Afterglows of gamma-ray bursts (GRBs) are emitted from expanding forward shocks, which are expected to have magnetic fields much stronger than the interstellar field, although the origin of the field is a long-standing problem. Two field amplification mechanisms, plasma kinetic instabilities and magnetohydrodynamic instabilities, have been discussed so far. The coherence-length scales of the fields amplified by these two processes are different by 7–10 orders of magnitude, and the polarimetric observations may distinguish them. We construct a semi-analytic model of the forward-shock afterglow polarization under the assumption of hydrodynamic-scale turbulent magnetic field. We perform numerical calculations of synchrotron polarization for the isotropic turbulence and the zero viewing angle. We find that the polarization degrees are ∼1% when the field coherence-length scale in the fluid co-moving frame is of the order of the thickness of the shocked regions. This range of polarization degree is comparable to that of the observed late-phase optical afterglows. Our model also shows that the radio polarization degrees are comparable to the optical ones on average but can be higher than the optical ones at some time intervals. The polarization angles are shown to vary randomly and continuously. These polarimetric properties are clearly different from the case of plasma kinetic instability. Simultaneous polarimetric observations of GRB afterglows at the radio and optical bands have recently started, which will help us constrain the magnetic field amplification mechanism.

Gamma-ray bursts (GRBs) are the most luminous transients in the universe and are utilized as probes of early stars, gravitational wave counterparts, and collisionless shock physics.

Gamma-ray bursts (GRBs) are the most luminous gamma-ray transients in the universe, and are utilized as probes of early stars, gravitational wave counterparts, and collision less shock physics. For understanding the fundamental physical quantities of GRB jets and their environments as well as their emission mechanism, coordinated multi-wavelength (semi-)simultaneous measurements are crucial as the global communities demonstrated in the past three decades. In spite of studies on polarimetry of GRBs in individual wavelengths that characterized intriguing properties of prompt emission and afterglow, no coordinated multi-wavelength measurements has yet been performed. Here, we report the first coordinated simultaneous polarimetry in the optical and radio bands for the afterglow associated to the typical long GRB 191221B. Our observations successfully caught the radio emission, which is not affected by synchrotron self-absorption, and show that the emission is depolarized in the radio band in comparison with the optical one. This result excludes a simple one-zone model that the polarization degree is nearly constant above the synchrotron self-absorption frequency, and has important implications for plasma-scale turbulent magnetic fields and existence of cool electrons. Our simultaneous polarization angle measurement supports the latter model rather than the former one. The existence of cool electrons increases the estimate of the total jet energy by a factor of > 2 for this typical GRB. Further coordinated multi-wavelength polarimetric campaigns would improve our understanding of the total jet energies and magnetic field configurations in the emission regions of various types of GRBs, which are required to comprehend the mass scales of their progenitor systems and the physics of collisionless shocks.

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