Photon Scattering by Relativistic Flows in Schwarzschild Spacetimes. I. The Generation of Power-Law Spectra

We study the spectra generated as a result of bulk Comptonization by relativistic electrons in radial flows onto compact objects. We solve numerically the general-relativistic radiative transfer equation in the Schwarzschild spacetime, in steady-state and under minimal assumptions. We show that power-law spectra result from multiple scatterings, in a way similar to thermal Comptonization. We also find that photon-electron interactions taking place near the black-hole event horizon affect very little the emerging spectra. We, therefore, argue that bulk Comptonization spectra do not carry distinguishing signatures of the compact object around which they are produced. We examine the dependence of the spectra on simplifications often employed regarding the spacetime geometry, the distribution of photon sources, and the boundary conditions. We show that the existence of trapped characteristics around a black hole reduces the efficiency of Comptonization and that general relativistic effects identically cancel bulk Comptonization effects for a free-falling flow and in the limit of infinitesimal mean-free path. As a result, we find that neglecting the curved spacetime geometry leads to overestimating the high-energy flux by up to an order of magnitude. Finally, we demonstrate that the spectrum from accretion onto a neutron star depends sensitively on the imposed boundary conditions, while that from a black hole is immune to such choices.