Oscillations Of Neutron Stars Research Articles

Impact of the equation of state on f - and p - mode oscillations of neutron stars

We investigate the impact of the neutron-star matter equation of state on the $f$- and $p_1$-mode oscillations of neutron stars obtained within the Cowling approximation and linearized general relativity. The $f$- and $p_1$-mode oscillation frequencies, and their damping times are calculated using representative sets of Skyrme Hartree-Fock and relativistic mean-field models, all of which reproduce nuclear systematics and support $2M_\odot$ neutron stars. Our study shows strong correlations between the frequencies of $f$- and $p_1$-modes and their damping times with the pressure of $\beta$-equilibrated matter at densities equal to or slightly higher than the nuclear saturation density $\rho_0$. Such correlations are found to be almost independent of the composition of the stars. The frequency of the $p_1$-mode of $1.4M_\odot$ star is strongly correlated with the slope of the symmetry energy $L_0$ and $\beta$-equilibrated pressure at density $\rho_0$. Compared to GR calculations, the error in the Cowling approximation for the $f$-mode is about 30\% for neutron stars of low mass, whereas it decreases with increasing mass. The accuracy of the $p_1$-mode is better than 15\% for neutron stars of maximum mass, and improves for lower masses and higher number of radial nodes.

General relativistic treatment of f -mode oscillations of hyperonic stars

We present a systematic study of $f$-mode oscillations in neutron stars containing hyperons, extending recent results obtained within the Cowling approximation to linearized general relativity. Employing a relativistic mean-field model, we find that the Cowling approximation can overestimate the quadrupolar $f$-mode frequency of neutron stars by up to 30% compared to the frequency obtained in the linearized general relativistic formalism. Imposing current astrophysical constraints, we derive updated empirical relations for gravitational wave asteroseismology. The frequency and damping time of quadrupole $f$-mode oscillations of hyperonic stars are found to be in the range of 1.47--2.45 kHz and 0.13--0.51 s, respectively. Our correlation studies demonstrate that among the various parameters of the nucleonic and hyperonic sectors of the model, the nucleon effective mass shows the strongest correlation with mode characteristics and neutron star observables. Estimates for the detectability of $f$ modes in a transient burst of gravitational waves from isolated hyperonic stars is also provided.

Constraining the nuclear equation of state from rotating neutron stars

We demonstrate how observables of slowly rotating neutron stars can be used to constrain the nuclear equation of state. By building a Bayesian framework we demonstrate how combining different types of neutron star measurements, motivated by the upcoming multi-messenger era, provide informative posterior distributions of commonly used equation of state parametrizations. Exemplarily, we chose the Read et al. four parameter model that is widely used to represent realistic equations of states in neutron star physics. Since future observational campaigns will not only provide mass, radius and rotation rate measurements, but also neutron star oscillation modes, a unified framework to analyze the joint knowledge becomes necessary. While several attempts exist in the literature, the here presented framework explicitly takes into account rotational effects by using state-of-the-art universal relations for their oscillation spectra. To demonstrate its performance we apply it to observables that take into account rotational effects to best possible precision and use our independent model for the reconstruction. Only a few high precision neutron star measurements are required to put tight constraints on the underlying equation of state.

Using machine learning to parametrize postmerger signals from binary neutron stars

There is growing interest in the detection and characterization of gravitational waves from postmerger oscillations of binary neutron stars. These signals contain information about the nature of the remnant and the high-density and out-of-equilibrium physics of the postmerger processes, which would complement any electromagnetic signal. However, the construction of binary neutron star postmerger waveforms is much more complicated than for binary black holes: (i) there are theoretical uncertainties in the neutron-star equation of state and other aspects of the high-density physics, (ii) numerical simulations are expensive and available ones only cover a small fraction of the parameter space with limited numerical accuracy, and (iii) it is unclear how to parametrize the theoretical uncertainties and interpolate across parameter space. In this work, we describe the use of a machine-learning method called a conditional variational autoencoder (CVAE) to construct postmerger models for hyper/massive neutron star remnant signals based on numerical-relativity simulations. The CVAE provides a probabilistic model, which encodes uncertainties in the training data within a set of latent parameters. We estimate that training such a model will ultimately require $\ensuremath{\sim}{10}^{4}$ waveforms. However, using synthetic training waveforms as a proof-of-principle, we show that the CVAE can be used as an accurate generative model and that it encodes the equation of state in a useful latent representation.

