1. Magnetized Shocks & Prompt GRB Emission
Ramesh Narayan
Pawan Kumar
Sasha Tchekhovskoy
Jonathan McKinney

2. Introduction
Prompt gamma-ray emission differs greatly from afterglow emission
Afterglow is from external shock, so prompt emission is from elsewhere:
Internal shocks, or
Reverse shock (+turbulence), or
Photosphere
We will assume that the radiation is from Shock-Accelerated Electrons

3. Magnetized Jet Model 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
McKinney
Tchekhovskoy

4. Acceleration:  Problem
Cold magnetically-dominated jets do not accelerate efficiently
Magnetization Parameter:
 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

5. However,…
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

6. Observations
From estimates of jet Lorentz factor (j) and opening angle (j) we obtain a lower limit on final (Tchekhovskoy et al. 2010):
From energy radiated in –rays (E) and afterglow energy (EK) we obtain the efficiency of prompt emission:

7. DATA
P&K (2002):
970508, , , , , C, , ,
HETE II:
021004
Fermi:
080916C,
(i)  is within a factor of a few of unity (ii)  is large, i.e., -ray emission is efficient

8. Internal Shock Model
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  

9. Distribution of e From Afterglow Modeling

10. =10 2
=199
1.4
1.2
1.1
1.05
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

11. Reverse Shock
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
Cold ISM
  0
1=1
Hot ISM
2=3
Hot Ejecta
Cold Jet Ejecta 
j=4

12. Sari & Piran (1995)

13. =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

14. 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

15. DATA What is the Solution? P&K (2002):
970508, , , , , C, , ,
HETE II:
021004
Fermi:
080916C,
What is the Solution?
Reliability of the data: j, j, E, EK ?
Can estimates change orders of magnitude?

16. What is the Solution?
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)

17. What is the Solution?
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 

18. But Inter-Blob Shocks? 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 

19. Other Solutions? Perhaps it is the Forward Shock?
Both prompt emission and afterglow
Perhaps high  outflows accelerate particles by something other than shocks, e.g., Reconnection? (Medvedev)
Perhaps it is a hot jet?
Hydrodynamic: Back to the fireball model!
Perhaps it is photospheric quasi-thermal emission?

20. Standard Picture Simpler Scenario Magnetic Jet/Fireball
Bulk KE of Baryons
Non-Thermal PL Electrons
Electron Thermal Energy
Non-Thermal PL Electrons

21. Summary
Steady magnetized jet model cannot explain the observed prompt –ray emission via shock acceleration
My favorite solutions
Reconnection or something like it
Hot jet, or fireball model
Photospheric emission (Band function?)
Blobby jet (fine-tuned?)