Diffusion and convection of relativistic electrons in non-thermal sources: Steady-state solutions

In this paper we study the propagation of relativistic electrons in stationary spherically-symmetric models of non-thermal sources. Electrons are injected by a collapsed object in the centre and then diffuse away in the presence of a flux of accreting matter. We calculate the electron density taking into account both the outward diffusion and the inward convection: it is assumed that the diffusion coefficient and the velocity field have a power dependence on the radial coordinate. In Section 3 the transport equation is solved for the particular case where the electron energy is constant; while Section 4 treats the case in which the particles suffer synchrotron or inverse-Compton losses. The effects due to the convection are then discussed in comparison with the purely diffusive case.