Effects of relativistic parameter sets on tidal deformabilities and f-mode oscillations of neutron stars

The implications of relativistic parameter sets established at saturation density on the tidal deformabilities and f-mode oscillations of neutron stars (NSs) are examined using constraints from the gravitational wave (GW) event GW170817 and NICER. According to our findings, the isovector saturation parameters have a greater impact on the radii and tidal deformabilities of NSs than the isoscalar saturation parameters. Our analysis also examines the impact of saturation properties on f-mode frequencies and finds that f-mode frequencies with 1.4 M ⊙ (solar mass) are roughly between 1.95 and 2.15 kHz. These findings could be confirmed by future advanced GW detectors. A good linear parameter-independent correlation between f-mode frequencies inferred from saturation parameters in the entire region is also observed, and we attempt to fit an updated version of this universal relationship. Furthermore, we used chiral effective theory (χ EFT) together with the multi-messenger astronomy constraints to further reinforce the rationality of the conclusions we have reached.

Neutron star oscillations in pseudo-Newtonian gravity

ABSTRACT We investigate the oscillations of neutron stars using a purely Newtonian approach and three other pseudo-Newtonian formulations. Our work is motivated by the fact that pseudo-Newtonian formulations are commonly used in core-collapse supernova (CCSN) simulations. We derive and solve numerically the radial and non-radial perturbation equations for neutron star oscillations using different combinations of modified Newtonian hydrodynamics equations and gravitational potentials. We pay special attention to the formulation proposed recently by Zha et al. that implements the standard Case A effective potential in CCSN simulations with an additional lapse-function correction to the hydrodynamics equations. We find that this ‘Case A + lapse’ formulation can typically approximate the frequency of the fundamental radial mode of a 1.4-M⊙ neutron star computed in general relativity to about a few tens of per cent for our chosen EOS models. For the non-radial quadrupolar f mode, which is expected to contribute strongly to the gravitational waves emitted from a protoneutron star, the Case A + lapse formulation performs much better and can approximate the f-mode frequency to within about a few per cent even for the maximum-mass configuration in general relativity.

Radial oscillations in neutron stars from QCD

We study the stability against infinitesimal radial oscillations of neutron stars generated by a set of equations of state obtained from first-principle calculations in cold and dense QCD and constrained by observational data. We consider mild and large violations of the conformal bound, $c_{s} = 1/\sqrt{3}$, in stars that can possibly contain a quark matter core. Some neutron star families in the mass-radius diagram become dynamically unstable due to large oscillation amplitudes near the core.

Oscillation dynamics of scalarized neutron stars

Scalar-tensor theories are well-studied extensions of general relativity that offer deviations which are yet within observational boundaries. We present the time evolution equations governing the perturbations of a nonrotating scalarized neutron star, including a dynamic spacetime as well as scalar field within the framework of such scalar-tensor theories. We employ a theory that allows for a massive scalar field or a self-interaction term and we study the impact of those parameters on the nonaxisymmetric $f$-mode. The time evolution approach allows for a comparatively simple implementation of the boundary conditions. We find that the $f$-mode frequency is no longer a simple function of the star's average density when a scalar field is present. We also evaluate the accuracy of different variants of the Cowling approximation commonly used in previous studies of neutron star oscillation modes in alternative theories of gravity and demonstrate that it can give us not only qualitatively correct results, but in some cases also good quantitative estimates of the oscillations frequencies.

Constraining Dense Matter Physics Using f-Mode Oscillations in Neutron Stars

In this paper, an investigation of the role of nuclear saturation parameters on f-mode oscillations in neutron stars is performed within the Cowling approximation. It is found that the uncertainty in the effective nucleon mass plays a dominant role in controlling the f-mode frequencies. The effect of the uncertainties in saturation parameters on previously-proposed empirical relations of the frequencies with astrophysical observables relevant for asteroseismology are also investigated. These results can serve as an important tool for constraining the nuclear parameter space and understand the behaviour of dense nuclear matter from the future detection of f-modes.

