Constraining the magnetic field in GRB relativistic collisionless shocks using radio data

Abstract

Using gamma-ray burst (GRB) radio afterglow observations, we calculate the fraction of shocked plasma energy in the magnetic field in relativistic collisionless shocks (∈B). We obtained ∈B for 38 bursts by assuming that the radio afterglow light curve originates in the external forward shock, and that its peak at a few to tens of days is due to the passage of the minimum (injection) frequency through the radio band. This allows for the determination of the peak synchrotron flux of the external forward shock, fp, which is fp α ∈ 1/2 B . The obtained value of ∈B is conservatively a minimum if the time of the 'jet break' is unknown, since after the 'jet break' fp is expected to decay with time faster than before it. Claims of 'jet breaks' have been made for a subsample of 23 bursts, for which we can estimate a measurement of ∈B. Our results depend on the blast wave total energy, E, and the density of the circumstellar medium (CSM), n, as ∈B α E-2n-1. However, by assuming a CSM magnetic field (~10 μG), we can express the lower limits/measurements on ∈B as a density-independent ratio, B/Bsc, of the magnetic field behind the shock to the CSM shock-compressed magnetic field.We find that the distribution on both the lower limit on and the measurement of B/Bsc spans ~3.5 orders of magnitude and both have a median of B/Bsc ~ 30. This suggests that some amplification, beyond simple shock compression, is necessary to explain these radio afterglow observations. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.