On electron acceleration by mildly-relativistic shocks: PIC simulations

Radio observations revealed a presence of relativistic supernovae - a class of objects intermediate between the regular supernovae and gamma-ray bursts. The typical Lorentz-factors of plasma flows in relativistic radio-bright supernovae were estimated to be about 1.5. Mildly relativistic shocks in electron-ion plasmas are known to efficiently accelerate radio-emitting electrons if the shock is subluminous. The inclination angle of the velocity of subluminous shock to the ambient magnetic field should be below a critical angle which depends on the Mach number and the plasma magnetization parameter. In this paper we present particle-in-cell modeling of electron acceleration by mildly-relativistic collisionless shock of different obliquity in a plasma with ratio of the magnetic energy to the bulk kinetic energy σ ≈ 0.004 which is of interest for the relativistic supernovae modeling. It was shown earlier that a development of the ion scale Bell-type instability in electron-ion relativistic shock may have a strong influence on the electron injection and acceleration. In the time period of about 1500 ω p i − 1 ( ω pi is the ion plasma frequency) after the shock initialization the magnetic field fluctuations generated by Bell’s instability may significantly decreases number of accelerated electrons even in a sub-luminous shock. We study here the evolution of the electron spectra of subluminous shocks of different obliquity. This is important to for modeling of synchrothron spectra from relativistic supernovae.