Shear Acceleration in Expanding Flows

Shear flows are naturally expected to occur in astrophysical environments and potential sites of continuous non-thermal Fermi-type particle acceleration. Here we investigate the efficiency of expanding relativistic outflows to facilitate the acceleration of energetic charged particles to higher energies. To this end, the gradual shear acceleration coefficient is derived based on an analytical treatment. The results are applied to the context of the relativistic jets of active galactic nuclei. The inferred acceleration timescale is investigated for a variety of conical flow profiles (i.e., power law, Gaussian, Fermi-Dirac) and compared to the relevant radiative and non-radiative loss timescales. The results exemplify that relativistic shear flows are capable of boosting cosmic-rays to extreme energies. Efficient electron acceleration, on the other hand, requires weak magnetic fields and may thus be accompanied by a delayed onset of particle energization and affect the overall jet appearance (e.g., core, ridge line and limb-brightening).