Compton scattering in static and moving media. II. System-frame solutions for spherically symmetric flows

I study the formation of Comptonization spectra in spherically symmetric, fast-moving media in a flat spacetime. I analyze the mathematical character of the moments of the transfer equation in the system frame and describe a numerical method that provides fast solutions of the time-independent radiative transfer problem that are accurate in both the diffusion and free-streaming regimes. I show that even if the flows are mildly relativistic (V ∼ 0.1, where V is the electron bulk velocity in units of the speed of light), terms that are second order in V alter the emerging spectrum both quantitatively and qualitatively. In particular, terms that are second order in V produce power-law spectral tails, which are the dominant feature at high energies, and therefore cannot be neglected. I further show that photons from a static source are upscattered by the bulk motion of the medium even if the velocity field does not converge. Finally, I discuss these results in the context of radial accretion onto and outflows from compact objects.