2019MNRAS.487.5335L

Negative and positive correlations between the X-ray photon index and the Eddington-scaled X-ray luminosity were found in the decay phase of X-ray binary outbursts and a sample of active galactic nuclei in former works. We systematically investigate the evolution of the X-ray spectral index, along with the X-ray flux and Eddington ratio, in eight outbursts of four black-hole X-ray binaries, where all selected outbursts have observational data from the Rossi X-ray Timing Explorer in both rise and decay phases. In the initial rise phase, the X-ray spectral index is anticorrelated with the flux and the X-ray spectrum quickly softens when the X-ray flux is approaching the peak value. In the decay phase, the X-ray photon index and the flux follow two different positive correlations and they become anticorrelated again when the X-ray flux is below a critical value, where the anticorrelation part follows the same trend as found in the initial rise phase. Compared with other X-ray binaries, GRO J1655-40 has an evident lower critical Eddington ratio for the anticorrelation and positive transition, which suggests that its black-hole mass and distance are not well constrained, or its intrinsic physics is different.