F-mode Frequencies Research Articles

Fundamental Oscillation Modes in Neutron Stars with Hyperons and Delta Baryons

For a new parameterization of the modified effective chiral model, developed primarily to regulate the density content of the symmetry energy and its higher order terms, equations of state (EoSs) for hyperon-rich matter (H) and delta baryon matter (Δ) were obtained. The models were used to investigate the emission of gravitational waves (GWs) through f-mode oscillations in the corresponding neutron stars. We obtained the stellar structure, f-mode frequency and tidal deformability Λ for our models. We report that the Δ EoS is stiffer compared to the H EoS. We also analyzed the velocity of sound in these media. The corresponding mass–radius relationships were obtained and compared with various observations. We studied the dependence of f-mode frequencies on the stellar mass, redshift and tidal deformability. We employed the well known Cowling approximation to obtain the f-mode frequencies for l=2,3 and 4 modes of oscillation. We found that the f-mode frequencies of the H and Δ EoSs were almost the same in the lower mass region, while we observed a substantial difference between them in the high-mass region. We also obtained an empirical relation for the EoSs considered. The various attributes obtained for our models showed close agreement with various observational constraints from pulsars and GW events.

Exploring non-radial oscillation modes in dark matter admixed neutron stars

Because of their extreme densities and consequently, gravitational potential, compact objects such as neutron stars can prove to be excellent captors of dark matter particles. Considering purely gravitational interactions between dark and hadronic matter, we construct dark matter admixed stars composed of two-fluid matter subject to current astrophysical constraints on maximum mass and tidal deformability. We choose a wide range of parameters to construct the dark matter equation of state, and the DDME2 parameterization for the hadronic equation of state. We then examine the effect of dark matter on the stellar structure, tidal deformability and non-radial modes considering the relativistic Cowling approximation. We find the effect on p-modes is substantial, with frequencies decreasing up to the typical f-mode frequency range for most stars with a dark matter halo. The effects on the f-mode frequency are less extreme. Finally, we find the most probable values of the dark matter parameters that satisfy the observational constraints.

Constraining neutron star properties and dark matter admixture with the NITR-I equation of state: Insights from observations and universal relations

A recent observational study has set a constraint on the maximum mass of neutron stars (NSs), specifically focusing on PSR J0952-0607 and the compact star remnant HESS J1731-347, particularly within the low-mass regime. In our recent study, Ref. 1 , we developed an energy density functional named NITR, which successfully produced the mass limit of the aforementioned pulsar but did not fully meet other observational constraints, such as those from NICER+XMM and GW170817. In this study, we introduce a new EDF named “NITR-I”, which not only reproduces the mass limit of PSR J0952-0607 but also aligns its canonical radius with NICER+XMM data, and its canonical dimensionless tidal deformability is consistent with the GW170817 event, thereby demonstrating the robustness of our model. The low-mass constraint associated with HESS J1731-347 suggests various possible compositions for the NS. The NITR-I model alone does not satisfy the HESS J1731-347 constraint; thus, we explore the possibility of incorporating dark matter (DM) inside the NS to meet this constraint. This approach proves successful when a specific value of Fermi momentum is considered. We also examine the impact of DM with varying Fermi momentum on different NS properties, such as tidal deformability and nonradial f-mode oscillation, using various relativistic mean-field (RMF) models. For the NITR-I EOS, the f-mode frequency is about 2.15[Formula: see text]kHz at 1.4 [Formula: see text] when [Formula: see text][Formula: see text]GeV, and it slightly increases to around 2.32[Formula: see text]kHz with [Formula: see text][Formula: see text]GeV. This increase in frequency due to DM suggests a possible reduction in tidal deformability, indicating that neutron stars with higher DM content are less susceptible to deformation by tidal forces which could be detectable in gravitational wave signals from neutron star mergers. Finally, we explore various universal relations (URs) for DM-admixed NSs, such as the relation between compactness and tidal deformability, the f-mode frequency and tidal deformability, and estimate the canonical values corresponding to both compactness and f-mode frequency using the GW170817 data.

