The Origin of Power-law Spectra in Relativistic Magnetic Reconnection

Abstract Magnetic reconnection is often invoked as a source of high-energy particles, and in relativistic astrophysical systems it is regarded as a prime candidate for powering fast and bright flares. We present a novel analytical model—supported and benchmarked with large-scale three-dimensional kinetic particle-in-cell simulations in electron–positron plasmas—that elucidates the physics governing the generation of power-law energy spectra in relativistic reconnection. Particles with Lorentz factor γ ≳ 3 σ (here, σ is the magnetization) gain most of their energy in the inflow region, while meandering between the two sides of the reconnection layer. Their acceleration time is t acc ∼ γ η rec − 1 ω c − 1 ≃ 20 γ ω c − 1 , where η rec ≃ 0.06 is the inflow speed in units of the speed of light and ω c = eB 0 / mc is the gyrofrequency in the upstream magnetic field. They leave the region of active energization after t esc , when they get captured by one of the outflowing flux ropes of reconnected plasma. We directly measure t esc in our simulations and find that t esc ∼ t acc for σ ≳ few. This leads to a universal (i.e., σ -independent) power-law spectrum dN free / d γ ∝ γ − 1 for the particles undergoing active acceleration, and dN / d γ ∝ γ − 2 for the overall particle population. Our results help to shed light on the ubiquitous presence of power-law particle and photon spectra in astrophysical nonthermal sources.