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.
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