Magnetic Field Amplification and Particle Acceleration in Weakly Magnetized Transrelativistic Electron–Ion Shocks

Key findings from this study

• The study found that shock precursor structure transitions from Bell instability dominance at magnetizations above approximately 10^-3 to Weibel instability dominance below approximately 10^-4.
• The authors report that Bell-dominated shocks convert roughly 20 percent of upstream energy into nonthermal ions with Bohm scaling but accelerate electrons much less efficiently.
• The researchers demonstrate that Weibel-dominated shocks produce comparable nonthermal ion and electron fractions of approximately 10 percent each, with maximum energy scaling as the square root of time.

Overview

This study examines the microphysics of quasi-parallel transrelativistic shocks in weakly magnetized plasmas using long-duration two-dimensional particle-in-cell simulations. The research identifies a transition between two distinct regimes governed by competing plasma instabilities that shape the shock precursor structure. At relatively high magnetizations, the Bell instability dominates, whereas at lower magnetizations, the Weibel instability prevails. The findings characterize how these regimes differ in particle acceleration efficiency and maximum energy scaling for both ions and electrons. The results apply to astrophysical contexts including extragalactic jet termination shocks, late-stage gamma-ray burst afterglows, and fast blue optical transients.

Methods and approach

The authors conducted two-dimensional particle-in-cell simulations using the OSIRIS code to investigate transrelativistic shocks with expected Lorentz factors of approximately a few. The simulations examined quasi-parallel shock configurations propagating through weakly magnetized plasmas across a range of magnetization parameters. Long-duration runs enabled characterization of shock precursor structure and particle acceleration over extended timescales. The computational approach allowed direct comparison of Bell instability and Weibel instability contributions to magnetic field amplification and energy conversion into nonthermal particle populations.

Results

The simulations reveal a clear transition between two instability-dominated regimes at a magnetization threshold near σ between 10^-4 and 10^-3. In the Bell-dominated regime at higher magnetizations (σ ≳ 10^-3), shocks convert approximately 20 percent of upstream flow energy into downstream nonthermal ion energy, with nonthermal ion maximum energy exhibiting Bohm scaling proportional to time. Electron acceleration in this regime is substantially less efficient, with energy conversion fractions well below 10 percent.

In the Weibel-dominated regime at lower magnetizations (σ ≲ 10^-4), both ions and electrons achieve comparable nonthermal energy fractions of approximately 10 percent each. However, the maximum energy scaling is slower in this regime, following a square-root-of-time dependence rather than linear Bohm scaling. This regime produces significantly enhanced nonthermal electron populations compared to Bell-dominated shocks, which has implications for observable synchrotron emission from transrelativistic astrophysical shocks.

Implications

The transition between instability regimes explains discrepancies in expected electron acceleration efficiency for transrelativistic shocks propagating through different environments. For weakly magnetized media characteristic of interstellar conditions (σ ~ 10^-9), the Weibel-dominated regime predicts substantially higher nonthermal electron fractions than previously estimated from Bell-dominated models. This enhanced electron acceleration may resolve the apparent deficit in electron heating needed to explain bright X-ray emission observed from events like the binary neutron star merger GW170817 at late times. The findings suggest that transrelativistic shocks in different astrophysical contexts may exhibit qualitatively different particle acceleration signatures depending on ambient magnetization.

The distinct maximum energy scaling laws between regimes have consequences for cosmic ray production and emission spectra. Bell-dominated shocks achieve higher maximum particle energies over comparable timescales due to Bohm scaling, favoring efficient ion acceleration for cosmic ray production. Weibel-dominated shocks produce more balanced ion-electron acceleration with slower energy gain, potentially yielding different spectral signatures. These results provide quantitative predictions for interpreting observations of fast blue optical transients, late-stage gamma-ray burst afterglows, and extragalactic jet termination shocks across different environmental conditions and evolutionary stages.

Scope and limitations

This summary is based on the study abstract and available metadata. It does not include a full analysis of the complete paper, supplementary materials, or underlying datasets unless explicitly stated. Findings should be interpreted in the context of the original publication.