The most probable cause for the high gamma-ray polarization in GRB 021206

The exciting detection of a very high degree of linear polarization, P = 80% ± 20%, in the prompt γ-ray emission of the recent gamma-ray burst GRB 021206 provides strong evidence that synchrotron emission is the dominant radiation mechanism. Besides this immediate implication, there were also claims that this implies a magnetic field that is ordered on large scales within the ejecta and must therefore be produced at the source, which in turn was used as an argument in favor of magnetic fields playing an active role in the production of GRB jets. However, an alternative explanation was also suggested: a very narrow jet, of opening angle θ_j ∼ 1/γ, where γ ∼ 100 is the Lorentz factor during the GRB, viewed slightly outside its edge, at θ_j < θ_obs ≲ θ_j + 1/γ. This explanation also works with a magnetic field that is generated in the internal shocks and does not originate at the source. We calculate the expected degree of polarization for these two scenarios and find that it is significantly easier to produce P ∼ 50% with an ordered field. More specifically, we obtain P ∼ 43%-61% for an ordered transverse magnetic field, B_ord, whereas a shock-produced field that is random but fully within the plane of the shock, B_⊥, can produce up to P ≲ 38%-54% for a single pulse in the GRB light curve, but the integrated emission over many pulses (as measured in GRB 021206) is expected to be a factor of ∼2 lower. A magnetic field normal to the shock front, B_||, can produce P ∼ 35%-62% for the emission integrated over many pulses. However, polarization measurements from GRB afterglows suggest a more isotropic configuration for the shock-produced field that should reduce P by a factor of ∼2-3. Therefore, an ordered magnetic field, B _ord, that originates at the source can produce the observed polarization most naturally, while B_|| is less likely, and B _⊥ is the least likely of the above.