Transcript Probing the Magnetic Field Structure in g
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