**Publication date:** Jun 2015

**Abstract:**

The Resonant Switch (RS) model of twin high-frequency quasi-periodic

oscillations (HF QPOs) observed in neutron star binary systems, based on

switch of the twin oscillations at a resonant point, has been applied to

the atoll source 4U 1636-53 under assumption that the neutron star

exterior can be approximated by the Kerr geometry. Strong restrictions

of the neutron star parameters M (mass) and a (spin) arise due to

fitting the frequency pairs admitted by the RS model to the observed

data in the regions related to the resonant points. The most precise

variants of the RS model are those combining the relativistic precession

frequency relations with their modifications. Here, the neutron star

mass and spin estimates given by the RS model are confronted with a

variety of equations of state (EoS) governing structure of neutron stars

in the framework of the Hartle-Thorne theory of rotating neutron stars

applied for the observationally given rotation frequency

f_{rot}≍580 Hz (or alternatively f_{rot}≍290 Hz) of the

neutron star in 4U 1636-53. It is shown that only two variants of the RS

model based on the Kerr approximation are compatible with two EoS

applied in the Hartle-Thorne theory for f_{rot}≍580 Hz, while no

variant of the RS model is compatible for f_{rot}≍290 Hz. The

two compatible variants of the RS model are those giving the best fits

of the observational data. However, a self-consistency test by fitting

the observational data to the RS model with oscillation frequencies

governed by the Hartle-Thorne geometry described by three spacetime

parameters M,a and (quadrupole moment) q related by the two available

EoS puts strong restrictions. The test admits only one variant of the RS

model of twin HF QPOs for the Hartle-Thorne theory with the EoS

predicting the parameters of the neutron star M≍2.10 M_{☉},

a≍0.208, and q/a^{2}≍1.77.

**Authors:**

Stuchlìk, Z.; Urbanec, M.; Kotrlovà, A.; Török, G.; Goluchovà, K.;