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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 )

Probing Magnetic Field Structure in GRBs Through Dispersive Plasma Effects on the Afterglow Polarization Amir Sagiv, Eli Waxman & Abraham Loeb GRBs in

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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

4th WorkshopOctober 2004

Rome

ApJ Nov. 2004 in press( astro-ph/0401620 )

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. Ek )

• Collisionless shock wave physics

Transfer of polarized light

equation of

transfer:

V

U

Q

I

h

hf

fq

q

V

U

Q

I

s

V

Q

I

00

0

0

00

0d

d

Stokes prmsemissivities absorptionpropagationpropagation

Transverse EM waves in magnetized plasma :

22

2

2

B

B

ijijpnEnE

• birefringence

• circularly polarized

nc

f

Faraday rotation

h

Values of propagation coefficients (f , h )

“cold” plasma :

relativistic plasma :

)~(

cos~~

22

2

B

Bpcold c

f

)~(2

sin~~

22

222

B

Bpcold c

h

22

2lncos~~

e

eBprel c

f

syn

p

esyn

pe

synesyn

e

Bprel c

h

if)(2-p

2

if)(2

2

sin~~2/)2(

)2(

3

222

Calculating propagation effects on afterglow polarization

• Fireball parameters :

Eiso = 1054 erg , T = 10 s , i = 350 , e ,B = 0.1 , p = 2.2

nISM = 1 cm-3 , , vw = 103

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∙

Observation consequences

• At low freq. :L suppressed

C dominant

• Transition C L :Fwd. shock : 1 GHz (radio) Rev. shock : 31013

Hz (IR)

• At high freq. :“Cannonical” L

(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 , for 31013 < < 1015 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 )

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)

END

Fireball geometry, viewing geometry, etc. . .

B|| B

k

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

Faraday effect

Magnetized plasma( B z )

• birefringence

Transverse EM waves :

3

12

21

00

0

0

i

i

ij

2

2

3

22

2

2

22

2

1

1

1

p

B

pB

B

p

22

2

2

B

B

ijijpnEnE

• circularly polarized

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 : 31013

Hz (IR)

• Minimal polarization at transition frequency (10-20%)

forward

reverse

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 ?

Important frequencies (Hz)

ISM WindForward Reverse Forward Reverse

Fa

trans

a

p

syn(m)

B~B

~p

7.0 1018

3.7 1010

2.9 107 1.5 1098.5 1082.8 106

1.04 10149.6 1018 2.6 1015

3.7 1010 1.6 1011 1.6 1011

7.6 105 2.3 108 7.8 106 4.0 108

5.1 1097.1 1081.9 1091.0 109

3.3 108

1.6 109

1.0 109 3.5 1013 3.0 10134.5 109

7.0 1013 3.0 1013

2.8 1015 1.6 10169.7 109

5.7 109

Important plasma parameters

ISM WindForward Reverse Forward Reverse

135

1.3 103

4.0 1013 4.0 10139.8 10139.8 1013

328328 135

4.0 105 3.4 105 1.8 107

40.2 40.2 418 418

1055.4 103431.3 104

10-2 3.4 3.0 10-26 10-4

m

ne

W

zcool / W `

`

`

`

`

`

r (cm)

710 910 1210 1710 1810

x opt IR radio

compact

object

acceleration constant ~

350

internal

collisions:

GR

B

transition phase:

Forward -R

everse

shocks

Afterglow

Jet break

time

sub-

relativistic