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

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

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

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

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

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:

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 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  

Distribution of e From Afterglow Modeling

=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

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

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 What is the Solution? Reliability of the data: j, j, E, EK ? Can estimates change orders of magnitude?

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)

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 

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 

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?

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

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?)