Particles acceleration with magnetic reconnection in large scale RMHD simulations–II. Particle spectra

ABSTRACT We extend the sub-grid model of Nurisso et al. (2023) to include particle acceleration and to predict the resulting energy spectra produced by magnetic reconnection events in large-scale relativistic magnetohydrodynamic (RMHD) simulations. Our method is consistently calibrated on particle-in-cell results and employs a particle-tracking approach that builds upon Vaidya et al. (2018). In this framework, the non-thermal spectral distribution of each macro-particle – representing an electron cloud – is updated by solving the relativistic cosmic-ray transport equation using the local fluid conditions. The proposed model predicts the slope and the maximum energy of the macro particle spectral distribution from the sampled values of plasma $\beta$ and $\sigma$ (magnetization) parameters, and it estimates the amount of magnetic energy feeding the non-thermal population including the contribution given by the guide field. A convolution method similar to the one proposed by Mukherjee et al. (2021) is employed in order to account for multiple acceleration episodes. The method has been implemented in the new GPU-ready version of the pluto code. We demonstrate its validity to predict particle spectra for a stationary current sheet. Furthermore, an application to a 3D unstable plasma column, where multiple current sheets are formed as by-product of the current-driven instability, is presented. Our results indicate an early-time cumulative power law with spectral index $p\sim 2.7$ which evolves in a broken power-law at later stages (with a high energy tail slope $p\sim 4$). Lastly, we demonstrate the capability of the module to predict the non-thermal emission intensity, polarization angle and degree of the system for two line of sights.