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Relativistic Collisionless Shocks in the Unmagnetized Limit
Milos MilosavljevicDepartment of Astronomy, The University of Texas at Austin
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Plan
• Summary of: Milosavljevic & Nakar, “Weibel Filament Decay and Thermalization in Collisionless Shocks and Gamma-Ray Burst Afterglows” 2006 ApJ, 641, 978.
• Summary of: Milosavljevic & Nakar, “The Cosmic Ray Precursor of Collisionless Shocks: A Missing Link in Gamma-Ray Burst Afterglows” 2006, ApJ, 651, 979.
• Outlook.
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Anatomy of a Weibel Filament(Alfven 1939, Hammer & Rostoker 1970)
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The Weibel Tissue (Pair Plasma)
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The Lining (Pair Plasma)
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Spitkovsky 2006
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The Lining (Pair Plasma)
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Spitkovsky 2006
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Validity of the Fluid Theorye.g., Zenitani & Hoshino, “Relativistic Particle Acceleration
in a Folded Current Sheet” 2005, ApJ 618, L111
Caution (Jon Arons, priv. comm.): It still remains to be checked whether the magnetic walls are stabilized by the shear (bulk streaming of the plasma) on the sides of the filament. Shear stabilization could prevent a pressure-driven instability, but the filaments could still be disrupted by another instability.
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Where is the shock?
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Frederisken et al. 2004
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electrons
ions
Frederisken et al. 2004
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Can Coulomb shielding prevent decay in electron-ion shocks?
If decay is pressure driven and not Coulomb or
Ampere driven, shielding does not prevent decay.
Hededal et al. 2005
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Deconfinement
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Long Term Evolution of Weibel Turbulence
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Long Term Evolution of Weibel Turbulence
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Summary of Part I
• Weibel “filaments” (at least in pair shocks) are a really network of skin-depth thick magnetic walls with field-free interior.
• Optimistically granting Coulomb shielding and negligible Ampere interactions, the “filaments” are MHD unstable (sausage-kink, etc.) and move (but see the caveat on page 7).
• Synchrotron emission in the small-scale field depolarizes.
• Instability compromises the confining power of the magnetic walls. The particles drift, escape, and isotropize. The magnetic field decays.
• In electron-ion shocks, the decay time scale is unknown. Simulations will measure the decay time scale, but published electron-ion simulations have not converged.
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The Weibel Shock: The Scorecard
• Shock transition?
• Persistent strong magnetic field?
• Particle acceleration beyond electron-ion equilibration?
Are we missing something?
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energetic ions running ahead of the shock
p
shock at t
e-
e-
p
shoc
k m
oves
in th
is d
irec
tion
shock at t+Dt
The Upstream frame
p
e-
e-
p
The Shock frame
scattering
Energy growsby x2 each time around
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Bell’s Precursor• Assume that the shock accelerates
electrons and ions.• Electrons cool efficiently but ions do
not.• The cosmic rays carry a current into
the shock upstream.• Thermal electron Debye screen the
cosmic ray protons, and carry an equal and opposite return current.
• A seed field in the shock upstream interacts with the return current, and the upstream thermal plasma accelerated sideways.
• Nonlinear magnetic field growth is possible, but not proven.
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Bell 2004
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• In relativistic and Newtonian shocks, cosmic rays going into the shock upstream can drive different processes:– Bell / Bell & Lucek
– Firehose
– Gyroresonant
• If magnetic fields are amplified in the precursor, the amplification length is much larger than the plasma skin depth, and decays resistively.
• The amplified field prevents the Weibel instability! (e.g., Hededal & Nishikawa 2005). The shock is mediated by cosmic rays interacting with large-scale magnetic fields. Other processes must equilibrate the plasma.
• In relativistic external GRB shocks, the maximum magnetic field length scale is ~ R/2. This field is insufficient to confine UHECR, and thus UHECR are not accelerated in external GRB shocks.
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Summary of Part II
• If the shock generates a power-law spectrum of accelerated particles, the ions will go farther than the electrons.
• The ion cosmic ray precursor of the shock may excite disturbances in the shock upstream, e.g., by current-driven interactions.
• In GRB afterglows, the precursor has enough energy to drive turbulence in the shock upstream, but the outcome of the precursor-upstream interaction is not well understood.
• If upstream turbulence is excited, it could generate a magnetic field on scales much larger than the plasma skin depth, which could in turn quench the Weibel instability, and yield a very different shock structure.