Estimating the masses of three neutron stars by twin kilohertz quasi-periodic oscillations and innermost stable circular orbits: constraining equations of state

We test the magnetohydrodynamics (MHD) model derived by Shi, Zhang and Li by the like-standard deviations of the twin kilohertz (kHz) quasi-periodic oscillation (QPO) frequencies when the modes of the MHD waves in the MHD model are recalculated. A group of approximate equations derived from the MILD equations in the MILD model are proposed. Consequently, the dependence of the twin kHz QPO frequencies on several neutron star (NS) parameters is determined by the approximate equations. Based on the selection criterion that NS parameters corresponding to the minimum like-standard deviation are the most reasonable parameters, the masses of the three NSs in 4U 0614+09, 4U 1636-53 and 4U 1608-52 are estimated as M < 2.60 M-circle dot, 2.00 M-circle dot < M < 2.31 M-circle dot and 2.17 M-circle dot < M < 2.62 M-circle dot, respectively. According to these NS masses, some equations of state for the nuclear matter in compact stars can be ruled out.