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Equations of State in the Hartle-Thorne Model of Neutron Stars Selecting Acceptable Variants of the Resonant Switch Model of Twin HF QPOs in the Atoll Source 4U 1636-53

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

Acta Astronomica

2015

Vol. 65, No. 2

169--195

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.

Test of the Resonant Switch Model by Fitting the Data of Twin-Peak HF QPOs in the Atoll Source 4U 1636-53

Stuchlìk Z., Kotrlovà A., Török G., Goluchovà K.

Acta Astronomica

2014

Vol. 64, No. 1

45--64

Resonant Switch (RS) model has recently been proposed as an alternative to the standard models of twin-peak high-frequency quasi-periodic oscillations (HF QPOs) observed in low-mass X-ray binaries containing a neutron star. The model assumes switch of twin oscillations at a resonant point, where frequencies of the upper and lower oscillations νU and νL become commensurable and one pair of the oscillating modes (corresponding to a specific model of HF QPOs) changes to some other pair due to non-linear resonant phenomena. We test the RS model for the atoll source 4U 1636-53, where we assume two resonant points observed at frequency ratios νU:νL=3:2, 5:4, by fitting the pairs of the oscillatory modes to the observed data in the regions related to the resonant points. Among acceptable variants of the RS model the most promising are those combining the relativistic precession (RP) and the total precession (TP) frequency relations or their modifications. The precision of the fits is shown to be strongly increased in comparison to fits realized by individual pairs along the whole data range. We demonstrate that the χ2 test is significantly improved. Fitting of the HF QPO data in the source 4U 1636-53 by the RP1-RP variant of the RS model gives the best results and implies that the neutron star mass and dimensionless spin are M≈2.2 Msun and a≈0.27.