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 4 th Workshop October 2004 Rome

Origin, structure & strength of

B

OPEN QUESTIONS !

• Progenitor • Outflow ( e.g. Poynting flux vs. E k ) • Collisionless shock wave physics in GRB shocks : Plasma effects : • change polarization properties • sensitive to B structure and strength Polarization measurement of early afterglow in

radio

&

IR

can unveil

B

structure ( and constrain strength )

equation of transfer:

Transfer of polarized light

I

d d

s

 

Q



U V

       0

Q I

  

V

   

q

0 0 

q



f

0 0 

f



h

0 0

h

  

I

 

Q U

 

V

Transverse EM waves in magnetized plasma : 

ij E j



n

2

E i

 

n

     2

p

2  

B



B

2  • circularly polarized • birefringence

f

propagation 

c



n

Faraday rotation

h

Values of propagation coefficients (f , h )

“cold” plasma :

f cold

 2

p c

(  2

B

 cos 

B

2 )

h cold

 2

p

2

c

 2

B

(  2 sin  2 

B

2 ) relativistic plasma :

f rel



p

2

B c

 2 cos 

h rel



p

2 2 sin

B

2

c

 3 2  ln  

e

2

e

          2 p 2      2

e

    

e

 (

p

 2 )    

syn

  ( 

syn



e

) (     

e

)     (

p

 2 ) / 2 if if   

syn

  

syn

Calculating propagation effects on afterglow polarization

• Fireball parameters :

E iso

= 10 2.2 54 erg ,

T

∙ = 10 s , G

i -5 M



yr -1

= 350 ,  e ,  B = 0.1 , p =

n ISM

= 1 cm -3 , , v w = 10 3 • Uniform field across emitting slab km s -1 • Early AG ( F / R shocks ) : G >  jet -1

(typ. jet)

• Uniform-density ISM / Wind ( n ~ r -2 ) • Cooling - synchrotron losses • Integration of transfer equation

Observation consequences

• At low freq. : P

L

suppressed P

C

dominant • Transition

C

Fwd. shock : 

L

1 GHz (radio) Rev. shock : 3  10 13 Hz (IR) : • At high freq. : “Cannonical” P

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 n , for 3  10 13 < n < 10 15 Hz  circ. polarization !

• Probe on field strength : Uniform B 10 -4  decrease (factor 10) in n trans • Probe on field structure : with  B = 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  polarization, feasible when fast alerts become available (SWIFT) • Stringent constraints on models of field origin • Probing collisionless shock physics and GRB progenitors

END

Fireball geometry, viewing geometry, etc. . .

Typical jet :  j » G -1  0 J    f » h  pol :  Uniform B  (L+R) Far. depol.

p /2

B ||

J

k B

^ J Narrow jet :   h » f   j

~

G -1 Uniform B   pol :  & ^ if

B

^  J  p /2  no Far. depol.

B ||

J

k

J

B

^ Random B in narrow jet  high P L

Magnetized plasma (

B



z

)

Faraday effect



ij

      1

i

 2 0

i

 2  1 0 0 0    3   2  1 3  1    

B

 2 

p

2  

B

2  2 

p

2  

B

2  1   2

p

 2 Transverse EM waves : 

ij E j



n

2

E i

 

n

     2

p

2  

B



B

2  • circularly polarized • birefringence

Observational Consequences

forward • 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%) reverse • High frequencies : “ canonical ” Linear polarization (50% , 75%)

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

?

particle acceleration ?

RANDOM FIELD High P L generated by instabilities at shock possible for a jet observed off-axis

n syn (  m ) n B ~ B n p ~ p n a n Fa n trans

Important frequencies (Hz)

Forward

ISM

Reverse 9.6  10 18 1.04  10 14

Wind

Forward 7.0  10 18 Reverse 2.6  10 15 2.8  10 6 3.7  10 10 7.6  10 5 1.0  10 9 3.3  10 8 8.5  10 8 3.7  10 10 2.3  10 8 1.9  10 9 7.0  10 13 2.9  10 7 1.6  10 11 7.8  10 6 7.1  10 8 5.7  10 9 1.5  10 9 1.6  10 11 4.0  10 8 5.1  10 9 3.0  10 13 1.6  10 9 1.0  10 9 2.8  10 15 3.5  10 13 9.7  10 9 4.5  10 9 1.6  10 16 3.0  10 13

G W ` n e ` B `  m ` z ` / W `

Important plasma parameters

Forward

ISM

Reverse 328 328

Wind

Forward 135 Reverse 135 9.8  10 13 1.3  10 3 9.8  10 13 4.0  10 5 4.0  10 13 3.4  10 5 4.0  10 13 1.8  10 7 40.2

1.3  10 4 10 -2 40.2

43 3.4

418 5.4  10 3 6  10 -4 418 105 3.0  10 -2

 x opt IR radio r (cm) 10 7 10 9 10 12 10 17 10 18 Afterglow