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 \emph{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 $\Gamma$ 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 $\Gamma$ and the X-ray luminosity log$L_{\rm X}$, when it is in the bright hard state. More specifically, the $\Lambda$-shaped correlation between $\Gamma$ and log$L_{\rm X}$ is observed, as the luminosity decreases by a factor of 3 in a narrow range from $\sim 10^{38}$ to $10^{37.5}$ $\rm erg~s^{-1}$. 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.