Fundamental oscillation modes of neutron stars: Validity of universal relations (original) (raw)
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Gravitational waves from neutron stars described by modern EOS
The frequencies and damping times of neutron star (and quark star) oscillations have been computed using the most recent equations of state available in the literature. We find that some of the empirical relations that connect the frequencies and damping times of the modes to the mass and radius of the star, and that were previously derived in the literature need to be modified.
The imprint of the equation of state on the axial w-modes of oscillating neutron stars
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Gravitational wave asteroseismology of fast rotating neutron stars with realistic equations of state
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In the present paper we study the oscillations of fast rotating neutron stars with realistic equations of state (EoS) within the Cowling approximation. We derive improved empirical relations for gravitational wave asteroseismology with f -modes and for the first time we consider not only quadrupolar oscillations but also modes with higher spherical order (l = |m| = 3, 4). After performing a systematic comparison with polytropic EoS, it is shown that the empirical relations found in this case approximately also hold for realistic EoS. Even more, we show that these relations will not change significantly even if the Cowling approximation is dropped and the full general relativistic case is considered, although the normalization used here (frequencies and damping times in the nonrotating limit) could differ considerably. We also address the inverse problem, i.e. we investigate in detail what kind of observational data is required in order to determine characteristical neutron star parameters. It is shown that masses, radii and rotation rates can be estimated quite accurately using the derived asteroseismology relations. We also compute the instability window for certain models, i.e. the limiting curve in a T − Ω-plane where the secular Chandrasekhar-Friedman-Schutz (CFS) instability overcomes dissipative effects, and show that some of the modern realistic EoS will lead to a larger instability window compared to all of the polytropic ones presented so far in the literature. Additionally, we calculate the r-mode instability window and compare it with the f -mode-case. The overall results for the instability window suggest that it is vital to take into account oscillations with l = 3, 4 when considering gravitational wave asteroseismology using the f -mode in rapidly rotating neutron stars, as these modes can become CFS unstable for a much larger range of parameters than pure quadrupolar oscillations.
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Physical Review D, 2013
We study the dynamical evolution of the gravitational-wave driven instability of the f -mode in rapidly rotating relativistic stars. With an approach based on linear perturbation theory we describe the evolution of the mode amplitude and follow the trajectory of a newborn neutron star through its instability window. The influence on the f -mode instability of the magnetic field and the presence of an unstable r-mode is also considered. Two different configurations are studied in more detail; a standard N = 1 polytrope with a typical mass and radius and a more extreme polytropic N = 2/3 model which describes a supramassive neutron star. We study several evolutions with different initial rotation rates and temperature and determine the gravitational waves radiated during the instability. For reasonable values of the mode saturation amplitude, i.e. with a mode energy of about 10 −6 M c 2 , the gravitational-wave signal can be detected by the Einstein Telescope detector from the Virgo cluster. The magnetic field affects the evolution and then the detectability of the gravitational radiation when its strength is higher than 10 12 G, while the effects of an unstable rmode become dominant when this mode reaches the maximum saturation value allowed by non-linear mode couplings. However, the relative saturation amplitude of the f -and r-modes must be known more accurately in order to provide a definitive answer to this issue. From the thermal evolution we find also that the heat generated by shear viscosity during the saturation phase completely balances the neutrinos' cooling and prevents the star from entering the regime of mutual friction. The evolution time of the instability is therefore longer and the star loses significantly larger amounts of angular momentum via gravitational waves.
Nonlinear Evolution of the r-Modes in Neutron Stars
Physical Review Letters, 2001
The evolution of a neutron-star r-mode driven unstable by gravitational radiation (GR) is studied here using numerical solutions of the full nonlinear fluid equations. The dimensionless amplitude of the mode grows to order unity before strong shocks develop which quickly damp the mode. In this simulation the star loses about 40% of its initial angular momentum and 50% of its rotational kinetic energy before the mode is damped. The nonlinear evolution causes the fluid to develop strong differential rotation which is concentrated near the surface and poles of the star.
Oscillations of hot, young neutron stars: Gravitational wave frequencies and damping times
Arxiv preprint arXiv: …, 2011
We study how the frequencies and damping times of oscillations of a newly born, hot proto-neutron star depend on the physical quantities which characterize the star quasi-stationary evolution which follows the bounce. Stellar configurations are modeled using a microscopic equation of state obtained within the Brueckner-Hartree-Fock, nuclear many-body approach, extended to the finite-temperature regime. We discuss the mode frequency behaviour as function of the lepton composition, and of the entropy gradients which prevail in the interior of the star. We find that, in the very early stages, gravitational wave emission efficiently competes with neutrino processes in dissipating the star mechanical energy residual of the gravitational collapse.
Asteroseismology: Radial oscillations of neutron stars with realistic equation of state
Physical Review D, 2020
We study radial oscillations of non-rotating neutron stars (NSs) in four-dimensional General Relativity. The interior of the NS was modelled within a recently proposed multicomponent realistic equation of state (EoS) with the induced surface tension (IST). In particular, we considered the IST EoS with two sets of model parameters, that both reproduce all the known properties of normal nuclear matter, give a high quality description of the proton flow constraint, hadron multiplicities created in nuclear-nuclear collisions, consistent with astrophysical observations and the observational data from the NS-NS merger. We computed the 12 lowest radial oscillation modes, their frequencies and corresponding eigenfunctions, as well as the large frequency separation for six selected fiducial NSs (with different radii and masses of 1.2, 1.5 and 1.9 solar masses) of the two distinct model sets. The calculated frequencies show their continuous growth with an increase of the NS central baryon density. Moreover, we found correlations between the behaviour of first eigenfunction calculated for the fundamental mode, the adiabatic index and the speed of sound profile, which could be used to probe the internal structure of NSs with the asteroseismology data.
Classical and Quantum Gravity, 2006
We briefly review the properties of quasi-normal modes of neutron stars and black holes. We analyze the consequences of a possible detection of such modes via the gravitational waves associated with them, specially addressing our study to the Brazilian spherical antenna, on which a possible detection would occur at 3.0-3.4 kHz. A question related to any putative gravitational wave detection concerns the source that produces it. We argue that, since the characteristic damping times for the gravitational waves of neutron stars and black holes are different, a detection can distinguish between them; and also distinguish the neutron star's oscillating modes. Moreover, since the source can be identified by its characteristic damping time, we are able to extract information about the neutron star or black hole. This information would lead, for example, to a strong constrain in the nuclear matter equation of state, namely, the compression modulus should be K ≈ 220M eV .
Quasi‐normal Modes of Rotating Relativistic Stars: Neutral Modes for Realistic Equations of State
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.