Impact of a dark boson mediated feeble interaction between dark matter and hadronic matter on the f -mode oscillation of neutron stars

We studied the possible presence of dark matter (DM) in neutron stars (NSs) and the structural properties of the DM admixed NSs (DMANSs) in one of our recent works [1]. The feeble interaction between the fermionic DM (χ) with the hadronic matter is introduced through a dark scalar (ϕ) and a dark vector (ξ) boson as mediators. The allowed range of the mass of the fermionic DM (mχ), for a particular range of DM Fermi momentum (kFχ), was obtained in the same work [1] with respect to the various astrophysical constraints on the structural properties of compact stars viz., the mass, radius, and tidal deformability. The present work is dedicated to the calculation and study of nonradial oscillation of the DMANSs using Cowling approximation. We particularly investigate the effect of the presence of DM on the fundamental (f) mode oscillation frequencies of the DMANSs utilizing the previously obtained range of mχ for four different hadronic models. In this work we thoroughly investigate how the individual and combined effects of mχ and kFχ affect the f-mode oscillation frequency. Within the framework of our DMANS models, for a particular value of kFχ, the range of fmaxDMANS, with respect to the allowed range of mχ, is also obtained in the present work for four different hadronic models. Since in the present era, the 1.4 and 2.01M⊙ NSs are of special interest after the detection of GW170817 and PSR J0740+6620, we particularly investigate, for the four hadronic models, the range of f1.4DMANS and f2.01DMANS with respect to the acceptable range of mχ corresponding to the range of kFχ. Published by the American Physical Society 2024

Universal relations for anisotropic interacting quark stars

Interacting quark stars, which are entirely composed of interacting quark matter including perturbative QCD corrections and color superconductivity, can meet constraints from various pulsar observations. In realistic scenarios, pressure anisotropies are expected in the star's interior. Recently, the stellar structural properties of anisotropic interacting quark stars have been investigated. In this study, we further explore the universal relations (URs) related to the moment of inertia I, tidal deformability Λ, compactness C, and the f-mode nonradial pulsation frequency for such stars. Our results reveal that these approximate URs generally hold, being insensitive to both the EOS variations as well as to the presence of anisotropy. In contrast to previous studies on anisotropic neutron stars, we find that more positive anisotropy tends to enhance the I-Λ and I-C URs, but weakens the C-Λ UR. For all the URs involving f-mode frequency, we find that they are enhanced by the inclusion of anisotropy (whether positive or negative). Utilizing these URs and the tidal deformability constraint from the GW170817 event, we put limits on the structural properties of isotropic and anisotropic quark stars, such as the moment of inertia I 1.4, the canonical radius R 1.4 and the canonical f-mode frequency f f,1.4, all of which are very different compared to those of neutron stars.

Exploring the macroscopic properties of proto-neutron stars: Effects of entropy and lepton fraction

Neutron stars (NSs) have generally been considered as cold, zero-temperature entities. Recent progress in computational methods and theoretical modelling has opened up the exploration of finite temperature effects, marking an important research frontier. We examine the macroscopic properties of Proto-Neutron Stars (PNS) using different parametrizations of relativistic mean field (RMF) models. We adopt a constant entropy approach by fixing entropy per baryon, S=1 and 2. Higher S elevates the maximum mass for PNS and flattens the mass-radius curves. The higher lepton fraction (Yl) leads to a decrease in maximum mass and an increase in the canonical radius. Furthermore, both the S and Yl influence the dimensionless tidal deformability (Λ). We note that the f-mode frequencies in PNSs increase as S decreases and the Yl increases at maximum mass. We find that the macroscopic properties of the PNS exhibit the same trend, irrespective of the parameter sets employed for the variation of S and Yl.

Universal relations for compact stars with exotic degrees of freedom

The nature of the highly dense matter inside the supernova remnant compact star is not constrained by terrestrial experiments and hence modeled phenomenologically to accommodate the astrophysical observations from compact stars. The observable properties of the compact stars are highly sensitive to the microscopic model of highly dense matter. However, some universal relations exist between some macroscopic properties of compact stars independent of the matter model. We study the universal relation including the stars containing exotic degrees of freedom such as heavier strange and non-strange baryons, strange quark matter in normal and superconducting phases, etc. We examine the universal relations for quantities moment of inertia - tidal love number - quadrupole moment. We also study the correlation of non-radial f-mode and p-mode frequencies with stellar properties. We find the f-mode frequency observes the universal relation with dimensionless tidal deformability but the p-mode frequency does not show a good correlation with stellar properties. The p-mode frequency is sensitive to the composition of the matter. We find that universal relation is also applicable for stars with exotic matter in the core of the star with several models of exotic matter.

