Impact of the returning radiation on X-ray reflection spectroscopy measurements: the case of Galactic black holes

The effect of the returning radiation has long been ignored in the analysis of the reflection spectra of Galactic black holes and active galactic nuclei and only recently has been implemented in the relxill package. Here we present a study on the impact of the returning radiation on the estimate of the parameters of Galactic black holes. We consider high-quality NuSTAR spectra of three Galactic black holes (GX 339-4, Swift J1658.2-4242, and MAXI J1535-571) and we fit the data with the lamppost model in the latest version of relxill, first without including the returning radiation and then including the returning radiation. We do not find any significant difference in the estimate of the parameters of these systems between the two cases, even if all three sources are fast-rotating black holes and for two sources the estimate of the height of the corona is very low, two ingredients that should maximize the effect of the returning radiation. We discuss our results and the approximations in relxill.