Particle acceleration in relativistic magnetized collisionless electron-ion shocks

Lorenzo Sironi, Anatoly Spitkovsky

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159 Scopus citations


We investigate shock structure and particle acceleration in relativistic magnetized collisionless electron-ion shocks by means of 2.5-dimensional particle-in-cell simulations with ion-to-electron mass ratios (m i/me) ranging from 16 to 1000. We explore a range of inclination angles between the pre-shock magnetic field and the shock normal. In "subluminal" shocks, where relativistic particles can escape ahead of the shock along the magnetic field lines, ions are efficiently accelerated via the first-order Fermi process. The downstream ion spectrum consists of a relativistic Maxwellian and a high-energy power-law tail, which contains ∼5% of ions and ∼30% of ion energy. Its slope is-2.1±0.1. The scattering is provided by short-wavelength non-resonant modes produced by Bell's instability, whose growth is seeded by the current of shock-accelerated ions that propagate ahead of the shock. Upstream electrons enter the shock with lower energy than ions (albeit by only a factor of ∼5 ≪ mi/me), so they are more strongly tied to the field. As a result, only ∼1% of the incoming electrons are accelerated at the shock before being advected downstream, where they populate a steep power-law tail (with slope-3.5 ± 0.1). For "superluminal" shocks,where relativistic particles cannot outrun the shock along the field, the self-generated turbulence is not strong enough to permit efficient Fermi acceleration, and the ion and electron downstream spectra are consistent with thermal distributions. The incoming electrons are heated up to equipartition with ions, due to strong electromagnetic waves emitted by the shock into the upstream. Thus, efficient electron heating (≳15% of the upstream ion energy) is the universal property of relativistic electron-ion shocks, but significant nonthermal acceleration of electrons (≳2% by number, ≳10% by energy, with slope flatter than-2.5) is hard to achieve in magnetized flows and requires weakly magnetized shocks (magnetization s ≲ 10-3), where magnetic fields self-generated via theWeibel instability are stronger than the background field. These findings place important constraints on the models of gamma-ray bursts and jets from active galactic nuclei that invoke particle acceleration in relativistic magnetized electron-ion shocks.

Original languageEnglish (US)
JournalAstrophysical Journal
Issue number2
StatePublished - Jan 10 2011

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Acceleration of particles
  • Cosmic rays
  • Galaxies: jets
  • Gamma-ray burst: general
  • Shock waves


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