2014ApJ...785...29S

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 ε_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 ε_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/cm3, the distribution of ε_Bmeasurements (upper limits) for our optical (X-ray) sample has a range of ∼10^–8-10^–3 (∼10^–6-10^–3) and median of ∼fewx10^–5 (∼fewx10^–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.