Accretion geometry in neutron star low-mass X-ray binaries during the hard spectral state

We investigate the accretion geometry in neutron star low-mass X-ray binaries (LMXBs) in the hard spectral state. It is commonly accepted that, for low mass transfer rates, an advection-dominated accretion flow (ADAF) is present in the inner region. But the observed relativistically broadened emission lines in the reflection spectra clearly indicate the existence of discs near the innermost stable circular orbit $(R_{\rm{ISCO}})$. We investigate the interaction between the coronal flow and the disc in neutron star LMXBs, and find that gas condensation from the dominant, coronal accretion flow to an inner disc is enhanced as compared to that in black hole LMXBs as a consequence of irradiation of the corona by the neutron star surface. Computations show that for low mass transfer rates ($\sim 0.005-0.02$ Eddington rate) a persistent weak disc can coexist with a coronal flow in the innermost region, where a pure ADAF would have been expected. The inner disc extends outwards from $R_{\rm{ISCO}}$ to $\sim 10 R_{\rm{ISCO}}$ for Eddington ratios ($L/L_{\rm{Edd}}$) as low as $\sim 0.002$, covers a larger region for higher Eddington ratios, and eventually connects to the outer disc at $L/L_{\rm{Edd}} \sim 0.02$, thereby transiting to a soft state. We demonstrate that the observationally inferred region of the broad iron lines in the hard-state sources generally lies within the extension of the inner discs predicted by the condensation model. Disappearance of the broad iron lines is predicted at very low luminosities, either caused by very low accretion rates or disc truncation by strong magnetic fields.