2020MNRAS.496.2704Q

Observationally, an anticorrelation between the X-ray photon index Γ (obtained by fitting the X-ray spectrum between 0.5 and 10 keV with a single power law) and the X-ray luminosity L_0.5-10 keV_, i.e. a softening of the X-ray spectrum with decreasing L_0.5-10 keV_, is found in neutron star low-mass X-ray binaries (NS-LMXBs) in the range of L_ 0.5-10keV_∼10³⁴-10³⁶ erg s^–1. In this paper, we explain the observed anticorrelation between Γ and L_0.5-10 keV_ within the framework of the self-similar solution of the advection-dominated accretion flow (ADAF) around a weakly magnetized NS. The ADAF model intrinsically predicts an anticorrelation between Γ and L_0.5-10 keV_. In the ADAF model, there is a key parameter, f_th, which describes the fraction of the ADAF energy released at the surface of the NS as thermal emission to be scattered in the ADAF. We test the effect of f_th on the anticorrelation between Γ and L_0.5-10 keV_. It is found that the value of f_th can significantly affect the anticorrelation between Γ and L_0.5-10 keV_. Specifically, the anticorrelation between Γ and L_0.5-10 keV_ becomes flatter with decreasing f_th as taking f_th = 0.1, 0.03, 0.01, 0.005, 0.003, and 0, respectively. By comparing with a sample of non-pulsating NS-LMXBs with well measured Γ and L_0.5-10 keV_, we find that indeed only a small value of 0.003 <= f_th <= 0.1 is needed to match the observed anticorrelation between Γ and L_0.5-10 keV_. Finally, we argue that the small value of f_th <= 0.1 derived in this paper further confirms our previous conclusion that the radiative efficiency of NSs with an ADAF accretion may not be as high as ε∼{dot}M GM / R_*/{dot}M c²∼0.2.