Polarization lightcurves and position angle variation of beamed gamma-ray bursts

The recently detected linear polarization in the optical lightcurve of GRB 990510 renewed the interest on how polarization can be produced in gamma-ray burst fireballs. Here we present a model based on the assumption that we are seeing a collimated fireball, observed slightly off-axis. This introduces some degree of anisotropy, and makes it possible to observe a linearly polarized flux even if the magnetic field is completely tangled in the plane orthogonal to the line of sight. We construct the lightcurve of the polarization flux, showing that it is always characterized by two maxima, with the polarization position angle changing by 90 deg. between the first and the second maximum. The very same geometry here assumed implies that the total flux initially decays in time as a power law, but gradually steepens as the bulk Lorentz factor of the fireball decreases.