Investigation of the emission radii of kHz QPOs for the accreting millisecond X-Ray pulsars, Atoll and Z sources

We infer the emission positions of twin kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low-mass X-ray binaries (NS-LMXBs) based on the Alfvén wave oscillation model (AWOM). For most sources, the emission radii of kHz QPOs cluster around a region of 16–19 km with the assumed NS radii of 15 km. Cir X-1 has the larger emission radii of 23 ∼ 38 km than those of the other sources, which may be ascribed to its large magnetosphere-disc radius or strong NS surface magnetic field. SAX J1808.4−3658 is also a particular source with the relative large emission radii of kHz QPOs of 20 ∼ 23 km, which may be due to its large inferred NS radius of 18 ∼ 19 km. The emission radii of kHz QPOs for all the sources are larger than the NS radii, and the possible explanations of which are presented. The similarity of the emission radii of kHz QPOs (∼16–19 km) for both the low/high luminosity Atoll/Z sources is found, which indicates that both sources share the similar magnetosphere-disc radii.