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 epsilonB (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 the 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 epsilonB n2/(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 epsilonB 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 x 10-5 (~few x 10-5). To characterize how much amplification is needed, beyond shock compression of a seed magnetic field ~10 muG, we expressed our results in terms of an amplification factor, AF, which is very weakly dependent on n (AF propto n0.21 ). 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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