Modes Of Neutron Stars Research Articles

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.

Shear and interface modes in neutron stars with pasta structures

We carefully examine the shear and interface modes, which are excited due to the presence of crust elasticity, in neutron stars with pasta structures, adopting the relativistic Cowling approximation. We find that the shear modes are independent of the presence of the cylindrical-hole and spherical-hole nuclei at least up to a few kilohertz, while the interface modes strongly depend on the presence of the cylindrical-hole and spherical-hole nuclei. In addition, we find empirical relations for the interface mode frequencies multiplied by the stellar mass and for the shear mode frequencies multiplied by the stellar radius. These relations are expressed as a function of the stellar compactness almost independently of the stiffness in a higher-density region inside the neutron star, once one selects the crust equation of state. Thus, if one would simultaneously observe the shear and interface modes from a neutron star, one might extract the neutron star mass and radius with the help of the constraint on the crust stiffness obtained from terrestrial experiments.

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.

Pseudo Nambu–Goldstone modes in neutron stars

If quarks and gluons are either gapped or confined in neutron stars (NSs), the most relevant light modes are Nambu–Goldstone (NG) modes. We study NG modes within a schematic quark model whose parameters at high density are constrained by the two-solar mass constraint. Our model has the color-flavor-locked phase at high density, with the effective couplings as strong as in hadron physics. We find that strong coupling effects make NG modes more massive than in weak coupling predictions, and would erase several phenomena caused by the stressed pairings in mismatched Fermi surfaces. For instance, we found that charged kaons, which are dominated by diquark and anti-diquark components, are not light enough to condense at strong coupling. Implications for gravitational wave signals for NS–NS mergers are also briefly discussed.

A new mechanism for saturating unstable r modes in neutron stars

We consider a new mechanism for damping the oscillations of a mature neutron star. The new dissipation channel arises if superfluid vortices are forced to cut through superconducting fluxtubes. This mechanism is interesting because the oscillation modes need to exceed a critical amplitude in order for it to operate. Once it acts the effect is very strong (and nonlinear) leading to efficient damping. The upshot of this is that modes are unlikely to ever evolve far beyond the critical amplitude. We consider the effect of this new dissipation channel on the r-modes, that may be driven unstable by the emission of gravitational waves. Our estimates show that the fluxtube cutting leads to a saturation threshold for the instability that can be smaller than that of other proposed mechanisms. This suggests that the idea may be of direct astrophysical relevance.

How to adapt broad-band gravitational-wave searches forr-modes

Up to now there has been no search for gravitational waves from the $r$-modes of neutron stars in spite of the theoretical interest in the subject. Several oddities of $r$-modes must be addressed to obtain an observational result: The gravitational radiation field is dominated by the mass current (gravitomagnetic) quadrupole rather than the usual mass quadrupole, and the consequent difference in polarization affects detection statistics and parameter estimation. To astrophysically interpret a detection or upper limit it is necessary to convert the gravitational-wave amplitude to an $r$-mode amplitude. Also, it is helpful to know indirect limits on gravitational-wave emission to gauge the interest of various searches. Here I address these issues, thereby providing the ingredients to adapt broad-band searches for continuous gravitational waves to obtain $r$-mode results. I also show that searches of existing data can already have interesting sensitivities to $r$-modes.

Transport parameters in neutron stars from in-mediumNNcross sections

We present a numerical study of shear viscosity and thermal conductivity of symmetric nuclear matter, pure neutron matter and $\beta$-stable nuclear matter, in the framework of the Brueckner theory. The calculation of in-medium cross sections and nucleon effective masses is performed with a consistent two and three body interaction. The investigation covers a wide baryon density range as requested in the applications to neutron stars. The results for the transport coefficients in $\beta$-stable nuclear matter are used to make preliminary predictions on the damping time scales of non radial modes in neutron stars.

Imprints of the nuclear symmetry energy on gravitational waves from the axialw-modes of neutron stars

The eigenfrequencies of the axial $w$-modes of oscillating neutron stars are studied using the continued fraction method with an equation of state (EOS) partially constrained by the recent terrestrial nuclear laboratory data. It is shown that the density dependence of the nuclear symmetry energy ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ affects significantly both the frequencies and the damping times of these modes. Besides confirming the previously found universal behavior of the mass-scaled eigenfrequencies as functions of the compactness of neutron stars, we explored several alternative universal scaling functions. Moreover, the ${w}_{\mathit{II}}$-mode is found to exist only for neutron stars having a compactness of $M/R\ensuremath{\geqslant}0.1078$ independent of the EOS used.

Resonant tidal excitations of inertial modes in coalescing neutron star binaries

We study the effect of resonant tidal excitation of inertial modes in neutron stars during binary inspiral. For spin frequencies less than 100 Hz, the phase shift in the gravitational waveform associated with the resonance is small and does not affect the matched filtering scheme for gravitational wave detection. For higher spin frequencies, the phase shift can become significant. Most of the resonances take place at orbital frequencies comparable to the spin frequency, and thus significant phase shift may occur only in the high-frequency band (hundreds of Hertz) of gravitational waves. The exception is a single odd-parity $m=1$ mode, which can be resonantly excited for misaligned spin-orbit inclinations, and may occur in the low-frequency band (tens of Hertz) of gravitational waves and induce significant ($\ensuremath{\gg}1\text{ }\text{ }\mathrm{radian}$) phase shift.

