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 particle-in-cell simulations - that elucidates the physics governing the generation of power-law energy spectra in relativistic reconnection. Particles with Lorentz factor $\gamma \gtrsim 3\sigma$ (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 $t_{\mathrm{acc}}\sim \gamma {\eta }_{\mathrm{rec}}^{-1}{\omega }_{\mathrm{c}}^{-1}\simeq 20\gamma {\omega }_{\mathrm{c}}^{-1}$, where ${\eta }_{\mathrm{rec}}\simeq 0.06$ is the inflow speed in units of the speed of light and ${\omega }_{\mathrm{c}}=e{B}_0/mc$ is the gyrofrequency in the upstream magnetic field. They leave the region of active energization after $t_{\mathrm{esc}}$, when they get captured by one of the outflowing flux ropes of reconnected plasma. We directly measure $t_{\mathrm{esc}}$ in our simulations and find that $t_{\mathrm{esc}}\sim t_{\mathrm{acc}}$ for $\sigma \gtrsim \mathrm{few}$. This leads to a universal (i.e., $\sigma$-independent) power-law spectrum $d{N}_{\mathrm{free}}/d\gamma \propto {\gamma }^{-1}$ for the particles undergoing active acceleration, and $dN/d\gamma \propto {\gamma }^{-2}$ for the overall particle population. Our results help shedding light on the ubiquitous presence of power-law particle and photon spectra in astrophysical non-thermal sources.

8 pages, 8 figures, submitted