The Steady Growth of the High-Energy Spectral Cutoff in Relativistic Magnetic Reconnection

TL;DR

This study uses large-scale simulations to show that in relativistic magnetic reconnection, the high-energy spectral cutoff of accelerated particles grows steadily over time, challenging previous saturation claims and supporting its role in astrophysical high-energy emission.

Contribution

It reveals that the high-energy spectral cutoff in relativistic reconnection continuously increases with time, following a sqrt(t) scaling, and details the particle dynamics within plasmoids that drive this growth.

Findings

High-energy spectral cutoff grows as √t, not saturating at 4σ.

Particles at the cutoff reside in magnetized rings around plasmoids.

Spectrum slope evolves from hard to approximately 2 over time.

Abstract

Magnetic reconnection is invoked as an efficient particle accelerator in a variety of astrophysical sources of non-thermal high-energy radiation. With large-scale two-dimensional particle-in-cell simulations of relativistic reconnection (i.e., with magnetization $\sigma\gg1$) in pair plasmas, we study the long-term evolution of the power-law slope and high-energy cutoff of the spectrum of accelerated particles. We find that the high-energy spectral cutoff does not saturate at $\gamma_{\rm cut}\sim 4\sigma$, as claimed by earlier studies, but it steadily grows with time as long as the reconnection process stays active. At late times, the cutoff scales approximately as $\gamma_{\rm cut}\propto \sqrt{t}$, regardless of the flow magnetization and initial temperature. We show that the particles dominating the high-energy spectral cutoff reside in plasmoids, and in particular in a strongly magnetised ring around the plasmoid core. The growth of their energy is driven by the increase in the local field strength, coupled with the conservation of the first adiabatic invariant. We also find that the power-law slope of the spectrum ($p=-{\rm d}\log N/{\rm d}\log \gamma$) evolves with time. For $\sigma\gtrsim10$, the spectrum is hard at early times ($p\lesssim 2$), but it tends to asymptote to $p\sim 2$; the steepening of the power-law slope allows the spectral cutoff to extend to higher and higher energies, without violating the fixed energy budget of the system. Our results demonstrate that relativistic reconnection is a viable candidate for accelerating the high-energy particles emitting in relativistic astrophysical sources.