Implications of the γ-ray Polarization of GRB 021206

We compare two possible scenarios for the producing of high level of polarization within the prompt emission of a GRB: synchrotron emission from a relativistic jet with a uniform (in space and time) magnetic field and synchrotron emission from a jet with a random magnetic field in the plane of the shock. Somewhat surprisingly we find that both scenarios can produce a comparable level of polarization ($\sim 45-50$% for the uniform field and $\sim 30-35$% for a random field). Uniform time independent field most naturally arises by expansion of the field from the compact object. It requires a $10^{12}$G field at the source and a transport of the field as $\propto R^{-1}$. It {\it does not} imply Poynting flux domination of the energy of the wind. There is a serious difficulty however, within this scenario, accounting for particle acceleration (which requires random magnetic fields) both for Poynting flux and non-Poynting flux domination. Significant polarization can also arise from a random field provided that the observer is located within $1/\Gamma$ orientation from a narrow ($\theta_j \sim 1/\Gamma$) jet. While most jets are wider, the jet of GRB 021206 from which strong polarization was recently observed, was most likely very narrow. GRB 021206 is among the strongest bursts ever. Adopting the energy-angle relation we find an estimated angle of $<1/40$rad or even smaller. Thus, for this particular burst the required geometry is not unusual. We conclude that the RHESSI observations suggest that the prompt emission results from synchrotron radiation. However, in view of the comparable levels of polarizations predicted by both the random field and the homogeneous field scenarios these observations are insufficient to rule out or confirm either one.