1. Probing Magnetic Field Structure in GRBs Through Dispersive Plasma Effects on the Afterglow Polarization Amir Sagiv, Eli Waxman & Abraham Loeb GRBs in the Afterglow Era 4 th Workshop October 2004 Rome ApJ Nov. 2004 in press ( astro-ph/0401620 )

2. Polarization measurement of early afterglow in radio & IR can unveil B structure ( and constrain strength ) Origin, structure & strength of B in GRB shocks : OPEN QUESTIONS ! Plasma effects : change polarization properties sensitive to B structure and strength Progenitor Outflow ( e.g. Poynting flux vs. E k ) Collisionless shock wave physics

3. Transfer of polarized light equation of transfer: Stokes prms emissivitiesabsorption propagation Transverse EM waves in magnetized plasma : birefringence circularly polarized Faraday rotation

4. Values of propagation coefficients (f, h ) “cold” plasma : relativistic plasma :

5. Calculating propagation effects on afterglow polarization Fireball parameters : E iso = 10 54 erg, T = 10 s,  i = 350,  e,  B = 0.1, p = 2.2 n ISM = 1 cm -3,, v w = 10 3 km s -1 Uniform field across emitting slab Early AG ( F / R shocks ) :  >  jet -1 (typ. jet) Uniform-density ISM / Wind ( n ~ r -2 ) Cooling - synchrotron losses Integration of transfer equation M = 10 -5 M  yr -1 ∙

6. Observation consequences At low freq. :  L suppressed  C dominant Transition C  L : Fwd. shock : 1 GHz (radio) Rev. shock : 3  10 13 Hz (IR) At high freq. : “Cannonical”  L (50%, 75%)

7. Observation consequences (cont.) Results insensitive of ambient density (ISM vs. wind) In reverse shocks only : 180° oscillations of polarization position angle as function of, for 3  10 13 < < 10 15 Hz  circ. polarization ! Probe on field strength : Uniform B with  B = 10 -4  decrease (factor 10) in trans  no  ( ) oscillations in reverse shocks Probe on field structure : No propagation effect if field is entangled over small length scales (  coh « width of slab )

8. Summary Constraining B structure & strength through Radio & IR observations of early afterglow (particularly reverse shock) Distinct polarization fingerprints of uniform field Stringent constraints on models of field origin Probing collisionless shock physics and GRB progenitors Complementary to measurement of  polarization, feasible when fast alerts become available (SWIFT)

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10. Fireball geometry, viewing geometry, etc... B || BB k B || BB k Typical jet :  j »  -1  0 <  <   /2  f » h  pol :  (L+R)  if B    /2  Uniform B  Far. depol. Narrow jet :  j ~  -1   h » f  pol :  &    Uniform B  no Far. depol. Random B in narrow jet  high  L

11. Faraday effect Magnetized plasma ( B  z ) birefringence Transverse EM waves : circularly polarized

12. Observational Consequences High frequencies : “ canonical ” Linear polarization (50%, 75%) Suppression of linear pol. at low frequencies Transition circular  linear : Forward shock : 1 GHz (radio) Reverse shock : 3  10 13 Hz (IR) Minimal polarization at transition frequency (10-20%) forward reverse

13. GRB 021206 : linear polarization of  -rays High degree of linear polarization ( 80% ± 20% ) Position angle constant throughout burst  Synchrotron emission ! UNIFORM FIELD ?  advected from source  Poynting-flux dominated outflow ? High  L possible for a jet observed off-axis RANDOM FIELD generated by instabilities at shock particle acceleration ?

14. Important frequencies (Hz) ISMWind ForwardReverseForwardReverse Fa trans a p syn (  m ) B ~ B ~ p 7.0  10 18 3.7  10 10 2.9  10 7 1.5  10 9 8.5  10 8 2.8  10 6 1.04  10 14 9.6  10 18 2.6  10 15 3.7  10 10 1.6  10 11 7.6  10 5 2.3  10 8 7.8  10 6 4.0  10 8 5.1  10 9 7.1  10 8 1.9  10 9 1.0  10 9 3.3  10 8 1.6  10 9 1.0  10 9 3.5  10 13 3.0  10 13 4.5  10 9 7.0  10 13 3.0  10 13 2.8  10 15 1.6  10 16 9.7  10 9 5.7  10 9

15. Important plasma parameters ISMWind ForwardReverseForwardReverse 135 1.3  10 3 4.0  10 13 9.8  10 13 328 135 4.0  10 5 3.4  10 5 1.8  10 7 40.2 418 105 5.4  10 3 43 1.3  10 4 10 -2 3.4 3.0  10 -2 6  10 -4  mm nene  W z cool / W ` ` ` ` ` `

16. r (cm) xoptIR  radio compact object acceleration constant  ~ 350 internal collisions:GRB transition phase:Forward -Reverseshocks Afterglow Jet break time   sub-relativistic