0 v 1 2 2 M ay 2 00 3 Polarization of prompt GRB emission : evidence for electromagnetically - dominated outflow

Observations by the RHESSI satellite of large polarization of the prompt γ-ray emission from the Gamma Ray Burst GRB0212206 (Coburn & Boggs 2003) imply that the magnetic field coherence scale is larger than the size of the visible emitting region, ∼ R/Γ, where R is the radius of the flow, Γ is the associated Lorentz factor. Such fields cannot be generated in a causally disconnected, hydrodynamically dominated outflow. Electromagnetic models of GRBs (Lyutikov & Blandford 2002), 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/Γ 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/dǫ ∝ ǫ −3). The maximum polarization is smaller than the theoretical upper limit for a stationary plasma in uniform magnetic field due to relativistic kinematic effects.