$f$-mode oscillations of compact stars with realistic equations of state in dynamical spacetime

Anshu Gupta; Fatemeh Hossein Nouri; Swarnim Shashank

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$f$-mode oscillations of compact stars with realistic equations of state in dynamical spacetime

Swarnim Shashank, Fatemeh Hossein Nouri, Anshu Gupta

General Relativity and Quantum Cosmology · Submitted 10 Aug 2021

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The authors' main claim We also show that even using perturbed single star simulations can provide good agreement with $f$-modes extracted from inspiral phase of binary neutron star simulations which are computationally more expensive.

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arXiv ID2108.04643 (version 3)

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CitationAnshu Gupta, Fatemeh Hossein Nouri, Swarnim Shashank. "$f$-mode oscillations of compact stars with realistic equations of state in dynamical spacetime." arXiv:2108.04643 (2021). https://pith.science/paper/H4WXFFD4

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In this study, we perform full three dimensional numerical relativity simulations of non-rotating general relativistic stars. Extending the studies for polytropic equation of state, we investigate the accuracy and robustness of numerical scheme on measuring fundamental ($f$)-mode frequency for realistic equations of state (EoS). We use various EoS with varying range of stiffness and numerically evolve perturbed stellar models for several mass configurations (in the range of $1.2 - 2.0$ $M_{\odot}$) for each of these EoS. Using the gravitational waveform obtained from the simulations we extract the $f$-modes of the stars. The obtained results are tested against the pre-existing perturbation methods and find good agreement. Validity and deviation of universal relations have been carried out and are compared with earlier results under Cowling approximation as well as perturbative approaches. We also show that even using perturbed single star simulations can provide good agreement with $f$-modes extracted from inspiral phase of binary neutron star simulations which are computationally more expensive.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this study, we perform full three dimensional numerical relativity simulations of non-rotating general relativistic stars.	method 0.61	0.96	0.02	asserted 0.97
s1	Extending the studies for polytropic equation of state, we investigate the accuracy and robustness of numerical scheme on measuring fundamental ($f$)-mode frequency for realistic equations of state (EoS).	contribution 0.94	0.79	0.07	asserted 0.76
s2	We use various EoS with varying range of stiffness and numerically evolve perturbed stellar models for several mass configurations (in the range of $1.2 - 2.0$ $M_{\odot}$) for each of these EoS.	method 1.00	0.96	0.04	asserted 0.96
s3	Using the gravitational waveform obtained from the simulations we extract the $f$-modes of the stars.	method 1.00	0.96	0.05	asserted 0.99
s4	The obtained results are tested against the pre-existing perturbation methods and find good agreement.	result 0.97	0.92	0.15	asserted 1.00
s5	Validity and deviation of universal relations have been carried out and are compared with earlier results under Cowling approximation as well as perturbative approaches.	result 0.59	0.86	0.13	asserted 0.84
s6	We also show that even using perturbed single star simulations can provide good agreement with $f$-modes extracted from inspiral phase of binary neutron star simulations which are computationally more expensive.	result 0.94	0.91	0.30	asserted 0.94

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Original abstract

In this study, we perform full three dimensional numerical relativity simulations of non-rotating general relativistic stars. Extending the studies for polytropic equation of state, we investigate the accuracy and robustness of numerical scheme on measuring fundamental ($f$)-mode frequency for realistic equations of state (EoS). We use various EoS with varying range of stiffness and numerically evolve perturbed stellar models for several mass configurations (in the range of $1.2 - 2.0$ $M_{\odot}$) for each of these EoS. Using the gravitational waveform obtained from the simulations we extract the $f$-modes of the stars. The obtained results are tested against the pre-existing perturbation methods and find good agreement. Validity and deviation of universal relations have been carried out and are compared with earlier results under Cowling approximation as well as perturbative approaches. We also show that even using perturbed single star simulations can provide good agreement with $f$-modes extracted from inspiral phase of binary neutron star simulations which are computationally more expensive.

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4 arXiv papers cite this in 5 sentences

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There are a few efforts to investigate the effect on $f$-modes of the inclusion of exotic forms of matter (hyperon or quark matter) [ref] or to improve the asteroseismology relations with current astrophysical constraints [ref] .

General relativistic treatment of $f$-mode oscillations of hyperonic stars · Summary of this work · 0.88

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Uses the method or tool of 13 papers

Thus, we choose the recently established relations, which use compactness and effective compactness for calculating the damping times [ref] :

Fundamental oscillation modes of neutron stars: validity of universal relations · Calculation of damping times · 0.98
Thus, we choose the recently established relations, which use compactness and effective compactness for calculating the damping times [ref] :

Universal and approximate relations for the gravitational-wave damping timescale of $f$-modes in neutron stars · Calculation of damping times · 0.98
For this computation we integrate Eq. (15) from [ref] for the metric perturbation function $H$, from center to surface using fourth order Runge-Kutta method.

Tidal Love numbers of neutron stars · Universal Relations · 1.00

Compares with 8 papers

We further note that even by interpolating the mass vs $f$-mode data based on our simulations to get the $f$-mode frequency at $1.35 M_⊙$, the value which we get differs only by $0.9%$ for the SLy EoS from the one reported in Ref. [ref] .

Spin effects on neutron star fundamental-mode dynamical tides: phenomenology and comparison to numerical simulations · Comparison with compact binary merger simulations · 0.99
Further, the computed frequencies match very well with the studies performed by other groups while studying the fundamental modes during the binary neutron star merger [ref] , as well as the frequencies extracted through perturbative studies [ref] .

Fundamental oscillation modes of neutron stars: validity of universal relations · Conclusions · 0.98
The evolution equation of state becomes: [equation] We find that the results obtained from the hybrid equation of state method for our $1.4M_⊙$ polytrope to be consistent with the results from Ref. [ref] .

Probing neutron star structure via f-mode oscillations and damping in dynamical spacetime models · Equations of State · 0.97

Cites as background 38 papers

Recently, Rosofsky et al. [ref] carried out studies in the fully dynamical spacetime and extracted the fundamental modes for the polytropic equations of state.

Probing neutron star structure via f-mode oscillations and damping in dynamical spacetime models · Introduction · 0.87
The $f$-mode oscillations have also been studied using numerical simulations, employing the cowling approximation i.e. by evolving hydrodynamic equations in the fixed background of general relativistic spacetime for a single perturbed neutron star [ref] , also in full GR to study bar mode instability [ref] , as well as under conformally flatness condition (CFC) [ref] , where the 3-metric is assumed to be conformally flat and the spacetime dynamics is coupled with fluid dynamics.

GRMHD in axisymmetric dynamical spacetimes: the X-ECHO code · Introduction · 0.95
The $f$-mode oscillations have also been studied using numerical simulations, employing the cowling approximation i.e. by evolving hydrodynamic equations in the fixed background of general relativistic spacetime for a single perturbed neutron star [ref] , also in full GR to study bar mode instability [ref] , as well as under conformally flatness condition (CFC) [ref] , where the 3-metric is assumed to be conformally flat and the spacetime dynamics is coupled with fluid dynamics.

On the saturation amplitude of the f-mode instability · Introduction · 0.95

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