**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

frot≍580 Hz (or alternatively frot≍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

frot≍580 Hz, while no variant of the RS model is

compatible for frot≍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/a2≍1.77.

**Authors:**

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