Equation of state and radial oscillations of neutron stars

We investigate radial oscillations of pure neutron stars and hybrid stars, employing equations of state of nuclear matter from Brueckner-Hartree-Fock theory, and of quark matter from the Dyson-Schwinger quark model, performing a Gibbs construction for the mixed phase in hybrid stars. We calculate the eigenfrequencies and corresponding oscillation functions. Our results for the zero points of the first-order radial oscillation frequencies give the maximum mass of stable neutron stars, consistent with the common criterion $dM/d\rho_c=0$. Possible observations of the radial oscillation frequencies could help to learn more about the equation of state, predict the maximum mass of neutron stars more precisely, and indicate the presence of quark matter.

Effect of hyperons on f -mode oscillations in neutron stars

As the densities in the interior of neutron stars exceed those of terrestrial nuclear experiments, they provide a scope for studying the nature of dense matter under extreme conditions. The composition of the inner core of neutron stars is highly uncertain, and it is speculated that exotic forms of matter such as hyperons may appear there. Gravitational waves emitted by unstable oscillation modes in neutron stars contain information about their interior composition and therefore allow us to probe the interior directly. Recently, a systematic investigation of $f$-mode oscillations in neutron stars revealed the role of the uncertainty in nuclear saturation parameters, particularly the effective nucleon mass, on its frequency. In this work, we study the influence of the appearance of hyperons on $f$-mode oscillation frequencies and therefore on the emission of gravitational waves. We also speculate whether a future detection of $f$-mode frequencies could provide a possibility of probing the presence of hyperons in the neutron star core.

Entrainment matrix for BSk energy-density functionals

The entrainment matrix is an important parameter of superfluid hydrodynamics and is extensively used to model, e.g., neutron-star oscillations and glitches. Here we present a detailed step-by-step algorithm to calculate this matrix for a series of modern BSk energy-density functionals. Using it, both the entrainment matrix and equation of state can be determined self-consistently, within the same microscopic approach.

Diffusion as a damping mechanism for neutron-star oscillations

We study the effects of diffusion on damping of oscillations in the neutron star cores. This dissipation mechanism is usually ignored in the literature. As we show, the effect of diffusion is always smaller than viscous dissipation if the normal (nonsuperfluid and nonsuperconducting) matter of neutron stars is considered. However, we argue that for superconducting stars the role of diffusion may increase.

Asteroseismology: Radial oscillations of neutron stars with realistic equation of state

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.

Crustal torsional oscillations inside the deeper pasta structures

AbstractThe quasiperiodic oscillations (QPOs) have been discovered in the afterglow of the giant flares observed in the soft‐gamma repeaters. As QPOs are strongly associated with the neutron star oscillations, one could extract the neutron star properties via identification of QPOs as specific neutron star oscillations. In this study, we take into account the torsional oscillations inside the phase composed of cylindrical holes (tubes) and spherical holes (bubbles), which correspond to the inner layer in the neutron star crust. We remark that such oscillations are independent of the oscillations inside the phase composed of spherical and cylindrical nuclei, which correspond to the outer layer. Then, we find that all the observed QPOs can be explained with torsional oscillations excited in either layer, which is consistent with the severe constraint on the slope parameter, L, of nuclear symmetry energy as L ≃ 58 − 73 MeV obtained in our previous study.

R-mode stabilization in neutron stars with hyperon cores

R-mode oscillations of neutron stars are known to be generally unstable with respect to the emission of gravitational waves. This instability can be suppressed by dissipative processes in the neutron star core. The standard minimal nucleonic model of the core cannot stabilize r-modes for many observed neutron stars, at the same time the probability to observe them unstable should be very low. One of the solutions to this problem is to account for possible presence of hyperons in the stellar core. Hyperons strongly enhance bulk viscosity in the core, which effectively suppresses the r-mode instability. We revisit the bulk viscosity calculations in the non-superfluid hyperon matter and briefly discuss the effect of baryon superfluidity. Our results suggest that the hyperon solution to the r-mode problem is more promising than it was thought before.

