The $\beta$-Dependence of Particle Spectra in Relativistic Turbulent Reconnection

TL;DR

This study uses numerical simulations to explore how plasma beta influences particle energy spectra in relativistic turbulent magnetic reconnection, revealing a systematic steepening of spectra with increasing beta.

Contribution

It introduces empirical scaling relations showing how the spectral exponent depends on plasma beta in relativistic reconnection, highlighting relativistic physics effects.

Findings

Spectral slope increases with plasma beta, following a power-law relation.

Relativistic effects cause a greater steepening of spectra compared to non-relativistic cases.

The results help interpret diverse astrophysical non-thermal radiation spectra.

Abstract

We perform numerical simulations of particle acceleration in relativistic, self-driven turbulent magnetic reconnection using the MHD-PIC method. We systematically investigate the dependence of the non-thermal particle spectral exponent on the plasma $\beta$. We find that particle acceleration proceeds in two stages: an initial, efficient first-order Fermi phase where momentum gains are comparable in parallel and perpendicular directions, followed by a slower drift-dominated phase. The power-law slope of the non-thermal spectrum is established during the Fermi phase, as found in previous studies. Our results demonstrate a systematic steepening of the accelerated particle energy spectrum with increasing $\beta$. We derive empirical scaling relations: the spectral exponent $\alpha \propto \beta^{0.5}$ in the relativistic regime, compared to $\alpha \propto \beta^{0.3}$ in the non-relativistic case. This marked difference is rooted in relativistic physics: the increased inertial mass density ($\rho h$) in high-$\beta$ plasmas acts as an energy sink, reducing the Alfv\'en velocity and thereby altering the dynamics of magnetic energy release and its partition efficiency. The derived scaling provides a unified physical framework for interpreting the diversity of non-thermal radiation spectra observed in astrophysical sources, including black hole corona X-ray flares, gamma-ray bursts, and active galactic nucleus jets.