Linear Polarization in GRB Afterglows: The Case for an Ordered Magnetic Field

Linear polarization at the level of $\sim 1-3%$ has by now been measured in several gamma-ray burst (GRB) afterglows. Whereas the degree of polarization, $P$, was found to vary in some sources, the position angle, $\theta_p$, was roughly constant in all cases. Until now, the polarization has been commonly attributed to synchrotron radiation from a jet with a tangled magnetic field that is viewed somewhat off axis. However, such a model predicts a $90^\circ$ change in $\theta_p$ around the ``jet break'' time in the lightcurve, for which there has so far been no observational confirmation. We propose an alternative interpretation, wherein the polarization is attributed, at least in part, to a large-scale, ordered magnetic field in the medium into which the afterglow-emitting shock propagates. This field component is amplified by compression (possibly enhanced by cooling) in the shock, and may dominate the measured polarization. The total emissivity is, however, likely dominated by a tangled field component generated by postshock turbulence. In this picture, the near constancy of $\theta_p$ is a consequence of the approximate uniformity of the ambient field direction, whereas the observed variations in $P$ result from expected changes in the ratio of the ordered-to-random mean-squared field amplitudes. The radiation from the original ejecta, which includes the prompt $\gamma$-ray emission and the emission from the reverse shock (the 'optical flash' and 'radio flare'), could potentially exhibit a high degree of polarization (up to $\sim 60%$) induced by an ordered transverse magnetic field advected from the central source.