Non-linear r modes in neutron stars: a hydrodynamical limitation on r-mode amplitudes

Previously we found that large amplitude $r$-modes could decay catastrophically due to nonlinear hydrodynamic effects. In this paper we found the particular coupling mechanism responsible for this catastrophic decay, and identified the fluid modes involved. We find that for a neutron star described by a polytropic equation of state with polytropic index $\Gamma=2$, the coupling strength of the particular three-mode interaction causing the decay is strong enough that the usual picture of the $r$-mode instability with a flow pattern dominated by that of an $r$-mode can only be valid for the dimensionless $r$-mode amplitude less than $O(10^{-2})$.

R-modes of accreting hyperon stars as persistent sources of gravitational waves

The $r$-modes of accreting neutron stars could be a detectable source of persistent gravitational waves if the bulk viscosity of the stellar matter can prevent a thermal runaway. This is possible if exotic particles such as hyperons are present in the core of the star. We compute bulk viscous damping rates and critical frequencies for $r$-modes of neutron stars containing hyperons in the framework of relativistic mean field theory. We combine the results of several previous calculations of the microphysics, include for the first time the effect of rotation, and explore the effects of various parameters on the viability of persistent gravitational wave emission. We find that persistent emission is quite robust, although it is disfavored in stars below 1.3--1.5 ${M}_{\ensuremath{\bigodot}}$ depending on the equation of state. In some cases persistent emission is compatible with temperatures as low as ${10}^{7}\text{ }\text{ }\mathrm{K}$, observed in some accreting neutron stars in quiescence.

Magnetic effects on the viscous boundary layer damping of ther-modes in neutron stars

This paper explores the effects that magnetic fields have on the viscous boundary layers (VBLs) that can form in neutron stars at the crust-core interface, and it investigates the VBL damping of the gravitational-radiation driven r-mode instability. Approximate solutions to the magnetohydrodynamic equations valid in the VBL are found for ordinary-fluid neutron stars. It is shown that magnetic fields above ${10}^{9}{(10}^{10} \mathrm{K}/T)\mathrm{G}$ significantly change the structure of the VBL, and that magnetic fields decrease the VBL damping time. Furthermore, VBL damping completely suppresses the r-mode instability for $B\ensuremath{\gtrsim}{10}^{12} \mathrm{G}$ (independent of the temperature). These bounds refer to the strength of the radial component of the equilibrium field at the location of the core radius. Magnetic effects on the VBL vanish wherever the radial component of the equilibrium field vanishes. Thus, magnetic fields will profoundly affect the VBL damping of the r-mode instability in hot young pulsars (that are cool enough to have formed a solid crust). One can speculate that magnetic fields can affect the VBL damping of this instability in low-mass x-ray binary systems and other cold old pulsars (if they have sufficiently large internal fields).

R‐Modes in Neutron Stars with Crusts: Turbulent Saturation, Spin‐down, and Crust Melting

Rossby waves (r-modes) have been suggested as a means to regulate the spin periods of young or accreting neutron stars, and also to produce observable gravitational wave radiation. R-modes involve primarily transverse, incompressive motions of the star's fluid core. However, neutron stars gain crusts early in their lives: therefore, r-modes also imply shear in the fluid beneath the crust. We examine the criterion for this shear layer to become turbulent, and derive the rate of dissipation in the turbulent regime. Unlike dissipation from a viscous boundary layer, turbulent energy loss is nonlinear in mode energy and can therefore cause the mode to saturate at amplitudes typically much less than unity. This energy loss also reappears as heat below the crust. We study the possibility of crust melting as well as its implications for the spin evolution of low-mass X-ray binaries. Lastly, we identify some universal features of the spin evolution that may have observational consequences.

Radiative falloff in neutron star spacetimes

We systematically study late-time tails of scalar waves propagating in neutron star spacetimes. We consider uniform density neutron stars, for which the background spacetime is analytic and the compaction of the star can be varied continously between the Newtonian limit 2M/R << 1 and the relativistic Buchdahl limit 2M/R = 8/9. We study the reflection of a finite wave packet off neutron stars of different compactions 2M/R and find that a Newtonian, an intermediate, and a highly relativistic regime can be clearly distinguished. In the highly relativistic regime, the reflected signal is dominated by quasi-periodic peaks, which originate from the wave packet bouncing back and forth between the center of the star and the maximum of the background curvature potential at R ~ 3 M. Between these peaks, the field decays according to a power-law. In the Buchdahl limit 2M/R -> 8/9 the light travel time between the center and the maximum or the curvature potential grows without bound, so that the first peak arrives only at infinitely late time. The modes of neutron stars can therefore no longer be excited in the ultra-relativistic limit, and it is in this sense that the late-time radiative decay from neutron stars looses all its features and gives rise to power-law tails reminiscent of Schwarzschild black holes.

Second-order rotational effects on ther-modes of neutron stars

Techniques are developed here for evaluating the r-modes of rotating neutron stars through second order in the angular velocity of the star. Second-order corrections to the frequencies and eigenfunctions for these modes are evaluated for neutron star models. The second-order eigenfunctions for these modes are determined here by solving an unusual inhomogeneous hyperbolic boundary-value problem. The numerical techniques developed to solve this unusual problem are somewhat non-standard and may well be of interest beyond the particular application here. The bulk-viscosity coupling to the r-modes, which appears first at second order, is evaluated. The bulk-viscosity time scales are found here to be longer than previous estimates for normal neutron stars, but shorter than previous estimates for strange stars. These new time scales do not substantially affect the current picture of the gravitational radiation driven instability of the r-modes either for neutron stars or for strange stars.