Oscillations Of Neutron Stars Research Articles

Torsional oscillations of magnetized neutron stars: Impacts of Landau-Rabi quantization of electron motion

Torsional oscillations of magnetized neutron stars: Impacts of Landau-Rabi quantization of electron motion

Probing hadron–quark phase transition in twin stars using f-modes

ABSTRACT Although it is conjectured that a phase transitions from hadronic to deconfined quark matter in the ultrahigh-density environment of neutron stars (NS), the nature of phase transition remains an unresolved mystery. Furthermore, recent efforts reveal that the finite surface tension effects can lead to a mixed phase with different geometric shapes (so-called ‘pasta’ phases), leading to a smooth phase transition from hadronic to quark matter in the NS interior. Depending on whether there is a strong or a pasta-induced smooth first-order phase transition, one may expect a third family of stable, compact stars or ‘twin stars’ to appear, with the same mass but different radii compared to NSs. The possibility of identifying twin stars using astrophysical observations has been a subject of interest. This study investigates the potential of probing the nature of the hadron–quark phase transition through future gravitational wave (GW) detections from fundamental (f-) mode oscillations in NSs. Using a newly developed model that parametrizes the hadron–quark phase transition with ‘pasta phases’, we calculate f-mode characteristics within a full general relativistic framework. We then use universal relations in GW asteroseismology to derive stellar properties from the detected mode parameters. Our findings suggest that detecting GWs from f modes with third-generation GW detectors offers a promising scenario for the existence of twin stars. However, we also estimate various uncertainties in determining the mode parameters and conclude that these uncertainties make it more challenging to identify the nature of the hadron–quark phase transition.

Magnetar QPOs and Neutron Star Crust Elasticity

The crust region is a tiny fraction of neutron stars, but it has a variety of physical properties and plays an important role in astronomical observations. One of the properties characterizing the crust is elasticity. In this review, with the approach of asteroseismology, we systematically examine neutron star oscillations excited by crust elasticity, adopting the Cowling approximation. In particular, by identifying the quasi-periodic oscillations observed in magnetar flares with the torsional oscillations, we make a constraint on the nuclear saturation parameters. In addition, we also discuss how the shear and interface modes depend on the neutron star properties. Once one detects an additional signal associated with neutron star oscillations, one can obtain a more severe constraint on the saturation parameters and/or neutron star properties, which must be a qualitatively different constraint obtained from terrestrial experiments and help us to complementarily understand astrophysics and nuclear physics.

Radial oscillations of hybrid stars and neutron stars including delta baryons: the effect of a slow quark phase transition

We study radial oscillations of hybrid neutron stars composed of hadronic external layers followed by a quark matter core. We employ a density-dependent relativistic mean-field model including hyperons and Δ baryons to describe hadronic matter, and a density-dependent quark model for quark matter. We obtain the ten lowest eigenfrequencies and the corresponding oscillation functions of N, N+Δ, N+H, and N+H+Δ equations-of-state with a phase transition to the quark matter at 1.4 and 1.8 M ⊙, focusing on the effects of a slow phase transition at the hadron-quark interface. We observe that the maximum mass is reached before the fundamental mode's frequency vanishes for slow phase transitions, suggesting that some stellar configurations with higher central densities than the maximum mass remain stable even when they undergo small radial perturbations. Future gravitational wave detectors and multi-messenger astronomy, complemented by robust microscopic models enabling exploration of various neutron star compositions, including hyperon content, are anticipated to impose precise limitations on the equation of state of baryonic matter under high-density conditions.

Search for Gravitational-wave Transients Associated with Magnetar Bursts in Advanced LIGO and Advanced Virgo Data from the Third Observing Run

