Early-time polarized optical light curve of GRB 131030A

We report the polarized optical light curve of a gamma-ray burst afterglow obtained using the RoboPol instrument. Observations began 655 seconds after the initial burst of gamma-rays from GRB131030A, and continued uninterrupted for 2 hours. The afterglow displayed a low, constant fractional linear polarization of $p = (2.1 \pm 1.6)\,\%$ throughout, which is similar to the interstellar polarization measured on nearby stars. The optical brightness decay is consistent with a forward-shock propagating in a medium of constant density, and the low polarization fraction indicates a disordered magnetic field in the shock front. This supports the idea that the magnetic field is amplified by plasma instabilities on the shock front. These plasma instabilities produce strong magnetic fields with random directions on scales much smaller than the total observable region of the shock, and the resulting randomly-oriented polarization vectors sum to produce a low net polarization over the total observable region of the shock.