Cosmic-Ray Acceleration in Radio-jet Shear Flows: Scattering Inside and Outside the Jet

Abstract

Abstract A steady-state, analytical model of energetic particle acceleration in radio-jet shear flows due to cosmic-ray viscosity is explored, including particle scattering both into and out of the shear flow acceleration region. This involves solving a mixed Dirichlet–Von Neumann boundary value problem at the edge of the jet. The spectrum of the accelerated particles is harder than the free-escape case from the edge of the jet. The flow velocity u = u(r) e z is along the axis of jet (the z-axis). u is independent of distance z along the jet axis, and u(r) is a monotonically decreasing function of cylindrical radius r from the jet axis. The scattering time where p is the particle momentum in the fluid frame in the shear flow region 0 < r < r 2, and outside the jet (r > r 2). Green’s functions are obtained for monoenergetic injection of particles with momentum p = p 0 at radius r = r 1 (0 < r 1 < r 2). The Green’s function and Green’s formula are used to determine solutions for a general spectrum of particles at . Solutions are obtained corresponding to a monoenergetic spectrum at infinity. We discuss the implications of these results for the acceleration of ultra-high-energy cosmic-rays in active galactic nucleus jet sources. Leaky box models of particle acceleration in shear flows, including synchrotron losses and particle escape, are used to describe the momentum spectrum of accelerated particles. The use of the relativistic telegrapher transport equation model is discussed.