Transcript ppt

Magnetized Shocks &
Prompt GRB Emission
Ramesh Narayan
Pawan Kumar
Sasha Tchekhovskoy
Jonathan McKinney
Introduction
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Prompt gamma-ray emission differs
greatly from afterglow emission
Afterglow is from external shock, so
prompt emission is from elsewhere:
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Internal shocks, or
Reverse shock (+turbulence), or
Photosphere
We will assume that the radiation is
from Shock-Accelerated Electrons
Magnetized Jet Model
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GRBs have jets with very large j
Leading paradigm for producing such
jets: magnetic fields attached to
spinning BHs or NSs
Initially, energy flows out as Poynting
flux, then gradually converted to KE
Talks at this meeting
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McKinney
Tchekhovskoy
Acceleration:
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Cold magnetically-dominated jets do not
accelerate efficiently
Magnetization Parameter:

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Problem
cE  B / 4
EM Energy Flux
= 2 2 
 v c
Mass Energy Flux
problem: For a steady, axisymmetric jet,
only a small fraction of EM energy is
converted to mass KE: final  1
Jet which is confined and then deconfined
can give final ~ 1 (Tchekhovskoy)
 50% of magnetic energy can be tapped
However,…
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Shocks involving magnetized fluid are not
very efficient at converting bulk kinetic
energy to thermal energy
When  is large (or even when it is
modest), if the field is “perpendicular”,
the conversion is inefficient (Kennel &
Coroniti 1984)
How inefficient? We have solved the
jump conditions for internal shocks and
reverse shock to answer this question
Observations
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From estimates of jet Lorentz factor (j)
and opening angle (j) we obtain a lower
limit on final (Tchekhovskoy et al. 2010):
 final
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  j sin  j 


 15 
2
From energy radiated in –rays (E) and
afterglow energy (EK) we obtain the
efficiency of prompt emission:
 
E
E  EK
DATA
P&K (2002):
970508, 990123,
990510, 991208,
991216, 000301C,
000418, 000926,
010222
HETE II:
021004
Fermi:
080916C, 090510
(i)  is within a factor of a few of unity
(ii)  is large, i.e., -ray emission is efficient
Internal Shock Model
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Two cold magnetized
blobs, with magnetization
, Lorentz factors + and  in CM frame (relative
Lorentz factor )
Assume a fraction e of
thermal energy goes into
relativistic electrons
Assume fast cooling
Parameters: , , e

Cold

Hot
Hot
Cold
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Distribution of e From
Afterglow Modeling
1.1
1.05
1.4
1.2
=10
2
=199
1.21
e=0.2
e=1
If we consider a reasonable e = 0.2, not a single GRB in our sample is
consistent with internal shock, not even for  = 10 (or  = 199)
e = 1 improves the situation a bit, but it is still very unsatisfactory
Reverse Shock
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Jet ejecta (magnetization
parameter ) with Lorentz
factor j=4, and relativity
parameter =(R/Rs)1/2
(Sari & Piran 1995),
collides with cold ISM
Assume fraction e of
thermal energy in reverse
shock goes into relativistic
electrons
Assume fast cooling
Parameters: , j, , e
1=1
Cold ISM
0
Hot ISM
2=3
Hot Ejecta
Cold Jet Ejecta
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j=4
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2
cE  B / 4
EM Energy Flux
= 2 2 
   j sin  j 
 v c
Mass Energy Flux
1/2
 3n4

 R 
l 
4/3
   
     2 1    

  j n1

 Rs 
  1: Newtonian shock (Inefficient)
1/2
1/2
  1: Relativistic shock (Efficient)
Sari &
Piran
(1995)
=0.01
0.1
1
3.16
j=300, e=0.2
j=300, e=1
If we consider a reasonable e = 0.2, not a single GRB in our sample is
consistent with the reverse shock, not even for  = 0.01
e = 1 improves the situation a bit, but it is still very unsatisfactory
What Does this Mean?
If GRB jets are produced by steady, cold,
magnetically-accelerated jets, then the
thermal energy produced either by the
reverse shock or by internals shocks,
is insufficient to power
the prompt –ray emission
DATA
What is the Solution?
P&K (2002):
970508, 990123,
990510, 991208,
991216, 000301C,
000418, 000926,
010222
HETE II:
021004
Fermi:
080916C, 090510
Reliability of the data: j, j, E, EK ?
Can estimates change orders of magnitude?
What is the Solution?
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Perhaps relativistic magnetized shocks
can achieve e1, whereas
unmagnetized shocks only have e~0.2
However, particle-in-cell simulations of
shock acceleration suggest that
(perpendicular) magnetic fields kill
acceleration
Requires   10-3 for decent acceleration
(Sironi & Spitkovsky 2009, 2011)
What is the Solution?
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Perhaps we don’t have a
steady jet, but a blobby
jet, with impulsive
acceleration (Granot et
al. 2011)
Blobs expand and their
front surfaces accelerate
efficiently to large final
(like fireball model)
Can beat the  problem
Modest
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But Inter-Blob Shocks?
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Blobs have to expand
a lot to reduce 
With multiple blobs,
we get internal shocks
(which is good)
But they will be high 
shocks  inefficient
We can avoid this only
with Fine-Tuning
Modest
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Other Solutions?
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Perhaps it is the Forward Shock?
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Perhaps high  outflows accelerate
particles by something other than
shocks, e.g., Reconnection? (Medvedev)
Perhaps it is a hot jet?
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Both prompt emission and afterglow
Hydrodynamic: Back to the fireball model!
Perhaps it is photospheric quasi-thermal
emission?
Standard Picture
Simpler Scenario
Magnetic Jet/Fireball
Magnetic Jet/Fireball
Bulk KE of Baryons
Non-Thermal PL Electrons
Electron Thermal Energy
Non-Thermal PL Electrons
Summary
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Steady magnetized jet model cannot
explain the observed prompt –ray
emission via shock acceleration
My favorite solutions
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Reconnection or something like it
Hot jet, or fireball model
Photospheric emission (Band function?)
Blobby jet (fine-tuned?)