Constraining the magnetic field structure in collisionless relativistic shocks with a radio afterglow polarization upper limit in GW 170817. Issue 4 (28th November 2019)

• Record Type: Journal Article
• Authors: Gill, Ramandeep; Granot, Jonathan
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 491:Issue 4(2020)
• Page Start: 5815
• Page End: 5825
• Publication Date: 2019-11-28
• Subjects: magnetic fields -- plasmas -- polarization -- relativistic processes -- shock waves -- gamma-ray burst: individual: GRB 170817A/GW 170817; Astronomy -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnras/stz3340
• Languages: English
• ISSNs: 0035-8711

Abstract

ABSTRACT: 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 $\boldsymbol {B}$ is produced by the two-stream and/or Weibel instabilities on plasma skin-depth scales ( c /ω p ), and is oriented predominantly within the shock plane ( B ⊥ ; transverse to the shock normal, $\hat{\boldsymbol {n}}_{\rm {sh}}$ ), and is often approximated to be completely within it ($B_\parallel \equiv \hat{\boldsymbol {n}}_{\rm {sh}}\, \cdot \, \boldsymbol {B}=0$ ). Current 2D/3D particle-in-cell simulations are limited to short time-scales and box sizes ≲10 4 ( c /ω p ) ≪ R /Γsh much smaller than the shocked region's comoving width, and hence cannot probe the asymptotic downstream $\boldsymbol {B}$ structure. We constrain the latter using the linear polarization upper limit, $\vert \Pi \vert \lt 12{{\ \rm per\ cent}}$, on the radio afterglow of GW $170817$ / GRB 170817A. Afterglow polarization depends on the jet's angular structure, our viewing angle, and the $\boldsymbol {B}$ 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 $\boldsymbol {B}$ as an isotropic field in 3D that is stretched along $\hat{\boldsymbol {n}}_{\rm {sh}}$ by a factor ξ ≡ $B_\parallel $ / B ⊥, whose initial value ξ f ≡ $B_\parallel, $ f / B ⊥, f describes the field that survives downstream on plasma scales ≪ R /Γsh . We calculate Π(ξ f ) 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 ξ downstream). We find that independent of the exact jet structure, $\boldsymbol {B}$ 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 $\boldsymbol {B}$ structure in relativistic collisionless shocks, it may be consistent with turbulence amplified magnetic field.