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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).

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slide1
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

slide2
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 !

slide3
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.

slide4
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.

slide5
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

slide6
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

slide7
Linear Polarization

Synchrotron model

Band function

Compton drag model

slide8
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.)

slide9
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

slide10
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.

slide11
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

slide12
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

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

slide13
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.

slide14
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%

slide15
gqj > 1

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.

slide16
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 > (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.

slide17
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
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