Abstract
Mon. Not. Roy. Astron. Soc. 442 (2014) 3147-3154 Using GRB radio afterglow observations, we calculate the fraction of shocked
plasma energy in the magnetic field in relativistic collisionless shocks
($\epsilon_B$). We obtained $\epsilon_B$ 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, $f_p$, which is
$f_p \propto \epsilon_B^{1/2}$. The obtained value of $\epsilon_B$ is
conservatively a minimum if the time of the "jet break" is unknown, since after
the "jet break" $f_p$ 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 $\epsilon_B$. Our results depend on the blast
wave total energy, $E$, and the density of the circum-stellar medium (CSM),
$n$, as $\epsilon_B \propto E^{-2}n^{-1}$. However, by assuming a CSM magnetic
field ($\sim 10$ $\mu$G), we can express the lower limits/measurements on
$\epsilon_B$ as a density-independent ratio, $B/B_{sc}$, 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 $B/B_{sc}$ spans
$\sim 3.5$ orders of magnitude and both have a median of $B/B_{sc} \sim 30$.
This suggests that some amplification, beyond simple shock-compression, is
necessary to explain these radio afterglow observations.