MAGNETIC FIELDS IN RELATIVISTIC COLLISIONLESS SHOCKS

Abstract

We present a systematic study on magnetic fields in gamma-ray burst (GRB) external forward shocks (FSs). There are 60 (35) GRBs in our X-ray (optical) sample, mostly from Swift . We use two methods to study B (fraction of energy in magnetic field in the FS): (1) for the X-ray sample, we use the constraint that the observed flux at the end of the steep decline is ⩾ X-ray FS flux; (2) for the optical sample, we use the condition that the observed flux arises from the FS (optical sample light curves decline as ∼ t −1 , as expected for the FS). Making a reasonable assumption on E (jet isotropic equivalent kinetic energy), we converted these conditions into an upper limit (measurement) on B n 2/( p + 1) for our X-ray (optical) sample, where n is the circumburst density and p is the electron index. Taking n = 1 cm −3 , the distribution of B measurements (upper limits) for our optical (X-ray) sample has a range of ∼10 −8 –10 −3 (∼10 −6 –10 −3 ) and median of ∼few × 10 −5 (∼few × 10 −5 ). To characterize how much amplification is needed, beyond shock compression of a seed magnetic field ∼10 μG, we expressed our results in terms of an amplification factor, AF, which is very weakly dependent on n (AF∝ n 0.21 ). The range of AF measurements (upper limits) for our optical (X-ray) sample is ∼1–1000 (∼10–300) with a median of ∼50 (∼50). These results suggest that some amplification, in addition to shock compression, is needed to explain the afterglow observations.