The exciting detection of a very high degree of linear polarization, , in the prompt g-ray P p 80% 20% 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 , where is the v ∼ 1/ gg 100 j Lorentz factor during the GRB, viewed slightly outside its edge, at . This explanation also works v ! v v 1/g j obs j 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 with an ordered field. More specifically, we obtain for an ordered transverse magnetic P 50% P ∼ 43%–61% field, , whereas a shock-produced field that is random but fully within the plane of the shock, , can produce B B ord ⊥ up to for a single pulse in the GRB light curve, but the integrated emission over many pulses (as P 38%–54% measured in GRB 021206) is expected to be a factor of ∼2 lower. A magnetic field normal to the shock front, , can produce for the emission integrated over many pulses. However, polarization measurements BP ∼ 35%–62% k 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, , that originates at the source can produce the observed Bord polarization most naturally, while is less likely, and is the least likely of the above. BB k
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