Constraining the magnetic field structure in collisionless relativistic shocks with a radio afterglow polarization upper limit in GW 170817

Gamma-ray burst (GRB) afterglow arises from a relativistic shock driven into the ambient medium, which generates tangled magnetic fields and accelerates relativistic electrons that radiate the observed synchrotron emission. In relativistic collisionless shocks the post-shock magnetic field {B} is produced by the two-stream and/or Weibel instabilities on plasma skin-depth scales, and is oriented predominantly within the shock plane; transverse to the shock normal and is often approximated to be completely within it Current 2D/3D particle-in-cell simulations are limited to short time-scales and box sizes much smaller than the shocked region's comoving width, and hence cannot probe the asymptotic downstream {B} structure. We constrain the latter using the linear polarization upper limit, cent}}, on the radio afterglow of GW 170817 GRB 170817A. Afterglow polarization depends on the jet's angular structure, our viewing angle, and the {B} structure. In GW 170817 GRB 170817A the latter can be tightly constrained since the former two are well-constrained by its exquisite observations. We model {B} as an isotropic field in 3D that is stretched along by a factor ζ, whose initial value ζf, describes the field that survives downstream on plasma scales sh. We calculate Π(ζf) by integrating over the entire shocked volume for a Gaussian or power-law core-dominated structured jet, with a local Blandford-McKee self-similar radial profile (used for evolving ζ downstream). We find that independent of the exact jet structure, {B} has a finite, but initially sub-dominant, parallel component: 0.57 0.89, making it less anisotropic. While this motivates numerical studies of the asymptotic {B} structure in relativistic collisionless shocks, it may be consistent with turbulence amplified magnetic field.