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Comparison of the Hartle-Thorne Model of Neutron Stars with its Kerr Approximation by using Resonant Switch Model

Stuchlík Z., Klimovičová K., Schee J., Török G., Kotrlová A.

Acta Astronomica

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2021

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Vol. 71, No. 4

311--141

EN

The Hartle-Thorne (H-T) models of slowly rotating neutron or quark stars, characterized by the mass M, dimensionless spin a, and reduced quadrupole moment q, are constructed for the observationally given rotational frequency frot=580 Hz (290 Hz) of the compact star in the atoll source 4U 1636-53, and a wide range of equations of state (EoS) giving sequences of allowed states governed by the relations a(M), q(M). These sequences are used in the framework of the resonant switch (RS) model combining pairs of geodesic oscillation models to match the data of the twin high-frequency quasi-periodic oscillations observed in the 4U 1636-53 source. The results of the matching procedure using the H-T models are compared to those based on the Kerr approximation of the exterior of the neutron stars. The best H-T matches fix the only variant of the RS model combining particular modifications of the relativistic precession model, exclude the rotation frequency frot=290 Hz, restrict the considered EoS to six of them, excluding the strange quark stars, and significantly improve precision of the matches given by any single geodesic oscillations model. The Kerr matching allows two variants of the RS model, thus, giving false information, and only three EoS, thus, giving insufficient information. Our results demonstrate that in the matching procedure, the Kerr approximation can be used only for neutron stars governed by the H-T models with q<2, implying an important restriction on the applicability of the Kerr approximation for description of the oscillatory phenomena around neutron stars. On the other hand, the RS model is sufficiently discriminating for the spacetime metric to be largely determined by fitting to the data. The ranges of the external spacetime parameters of the neutron stars related to the best H-T matches are determined to be M≈2.10-2.13 Mo, a≈0.21-0.25, q≈1.8-2.3. Most compact neutron star is predicted by the Gandolfi EoS, when M≈2.10 Mo, a≈0.21, q≈1.8, with the equatorial radius R≈10.83 km and eccentricity ε=0.03.

2

Multi-Resonance Orbital Model Applied to High-Frequency Quasi-Periodic Oscillations Observed in Sgr A*

Kotrlová A., Stuchlík Z., Török G.

Acta Astronomica

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2013

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Vol. 63, No. 2

275--292

EN

The multi-resonance orbital model of high-frequency quasi-periodic oscillations (HF QPOs) enables precise determination of the black hole dimensionless spin a if observed set of oscillations demonstrates three (or more) commensurable frequencies. The black hole spin a is related to the frequency ratio only, while its mass M is related to the frequency magnitude. The model is applied to the triple frequency set of HF QPOs observed in Sgr A* source with frequency ratio 3:2:1. Acceptable versions of the multi-resonance model are determined by the restrictions on the Sgr A* supermassive black hole mass. The version of strong resonances related to the black hole "magic" spin a=0.983 is acceptable but the version demonstrating the best agreement with the mass restrictions predicts spin a=0.980.

3

Resonant Switch Model of Twin Peak HF QPOs Applied to the Source 4U 1636-53

Stuchlík Z., Kotrlová A., Török G.

Acta Astronomica

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2012

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Vol. 62, No. 4

389--407

EN

Resonant Switch (RS) model of twin peak high-frequency quasi-periodic oscillations (HF QPOs) assumes switch of twin oscillations at a resonant point where frequencies of the upper and lower oscillations νU and νL become commensurable and the twin oscillations change from one pair of the oscillating modes (corresponding to a specific model of HF QPOs) to some other pair due to non-linear resonant phenomena. The RS model is used to determine range of allowed values of spin a and mass M of the neutron star located in the atoll source 4U 1636-53 where two resonant points are observed at frequency ratios νU:νL=3:2, 5:4. We consider the standard specific models of the twin oscillations based on the orbital and epicyclic geodetical frequencies. The resonant points are determined by the energy switch effect exhibited by the vanishing of the amplitude difference of the upper and lower oscillations. The predicted ranges of the neutron star parameters are strongly dependent on the twin modes applied in the RS model. We demonstrate that for some of the oscillatory modes used in the RS model the predicted parameters of the neutron star are unacceptable. Among acceptable RS models the most promising are those combining the Relativistic Precession and the Total Precession frequency relations or their modifications.

4

Black Holes Admitting Strong Resonant Phenomena

Stuchlík Z., Kotrlová A., Török G.

Acta Astronomica

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2008

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Vol. 58, No. 4

441--461

EN

High-frequency twin peak quasiperiodic oscillations (QPOs) are observed in four microquasars, i.e., Galactic black hole binary systems, with frequency ratio very close to 3:2. In the microquasar GRS 1915+105 the structure of QPOs exhibits additional frequencies and more than two frequencies are observed in the Galaxy nuclei Sgr A* or in some extragalactic sources (NGC 4051, MCG-6-30-15 and NGC 5408 X-1). The observed QPOs can be explained by a variety of the orbital resonance model versions assuming resonance of oscillations with the Keplerian frequency νK or the vertical epicyclic frequency νθ, and the radial epicyclic frequency νr, or some combinations of these frequencies. Generally, different resonances could arise at different radii of an accretion disk. However, we have shown that for special values of dimensionless black hole spin a strong resonant phenomena could occur when different resonances can be excited at the same radius, as cooperative phenomena between the resonances may work in such situations. The special values of a are determined for triple frequency ratio sets νK:νθ:νr=s:t:u with s,t,u being small integers. The most promising example of such a special situation arises for black holes with extraordinary resonant spin a=0.983 at the radius r=2.395 M, where νK:νθ:νr=3:2:1. We also predict that when combinations of the orbital frequencies are allowed, QPOs with four frequency ratio set 4:3:2:1 could be observed in the field of black holes with a=0.866,0.882 and 0.962. Assuming the extraordinary resonant spin a=0.983 in Sgr A*, its QPOs with observed frequency ratio ≈3:2:1 imply the black hole mass in the interval 4.3×106 Mʘ< M < 5.4×106 Mʘ, in agreement with estimates given by other, independent, observations.