The role of stochastic Fermi-type particle acceleration in the inner jets of Active Galactic Nuclei

High-resolution radio observations of nearby active galactic nuclei have revealed extended, limb-brightened structures in their inner jets. This ties in with other multi-wavelength observations from radio to X-ray and gamma-ray, indicating that a structured jet model is required. While electrons need to be kept energized to account for the observed features, the underlying particle acceleration mechanism is still unclear. We explore the role of stochastic Fermi-type particle acceleration, i.e., classical second-order Fermi and shear acceleration, for understanding the multi-wavelength observations of the inner jets of M87. An analytical Fokker-Planck description is adopted to infer characteristic spectral indices and cutoff energies for these two mechanisms. We focus on electron synchrotron radiation as the dominant emission process. We find that the multi-wavelength observations of M87 can be satisfactorily accounted for in a framework, where the X-rays are produced at a larger distance from the core than the radio emission region. This provides further support to multi-zone, broadband emission modelling. We use our findings to also comment on the acceleration of cosmic rays entrained in the sheath.