Electron and Proton Acceleration in Trans-Relativistic Magnetic Reconnection: Dependence on Plasma Beta and Magnetization

TL;DR

This study uses particle-in-cell simulations to explore how plasma beta and magnetization influence electron and proton acceleration during trans-relativistic magnetic reconnection, revealing key dependencies of particle spectra and acceleration mechanisms.

Contribution

It provides new empirical formulas for the spectral slope and acceleration efficiency as functions of plasma beta and magnetization, applicable to accretion disk models.

Findings

Electron spectra are non-thermal and modeled as power laws.

Spectral slope depends on plasma beta and magnetization, hardening with increasing sigma.

High beta near 1/4 sigma introduces an additional high-energy component.

Abstract

Non-thermal electron acceleration via magnetic reconnection is thought to play an important role in powering the variable X-ray emission from radiatively inefficient accretion flows around black holes. The trans-relativistic regime of magnetic reconnection, where the magnetization $\sigma$, defined as the ratio of magnetic energy density to enthalpy density, is $\sim 1$, is frequently encountered in such flows. By means of a large suite of two-dimensional particle-in-cell simulations, we investigate electron and proton acceleration in the trans-relativistic regime. We focus on the dependence of the electron energy spectrum on $\sigma$ and the proton $\beta$ (i.e., the ratio of proton thermal pressure to magnetic pressure). We find that the electron spectrum in the reconnection region is non-thermal and can be generally modeled as a power law. At $\beta \lesssim 3 \times 10^{-3}$, the slope, $p$, is independent of $\beta$ and it hardens with increasing $\sigma$ as $p\simeq 1.8 +0.7/\sqrt{\sigma}$. Electrons are primarily accelerated by the non-ideal electric field at X-points, either in the initial current layer or in current sheets generated in between merging magnetic islands. At higher values of $\beta$, the electron power law steepens for all values of $\sigma$. At values of $\beta$ near $\beta_{\rm max}\approx1/4\sigma$, when both electrons and protons are relativistically hot prior to reconnection, the spectra of both species display an additional component at high energies, containing a few percent of particles. These particles are accelerated via a Fermi-like process by bouncing in between the reconnection outflow and a stationary magnetic island. We provide an empirical prescription for the dependence of the power-law slope and the acceleration efficiency on $\beta$ and $\sigma$, which can be used in global simulations of collisionless accretion disks.