Gravitational waves are expected to be produced from neutron star oscillations associated with magnetar giant flares and short bursts. We present the results of a search for short-duration (milliseconds to seconds) and long-duration (∼100 s) transient gravitational waves from 13 magnetar short bursts observed during Advanced LIGO, Advanced Virgo, and KAGRA’s third observation run. These 13 bursts come from two magnetars, SGR 1935+2154 and Swift J1818.0−1607. We also include three other electromagnetic burst events detected by Fermi-GBM which were identified as likely coming from one or more magnetars, but they have no association with a known magnetar. No magnetar giant flares were detected during the analysis period. We find no evidence of gravitational waves associated with any of these 16 bursts. We place upper limits on the rss of the integrated incident gravitational-wave strain that reach 3.6 × 10−23 /Hz at 100 Hz for the short-duration search and 1.1 × 10−22 /Hz at 450 Hz for the long-duration search. For a ringdown signal at 1590 Hz targeted by the short-duration search the limit is set to 2.3 × 10−22 /Hz . Using the estimated distance to each magnetar, we derive upper limits on the emitted gravitational-wave energy of 1.5 × 1044 erg (1.0 × 1044 erg) for SGR 1935+2154 and 9.4 × 1043 erg (1.3 × 1044 erg) for Swift J1818.0−1607, for the short-duration (long-duration) search. Assuming isotropic emission of electromagnetic radiation of the burst fluences, we constrain the ratio of gravitational-wave energy to electromagnetic energy for bursts from SGR 1935+2154 with the available fluence information. The lowest of these ratios is 4.5 × 103.

Probing the impact of delta-baryons on nuclear matter and non-radial oscillations in neutron stars

Non-radial oscillations of Neutron Stars (NSs) provide a means to learn important details regarding their interior composition and equation of state. We consider the effects of Δ-baryons on non-radial f-mode oscillations and other NS properties within the Density-Dependent Relativistic Mean Field formalism. Calculations are performed for Δ-admixed NS matter with and without hyperons. Our study of the non-radial f-mode oscillations revealed a distinct increase in frequency due to the addition of the Δ-baryons with upto 20% increase in frequency being seen for canonical NSs. Other bulk properties of NSs, including mass, radii, and dimensionless tidal deformability (Λ) were also affected by these additional baryons. Comparing our results with available observational data from pulsars (NICER) and gravitational waves (LIGO-VIRGO collaboration), we found strong agreement, particularly concerning Λ.

Shear oscillations in neutron stars and the nuclear symmetry energy

Shear oscillations in neutron stars and the nuclear symmetry energy

R-modes as a new probe of dark matter in neutron stars

In this work, we perform the first systematic investigation of effects of the presence of dark matter on r-mode oscillations in neutron stars (NSs). Using a self-interacting dark matter (DM) model based on the neutron decay anomaly and a hadronic model obtained from the posterior distribution of a recent Bayesian analysis, we impose constraints on the DM self-interaction strength using recent multimessenger astrophysical observations. We also put new constraints on the DM fraction for this model of DM. The constrained DM interaction strength is then used to estimate DM self-interaction cross section and shear viscosity resulting from DM, which is found to be several orders of magnitude smaller than shear viscosity due to hadronic matter. Assuming chemical equilibrium among DM fermions and neutrons, we estimate the bulk viscosity resulting from the dark decay of neutrons considering different scenarios for the temperature dependence of the reaction rate and investigate the effect on the r-mode instability window. We conclude that DM shear and bulk viscosity may significantly modify the r-mode instability window compared with the minimal hadronic viscosities, depending on the temperature dependence of the process. We also found that for the window to be compatible with the X-ray and pulsar observational data, the rate for the dark decay process must be fast.

Radial oscillations of neutron stars with antikaon condensate

Radial oscillations of neutron stars with antikaon condensate

Probing the impact of WIMP dark matter on universal relations, GW170817 posterior, and radial oscillations

ABSTRACT In this study, we investigate the impact of weakly interacting massive particles (WIMPs) dark matter (DM) on C–Λ universal relations, GW170817 posterior, and radial oscillations of neutron stars (NSs) by considering the interactions of uniformly trapped neutralinos as a DM candidate with the hadronic matter through the exchange of the Higgs boson within the framework of the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The hadronic equation of state (EOS) is modelled using the relativistic mean-field (RMF) formalism with IOPB-I, G3, and quark–meson coupling (QMC)-RMF series parameter sets. The presence of DM softens the EOS at both the background and the perturbation levels that implies a small shift to the left in the posterior accompanied by a much larger jump in the left of the mass–radius curves with increasing DM mass. It is observed that EOSs with DM also satisfy the C–Λ universality relations among themselves but get slightly shifted to the right in comparison to that without considering DM. Additionally, we find that the inclusion of DM allows the mass–radius (M–R) curves to remain consistent with observational constraints for HESS J1731−347, indicating the possibility of classifying it as a dark matter-admixed neutron star (DMANS). Moreover, we explore the impact of DM on the radial oscillations of pulsating stars and investigate the stability of NSs. The results demonstrate a positive correlation between the mass of DM and the frequencies of radial oscillation modes.