Effect of viscosity and thermal conductivity on the radial oscillation and relaxation of relativistic stars

In this paper we present a generic formulation of the linearized dynamical equations governing small adiabatic radial oscillations of relativistic stars. The dynamical equations are derived by taking into consideration those effects of viscosity and thermal conductivity of neutron-star matter which directly determine the minimum period of observable pulsars. A variational principle is applied to determine a discrete set of eigenfunctions with complex eigenvalues. The real and imaginary parts of eigenvalues represent the squared natural frequencies and relaxation time of radial oscillations of non-rotating neutron stars, respectively. We provide a suitable framework which may be supplemented with various potential species of cold-nuclear-matter models to compute the spectra of the normalized eigenfrequencies with a certain numerical precision. In the last section, we provide a qualitative estimation of the rate at which viscosity and thermal conductivity drain the kinetic energy of radial oscillation mode in reasonably uniform neutron stars, without relying on explicit numerical computations.

The g-mode spectrum of reactive neutron star cores

Abstract We discuss the impact of nuclear reactions on the spectrum of gravity g-modes of a mature neutron star, demonstrating the anticipated disappearance of these modes when the timescale associated with the oscillations is longer than that of nuclear reactions. This is the expected result, but different aspects of the demonstration may be relevant for related problems in neutron star astrophysics. In particular, we develop the framework required for an explicit implementation of finite-time nuclear reactions in neutron star oscillation problems and demonstrate how this formulation connects with the usual bulk viscosity prescription. We also discuss implications of the absence of very high order g-modes for problems of astrophysical relevance.

Torsional oscillations of magnetized neutron stars with mixed poloidal-toroidal fields

The quasiperiodic oscillations found in the three giant flares of soft gamma-ray repeaters observed to date have been interpreted as torsional oscillations caused by a starquake related to a magnetospheric reconnection event. Motivated by these observations, we study the influence of the magnetic field geometry in the frequencies of the torsional oscillations of magnetized neutron stars. We use realistic tabulated equations of state for the core and crust of the stars and model their magnetic field as a dipole plus a toroidal component, using the relativistic Grad-Shafranov equation. The frequencies of the torsional modes are obtained by the numerical solution of the eigenvalue problem posed by the linear perturbation equations in the Cowling approximation. Our results show how the asteroseismology of these stars becomes complicated by the degeneracy in the frequencies due to the large relevant parameter space. However, we are able to propose approximately equation-of-state--independent relations that parametrize the influence of the magnetic field in the torsional oscillations, as well as a testable scenario in which the rearrangement of the magnetic field causes an evolution of the frequencies. Finally, we show that there is a magnetic field configuration that maximizes the energy in the perturbation at linear order, which could be related to the trigger of the giant flare.

Exploring the sensitivity of gravitational wave detectors to neutron star physics

The physics of neutron stars can be studied with gravitational waves emitted from coalescing binary systems. Tidal effects become significant during the last few orbits and can be visible in the gravitational-wave spectrum above 500 Hz. After the merger, the neutron star remnant oscillates at frequencies above 1 kHz and can collapse into a black hole. Gravitational-wave detectors with a sensitivity of ~10^{-24} strain/sqHz at 2-4 kHz can observe these oscillations from a source which is ~100 Mpc away. The current observatories, such as LIGO and Virgo, are limited by shot noise at high frequencies and have a sensitivity of > 2 * 10^{-23} strain/sqHz at 3 kHz. In this paper, we propose an optical configuration of gravitational-wave detectors which can be set up in present facilities using the current interferometer topology. This scheme has a potential to reach 7 * 10^{-25} strain/sqHz at 2.5 kHz without compromising the detector sensitivity to black hole binaries. We argue that the proposed instruments have a potential to detect similar amount of post-merger neutron star oscillations as the next generation detectors, such as Cosmic Explorer and Einstein Telescope. We also optimise the arm length of the future detectors for neutron star physics and find that the optimal arm length is ~20 km. These instruments have the potential to observe neutron star post-merger oscillations at a rate of ~30 events per year with a signal-to-noise ratio of 5 or more.