Constraining the magnetic field structure in collisionless relativistic shocks with a radio afterglow polarization upper limit in GW170817

TL;DR

This paper uses radio polarization limits from GW170817 to constrain the magnetic field structure in relativistic shocks, finding the magnetic field has a significant parallel component, informing models of shock magnetic turbulence.

Contribution

It introduces a method to constrain downstream magnetic field anisotropy using polarization upper limits, bridging simulation limitations and observational data.

Findings

The parallel magnetic field component is constrained to be between 0.57 and 0.89 times the perpendicular component.

The magnetic field is less anisotropic than previously assumed, with a significant parallel component.

Results suggest the magnetic field may be consistent with turbulence amplification mechanisms.

Abstract

Gamma-ray burst afterglows arise from relativistic collisionless shocks in which the postshock tangled magnetic field $\vec{B}$ is produced by the two-stream and/or Weibel instabilities on plasma skin-depth scales $(c/\omega_p)$. The field is expected to be oriented predominantly within the shock plane ($B_{\perp}$; transverse to the shock normal, $\hat{n}_{\rm{sh}}$), and is often approximated to be completely within it ($B_\parallel\equiv\hat{n}_{\rm{sh}}\,\cdot\,\vec{B}=0$). Current 2D/3D particle-in-cell simulations are limited to short timescales and box sizes $\lesssim10^4(c/\omega_p)\ll R/\Gamma_{\rm{sh}}$ much smaller than the shocked region's comoving width, and cannot probe the asymptotic downstream $\vec{B}$ structure. We constrain the latter using the linear polarization upper limit, $|\Pi|<12\%$, on the radio afterglow of GW170817/GRB170817A. Afterglow polarization depends on the jet's angular structure, our viewing angle, and the $\vec{B}$ structure. In GW170817/GRB170817A the latter can be tightly constrained since the former two are constrained from observations. We model $\vec{B}$ as an isotropic field in 3D that is stretched along $\hat{n}_{\rm{sh}}$ by a factor $\xi\equiv{}B_{\parallel}/B_{\perp}$, whose initial value $\xi_f\equiv{}B_{\parallel,f}/B_{\perp,f}$ describes the field that survives downstream on plasma scales $\ll{}R/\Gamma_{\rm{sh}}$. We calculate $\Pi(\xi_f)$ by integrating over the shocked volume for core-dominated structured jets, with a local Blandford-McKee self-similar radial profile. We find that independent of the exact jet structure, $\vec{B}$ has a finite, but initially sub-dominant, parallel component: $0.57\lesssim\xi_f\lesssim0.89$, making it less anisotropic. While this motivates numerical studies of the asymptotic $\vec{B}$ structure in relativistic collisionless shocks, it may be consistent with turbulence amplified magnetic field.