Analysis of Neutron Star f-mode Oscillations in General Relativity with Spectral Representation of Nuclear Equations of State

We study quasi-normal f-mode oscillations in neutron star (NS) interiors within a linearized general relativistic formalism. We utilize approximately 9000 nuclear equations of state (EOSs) using spectral representation techniques, incorporating constraints on nuclear saturation properties, chiral effective field theory for pure neutron matter, and perturbative quantum chromodynamics for densities pertinent to NS cores. The median values of the f-mode frequency, ν f (damping time, τ f ) for NSs with masses ranging from 1.4 to 2.0 M ⊙ lie between 1.80 and 2.20 kHz (0.13–0.22 s) for our entire EOS set. Our study reveals a weak correlation between f-mode frequencies and individual nuclear saturation properties, prompting the necessity for more intricate methodologies to unveil multiparameter relationships. We observe a robust linear relationship between the radii and f-mode frequencies for different NS masses. Leveraging this correlation alongside NICER observations of PSR J0740+6620 and PSR J0030+0451, we establish constraints that exhibit partial and minimal overlap for observational data from Riley et al. and Miller et al., respectively, with our nucleonic EOS data set. Moreover, NICER data align closely with the radius and frequency values for a few hadron–quark hybrid EOS models. This indicates the need to consider additional exotic particles such as deconfined quarks at suprasaturation densities. We conclude that future observations of the radius or f-mode frequency for more than one NS mass, particularly at the extremes of the viable NS mass scale, would either rule out nucleon-only EOSs or provide definitive evidence in its favor.

Non-radial oscillations in anisotropic dark energy stars

We study the non-radial f-mode oscillations of both isotropic and anisotropic dark energy stars by using the modified Chaplygin prescription of dark energy to model the stellar matter. The anisotropic pressure in the system is modeled with Bowers–Liang prescription. By solving the stellar structure equations in presence of anisotropy, we study the global properties of the dark energy star and compare the mass-radius profiles with data from GW events and milli-second pulsars. The stellar radial and anisotropic pressure profiles have also been investigated. We proceed to determine the prominent non-radial l=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l=2$$\\end{document}f-mode frequencies of the anisotropic dark energy star by employing the Cowling approximation and analyse and quantify the spectra by varying the anisotropic parameter. We report that f-mode spectra of dark energy star have distinctly different behaviour compared to neutron star and quark star, and this may possibly help in its future identification. Further, the tidal deformability factors of the anisotropic dark energy stars have also been analyzed.

The impact of anisotropy on neutron star properties: insights from 𝖨–𝖿–𝖢 universal relations

Anisotropy in pressure within a star emerges from exotic internal processes. In this study, we incorporate pressure anisotropy using the Quasi-Local model. Macroscopic properties, including mass (M), radius (R), compactness (C), dimensionless tidal deformability (Λ), the moment of inertia (I), and oscillation frequency (f), are explored for the anisotropic neutron star. Magnitudes of these properties are notably influenced by anisotropy degree. Universal I–f–C relations for anisotropic stars are explored in this study. The analysis encompasses various EOS types, spanning from relativistic to non-relativistic regimes. Results show the relation becomes robust for positive anisotropy, weakening with negative anisotropy. The distribution of f-mode across M–R parameter space as obtained with the help of C–f relation was analyzed for different anisotropic cases. Using tidal deformability data from GW170817 and GW190814 events, a theoretical limit for canonical f-mode frequency is established for isotropic and anisotropic neutron stars. For isotropic case, canonical f-mode frequency for GW170817 event is f 1.4 = 2.606+0.457 -0.484kHz; for GW190814 event, it is f 1.4 = 2.097+0.124 -0.149kHz. These relationships can serve as reliable tools for constraining nuclear matter EOS when relevant observables are measured.

The acoustic size of the Sun

ABSTRACT Analysis of f-mode frequencies has provided a measure of the radius of the Sun which is lower, by a few hundredths per cent, than the photospheric radius determined by direct optical measurement. Part of this difference can be understood by recognizing that it is primarily the variation of density well beneath the photosphere of the star that determines the structure of these essentially adiabatic oscillation modes, not some aspect of radiative intensity. In this paper we attempt to shed further light on the matter, by considering a differently defined, and dynamically more robust, seismic radius, namely one determined from p-mode frequencies. This radius is calibrated by the distance from the centre of the Sun to the position in the subphotospheric layers where the first derivative of the density scale height changes essentially discontinuously. We find that radius is more-or-less consistent with what is suggested by the f modes. In addition, the interpretation of the radius inferred from p modes leads us to understand more deeply the role of the total mass constraint in the structure inversions. This enables us to reinterpret the sound-speed inversion, suggesting that the positions of the photosphere and the adiabatically stratified layers in the convective envelope differ non-homologously from those of the standard solar model.

