Monte Carlo Simulations of Nonlinear Particle Acceleration in Parallel Trans-relativistic Shocks

TL;DR

This paper uses Monte Carlo simulations to study particle acceleration in shocks across nonrelativistic, trans-relativistic, and relativistic regimes, revealing how efficiency and shock structure change with shock speed.

Contribution

It introduces a simulation framework that models the transition between relativistic and nonrelativistic shocks, highlighting the impact on acceleration efficiency and shock compression ratios.

Findings

Acceleration efficiency varies significantly across shock regimes.

Shock smoothing reduces acceleration efficiency in ultra-relativistic shocks.

Transition occurs around shock Lorentz factor of 1.5.

Abstract

We present results from a Monte Carlo simulation of a parallel collisionless shock undergoing particle acceleration. Our simulation, which contains parameterized scattering and a particular thermal leakage injection model, calculates the feedback between accelerated particles ahead of the shock, which influence the shock precursor and "smooth" the shock, and thermal particle injection. We show that there is a transition between nonrelativistic shocks, where the acceleration efficiency can be extremely high and the nonlinear compression ratio can be substantially greater than the Rankine-Hugoniot value, and fully relativistic shocks, where diffusive shock acceleration is less efficient and the compression ratio remains at the Rankine-Hugoniot value. This transition occurs in the trans-relativistic regime and, for the particular parameters we use, occurs around a shock Lorentz factor = 1.5. We also find that nonlinear shock smoothing dramatically reduces the acceleration efficiency presumed to occur with large-angle scattering in ultra-relativistic shocks. Our ability to seamlessly treat the transition from ultra-relativistic to trans-relativistic to nonrelativistic shocks may be important for evolving relativistic systems, such as gamma-ray bursts and type Ibc supernovae. We expect a substantial evolution of shock accelerated spectra during this transition from soft early on to much harder when the blast-wave shock becomes nonrelativistic.