The models that seek to explain the reflection spectrum in black hole binaries usually invoke a point-like primary source of hard X-rays. This source illuminates the accretion disk and gives rise to the discrete (lines) and continuum-reflected components. The main goal of this work is to investigate whether the extended, mildly relativistic jet that is present in black hole binaries in the hard and hard-intermediate states is the hard X-ray source that illuminates the accretion disk. We use a Monte Carlo code that simulates the process of inverse Compton scattering in a mildly relativistic jet. Blackbody photons from the thin accretion disk are injected at the base of the jet and interact with the energetic electrons that move outward. Despite the fact that the jet moves away from the disk at a mildly relativistic speed, we find that approximately $15-20$% of the input soft photons are scattered back toward the accretion disk. The vast majority of the Comptonized, back-scattered photons escape very close to the black hole ($hlesssim 6 r_g$, where $r_g$ is the gravitational radius), but a non-negligible amount escape at a wide range of heights. At high heights, $hsim 500-2000,r_g$, the distribution falls off rapidly. The high-height cutoff strongly depends on the width of the jet at its base and is almost insensitive to the optical depth. The disk illumination spectrum is softer than the direct jet spectrum of the radiation that escapes in directions that do not encounter the disk. We conclude that an extended jet is an excellent candidate source of hard photons in reflection models.
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