Constraining Nuclear Parameters Using Gravitational Waves from f-mode Oscillations in Neutron Stars

Gravitational waves (GWs) emanating from unstable quasi-normal modes in neutron stars (NSs) could be accessible with the improved sensitivity of the current GW detectors or with the next-generation GW detectors and, therefore, can be employed to study the NS interior. Assuming f-mode excitation in isolated pulsars with typical energy of pulsar glitches and considering potential f-mode GW candidates for A+ (upgraded LIGO detectors operating at fifth observing run design sensitivity) and Einstein Telescope (ET), we demonstrate the inverse problem of NS asteroseismology within a Bayesian formalism to constrain the nuclear parameters and NS equation of state (EOS). We describe the NS interior within relativistic mean-field formalism. Taking the example of glitching pulsars, we find that for a single event in A+ and ET, among the nuclear parameters, the nucleon effective mass (m*) within 90% credible interval can be restricted within 10% and 5%, respectively. At the same time, the incompressibility (K) and the slope of the symmetry energy (L) are only loosely constrained. Considering multiple (10) events in A+ and ET, all the nuclear parameters are well constrained, especially m*, which can be constrained to 3% and 2% in A+ and ET, respectively. Uncertainty in the observables of a 1.4 M ⊙ NS such as radius (), f-mode frequency (), damping time (), and a few EOS properties including squared speed of sound (c s 2) are also estimated.

Investigating dark matter-admixed neutron stars with NITR equation of state in light of PSR J0952-0607

The fastest and heaviest pulsar, PSR J0952-0607, with a mass of M = 2.35±0.17 M ⊙, has recently been discovered in the disk of the Milky Way Galaxy. In response to this discovery, a new RMF model, 'NITR' has been developed. The NITR model's naturalness has been confirmed by assessing its validity for various finite nuclei and nuclear matter properties, including incompressibility, symmetry energy, and slope parameter values of 225.11, 31.69, and 43.86 MeV, respectively. These values satisfy the empirical/experimental limits currently available. The maximum mass and canonical radius of a neutron star (NS) calculated using the NITR model parameters are 2.355 M ⊙ and 13.13 km, respectively, which fall within the range of PSR J0952-0607 and the latest NICER limit. This study aims to test the consistency of the NITR model by applying it to various systems. As a result, its validity is extensively calibrated, and all the nuclear matter and NS properties of the NITR model are compared with two established models such as IOPB-I and FSUGarnet. In addition, the NITR model equation of state (EOS) is employed to obtain the properties of a dark matter admixed NS (DMANS) using two approaches (I) single-fluid and (II) two-fluid approaches. In both cases, the EOS becomes softer due to DM interactions, which reduces various macroscopic properties such as maximum mass, radius, tidal deformability, etc. The various observational data such as NICER and HESS are used to constrain the amount of DM in both cases. Moreover, we discuss the impact of dark matter (DM) on the nonradial f-mode frequency of the NS in a single fluid case only and try to constrain the amount of DM using different theoretical limits available in the literature.

Gravitational-wave signature of core-collapse supernovae

We calculate the gravitational-wave (GW) signatures of detailed 3D core-collapse supernova simulations spanning a range of massive stars. Most of the simulations are carried out to times late enough to capture more than 95% of the total GW emission. We find that the f/g-mode and f-mode of proto-neutron star oscillations carry away most of the GW power. The f-mode frequency inexorably rises as the proto-neutron star (PNS) core shrinks. We demonstrate that the GW emission is excited mostly by accretion plumes onto the PNS that energize modal oscillations and also high-frequency (``haze") emission correlated with the phase of violent accretion. The duration of the major phase of emission varies with exploding progenitor and there is a strong correlation between the total GW energy radiated and the compactness of the progenitor. Moreover, the total GW emissions vary by as much as three orders of magnitude from star to star. For black-hole formation, the GW signal tapers off slowly and does not manifest the haze seen for the exploding models. For such failed models, we also witness the emergence of a spiral shock motion that modulates the GW emission at a frequency near $\sim$100 Hertz that slowly increases as the stalled shock sinks. We find significant angular anisotropy of both the high- and low-frequency (memory) GW emissions, though the latter have very little power.

Radial Oscillations in Neutron Stars from Unified Hadronic and Quarkyonic Equation of States

We study radial oscillations in non-rotating neutron stars by considering the unified equation of states (EoSs), which support the 2 M⊙ star criterion. We solve the Sturm–Liouville problem to compute the 20 lowest radial oscillation modes and their eigenfunctions for a neutron star modeled with eight selected unified EoSs from distinct Skyrme–Hartree–Fock, relativistic mean field and quarkyonic models. We compare the behavior of the computed eigenfrequency for an NS modeled with hadronic to one with quarkyonic EoSs while varying the central densities. The lowest-order f-mode frequency varies substantially between the two classes of the EoS at 1.4 M⊙ but vanishes at their respective maximum masses, consistent with the stability criterion ∂M/∂ρc>0. Moreover, we also compute large frequency separation and discover that higher-order mode frequencies are significantly reduced by incorporating a crust in the EoS.

