic jets and kinetic physics in astrophysical systems
• On the maximum energy of shock-accelerated cosmic rays at ultra-relativistic shocks
• Radiation from sub-Larmor scale magnetic fields
• Particle acceleration, magnetization and radiation in relativistic shocks
• Non-linear collisionless damping of Weibel turbulence in relativistic blast waves
• Gamma-ray Burst Prompt Emission: Jitter Radiation in Stochastic Magnetic Field Revisited
• Long wavelength unstable modes in the far upstream of relativistic collisionless shocks
• Aperiodic magnetic turbulence produced by relativistic ion beams
• Impact of continuous particle injection on generation and decay of the magnetic field in collisionless shocks
• Prospects for ultra-high-energy particle acceleration at relativistic shocks
• The upstream magnetic field of collisionless GRB shocks: constraint by Fermi-LAT observations
• Diffusive acceleration in relativistic shocks: particle feedback
• Macroscopic magnetization of primordial plasma by virial shocks