The steady growth of the high-energy spectral cut-off in relativistic magnetic reconnection

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 >> 1) in pair plasmas, we study the long-term evolution of the power-law slope and high-energy cut-off of the spectrum of accelerated particles. We find that the high-energy spectral cut-off does not saturate at gamma(cut) similar to 4 sigma, as claimed by earlier studies, hut it steadily grows with time as long as the reconnection process stays active. At late times, the cut-off scales approximately as gamma(cut) alpha root t, regardless of the flow magnetization and initial temperature. We show that the particles dominating the high-energy spectral cut-off reside in plasmoids, and in particular in a strongly magnetized 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=-d log N/d log gamma) evolves with time. For sigma greater than or similar to 10, the spectrum is hard at early times (p greater than or similar to 2), but it tends to asymptote to p similar to 2; the steepening of the power-law slope allows the spectral cut-off 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.