Oscillations and tidal deformations of crystallized white dwarfs

ABSTRACTLong predicted more than 50 years ago, strong evidence for the existence of crystalline cores inside white dwarfs has recently been obtained by the Gaia space telescope. It is thus important to investigate how a crystalline core may affect the properties and dynamics of white dwarfs. In this paper, we first study the dependence of the frequencies of the fundamental (f), interfacial (i), and shear (s) oscillation modes on the size of the crystalline core. We find that the frequencies of the i and s modes depend sensitively on the size of the core, while the frequency of the f mode is affected only slightly by at most a few percent for our chosen white dwarf models. We next consider the tidal deformability of crystallized white dwarfs and find that the effect of crystallization becomes significant only when the radius of the core is larger than about 70 per cent of the stellar radius. The tidal deformability can change by a few to about 10 per cent when a white dwarf becomes fully crystallized. We also show that there exist approximate equation-of-state insensitive relations connecting the mass, moment of inertia, tidal deformability, and f-mode frequency for pure fluid white dwarfs. Depending on the stellar mass and composition, however, these relations can be affected by a few percent when the white dwarf is crystallized. These changes could leave an imprint on the gravitational waves emitted from the late inspiral or merger of white dwarf binaries, which may be detectable by future space-borne gravitational wave detectors.

Impact of updated multipole Love numbers and f -Love universal relations in the context of binary neutron stars

Neutron star (NS) equation of state (EoS) insensitive relations or universal relations (UR) involving neutron star bulk properties play a crucial role in gravitational-wave astronomy. Considering a wide range of equations of state originating from (i) phenomenological relativistic mean field models, (ii) realistic EoS models based on different physical motivations, and (iii) polytropic EoSs described by spectral decomposition method, we update the EoS-insensitive relations involving NS tidal deformability (Multipole Love relation) and the UR between f-mode frequency and tidal deformability (f-Love relation). We analyze the binary neutron star (BNS) event GW170817 using the frequency domain TaylorF2 waveform model with updated universal relations and find that the additional contribution of the octupolar electric tidal parameter and quadrupolar magnetic tidal parameter or the change of multipole Love relation has no significant impact on the inferred NS properties. However, adding the f-mode dynamical phase lowers the 90% upper bound on $\tilde{\Lambda}$ by 16-20% as well as lowers the upper bound of NSs radii by $\sim$500m. The combined URs (multipole Love and f-Love) developed in this work predict a higher median (also a higher 90% upper bound) for $\tilde{\Lambda}$ by 6% and also predict higher radii for the binary components of GW170817 by 200-300m compared to the URs used previously in the literature. We further perform injection and recovery studies on simulated events with different EoSs in $\rm A+$ detector configuration as well as with third generation (3G) Einstein telescope. In agreement with the literature, we find that neglecting f-mode dynamical tides can significantly bias the inferred NS properties, especially for low mass NSs. However, we also find that the impact of the URs is within statistical errors.

Oscillation modes and gravitational waves from strangeon stars

Abstract The strong interaction at low energy scales determines the equation of state (EOS) of supranuclear matters in neutron stars (NSs). It is conjectured that the bulk dense matter may be composed of strangeons, which are quark clusters with nearly equal numbers of u, d, and s quarks. To characterize the strong-repulsive interaction at short distance and the nonrelativistic nature of strangeons, a phenomenological Lennard-Jones model with two parameters is used to describe the EOS of strangeon stars (SSs). For the first time, we investigate the oscillation modes of non-rotating SSs and obtain their frequencies for various parameterizations of the EOS. We find that the properties of radial oscillations of SSs are different from those of NSs, especially for stars with relatively low central energy densities. Moreover, we calculate the f-mode frequency of nonradial oscillations of SSs within the relativistic Cowling approximation. The frequencies of the f-mode of SSs are found to be in the range from 6.7 kHz to $8.7\, \rm {kHz}$. Finally, we study the universal relations between the f-mode frequency and global properties of SSs, such as the compactness and the tidal deformability. The results we obtained are relevant to pulsar timing and gravitational waves, and will help to probe NSs’ EOSs and infer nonperturbative behaviours in quantum chromodynamics.

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.