NuSTAR View of the R - Γ Correlation in the Hard State of Black Hole Low-mass X-Ray Binaries

The power law and reflection emission have been observed in the X-ray spectra of both black hole X-ray binaries (BHXRBs) and active galactic nuclei (AGNs), indicating a common physical origin of the X-ray emission from these two types of sources. The relevant parameters describing the shape of both components and the potential correlation between these parameters can provide important clues on the geometric and physical properties of the disk and the corona in these sources. In this work, we present a positive correlation between the photon index Γ and the reflection strength R for the low-mass BHXRBs in the hard state by modeling NuSTAR data, which is qualitatively consistent with the previous studies. We compare our results with the predictions from different theoretical disk-corona models. We show that the R - Γ correlation found in this work seems to favor the moving corona model proposed by Beloborodov. Our results indicate that the coronal geometry varies significantly among BHXRBs. We further compare our results with that of AGNs. We find that the reflection strength R is smaller than unity in the hard state of BHXRBs, while it can be as large as ~5 in AGNs, which implies that the variations of the disk-coronal geometry of AGNs are more vigorous than that of the BHXRBs in the hard state.