Gamma-Ray Burst Afterglow: Polarization and Analytic Light Curves

GRB afterglow polarization is discussed. We find an observable, up to 10%, polarization, if the magnetic field coherence length grows at about the speed of light after the field is generated at the shock front. Detection of a polarized afterglow would show that collisionless ultrarelativistic shocks can generate strong large scale magnetic fields and confirm the synchrotron afterglow model. Non-detection, at a 1% level, would imply that either the synchrotron emission model is incorrect, or that strong magnetic fields, after they are generated in the shock, somehow manage to stay un-dissipated at ``microscopic'', skin depth, scales. Analytic lightcurves of synchrotron emission from an ultrarelativistic self-similar blast wave are obtained for an arbitrary electron distribution function, taking into account the effects of synchrotron cooling. The peak synchrotron flux and the flux at frequencies much smaller than the peak frequency are insensitive to the details of the electron distribution function; hence their observational determination would provide strong constraints on blast wave parameters.