Quasi-Radial Modes of Pulsating Neutron Stars: Numerical Results for General-Relativistic Rigidly Rotating Polytropic Models (original) (raw)
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We study the radial pulsation frequencies of slowly rotating neutron stars in general relativistic formalism using realistic equations of state. It is found that the pulsation frequencies are always an increasing function of rotation rate. The increasing rate of frequency depends on the nature of equations of state. Cameron [1] suggested that the vibration of neutron stars might excite motions that might have interesting astrophysical applications, which lead to a series of investigations of the vibrational properties of neutron stars. The earliest detailed calculations were done by Meltzer and Thorne [2] and Thorne [3], where they investigated the radial as well as nonradial oscillations using available equation of state, such as the Harrison-Walker-Wheeler equation of state. These and other early studies by Wheeler [4], Chau [5] and Occhionero [6] indicated that the majority
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The Astrophysical Journal, 1999
We compute zero-frequency (neutral) quasi-normal f -modes of fully relativistic and rapidly rotating neutron stars, using several realistic equations of state (EOSs) for neutron star matter. The zero-frequency modes signal the onset of the gravitational radiation-driven instability. We find that the l = m = 2 (bar) f -mode is unstable for stars with gravitational mass as low as 1.0 − 1.2M ⊙ , depending on the EOS. For 1.4M ⊙ neutron stars, the bar mode becomes unstable at 83% − 93% of the maximum allowed rotation rate. For a wide range of EOSs, the bar mode becomes unstable at a ratio of rotational to gravitational energies T /W ∼ 0.07 − 0.09 for 1.4M ⊙ stars and T /W ∼ 0.06 for maximum mass stars. This is to be contrasted with the Newtonian value of T /W ∼ 0.14. We construct the following empirical formula for the critical value of T /W for the bar mode, (T /W ) 2 = 0.115 − 0.048 M/M sph max , which is insensitive to the EOS to within 4 − 6%. This formula yields an estimate for the neutral mode sequence of the bar mode as a function only of the star's mass, M, given the maximum allowed mass, M sph max , of a nonrotating neutron star. The recent discovery of the fast millisecond pulsar in the supernova remnant N157B, supports the suggestion that a fraction of proto-neutron stars are born in a supernova collapse with very large initial angular momentum. If some neutron stars are born in an accretion-induced-collapse of a white dwarf, then they will also have very large angular momentum at birth. Thus, in a fraction of newly born neutron stars the instability is a promising source of continuous gravitational waves. It could also play a major role in the rotational evolution (through the emission of angular momentum) of merged binary neutron stars, if their post-merger angular momentum exceeds the maximum allowed to form a Kerr black hole.
Slowly rotating relativistic stars
Astrophysics and Space Science, 1973
Equations are given which determine the moment of inertia of a rotating relativistic fluid star to second order in the angular velocity with no other approximation being made. The equations also determine the moment of inertia of matter located between surfaces of constant density in a rotationally distorted star; for example, the moments of inertia of the crust and core of a rotationally distorted neutron star can be calculated in this way. The method is applied to n = ~-relativistic polytropes and to neutron star models constructed from the Baym-Bethe-Pethick-Sutherland-Pandbaripande equation of state.
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Cornell University - arXiv, 2014
We revisit the problem of radial pulsations of neutron stars by computing four general-relativistic polytropic models, in which "density" and "adiabatic index" are involved with their discrete meanings: (i) "rest-mass density" or (ii) "mass-energy density" regarding the density, and (i) "constant" or (ii) "variable" regarding the adiabatic index. Considering the resulting four discrete combinations, we construct corresponding models and compute for each model the frequencies of the lowest three radial modes. Comparisons with previous results are made. The deviations of respective frequencies of the resolved models seem to exhibit a systematic behavior, an issue discussed here in detail.
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Astronomy Reports, 2008
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Fast Rotating Neutron Stars with Realistic Nuclear Matter Equation of State
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Uniformly rotating neutron stars
arXiv: High Energy Astrophysical Phenomena, 2016
In this chapter we review the recent results on the equilibrium configurations of static and uniformly rotating neutron stars within the Hartle formalism. We start from the Einstein-Maxwell-Thomas-Fermi equations formulated and extended by Belvedere et al. (2012, 2014). We demonstrate how to conduct numerical integration of these equations for different central densities itrhoc{\it \rho}_citrhoc and angular velocities Omega\OmegaOmega and compute the static MstatM^{stat}Mstat and rotating MrotM^{rot}Mrot masses, polar RpR_pRp and equatorial RrmeqR_{\rm eq}Rrmeq radii, eccentricity epsilon\epsilonepsilon, moment of inertia III, angular momentum JJJ, as well as the quadrupole moment QQQ of the rotating configurations. In order to fulfill the stability criteria of rotating neutron stars we take into considerations the Keplerian mass-shedding limit and the axisymmetric secular instability. Furthermore, we construct the novel mass-radius relations, calculate the maximum mass and minimum rotation periods (maximum frequencies) of neutron star...
Rotating neutron stars: an invariant comparison of approximate and numerical space-time models
Monthly Notices of the Royal Astronomical Society, 2005
We compare three different models of rotating neutron star spacetimes: i) the Hartle-Thorne (1968) slow-rotation approximation, keeping terms up to second order in the stellar angular velocity; ii) the exact analytic vacuum solution of ; and iii) a numerical solution of the full Einstein equations. In the first part of the paper we estimate the limits of validity of the slow-rotation expansion by computing relative errors in the spacetime's quadrupole moment Q and in the corotating and counterrotating radii of Innermost Stable Circular Orbits (ISCOs) R ± . We integrate the Hartle-Thorne structure equations for five representative equations of state. Then we match these models to numerical solutions of the Einstein equations, imposing the condition that the gravitational mass and angular momentum of the models be the same. We find that the Hartle-Thorne approximation gives very good predictions for the ISCO radii, with R ± accurate to better than 1% even for the fastest millisecond pulsars. At these rotational rates the accuracy on Q is ∼ 20%, and better for longer periods. In the second part of the paper we focus on the exterior vacuum spacetimes, comparing the Hartle-Thorne approximation and the Manko analytic solution to the numerical models using Newman-Penrose (NP) coordinateindependent quantities. For all three spacetimes we introduce a physically motivated 'quasi-Kinnersley' NP frame. In this frame we evaluate a quantity, the speciality index S, measuring the deviation of each stellar model from Petrov Type D. Deviations from speciality on the equatorial plane are smaller than 5% at star radii for the faster rotating models, and rapidly decrease for slower rotation rates and with distance. We find that, at leading order, the deviation from Type D is proportional to (Q − Q Kerr ). Our main conclusion is that the Hartle-Thorne approximation is very reliable for most astrophysical applications.