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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
High Energy Astrophysical Phenomena · Submitted 1 Jul 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The test admits only one variant of the RS model of twin HF QPOs for the Hartle-Thorne theory with the Gandolfi et al. (2010) EoS predicting the parameters of the neutron star $M \sim 2.10 \mathrm{M}_{\odot}$, $a \sim 0.208$, and $q/a^2 \sim 1.77$.
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The abstract, sentence by sentence
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 at 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 Gandolfi et al. (2010) EoS predicting the parameters of the neutron star $M \sim 2.10 \mathrm{M}_{\odot}$, $a \sim 0.208$, and $q/a^2 \sim 1.77$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | background 0.72 | 0.39 | 0.02 | asserted 0.99 |
| s1 | 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. | result 0.94 | 0.67 | 0.06 | asserted 1.00 |
| s2 | The most precise variants of the RS model are those combining the relativistic precession frequency relations with their modifications. | result 0.72 | 0.35 | 0.06 | asserted 1.00 |
| s3 | 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 at 4U 1636-53. | method 0.68 | 0.84 | 0.06 | asserted 0.87 |
| s4 | 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. | result 1.00 | 0.90 | 0.37 | asserted 1.00 |
| s5 | The two compatible variants of the RS model are those giving the best fits of the observational data. | result 0.79 | 0.77 | 0.09 | asserted 1.00 |
| s6 | 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. | method 0.55 | 0.87 | 0.10 | asserted 1.00 |
| s7 | The test admits only one variant of the RS model of twin HF QPOs for the Hartle-Thorne theory with the Gandolfi et al. (2010) EoS predicting the parameters of the neutron star $M \sim 2.10 \mathrm{M}_{\odot}$, $a \sim 0.208$, and $q/a^2 \sim 1.77$. | result 1.00 | 0.90 | 0.82 | asserted 1.00 |
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The paper
Original 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 at 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 Gandolfi et al. (2010) EoS predicting the parameters of the neutron star $M \sim 2.10 \mathrm{M}_{\odot}$, $a \sim 0.208$, and $q/a^2 \sim 1.77$.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
What it cites · 35 sentences without a confident label
Uses the method or tool of 2 papers
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The results of the fitting procedure will be further tested by confrontation with detailed Hartle–Thorne theoretical models [ref] describing slowly rotating neutron stars that are constructed under the observationally given constraint of the rotation frequency $580 Hz$ (or $290 Hz$) relevant for the 4U 1636$-$53 neutron star [ref] , using the variety of widely accepted equations of state that were studied in [ref] .
Quadrupole moments of rotating neutron stars and strange stars · Application to the source 4U 1636$-$53 · 0.81
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Second, we define the orbital and epicyclic radial and vertical frequencies of the quasicircular geodesic motion in the Hartle–Thorne geometry, $ν_K(r;M,a,q)$, $ν_r(r;M,a,q)$, $ν_θ(r;M,a,q)$ [ref] .
The Hartle-Thorne circular geodesics · Self-consistency test by the Hartle–Thorne geometry · 0.95
Uses data or values from 1 paper
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Assuming the geodesic orbital and epicyclic frequencies related to the Kerr geometry, the fitting procedure applied to the RP model of the frequency-relation evolution implies mass–spin relation $M(a) = M_0[1 + k(a + a^2)]$ rather than concrete values of the neutron star parameters $M$ and $a$; for the Z-source Circinus X-1 there is $M_0 ∼2.2 M_⊙$ and $k ∼0.5$ [ref] .
On mass-constraints implied by the relativistic precession model of twin-peak quasi-periodic oscillations in Circinus X-1 · Introduction · 0.83
Cites as support 2 papers
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However, limiting the study to the resonant phenomena and frequencies of the geodesic origin, the number of free parameters of the model is restricted to the mass $M$ and dimensionless spin $a$ of the neutron star, as we are able to demonstrate that the predicted mass of the neutron star is large enough to guarantee with high precision independence of the geodesic frequencies on the quadrupole moment of the neutron star and applicability of the Kerr approximation in decribing the neutron star external geometry [ref] .
Quadrupole moments of rotating neutron stars and strange stars · Discussion · 0.97
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Such a simplification is correct with high accuracy for neutron (quark) stars with large masses, close to maximum allowed for a given equation of state [ref] , that can be assumed in the known atoll or Z-sources because of mass increasing due to the accretion.
On mass-constraints implied by the relativistic precession model of twin-peak quasi-periodic oscillations in Circinus X-1 · The RS model · 0.98
Cites as background 6 papers
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We briefly summarize the basic ideas of the RS model – for details see [ref] .
Multi-resonance orbital model of high-frequency quasi-periodic oscillations: possible high-precision determination of black hole and neutron star spin · The RS model · 0.95
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We briefly summarize the basic ideas of the RS model – for details see [ref] .
Resonant switch model of twin peak HF QPOs applied to the source 4U 1636-53 · The RS model · 0.95
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We consider a set of neutron-star matter equations of state that are based on various approaches – following the recent study of the neutron star properties related to the behavior of the quadrupole moment [ref] .
Quadrupole moments of rotating neutron stars and strange stars · Equations of state · 0.80
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