Ultra-High-Energy Cosmic Rays Accelerated by Magnetically Dominated Turbulence

Abstract

Ultra-High-Energy Cosmic Rays (UHECRs), particles characterized by energies exceeding $10^{18}$ eV, are generally believed to be accelerated electromagnetically in high-energy astrophysical sources. One promising mechanism of UHECR acceleration is magnetized turbulence. We demonstrate from first principles, using fully kinetic particle-in-cell simulations, that magnetically dominated turbulence accelerates particles on a short timescale, producing a power-law energy distribution with a rigidity-dependent, sharply defined cutoff well approximated by the form $f_{\mathrm{cut}}\left(E,E_{\mathrm{cut}}\right)=\text{sech}\left[(E/E_{\mathrm{cut}}{)}^2\right]$. Particle escape from the turbulent accelerating region is energy-dependent, with $t_{\mathrm{esc}}\propto E^{-\hat{I}´}$ and $\hat{I}´\sim 1/3$. The resulting particle flux from the accelerator follows $dN/dEdt\propto E^{-s}\text{sech}\left[(E/E_{\mathrm{cut}}{)}^2\right]$, with $s\sim 2.1$. We fit the Pierre Auger Observatory's spectrum and composition measurements, taking into account particle interactions between acceleration and detection, and show that the turbulence-associated energy cutoff is well supported by the data, with the best-fitting spectral index being $s=2.1_{-0.13}^{+0.06}$. Our first-principles results indicate that particle acceleration by magnetically dominated turbulence may constitute the physical mechanism responsible for UHECR acceleration.