X-Ray Spectral Correlations in a Sample of Low-mass Black Hole X-Ray Binaries in the Hard State

The power-law emission and reflection component provide valuable insights into the accretion process around a black hole. In this work, thanks to the broadband spectra coverage of the Nuclear Spectroscopic Telescope Array, we study the spectral properties for a sample of low-mass black hole X-ray binaries (BHXRBs). We find that there is a positive correlation between the photon index Γ and the reflection fraction R (the ratio of the coronal intensity that illuminates the disk to the coronal intensity that reaches the observer), consistent with previous studies, but except for MAXI J1820+070. It is quite interesting that this source also deviates from the well-known “V”-shaped correlation between the photon index Γ and the X-ray luminosity log L X , when it is in the bright hard state. More specifically, the Λ-shaped correlation between Γ and log L X is observed, as the luminosity decreases by a factor of 3 in a narrow range from ∼10 38 to 10 37.5 erg s −1 . Furthermore, we discover a strong positive correlation between R and the X-ray luminosity for BHXRBs in the hard state, which puts a constraint on the disk-corona coupling and the evolution.