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), Kuni

hito Ioka (KEK), Takashi Nakamura (Kyoto U)

Nanjing meeting; 2008, June, 22-27

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 !

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., Sage’s talk).

GRB 930131, GRB 960924: > 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.

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.

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)

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)

2D random field generated by shock

Toroidal field advected from engine

Dense soft photons

Linear Polarization

We calculate the linear polarization

- for instantaneous emission from a thin spherical shell

- moving with a Lorentz factor and an opening angle j

: emissivity normalization

: spectral shape

: local polarization degree in the lab frame

: local polarization angle in the lab frame

Linear PolarizationSynchrotron model

Band function

Compton drag model

Synchrotron with ordered field (SO model)Toroidal B field advected from engine

(Granot 03; Granot & Taylor 05)

Visible region: ~ 1/

(Toma et al. in prep.)

j > 1

j < 1

Synchrotron with random field (SR model)2D random B field generated by shock

(Granot 03)

/-1

/-1

GRB jet

Net polarization

Compton Drag Model (CD model)Dense soft photons

/-1

/-1

(Lazzati et al. 04)

CD model shows similar behavior to the SR model, but higher in general.

Monte Carlo SimulationsWe generate 10,000 GRB jets and random viewing angles v, and calculate fluences, spectra, and polarizations.

Simulated events compared to HETE-2 data

POET satellite project

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

60-500 keV

10-7 erg/cm2/s (in 2-400keV)

+- 60 degree

We consider two polarimeters, LEP and GRAPE, as realistic X-ray and gamma-ray polarimeters.

(2-15 keV) (60-500 keV)

50% Minimum Detectable Polarization (MDP) thresholds

50% of the polarizations of detectable bursts above these thresholds can be measured.

Results: Ep- diagram for detectable bursts

(2-15 keV) (60-500 keV)

Results: Ep- diagram for detectable bursts

Fractions of detectable events that are above the 50% MDP thresholds

SO model: 90%, 96%

SR model: 19%, 25%

CD model: 28%, 36%

Almost all the detectable events have j > 0.01, and in most cases v/j < 1.

High in the SR/CD models

The conditions j > 0.01 and v/j < 1 lead to 0.3 < < 0.5 and < 0.1 in the SO model and the SR/CD models, respectively.

j > 1

Detectable events by GRAPE

(2-15 keV) (60-500 keV)

The CD model shows distribution similar to the SR model, except that there are several events with > (+1)/(+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.

Results: Ep- diagram for detectable bursts

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 distribution peaks in the range of 0.3 < < 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