Particle Acceleration in Relativistic Shearing Flows: Energy Spectrum

Abstract We consider the acceleration of charged particles in relativistic shearing flows, with Lorentz factor up to ? 0 ? 20. present numerical solutions particle transport equation and compare these results from analytical calculations. show that highly limit energy spectrum approaches a power law, N ( E stretchy="false">) ? ? q ˜ , universal value $\tilde{q}=(1+\alpha )$?> = 1 + ? for slope this where ? parameterizes power-law momentum dependence mean free path. At mildly flow speeds, becomes softer sensitive underlying profile. explore different examples, including Gaussian power-law-type velocity profiles, showing latter yield comparatively harder spectra, producing $\tilde{q}\simeq 2$?> ? 2 ? 3 Kolmogorov turbulence. provide comparison simplified leaky-box approach derive an approximate relation estimating spectral index as function maximum shear speed. These are relevance jetted, high-energy astrophysical sources such active galactic nuclei, since is promising mechanism energies likely contribute radiation observed.