Constraints on kilohertz quasi-periodic oscillation models and stellar equations of state from SAX J1808.4–3658, Cyg X-2 and 4U 1820–30

Abstract

We test the relativistic precession model (RPM) and the magnetohydrodynamics Alfvén wave oscillation model (AWOM) for the kilohertz (kHz) quasi-periodic oscillations (QPOs) from sources with measured neutron star (NS) masses and twin kHz QPO frequencies. For the RPM, the derived NS masses of Cyg X-2, SAX J1808.4–3658 and 4U 1820–30 are 1.96 ± 0.10, 2.83 ± 0.04 and 1.85 ± 0.02 M⊙, respectively. These are, respectively, ∼30, 100 and 40 per cent higher than the measured results 1.5 ± 0.3, <1.4 and |$1.29^{+0.19}_{-0.07}$| M⊙. For the AWOM, where the free parameter of the model is the density of the star, we infer the NS radii to be around 10–20 km for the above three sources. Based on this, we can infer the matter compositions inside the NSs with the help of the equations of state. In particular, for SAX J1808.4–3658, the AWOM shows a lower mass density for its NS than those of the other known kHz QPO sources, with a radius range of 17–20 km, which excludes the strange quark matter inside its star.