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

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, ${\hat{n}}_{\mathrm{sh}}$), and is often approximated to be completely within it ($B_{\parallel }\equiv {\hat{n}}_{\mathrm{sh}}\cdot \vec{B}=0$). Current 2D/3D particle-in-cell simulations are limited to short timescales and box sizes $\lesssim 10^4(c/{\omega }_p)\ll R/{\Gamma }_{\mathrm{sh}}$ 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 ${\hat{n}}_{\mathrm{sh}}$ 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 $\ll R/{\Gamma }_{\mathrm{sh}}$. 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: $0.57\lesssim {\xi }_f\lesssim 0.89$, 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.

11 pages, 6 figures, Accepted to MNRAS

References in corpus (15)

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• The optical afterglow of GW170817 at one year post-merger
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• Synchrotron emission in the fast cooling regime: which spectra can be explained?
• Non-linear collisionless damping of Weibel turbulence in relativistic blast waves
• Shock Vorticity Generation from Accelerated Ion Streaming in the Precursor of Ultrarelativistic Gamma-Ray Burst External Shocks

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