Comments on the paper “ Polarimetric Constraints on the Optical Afterglow

GRB 990123 is the most luminous event detected so far, and in an important paper, Hjorth et al. (1999) reported an upper limit on the degree of linear polarization of the optical afterglow for this burst (P < 2.3%). One of the interprtations for this small value of P was that the emission was probably due a relativistic jet with ordered magnetic field, and the viewing angle in the lab frame θ <∼ Γ , where Γ is the bulk Lorentz factor of the jet at the time of the optical emission. We point out that this conclusion resulted from a confusion between the angles measured in the lab frame and in the plasma rest frame. For ordered magnetic field, one would actually obtain a large value of P because the above mentioned angle would correspond to a very large angle, θ <∼ π/2, in the plasma rest frame. And this is probably the case with the blazars. On the other hand, it is indeed possible to have P ≈ 0 if the magnetic field of GRB 990123 was completely chaotic and the viewing angle was considerably smaller than the semi-angle of the jet.