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

Ramandeep Gill; Jonathan Granot

doi:10.1093/mnras/stz3340

paper

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

arXiv:1910.05687 · doi:10.1093/mnras/stz3340

Abstract

Gamma-ray burst afterglows arise from relativistic collisionless shocks in which the postshock tangled magnetic field $B$ is produced by the two-stream and/or Weibel instabilities on plasma skin-depth scales $(c / ω_{p})$ . The field is expected to be oriented predominantly within the shock plane ( $B_{⊥}$ ; transverse to the shock normal, $n^_{sh}$ ), and is often approximated to be completely within it ( $B_{∥} \equiv n^_{sh} \cdot B = 0$ ). Current 2D/3D particle-in-cell simulations are limited to short timescales and box sizes $≲ 1 0^{4} (c / ω_{p}) ≪ R / Γ_{sh}$ much smaller than the shocked region's comoving width, and cannot probe the asymptotic downstream $B$ structure. We constrain the latter using the linear polarization upper limit, $∣Π∣ < 12%$ , on the radio afterglow of GW170817/GRB170817A. Afterglow polarization depends on the jet's angular structure, our viewing angle, and the $B$ structure. In GW170817/GRB170817A the latter can be tightly constrained since the former two are constrained from observations. We model $B$ as an isotropic field in 3D that is stretched along $n^_{sh}$ by a factor $ξ \equiv B_{∥} / B_{⊥}$ , whose initial value $ξ_{f} \equiv B_{∥, f} / B_{⊥, f}$ describes the field that survives downstream on plasma scales $≪ R / Γ_{sh}$ . We calculate $Π (ξ_{f})$ 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, $B$ has a finite, but initially sub-dominant, parallel component: $0.57 ≲ ξ_{f} ≲ 0.89$ , 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.

arXiv comment11 pages, 6 figures, Accepted to MNRAS

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

Abstract

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