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A thermal soft X-ray component is often detected in low-level accretingneutron stars (NSs), but is not detected in low-level accreting stellar-massblack holes (BHs). In this paper, we investigate the origin of such a thermalsoft X-ray component in the framework of the self-similar solution of theadvection-dominated accretion flow (ADAF) around NSs. It is assumed that afraction, $f_{\rm th}$, of the energy transferred onto the surface of the NS isthermalized at the surface of the NS as the soft photons to be scattered in theADAF. We self-consistently calculate the structure and the correspondingemergent spectrum of the ADAF by considering the radiative coupling between thesoft photons from the surface of the NS and the ADAF itself. We show that theCompton $y$-parameter of the ADAF for NSs is systematically lower than that ofBHs. Meanwhile, we find that the temperature of the thermal soft X-raycomponent in NSs decreases with decreasing mass accretion rate, which isqualitatively consistent with observations. We test the effect of $f_{\rm th}$on the structure, as well as the emergent spectrum of the ADAF. It is foundthat a change of $f_{\rm th}$ can significantly change the temperature of thethermal soft X-ray component as well as the spectral slope in hard X-rays.Finally, it is suggested that the value of $f_{\rm th}$ can be constrained byfitting the high-quality X-ray data, such as the $\it XMM$-$\it Newton$spectrum between 0.5-10 keV in the future work.

The advection-dominated accretion flow for the origin of the thermal soft X-ray component in low-level accreting neutron stars