1. 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

2. 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 !

3. Current Observational Situation
GRB : % (Coburn & Boggs 03)
This claim is controversial because of systematic uncertainties (Rutledge & Fox 2004; Wigger et al. 04; cf., Sage’s talk).
GRB , GRB : > 30% (Willis et al. 05)
GRB a: % (Kalemci et al. 07; McGlynn et al. 07)
They are also inconclusive because of instrumental systematic effects.

4. Current Observational Situation
Recently several X-ray & gamma-ray polarimeters with high sensitivity have been planned.
POET (2-15 keV & keV) McConnell et al.
POLAR ( keV) Produit et al.
PoGO ( 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.

5. 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
2D random field generated by shock
Synchrotron model with small-scale random B field (Waxman 03; Granot 03; Nakar et al. 03)
Compton drag model (Lazzati et al. 04; Eichler & Levinson 03)
Dense soft photons

6. Linear Polarization We calculate the linear polarization
for instantaneous emission from a thin spherical shell
moving with a Lorentz factor g >> 1 and an opening angle qj
: emissivity normalization
: local polarization degree in the lab frame
: spectral shape
: local polarization angle in the lab frame

7. Linear Polarization
Synchrotron model
Band function
Compton drag model

8. Synchrotron with ordered field (SO model)
(Granot 03; Granot & Taylor 05)
Toroidal B field advected from engine
gqj > 1
Visible region: ~ 1/g
gqj < 1
(Toma et al. in prep.)

9. 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

10. 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.

11. 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

12. POET satellite project
We consider two polarimeters, LEP and GRAPE, as realistic X-ray and gamma-ray polarimeters.
POET (POlarimeters for Energetic Transients)
(See Hill’s talk on Friday)
LEP
(Low Energy Polarimeter)
GRAPE
(Gamma-Ray Polarimeter Experiment)
Polarimetry
Detection limit
Field-of-View
2-15 keV
10-8 erg/cm2/s (in 2-400keV)
+-44 degree
keV
10-7 erg/cm2/s (in 2-400keV)
+- 60 degree

13. Results: Ep-P diagram for detectable bursts
P (2-15 keV)
P ( keV)
50% Minimum Detectable Polarization (MDP) thresholds
50% of the polarizations of detectable bursts above these thresholds can be measured.

14. Results: Ep-P diagram for detectable bursts
P (2-15 keV)
P ( keV)
Fractions of detectable events that are above the 50% MDP thresholds
SO model: 90%, 96%
SR model: 19%, 25%
CD model: 28%, 36%

15. gqj > 1 High P in the SR/CD models
Detectable events by GRAPE
High P in the SR/CD models
Almost all the detectable events have qj > 0.01, and in most cases qv/qj < 1.
The conditions qj > 0.01 and qv/qj < 1 lead to 0.3 < P < 0.5 and P < 0.1 in the SO model and the SR/CD models, respectively.

16. Results: Ep-P diagram for detectable bursts
P (2-15 keV)
P ( keV)
The CD model shows P distribution similar to the SR model, except that there are several events with P > (b+1)/(b+5/3) = 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.

17. 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 < P < 0.5.
If we detect a sufficiently large number of events, the SR and CD models may also be distinguished.
The SO model -> global B field advected from engine
The SR/CD models -> opening angle distribution