Dependence of Particle Acceleration Efficiency on Shock Velocity in Weakly Magnetized Electron-Ion Shocks

Using unprecedentedly long 2D particle-in-cell simulations, we study electron and ion acceleration in weakly magnetized quasi-parallel shocks, propagating at velocities ranging from transrelativistic to subrelativistic. At a fixed upstream magnetic field strength, low-velocity quasi-parallel shocks are dominated by the Bell instability, whereas high-velocity shocks are dominated by the Weibel instability. Both regimes accelerate ions with similar efficiency, with the Bell-dominated regime exhibiting faster growth in the maximum particle energy. The electron acceleration efficiency is strongly dependent on shock velocity. Weibel-dominated shocks have $\sim15\,\%$ of shock energy in nonthermal electrons, whereas in the Bell-dominated regime we attribute less than $\sim2\,\%$ of shock energy to nonthermal electrons. We discuss applications of our results to the bright X-ray emission from the late-stage afterglows of gamma-ray bursts, the radio emission from fast blue optical transients, and the X-ray variability in microquasars.
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