Magnetic Fields In Relativistic Collisionless Shocks

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 is an element of(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 similar to 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 is an element of(n2/(p+1))(B) 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 is an element of(B) measurements (upper limits) for our optical (X-ray) sample has a range of similar to 10 (8)-10 (3) (similar to 10 (6)-10 (3)) and median of similar to few x 10 (5) (similar to few x 10 (5)). To characterize how much amplification is needed, beyond shock compression of a seed magnetic field similar to 10 mu G, we expressed our results in terms of an amplification factor, AF, which is very weakly dependent on n (AF alpha n(0.21)). The range of AF measurements (upper limits) for our optical (X-ray) sample is similar to 1-1000 (similar to 10-300) with a median of similar to 50 (similar to 50). These results suggest that some amplification, in addition to shock compression, is needed to explain the afterglow observations.