Statistical Properties of GRB Polarization

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Statistical Properties of GRB Polarization
Kenji Toma
(National Astronomical Observatory of Japan)
Collaborated with Bing Zhang (Nevada U),
Takanori Sakamoto, Joanne Hill (GSFC), Ryo
Yamazaki (Hiroshima U), Kunihito Ioka (KEK),
Takashi Nakamura (Kyoto U)
Nanjing meeting 2008, June, 22-27
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GRB Polarization
One of new frontiers of GRB study will be
measuring polarizations.
Electromagnetic radiation has 4 measurable
quantities.

• Direction
• Intensity
• Frequency
• Polarization

GRB study has been developed mainly by measuring
3 quantities so far.
In spite of extensive efforts of the spectral and
lightcurve observations, the emission mechanism
of the prompt bursts is still unclear. Measuring
polarizations of the bursts will provide us with
new information !
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Current Observational Situation
GRB 021206 80-20 (Coburn Boggs 03)
This claim is controversial because of systematic
uncertainties (Rutledge Fox 2004 Wigger et al.
04 cf., Sages talk).
GRB 930131, GRB 960924 gt 30 (Willis et al. 05)
GRB 041219a 96-40 (Kalemci et al. 07 McGlynn
et al. 07)
They are also inconclusive because of
instrumental systematic effects.
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Current Observational Situation
Recently several X-ray gamma-ray polarimeters
with high sensitivity have been planned.

• POET (2-15 keV 60-500 keV) McConnell et al.
• POLAR (10-300 keV) Produit et al.
• PoGO (30-100 keV) Mizuno et al.
• XPOL (2-10 keV) Costa et al.

They will provide us with the first definitive
detections of the burst polarizations and enable
us to discuss their statistical properties.
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Emission Models
The polarization measurements of GRBs will be a
powerful tool to probe the emission mechanism.
Synchrotron model with globally ordered B field
(Lyutikov et al. 03 Granot 03 Nakar et al. 03)
Toroidal field advected from engine
Synchrotron model with small-scale random B field
(Waxman 03 Granot 03 Nakar et al. 03)
2D random field generated by shock
Compton drag model (Lazzati et al. 04 Eichler
Levinson 03)
Dense soft photons
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Linear Polarization
We calculate the linear polarization

• for instantaneous emission from a thin spherical
  shell
• moving with a Lorentz factor g gtgt 1 and an
  opening angle qj

emissivity normalization
local polarization degree in the lab frame
spectral shape
local polarization angle in the lab frame
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Linear Polarization
Synchrotron model
Band function
Compton drag model
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Synchrotron with ordered field (SO model)
(Granot 03 Granot Taylor 05)
Toroidal B field advected from engine
gqj gt 1
Visible region 1/g
gqj lt 1
(Toma et al. in prep.)
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Synchrotron with random field (SR model)
(Granot 03)
2D random B field generated by shock
q/g-1
q/g-1
GRB jet
Net polarization
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Compton Drag Model (CD model)
(Lazzati et al. 04)
Dense soft photons
q/g-1
q/g-1
CD model shows similar behavior to the SR model,
but higher P in general.
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Monte Carlo Simulations
We generate 10,000 GRB jets and random viewing
angles qv, and calculate fluences, spectra, and
polarizations.
Simulated events compared to HETE-2 data
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POET satellite project
We consider two polarimeters, LEP and GRAPE, as
realistic X-ray and gamma-ray polarimeters.
POET (POlarimeters for Energetic Transients)
(See Hills talk on Friday)
LEP (Low Energy Polarimeter)
GRAPE (Gamma-Ray Polarimeter Experiment)
Polarimetry Detection limit Field-of-View
60-500 keV 10-7 erg/cm2/s (in 2-400keV) - 60
degree
2-15 keV 10-8 erg/cm2/s (in 2-400keV) -44 degree
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Results Ep-P diagram for detectable bursts
P (2-15 keV)
P (60-500 keV)
50 Minimum Detectable Polarization (MDP)
thresholds
50 of the polarizations of detectable bursts
above these thresholds can be measured.
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Results Ep-P diagram for detectable bursts
P (2-15 keV)
P (60-500 keV)
Fractions of detectable events that are above the
50 MDP thresholds
SO model 90, 96 SR model 19, 25 CD
model 28, 36
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gqj gt 1
Detectable events by GRAPE
High P in the SR/CD models
Almost all the detectable events have qj gt 0.01,
and in most cases qv/qj lt 1.
The conditions qj gt 0.01 and qv/qj lt 1 lead to
0.3 lt P lt 0.5 and P lt 0.1 in the SO model and the
SR/CD models, respectively.
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Results Ep-P diagram for detectable bursts
P (2-15 keV)
P (60-500 keV)
The CD model shows P distribution similar to the
SR model, except that there are several events
with P gt (b1)/(b5/3) 0.75 (i.e., the upper
limit for synchrotron model).
If we detect a sufficiently large number of
events, the SR and CD models may also be
distinguished.
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Summary

• Recently there has been increasing interest in
  the measurement of X-ray and gamma-ray
  polarizations.
• The POET satellite may distinguish the SO, SR,
  and CD models for GRB emission mechanisms.
• Much more polarizations can be measured in
  detectable bursts in the SO model than in the
  SR/CD models, and the P distribution peaks in the
  range of 0.3 lt P lt 0.5.
• If we detect a sufficiently large number of
  events, the SR and CD models may also be
  distinguished.
• The SO model -gt global B field advected from
  engine
• The SR/CD models -gt opening angle distribution