Ambient magnetic field amplification in shock fronts of relativistic jets: an application to GRB afterglows

TL;DR

This study investigates magnetic field amplification at shock fronts of relativistic jets in GRB afterglows, combining analytical estimates and high-resolution RMHD simulations to explain observed magnetic field strengths and correlation lengths.

Contribution

It demonstrates that magnetic field pile-up at the contact discontinuity significantly amplifies fields, surpassing previous models and explaining observed intensities and correlation lengths.

Findings

Magnetic field amplification is mainly due to compression and pile-up at the contact discontinuity.

Maximum correlation length of amplified fields is up to 10^{14} cm, much larger than previous estimates.

Amplification efficiency depends on jet opening angle and ambient-to-jet density ratio.

Abstract

Strong downstream magnetic fields of order of $\sim 1$G, with large correlation lengths, are believed to cause the large synchrotron emission at the afterglow phase of gamma ray bursts (GRBs). Despite of the recent theoretical efforts, models have failed to fully explain the amplification of the magnetic field, particularly in a matter dominated scenario. We revisit the problem by considering the synchrotron emission to occur at the expanding shock front of a weakly magnetized relativistic jet over a magnetized surrounding medium. Analytical estimates and a number of high resolution 2D relativistic magneto-hydrodynamical (RMHD) simulations are provided. Jet opening angles of $\theta = 0^{\circ} - 20^{\circ}$, and ambient to jet density ratios of $10^{-4} - 10^2$ were considered. We found that most of the amplification is due to compression of the ambient magnetic field at the contact discontinuity between the reverse and forward shocks at the jet head, with substantial pile-up of the magnetic field lines as the jet propagates sweeping the ambient field lines. The pile-up is maximum for $\theta \rightarrow 0$, decreasing with $\theta$, but larger than in the spherical blast problem. Values obtained for certain models are able to explain the observed intensities. The maximum correlation lengths found for such strong fields is of $l_{\rm corr} \leq 10^{14}$ cm, $2 - 6$ orders of magnitude larger than the found in previous works.