Impact of ionization and electron density gradients in X-ray reflection spectroscopy measurements

The models currently used for the analysis of the reflection spectra of black holes usually assume a disk with constant ionization and electron density. However, there is some debate on the impact of these assumptions on the estimate of the properties of the sources, in particular when the fits suggest very steep emissivity profiles in the inner part of the accretion disk. In this work, we re-analyze a selected set of high-quality NuSTAR and Suzaku data of Galactic black holes and we fit the reflection component with three different models: RELXILL_NK, in which the ionization parameter and the electron density are constant, RELXILLION_NK, where the electron density is still constant but the ionization profile is described by a power law, and RELXILLDGRAD_NK, where the electron density profile is described by a power law and the ionization profile is calculated self-consistently from the electron density and the emissivity. While RELXILLION_NK may provide slightly better fits, we do not find any substantial difference in the estimate of the properties of the sources among the three models. Our conclusion is that models with constant electron density and ionization parameter are probably sufficient, in most cases, to fit the currently available X-ray data of accreting black holes.