The radiative efficiency of neutron stars at low-level accretion

Abstract

ABSTRACT When neutron star low-mass X-ray binaries (NS-LMXBs) are in the low-level accretion regime (i.e. $L_{\rm X}\lesssim 10^{36}\ \rm erg\ s^{-1}$), the accretion flow in the inner region around the NS is expected to exist in the form of the hot accretion flow, e.g. the advection-dominated accretion flow (ADAF) as that in black hole X-ray binaries. Following our previous studies in Qiao & Liu (2020a, b) on the ADAF accretion around NSs, in this paper, we investigate the radiative efficiency of NSs with an ADAF accretion in detail, showing that the radiative efficiency of NSs with an ADAF accretion is much lower than that of $\epsilon \sim {\dot{M} GM\over R_{*}}/{\dot{M} c^2}\sim 0.2$ despite the existence of the hard surface. As a result, given an X-ray luminosity LX (e.g. between 0.5 and 10 keV), $\dot{M}$ calculated by $\dot{M}=L_{\rm X}{R_{*}\over {GM}}$ is lower than the real $\dot{M}$ calculated within the framework of the ADAF accretion. The real $\dot{M}$ can be more than two orders of magnitude higher than that calculated by $\dot{M}=L_{\rm X}{R_{*}\over {GM}}$ with appropriate model parameters. Finally, we discuss that if applicable, the model of ADAF accretion around a NS can be applied to explain the observed millisecond X-ray pulsation in some NS-LMXBs (such as PSR J1023+0038, XSS J12270−4859, and IGR J17379−3747) at a lower X-ray luminosity of a few times of $10^{33}\ \rm erg\ s^{-1}$, since at this X-ray luminosity the calculated $\dot{M}$ with the model of ADAF accretion can be high enough to drive a fraction of the matter in the accretion flow to be channelled on to the surface of the NS forming the X-ray pulsation.