Relativistic photon mediated shocks

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Relativistic photon mediated shocks
Amir Levinson Tel Aviv University
With Omer Bromberg (PRL 2008)
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Motivation

• Strong shocks that form in regions where the
  Thomson depth exceeds unity are expected to be
  radiation dominated.
• Structure and spectrum of such shocks are
  different than those of collisionless shocks.
• May be relevant to a variety of systems
  including GRBs, microquasars, accretion flows,
  etc.

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Long GRBs and collapsars
Stellar core
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Hypernovae shock breakout
Bow shock source of keV photons r lt 1011
cm Radiation dominated
slow wind

• shocks that form during shock breakout phase are
  expected to be radiation dominated.
• Observational consequences (e.g., emission of VHE
  neutrinos, etc.) would depend on shock structure
  and population of nonthermal particles
  accelerated, if at all, at the shock front.

Emission of High energy Neutrinos?
Baryon poor fireball (BPJ) ?300
internal shocks Source of high-energy protons ?
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GRBs post breakout
external shock r 1015 cm collisionless
slow wind

• Shallow afterglow phase (SWIFT) ? prolonged
  emission?
• if true then implies extremely high radiative
  efficiency during prompt phase!
• - naturally accounted for by pure e? fireballs.
  Radiation dominated shocks formed on relevant
  scales can produce power law extension.

G-ray emission
BPJ
Afterglow emission
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Collisionless versus radiation dominated shocks
Collisionless mediated by collective plasma
process characteristic
scales c/?p , c/?B
Radiation dominated mediated by Compton
scattering
characteristic scale (?Tne)-1

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Non-relativistic case ( ß-ltlt 1)
Weaver, Blandford/Payne, Lyubarski, Riffert
Diffusion approximation is used. Equation of
state pradurad/3 provides a closure of shock
equations.
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Transmitted photon spectrum
1981
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Relativistic case ( G-gt1)

• diffusion approximation invalid
• equation of state pradurad/3 invalid.
• closure of shock equations ?
• ? pair production may be important

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Basic equations
(b)baryons, ( ?) pairs, (r) radiation
In the Thomson regime
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How to compute ?

• Integrate kinetic equation over energy and angle
  and then compute the shock structure
• Needs some scheme for the closure condition.
• Use shock profile as input in the kinetic
  equations to calculate transmitted spectrum.

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Infinite, plane-parallel shock
(Levinson/Bromberg, PRL 2008)
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Solve for net photon flux in fluid rest frame
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(No Transcript)
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Shock structure
Solution of moment equations. Closure
truncation at some order (bluesecond order, red
third order)
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Velocity profile (G-2)
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Velocity profile (G-10)
Closure Ggtgt1 - two beam approximation (from
upstream) Glt 2 - truncation at
some order (from downstream)
iterate until two branches are matched
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The photon spectrum work in progress

• Once the shock profile is known the spectrum can
  be computed by solving the transfer equation for
  the given profile, or performing MC simulations
• The spectrum extends up to the KN limit in the
  shock frame, and is very hard above the thermal
  peak.
• Preliminary results show that the equations have
  eigenfunctions of the sort A?(t) ??.

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Preliminary results
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Conclusions

• Relativistic radiation mediated shocks are
  expected to form in regions where the Thomson
  optical depth exceeds unity.
• The photon spectrum inside the shock has a hard,
  nonthermal tail extending up to the NK limit, as
  measured in the shock frame. For GRBs this may
  naturally account for a nonthermal spectral
  component extending up to tens of Mev. Doesnt
  require particle acceleration!
• The scale of the shock is a few Thomson m.f.p.
  This is typically much larger than skin depth and
  Larmor radii. Particle acceleration in such
  shocks would require diffusion length of
  macroscopic scale.
• Implications for VHE emission?
• e.g., site of prompt GeV photons?
• production of TeV neutrinos during shock breakout
  is questionable.
• May be relevant also to microquasars, accretion
  flows.