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A systematic study of the advection-dominated accretion flow for the origin of the X-ray emission in weakly magnetized low-level accreting neutron star

Observationally, the X-ray spectrum ($0.5-10$ keV) of low-level accreting neutron stars (NSs) 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 $η$ ($η\equiv L^{\rm power\ law}_{\rm 0.5-10\rm keV}/L_{\rm 0.5-10\rm keV}$) 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 $f_{\rm th}$ (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 ($\sim$ zero) with $L_{\rm 0.5-10\rm keV}$ for different $α$ with $f_{\rm th}=1$, which is inconsistent with observations. Meanwhile, it is found that a change of $f_{\rm th}$ can significantly change the relation of $η$ versus $L_{\rm 0.5-10\rm keV}$. By comparing with a sample of non-pulsating NS-LMXBs probably dominated by low-level accretion onto NSs, it is found that a small value of $f_{\rm th} \lesssim 0.1$ is needed to match the observed range of $η\gtrsim 10\%$ in the diagram of $η$ versus $L_{\rm 0.5-10\rm keV}$. Finally, we argue that the small value of $f_{\rm th} \lesssim 0.1$ implies that the radiative efficiency of NSs with an ADAF accretion may not be as high as the predicted result previously of $ε\sim {\dot M GM\over R_{*}}/{\dot M c^2}\sim 0.2$ despite the existence of the hard surface.