X-ray spectral formation in a converging fluid flow: Spherical accretion into black holes

We study Compton upscattering of low-frequency photons in a converging flow of thermal plasma. The photons escape diffusively, and electron scattering is the dominant source of opacity. We solve the equation of radiative transfer in the case of spherical, steady state accretion into black holes numerically and approximately analytically. Unlike previous work on this subject, we consider the inner boundary at a finite radius, and this has a significant effect on the emergent spectrum. It is shown that the bulk motion of the converging flow is more efficient in upscattering photons than thermal Comptonization, provided that the electron temperature in the flow is of order a few keV or less. In this case, the spectrum observed at infinity consists of a soft component coming from input photons that escaped after a few scatterings without any significant energy change and of a power law that extends to high energies and is made of those photons that underwent significant upscattering. The luminosity of the power law is relatively small compared to that of the soft component. The more reflective the inner boundary is, the flatter the power-law spectrum becomes. The spectral energy power-law index for black hole accretion is always higher than 1, and it is approximately 1.5 for high accretion rates. This result tempts us to say that bulk motion Comptonization might be the mechanism behind the power-law spectra seen in black hole X-ray sources.