Coherence scale of magnetic fields generated in early-time forward shocks of GRBs

We report the earliest-ever detection of optical polarization from a GRB forward shock (GRB 141220A), measured $129.5-204.3\,$s after the burst using the multi-colour RINGO3 optical polarimeter on the 2-m fully autonomous robotic Liverpool Telescope. The temporal decay gradient of the optical light curves from $86\,$s to $\sim 2200\,$s post-burst is typical of classical forward shocks with $\alpha = 1.091 \pm 0.008$. The low optical polarization $P_{BV} = 2.8_{- 1.6} ^{+ 2.0} \, \%$ (2$\sigma$) at mean time $\sim 168\,$s post-burst is compatible with being induced by the host galaxy dust ($A_{V, {\rm HG}}= 0.71 \pm 0.15 \,$mag), leaving low polarization intrinsic to the GRB emission itself -- as theoretically predicted for forward shocks and consistent with previous detections of low degrees of optical polarization in GRB afterglows observed hours to days after the burst. The current sample of early-time polarization data from forward shocks suggests polarization from (a) the Galactic and host galaxy dust properties (i.e. $P \sim 1\%-3\%$), (b) contribution from a polarized reverse shock (GRB deceleration time, jet magnetization) or (c) forward shock intrinsic polarization (i.e. $P \leq 2\%$), which depends on the magnetic field coherence length scale and the size of the observable emitting region (burst energetics, circumburst density).