Amir Sagiv, Eli Waxman & Abraham Loeb

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

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

Transfer of polarized light equation of transfer: Transverse EM waves in magnetized plasma : emissivities propagation propagation absorption Stokes prms Faraday rotation • circularly polarized • birefringence

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

∙ M = 10-5 M yr -1 Calculating propagation effects on afterglow polarization • Fireball parameters : Eiso = 1054 erg , T = 10 s , Gi = 350 , e ,B= 0.1 , p = 2.2 nISM = 1 cm-3, , vw = 103km s-1 • Uniform field across emitting slab • Early AG ( F / R shocks ) : G > qjet-1 (typ. jet) • Uniform-density ISM / Wind ( n ~ r-2) • Cooling - synchrotron losses • Integration of transfer equation

Observation consequences • At low freq. : • PLsuppressed • PCdominant • Transition CL : • Fwd. shock : • 1 GHz (radio) • Rev. shock : • 31013Hz (IR) • At high freq. : • “Cannonical” PL • (50%, 75%)

Observation consequences (cont.) • Results insensitive of ambient density (ISM vs. wind) • In reverse shocks only : • 180° oscillations of polarization position angle • as function of n, for 31013 < n < 1015 Hz •  circ. polarization ! • Probe on field strength : Uniform B with B = 10-4 •  decrease (factor 10) in ntrans •  no c(n) oscillations in reverse shocks • Probe on field structure : • No propagation effect if field is entangled • over small length scales (coh « width of slab )

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

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Fireball geometry, viewing geometry, etc. . . B|| B^ J J k B|| < < B^   J J k Typical jet :qj»G-1 J 0 p/2 f » h pol :  (L+R)  Uniform B  Far. depol. Narrow jet :qj~G-1 if B^ J  p/2 h » f pol :  &^  Uniform B  no Far. depol. Random B in narrow jet high PL

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

forward • Suppression of linear pol. • at low frequencies Observational Consequences • Transition circular  linear : • Forward shock : 1 GHz (radio) • Reverse shock : 31013Hz (IR) • Minimal polarization at • transition frequency (10-20%) • High frequencies : “canonical” • Linear polarization (50% , 75%) reverse

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

~ nB ~ np Important frequencies (Hz) ISM Wind Forward Reverse Forward Reverse nsyn(gm) 9.6  1018 1.04  1014 7.0  1018 2.6  1015 nB 2.8  106 8.5  108 2.9  107 1.5  109 3.7  1010 3.7  1010 1.6  1011 1.6  1011 np 7.6  105 2.3  108 7.8  106 4.0  108 1.0  109 1.9  109 7.1  108 5.1  109 na 3.3  108 7.0  1013 5.7  109 3.0  1013 nFa 1.6  109 2.8  1015 9.7  109 1.6  1016 ntrans 1.0  109 3.5  1013 4.5  109 3.0  1013

Important plasma parameters ISM Wind Forward Reverse Forward Reverse G 328 328 135 135 ` W 9.8  1013 9.8  1013 4.0  1013 4.0  1013 ne ` 1.3  103 4.0  105 3.4  105 1.8  107 ` B 40.2 40.2 418 418 gm ` 1.3  104 43 5.4  103 105 ` ` zcool / W 10-2 3.4 6  10-4 3.0  10-2

g x opt IR radio r (cm) sub-relativistic internal collisions: GRB transition phase: Forward -Reverse shocks Jet break time G > q -1 compact object acceleration constant G ~ 350 Afterglow

Amir Sagiv, Eli Waxman & Abraham Loeb