Polarization of prompt GRB emission: Evidence for electromagnetically - dominated outflow

-ray emission from the Gamma Ray Burst GRB021206 \citep{coburn03} imply that the magnetic field coherence scale is larger than the size of the visible emitting region,

\sim R/\Gamma

, where

R

is the radius of the flow,

\Gamma

is the associated Lorentz factor. Such fields cannot be generated in a causally disconnected, hydrodynamically dominated outflow. Electromagnetic models of GRBs \citep{lyutikov02}, in which large scale, dynamically dominant, magnetic fields are present in the outflow from the very beginning, provide a natural explanation of this large reported linear polarization. We derive Stokes parameters of synchrotron emission of a relativistically moving plasma with a given magnetic field configuration and calculate the pulse averaged polarization fraction of the emission from a relativistically expanding shell carrying global toroidal magnetic field. For viewing angles larger than

1/\Gamma

the observed patch of the emitting shell has almost homogeneous magnetic field, producing a large fractional polarization (

56%

for a power-law energy distribution of relativistic particles

dn/d\epsilon \propto \epsilon^{-3}

). The maximum polarization is smaller than the theoretical upper limit for a stationary plasma in uniform magnetic field due to relativistic kinematic effects.

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