Radial oscillations in neutron stars with delta baryons

We investigate the effect of $\mathrm{\ensuremath{\Delta}}$ baryons on the radial oscillations of neutron and hyperon stars, employing a density-dependent relativistic mean-field model. The spin-$3/2$ baryons are described by the Rarita-Schwinger Lagrangian density. The baryon-meson coupling constants for the spin-$3/2$ decuplet and the spin-$1/2$ baryonic octet are calculated using a unified approach relying on the fact that the Yukawa couplings present in the Lagrangian density of the mean-field models must be invariant under the SU(3) and SU(6) group transformations. We calculate the 20 lowest eigenfrequencies and corresponding oscillation functions of $\mathrm{\ensuremath{\Delta}}$-inclusive nuclear ($\mathrm{N}+\mathrm{\ensuremath{\Delta}}$) and hyperonic matter ($\mathrm{N}+\mathrm{H}+\mathrm{\ensuremath{\Delta}}$) by solving the Sturm-Liouville boundary value problem and also verifying its validity. We see that the lowest mode frequencies for $\mathrm{N}+\mathrm{\ensuremath{\Delta}}$ and $\mathrm{N}+\mathrm{H}$ EoSs are higher as compared to the pure nucleonic matter because of the deltas and hyperons present. Furthermore, the separation between consecutive modes increases with the addition of hyperons and $\mathrm{\ensuremath{\Delta}}$s.

Nonradial oscillations and gravitational wave emission of hybrid neutron stars

We investigate nonradial oscillations of pure and hybrid neutron 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. Characteristic differences between neutron-star and hybrid-star ${g}_{1}$-mode oscillation frequencies, damping times, and gravitational wave strains are pointed out. Prospects of observations are also discussed.

Radial oscillations of dark matter admixed neutron stars

Within the relativistic mean-field model, we investigate the properties of dark matter (DM) admixed neutron stars, considering non-rotating objects made of isotropic matter. We adopt the IOPB-I hadronic equation of state (EOS) by assuming that the fermionic DM within super-symmetric models has already been accreted inside the neutron star (NS). The impact of DM on the mass-radius relationships and the radial oscillations of pulsating DM admixed neutron stars (with and without the crust) are explored. It is observed that the presence of DM softens the EOS, which in turn lowers the maximum mass and its corresponding radius. Moreover, adding DM results in higher frequencies of pulsating objects and hence we show the linearity of fundamental mode frequency of canonical NS with DM Fermi momentum. We also investigate the profile of eigenfunctions solving the Sturm-Liouville boundary value problem, and verify its validity. Further, we study the stability of NSs considering the fundamental mode frequency variation with the mass of the star, and verify the stability criterion $\partial M/\partial\rho_c > 0$. Finally, the effect of the crust on the large frequency separation for different DM Fermi momenta is shown as well.

Simulating bulk viscosity in neutron stars. I. Formalism

The faithful inclusion of the effects of bulk viscosity induced by the presence of chemical reactions is an important issue for simulations of core-collapse supernovae, binary neutron star mergers, and neutron star oscillations, where particle abundances are locally pushed out of chemical equilibrium by rarefaction and compression of the fluid elements. In this work, we discuss three different approaches that can be used to implement bulk viscosity in general relativistic hydrodynamic simulations of neutron stars: the exact multi-component reacting fluid, and two M\"uller-Israel-Stewart theories, namely the second order Hiscock-Lindblom model and its linear limit, the Maxwell-Cattaneo model. After discussing the theory behind the three approaches, we specialize their dynamics equations to spherical symmetry in the radial gauge-polar slicing (i.e., Schwarzschild) coordinates. We also discuss a particular choice for the equation of state of the fluid and the associated neutrino emission rates, which are used in a companion paper for the numerical comparison of the three frameworks, and we obtain the effective sound speed for the Hiscock-Lindblom theory in the non-linear regime.

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.

