## Particle acceleration in mildly relativistic shocks

**Patrick Crumley**

(D. Caprioli, S. Markoff, A. Spitkovsky)

**Abstract:**

Many astrophysical objects such as radio supernovae, microquasars, and tidal disruption events launch supersonic outflows that travel at mildly relativistic speeds (v~c and Lorentz factor ~ 1). Shocks inside these mildly relativistic outflows have an advantage in producing high energy particles because the acceleration time is short, but the shock is subluminal for a larger range of upstream magnetic field inclinations compared to ultra-relativistic shocks. We study particle acceleration in weakly magnetized mildly relativistic shocks using fully kinetic particle-in-cell simulations. We find that quasi-parallel shocks are mediated by a filamentary non-resonant (Bell) instability driven by non-thermal ions, producing magnetic fluctuations on scales comparable to the ion gyro-radius. In quasi-parallel shocks, both electrons and ions are accelerated into non-thermal power-laws whose maximum energy grows linearly with time. Reflected non-thermal ions evacuate upstream cavities and amplify magnetic fields. At late times, 10% of the shockâs energy goes into non-thermal protons, 10% into magnetic fields, but only .05% of the energy goes into non-thermal electrons in a Mach number 15 quasi-parallel shock traveling at .75c. Increasing the velocity of such a shock from non-relativistic to relativistic increases the energy fraction in non-thermal electrons to several percent, while the energy fraction of ions is roughly constant. Therefore, the radiative efficiency of a quasi-parallel shock increases as its shock speed increases. In quasi-perpendicular shocks, no non-thermal power-law develops in ions or electrons. These findings have implications when modeling radiation from outflows that transition from relativistic to non-relativistic like the afterglows of GRBs.