  Very steep reflection emissivity profiles in the inner part of accretion
disks are commonly found in the analysis of X-ray observations of black hole
binaries and AGNs, but there is some debate about their exact origin. While
steep reflection emissivity profiles can be naturally produced by compact
coronae close to black holes, the measured radial emissivity parameter can be
further increased by the radial disk ionization profile when the theoretical
model assumes a disk with constant ionization. In this paper, we implement the
possibility of a radial disk ionization profile in the reflection model
RELXILL_NK and we analyze a NuSTAR observation of the black hole binary EXO
1846-031, which was previously found to have a very high inner emissivity
index. We find that the model with a radial disk ionization profile improves
the fit, but the impact on the estimate of the black hole spin parameter and on
the constraint of the deformation parameter is modest.
