ABSTRACT
Observationally, the X-ray spectrum (0.5–10 keV) of low-level accreting neutron stars (NSs) ($L_{\rm 0.5{-}10\,\rm kev}\lesssim 10^{36}\ \rm erg \ s^{-1}$) can generally be well fitted by the model with two components, i.e., a thermal soft X-ray component plus a power-law component. Meanwhile, the fractional contribution of the power-law luminosity η ($\eta \equiv L^{\rm power\ law}_{\rm 0.5{-}10\,\rm kev}/L_{\rm 0.5{-}10\,\rm kev}$) varies with the X-ray luminosity $L_{\rm 0.5{-}10\,\rm kev}$. In this paper, we systematically investigate the origin of such X-ray emission within the framework of the advection-dominated accretion flow (ADAF) around a weakly magnetized NS, in which the thermal soft X-ray component arises from the surface of the NS and the power-law component arises from the ADAF itself. We test the effects of the viscosity parameter α in the ADAF and thermalized parameter fth (describing the fraction of the ADAF energy released at the surface of the NS as thermal emission) on the relation of η versus $L_{\rm 0.5{-}10\,\rm kev}$. It is found that η is nearly a constant (∼zero) with $L_{\rm 0.5{-}10\,\rm kev}$ for different α with fth = 1, which is inconsistent with observations. Meanwhile, it is found that a change of fth can significantly change the relation of η versus $L_{\rm 0.5{-}10\,\rm kev}$. By comparing with a sample of non-pulsating NS-low mass X-ray binaries probably dominated by low-level accretion on to NSs, it is found that a small value of fth ≲ 0.1 is needed to match the observed range of $\eta \gtrsim 10{{\ \rm per\ cent}}$ in the diagram of η versus $L_{\rm 0.5{-}10\,\rm kev}$. Finally, we argue that the small value of fth ≲ 0.1 implies that the radiative efficiency of NSs with an ADAF accretion may not be as high as the predicted result previously of $\epsilon \sim {\dot{M} GM\over R_{*}}/{\dot{M} c^2}\sim 0.2$ despite the existence of the hard surface.
New Constraints on the Nuclear Equation of State from the Thermal Emission of Neutron Stars in Quiescent Low-mass X-Ray Binaries
