Download Collisionless Shocks

Relativistic Collisionless Shocks
in the Unmagnetized Limit
Milos Milosavljevic
Department of Astronomy, The University of Texas at Austin
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.
Anatomy of a Weibel Filament
(Alfven 1939, Hammer & Rostoker 1970)
The Weibel Tissue (Pair Plasma)
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 Theory
e.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.
Where is the shock?
electrons
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ions
Frederisken et al. 2004
Frederisken et al. 2004
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Can Coulomb shielding prevent decay in
electron-ion shocks?
Hededal et al. 2005
If decay is pressure driven and not Coulomb or
Ampere driven, shielding does not prevent decay.
Deconfinement
Long Term Evolution of Weibel Turbulence
Long Term Evolution of Weibel Turbulence
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.
The Weibel Shock: The Scorecard
• Shock transition?
• Persistent strong magnetic field?
• Particle acceleration beyond electron-ion
equilibration?
Are we missing something?
The Upstream frame
The Shock frame
Energy grows
by x2 each
time around
energetic ions
running
ahead of the
shock
scattering
shock at t+Dt
shock at t
e-
e-
p
p
e-
p
p
e-
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
• 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.
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 precursorupstream 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.