Long-Term Evolution of Magnetic Turbulence in Relativistic Collisionless Shocks: Electron-Positron Plasmas

By P. Chang, A. Spitkovsky, J. Arons. 2007

172 citations recorded by the source corpus.

We study the long term evolution of magnetic fields generated by an initially unmagnetized collisionless relativistic e+e− shock. Our two-dimensional particle-in-cell numerical simulations show that downstream of such a Weibel-mediated shock, particle distributions are approximately isotropic, relativistic Maxwellians, and the magnetic turbulence is highly intermittent spatially. The nonpropagating magnetic fields decay in amplitude and do not merge. The fields start with magnetic energy density ~ 0.1-0.2 of equipartition, but rapid downstream decay drives the fields to much smaller values, below ~10−3 of equipartition after ~103 skin depths. To construct a theory to follow field decay to these smaller values, we hypothesize that the observed damping is a variant of Landau damping. The model is based on the small value of the downstream magnetic energy density, which only weakly perturbs particle orbits, for homogeneous turbulence. Using linear kinetic theory, we find a simple analytic form for the damping rates for small-amplitude, subluminous electromagnetic fields. Our theory predicts that overall magnetic energy decays as (ωpt)−q with q ∼ 1, which compares with simulations. However, our theory predicts overly rapid damping of short-wavelength modes. Magnetic trapping of particles within the highly spatially intermittent downstream magnetic structures may be the origin of this discrepancy and may allow for some of this initial magnetic energy to persist. Absent additional physical processes that create longer wavelength, more persistent fields, we conclude that initially unmagnetized relativistic shocks in electron-positron plasmas are unable to form persistent downstream magnetic fields. These results put interesting constraints on synchrotron models for the prompt and afterglow emission from GRBs. We also comment on the relevance of these results for relativistic electron-ion shocks.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/80b5474997fb0d369cb91e2062d6e61535db27f5

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In Astronomy and Astrophysics

1. B. Metzger
2. Bing Zhang
3. E. Berger
4. L. Sironi
5. E. Quataert
6. Pawan Kumar
7. D. Giannios
8. A. Spitkovsky

In Nuclear and High Energy Physics

1. L. Sironi
2. A. Spitkovsky
3. D. Giannios
4. Bing Zhang
5. B. Metzger
6. J. Arons
7. E. Berger
8. U. Keshet

Citations in the corpus

• Nonrelativistic Collisionless Shocks in Unmagnetized Electron-Ion Plasmas (2008, background): “…simulations showed that the “Weibel-mediated” collisionless shocks can form at relativistic propagation speed in electron-positron plasmas (Kato 2007; Chang et al. 2008) and also in electron-ion plasmas (Spitkovsky 2008) without a background magnetic field; in these shocks the dissipation…”
• The Binary Neutron Star Event LIGO/Virgo GW170817 160 Days after Merger: Synchrotron Emission across the Electromagnetic Spectrum (2018, result): “These findings are consistent with the picture favored by magnetic field self-generated by the shock is not uniform in the post-shock region, but decays away from the shock (e.g., Spitkovsky 2008; Chang et al. 2008; Keshet et al. 2009; Martins et al. 2009; Haugbølle 2011; Sironi et al. 2013).”
• PARTICLE ACCELERATION IN RELATIVISTIC MAGNETIZED COLLISIONLESS ELECTRON–ION SHOCKS (2010, background): “Multi-dimensional PIC simulations of relativistic unmagnetized shocks have been presented by Spitkovsky (2005) for electron-positron flows (see also Chang et al. 2008; Keshet et al. 2009; Haugboelle 2010), and by Spitkovsky (2008a) for electron-ion flows.”
• WEIBEL, TWO-STREAM, FILAMENTATION, OBLIQUE, BELL, BUNEMAN...WHICH ONE GROWS FASTER? (2009, background): “…are currently extensively studied by means of PIC simulations (Medvedev & Loeb 1999; Silva et al. 2003; Nishikawa et al. 2003; Milosavljevic et al. 2006; Chang et al. 2008; Spitkovsky 2008a, 2008b; Martins et al. 2009), due to their role in the Fireball model for gamma-ray bursts (Piran 2000).”
• The physics of gamma-ray bursts & relativistic jets (2014, background): “This might be the reason for the small average AF inferred from afterglow observations; numerical simulations [388,389,387], and analysis of GRB afterglow data [390] support this general picture of strong field near the shock front and their decay down-stream.”
• PARTICLE ACCELERATION IN RELATIVISTIC MAGNETIZED COLLISIONLESS PAIR SHOCKS: DEPENDENCE OF SHOCK ACCELERATION ON MAGNETIC OBLIQUITY (2009, background): “PIC simulations of relativistic unmagnetized shocks have been presented by Spitkovsky (2005, 2008a), Chang et al. (2008) and Keshet et al. (2008); Spitkovsky (2008b) has shown that unmagnetized shocks naturally produce accelerated particles as part of the shock evolution.”
• THE MAXIMUM ENERGY OF ACCELERATED PARTICLES IN RELATIVISTIC COLLISIONLESS SHOCKS (2013, background): “Since the decay length of the Weibel turbulence in the downstream is still a matter of debate (Chang et al. 2008; Keshet et al. 2009), here we take LB,sat as our best estimate for the overall thickness of the turbulent region around the shock, including both upstream and downstream.”
• Particle Acceleration in Relativistic Collisionless Shocks: Fermi Process at Last? (2008, background): “PIC simulations of colliding relativistic shells have confirmed the general picture of the initial stages of the instability (Kazimura et al. 1998; Nishikawa et al. 2003, 2005; Silva et al. 2003; Frederiksen et al. 2004; Hededal et al. 2004), and have been evolved through the shock formation stage i”
• THE COSMOLOGICAL IMPACT OF LUMINOUS TeV BLAZARS. I. IMPLICATIONS OF PLASMA INSTABILITIES FOR THE INTERGALACTIC MAGNETIC FIELD AND EXTRAGALACTIC GAMMA-RAY BACKGROUND (2011, background): “Initially, the Weibel instability rapidly grows until the energy density of the generated magnetic field becomes of order the kinetic energy of the two beams (Silva et al. 2003; Frederiksen et al. 2004; Chang et al. 2008).”
• Relativistic Shocks: Particle Acceleration and Magnetization (2015, background): “2, one notably expects this turbulence to relax through collisionless damping on hundreds of c/ωp (Chang et al. 2008; Keshet et al. 2009; Lemoine 2015) while the electrons typically cool on much longer length scales.”
• The physics of galactic winds driven by active galactic nuclei (2012, background): “Importantly, though, the same simulations show that magnetic turbulence decays rapidly in the post-shock region (Chang et al. 2008).”