The energy injection and losses in the Monte Carlo simulations of a diffusive shock

TL;DR

This paper investigates how different prescribed scattering laws in Monte Carlo simulations affect energy injection, losses, and the resulting shock energy spectrum in diffusive shock acceleration models.

Contribution

It demonstrates that the prescribed scattering law intrinsically determines particle injection rates and influences shock energy spectrum slopes in self-consistent Monte Carlo simulations.

Findings

Anisotropic scattering results in low energy injection and high energy losses, producing a softer spectrum.

Isotropic scattering leads to higher energy injection and lower losses, resulting in a harder spectrum.

Energy injection and loss functions are directly correlated with the scattering law used.

Abstract

Although diffusive shock acceleration (DSA) could be simulated by some well-established models, the assumption of the injection rate from the thermal particles to the superthermal population is still a contentious problem. But in the self-consistent Monte Carlo simulations, because of the prescribed scattering law instead of the assumption of the injected function, hence particle injection rate is intrinsically defined by the prescribed scattering law. We expect to examine the correlation of the energy injection with the prescribed multiple scattering angular distributions. According to the Rankine-Hugoniot conditions, the energy injection and the losses in the simulation system can directly decide the shock energy spectrum slope. By the simulations performed with multiple scattering law in the dynamical Monte Carlo model, the energy injection and energy loss functions are obtained. As results, the case applying anisotropic scattering law produce a small energy injection and large energy losses leading to a soft shock energy spectrum, the case applying isotropic scattering law produce a large energy injection and small energy losses leading to a hard shock energy spectrum.