The Origin of Power-law Spectra in Relativistic Magnetic Reconnection

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 gamma greater than or similar to 3 sigma (here, sigma 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 tacc similar to gamma eta rec-1 omega c-1 similar or equal to 20 gamma omega c-1 , where eta rec similar or equal to 0.06 is the inflow speed in units of the speed of light and omega 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 similar to t acc for sigma greater than or similar to few. This leads to a universal (i.e., sigma-independent) power-law spectrum dNfree/d gamma proportional to gamma-1 for the particles undergoing active acceleration, and dN/d gamma proportional to gamma-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.