Probing phase transitions in neutron stars via the crust-core interfacial mode

Gravitational waves emitted from the binary neutron star (BNS) systems can carry information about the dense matter phase in these compact stars. The crust-core interfacial mode is an oscillation mode in a neutron star, and it depends mostly on the equation of state of the matter in the crust-core transition region. This mode can be resonantly excited by the tidal field of an inspiraling-in BNS system, thereby affecting the emitted gravitational waves and hence could be used to probe the equation of state in the crust-core transition region. In this work, we investigate, in detail, how the first-order phase transition inside the neutron star, if it exists, affects the properties of the crust-core interfacial mode using a Newtonian fluid perturbation theory on a general relativistic background solution of the stellar structure. Two possible types of phase transitions are considered: (1) the phase transitions happen in the fluid core but near the crust-core interface, which results in density discontinuities, and (2) the strong interaction phase transitions in the dense core (as in the conventional hybrid star case). We study how these phase transitions affect the properties of the neutron star oscillation mode excited at the interface, where there exists a shear modulus discontinuity (interfacial mode). In particular, the former phase transition has a minor effect on the mass-radius relation, and the adiabatic tidal deformability, but has the potential to significantly affect the interfacial mode frequency and thereby could be probed using gravitational waves. For the BNS systems, we discuss the possible observational signatures of these phase transitions in the gravitational waveforms and their detectability. Our work enriches the exploration of the physical properties of the crust-core interfacial mode and provides a promising method for probing the phase transition using the seismology of a compact star.

A new formulation of general-relativistic hydrodynamic equations using primitive variables

We present the derivation of hydrodynamical equations for a perfect fluid in General Relativity, within the decomposition of spacetime framework, using only primitive variables. Primitive variables are opposed to conserved variables, as defined in the widely used Valencia formulation of the same hydrodynamical equations. The equations are derived in a covariant way, so that they can be used to describe any configuration of the perfect fluid. Once derived, the equations are tested numerically. We implement them in an evolution code for spherically symmetric self-gravitating compact objects. The code uses pseudospectral methods for both the metric and the hydrodynamics. First, convergence tests are performed, then the frequencies of radial modes of polytropes are recovered with and without the Cowling approximation, and finally the performance of our code in the black hole collapse and migration tests are described. The results of the tests and the comparison with a reference core-collapse and neutron star oscillations code suggests that not only our code can handle very strong gravitational fields, but also that this new formulation helps gaining a significant amount of computational time in hydrodynamical simulations of smooth flows in General Relativity.

Self-similarity relations for torsional oscillations of neutron stars

ABSTRACT Self-similarity relations for torsional oscillation frequencies of neutron star crust are discussed. For any neutron star model, the frequencies of fundamental torsional oscillations (with no nodes of radial wavefunction, i.e. at n = 0, and at all possible angular wave numbers ℓ ≥ 2) is determined by a single constant. Frequencies of ordinary torsional oscillations (at any n > 0 with ℓ ≥ 2) are determined by two constants. These constants are easily calculated through radial integrals over the neutron star crust, giving the simplest method to determine full oscillation spectrum. All constants for a star of fixed mass can be accurately interpolated for stars of various masses (but the same equation of state). In addition, the torsional oscillations can be accurately studied in the flat space–time approximation within the crust. The results can be useful for investigating magneto-elastic oscillations of magnetars which are thought to be observed as quasi-periodic oscillations after flares of soft-gamma repeaters.

Effects of finite sizes of atomic nuclei on shear modulus and torsional oscillations in neutron stars

ABSTRACT The shear modulus of neutron star matter is one of the important properties used for determining torsional oscillations in neutron stars. We take into account the effects of finite sizes of spherical nuclei on the shear modulus and examine the frequencies of crustal torsional oscillations. The shear modulus decreases owing to the finite-size effect, which in turn decreases the frequencies of torsional oscillations. In particular, the finite-size effect becomes more crucial for oscillations with a larger azimuthal quantum number and for neutron star models with a weaker density dependence of nuclear symmetry energy. In practice, when one identifies quasi-periodic oscillations from a neutron star, where magnetic effects are negligible, with crustal torsional oscillations, the finite-size effect can be more significant at frequencies higher than ∼100 Hz.

Detectability of the gravitational-wave background produced by magnetar giant flares

We study the gravitational-wave background produced by f-mode oscillations of neutron stars triggered by magnetar giant flares. For the gravitational-wave energy, we use analytic formulae obtained via general relativistic magnetohydrodynamic simulations of strongly magnetized neutron stars. Assuming the magnetar giant flare rate is proportional to the star-formation rate, we show the gravitational-wave signal is likely undetectable by third-generation detectors such as the Einstein Telescope and Cosmic Explorer. We calculate the minimum value of the magnetic field and the magnetar giant flare rate necessary for such a signal to be detectable, and discuss these in the context of our current understanding of magnetar flares throughout the Universe.