Long-Time Evolution of Magnetic Fields in Relativistic Gamma-Ray Burst Shocks

Abstract

We investigate the long-time evolution of magnetic fields generated by the two-stream instability at ultra-and sub-relativistic astrophysical collisionless shocks. Based on 3D PIC simulation results, we introduce a 2D toy model of interacting current filaments. Within the framework of this model, we demonstrate that the field correlation scale in the region far downstream the shock grows nearly as the light crossing time, λ(t) ∼ ct, thus making the diffusive field dissipation inefficient. The obtained theoretical scaling is tested using numerical PIC simulations. This result extends our understanding of the structure of collisionless shocks in gamma-ray bursts and other astrophysical objects.

Are Gamma‐Ray Burst Shocks Mediated by the Weibel Instability?

“…On the contrary, such a small-scale magnetic field should decay (Gruzinov 2001). There is evidence for hierarchical merging of current filaments (Silva et al 2003;Frederiksen et al 2004;Medvedev et al 2005;Kato 2005), so might exceed unity. However, at the scale larger than the electron Larmor radius, which is of the order of $1/( 1/2 pp ), the field is already frozen into the electron gas; therefore, could hardly ever grow significantly beyond unity.…”

“…Many authors have therefore assumed that the shock somehow manufactures field energy to meet this requirement, but no convincing mechanism has been proposed to date. One mechanism discussed is the Weibel instability ( Medvedev & Loeb 1999;Silva et al 2003;Frederiksen et al 2004;Jaroschek et al 2005;Medvedev et al 2005;Kato 2005;Nishikawa et al 2005), which has the fastest growth rate and produces relatively strong small-scale magnetic field even in an initially nonmagnetized plasma. It is expected that the thermalization of the upstream flow could occur via scattering of particles on the magnetic fluctuations.…”

Shock Vorticity Generation from Accelerated Ion Streaming in the Precursor of Ultrarelativistic Gamma‐Ray Burst External Shocks

“…If, however, efficient compression commences only where the upstream interpenetrates the downstream thermalized plasma, the width of the compression layer may be as small as of the order of the skin depth. While in the preceding regions we expect a decrease in the mean magnetic field correlation length hki hkB 2 (k)i/hB 2 (k)i as the plasma approaches the shock, in the shock transition region we expect an opposite trend: the small-scale instabilities have reached saturation and the small field they have generated decays via a kinetic damping mechanism as the shocked plasma travels downstream (Gruzinov 2001;Medvedev et al 2005;Chang et al 2008;Keshet et al 2008;Spitkovsky 2008b). As the small-scale field decays, the residual field, which partakes in the synchrotron emission of the GRB afterglows (see, e.g., Panaitescu & Kumar 2002;Yost et al 2003) and must be much stronger than the shock-compressed preexisting magnetic field of the normal interstellar medium (see, e.g., Gruzinov 2001;Piran 2005b), is the larger scale field generated in regions 1Y3 above.…”

“…On the other hand, since max is much larger than the plasma skin depth c/! pla , the magnetic field that the turbulent dynamo generates will not be susceptible to the fast collisionless decay discussed by Chang et al (2008) that affects the much smaller scale field that kinetic instabilities can generate in the shock transition layer (e.g., Gruzinov 2001; Frederiksen et al 2004;Medvedev et al 2005;Keshet et al 2008;Spitkovsky 2008b and references therein).…”

Plasma Instabilities in Gamma‐Ray Bursts: Neutral Points and the Effect of Mode Coupling

“…This approach is also justified from the scenario in which magnetic fields are produced via the two-stream instability in the internal shocks of shells ejected from the source at different velocities (Medvedev & Loeb 1999). Because this instability grows very rapidly (Medvedev et al 2005), the system already carries a strong magnetic field when propagating into the surrounding interstellar medium (the so-called external shocks), which can be seen as the starting point for our investigation.…”