Amir Levinson

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Relativistic radiation mediated shocks
application to GRBs
Amir Levinson Tel Aviv University
LevinsonBromberg PRL 08 Bromberg et al. ApJ
11 Levinson ApJ 12
Katz et al. ApJ 10 Budnik et al. ApJ
10 NakarSari ApJ 10,11
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Motivation

• In GRBs a considerable fraction of the outflow
  bulk energy may dissipate beneath the
  photosphere.
• - dissipation mechanism shocks? magnetic
  reconnection ? other ? In this talk I consider
  sub-photospheric shocks
• 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
  vastly different than those of collisionless
  shocks.

Other examples shock breakout in SNs, LLGRB,
etc accretion flows
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Photospheric emission
GRB090902B
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Collapsar simulations
Lazzati et al. 2009
Substantial fraction of bulk energy dissipates
bellow the photosphere via collimation shocks
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A model with magnetic dissipation
Magnetic jets may be converted to HD jets above
the collimation zone
Levinson Begelman 13
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Internal shocks
Bromberg et al. 2011
Sub-photospheric shocks
Morsony et al. 2010
t
collisionless shocks
G
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What is a Radiation Mediated Shock?
Shock mechanism involves generation and
scattering of photons

• downstream energy dominated by radiation
• upstream plasma approaching the shock is
  decelerated by scattering of counter streaming
  photons

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Under which conditions a RMS forms ?
Radiation dominance downstream aTd4 gt nd
kTd From jump conditions numpc2?u2 ? aTd4
?
?u gt 410-5 (nu /1015 cm-3)1/6
In addition, photon trapping requires
Diffusion time tD shock crossing time tsh ?
? gt 1/?u
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RMS versus RRMS

• Non-relativistic RMS
• small energy gain De/eltlt1
• diffusion approximation holds. Used in most
  early treatments
• Zeldovich Raiser 1967 Weaver 1976 Blandford
  Pyne 1981
• Lyubarsky Sunyaev 1982 Riffert 1988

• Relativistic RMS
• photon distribution is anisotropic
• energy gain large De/e gt1
• optical depth depends on angle t a (1-b cosq)
• copious pair production
• Levinson Bromberg 08 Katz et al. 10 Budnik et
  al. 10 Nakar Sari 10,11 Levinson 12

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Photon source two regimes

• Photon production inside the shock (dominant in
  shock breakouts from stellar envelopes, e.g., SN,
  LLGRBs..)
• Photon advection by upstream fluid (dominant in
  GRBs Bromberg et al 11)

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Velocity profile for photon rich upstream
Levinson Bromberg 2008
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Solutions cold upstream (eg., shock breakout in
SN)
Velocity profile
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Collisionless shocks versus RMS

• Scale c/?p 1(n15)-1/2 cm , c/?B 3?(B6)-1 cm
• can accelerate particles to non-thermal
  energies.

collisionless
Plasma turbulence

• scale (?T n ?s)-1 109 n15-1 cm
• microphysics is fully understood
• cannot accelerate particles
  

RMS
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Detailed structure

• Shock transition fluid decelerates to terminal
  DS velocity
• Immediate DS radiation roughly isotropic but
  not in full equilibrium
• Far DS thermodynamic equilibrium is established

shock transition

• Very hard spectrum inside shock
• Thermal emission with local temp. downstream

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Thermalization depth
Photon generation Bremst. double Compton
Free-free t'ff 105?ff-1 (nu15)-1/8?u3/4
Double Compton t'DC 106 ?DC-1 (nu15)-1/2?u-1
Thermalization length gtgt shock width
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Temperature profile behind a planar shock (no
adiabatic cooling)
Thermalization by free-free double Compton
Levinson 2012
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Spectrum inside the shock (cold upstream)

• Temperature in immediate downstream is regulated
  by pair production
• Ts is much lower in shocks with photon rich
  upstream (as in GRBs)

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Prompt phase in GRBs shock in a
relativistically expanding outflow
?s/rph (r/ rph )2?-2
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Breakout and emission

• shock emerges from the photosphere and
  eventually becomes collisionless
• shells of shocked plasma that reach the
  photosphere start emitting
• time integrated spectrum depends on temperature
  profile behind the shock
• at the highest energies contribution from shock
  transition layer might be significant

photosphere
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Upstream conditions
Example adiabatic flow
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Computation of single shock emission
Integrate the transfer eq. for each shocked shell
to obtain its photospheric temperature
rph
rs
r0
Ts
Tph(rs)
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Time integrated SED a single relativistic shock
Contribution from the shock transition layer is
not shown
Uniform dissipation
?u2
?u10
?u5
?u const
?010 R6102
0.01
10
0.1
1
From Levinson 2012
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Dependence on dissipation profile
?u10, ?0100
?u10(?/?0)1/2
1
10
0.1
0.01
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Mildly relativistic shocks
Uniform dissipation (?uconst)
0.1
0.01
0.001
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Dependence on optical depth
Uniform dissipation
0.1
1
0.01
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Multipole shock emission

• Single shock emission produces thermal spectrum
  below the peak.
• Multiple shock emission can mimic a Band spectrum

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Several shocks with different velocities
Keren Levinson, in preparation
nEn a n1.4
Preliminary results
10-3
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Sum of 4 shocks (uniform velocity, equal spacing)
Keren Levinson in preparation
nEn a n1.2
Preliminary results
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Non-equal spacing
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post breakout
photosphere

• Shock becomes collisionless
• particle acceleration
• nonthermal emission from accelerated particles
• possible scattering of photospheric photons by
  nonthermal pairs

To be addressed in future work
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Conclusions

• Relativistic radiation mediated shocks are
  expected to form in regions where the Thomson
  optical depth exceeds unity.
• Time integrated SED emitted behind a single
  shock has a prominent thermal peak. The location
  of the peak depends mainly on upstream conditions
  and the velocity profile of the shock.
• The photon spectrum inside the shock has a hard,
  nonthermal tail extending up to the NK limit, as
  measured in the shock frame. Doesnt require
  particle acceleration!
• Multiple shock emission can mimic a Band
  spectrum