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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)
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 `
`
`
`
`
`