Instability In Neutron Stars Research Articles

Differential rotation in neutron stars at finite temperatures

IntroductionThis paper investigates the impact of differential rotation on the bulk properties and onset of rotational instabilities in neutron stars at finite temperatures up to 50 MeV.MethodsUtilizing the relativistic Brueckner-Hartree-Fock (RBHF) formalism in full Dirac space, the study constructs equation of state (EOS) models for hot neutron star matter, including conditions relevant for high temperatures. These finite-temperature EOS models are applied to compute the bulk properties of differentially rotating neutron stars with varying structural deformations.ResultsThe findings demonstrate that the stability of these stars against bar-mode deformation, a key rotational instability, is only weakly dependent on temperature. Differential rotation significantly affects the maximum mass and radius of neutron stars, and the threshold for the onset of bar-mode instability shows minimal sensitivity to temperature changes within the examined range.DiscussionThese findings are crucial for interpreting observational data from neutron star mergers and other high-energy astrophysical events. The research underscores the necessity of incorporating differential rotation and finite temperature effects in neutron star models to predict their properties and stability accurately.

Crust-core transition and dynamical instabilities in neutron stars for model with point-coupling interactions * *Supported by Changsha Municipal Natural Science Foundation (kq2007004) and the construct program of the key discipline in Hunan province

We explore the effects of the density dependence of symmetry energy on the crust-core phase transition and dynamical instabilities in cold and warm neutron stars in the relativistic mean field (RMF) theory with point-coupling interactions using the Vlasov approach. The role of neutrino trapping is also considered. The crust-core transition density and pressure, distillation effect, and cluster size and growth rates are discussed. The present work shows that the slope of symmetry energy at saturation, temperature, and neutrino trapping have non-negligible effects.

Transport Properties of Superfluid Phonons in Neutron Stars

We review the effective field theory associated with the superfluid phonons that we use for the study of transport properties in the core of superfluid neutrons stars in their low temperature regime. We then discuss the shear and bulk viscosities together with the thermal conductivity coming from the collisions of superfluid phonons in neutron stars. With regard to shear, bulk, and thermal transport coefficients, the phonon collisional processes are obtained in terms of the equation of state and the superfluid gap. We compare the shear coefficient due to the interaction among superfluid phonons with other dominant processes in neutron stars, such as electron collisions. We also analyze the possible consequences for the r-mode instability in neutron stars. As for the bulk viscosities, we determine that phonon collisions contribute decisively to the bulk viscosities inside neutron stars. For the thermal conductivity resulting from phonon collisions, we find that it is temperature independent well below the transition temperature. We also obtain that the thermal conductivity due to superfluid phonons dominates over the one resulting from electron-muon interactions once phonons are in the hydrodynamic regime. As the phonons couple to the Z electroweak gauge boson, we estimate the associated neutrino emissivity. We also briefly comment on how the superfluid phonon interactions are modified in the presence of a gravitational field or in a moving background.

Merger-inspired rotation laws and the low-T/W instability in neutron stars

ABSTRACTImplementing a family of differential rotation laws inspired by binary neutron-star merger remnants, we consider the impact of the rotation profile on the low-T/W instability. We use time evolutions of the linearized dynamical equations, in Newtonian gravity, to study non-axisymmetric oscillations and identify the unstable modes. The presence and evolution of the low-T/W instability is monitored with the canonical energy and angular momentum, while the growth time is extracted from the evolved kinetic energy. The results for the new rotation laws highlight similarities with the commonly considered j-constant law. The instability sets in when an oscillation mode corotates with the star (i.e. whenever there is a point at which the mode’s pattern speed matches the bulk angular velocity) and grows faster deep inside the co-rotation region. However, the new profiles add features, like an additional co-rotation point, to the problem, and these affect the onset of instability. The rotation laws have the most drastic influence on the oscillation frequencies of the l = m = 2 f mode in fast-rotating models, but affect the instability growth time at some level for any rotation rate. We also identify models where the low-T/W instability appears to be triggered by inertial modes. We discuss to what extent the inferred qualitative behaviour is likely to be of observational relevance.

Saturation of thef-mode instability in neutron stars. II. Applications and results

We present the first results on the saturation of the f-mode instability in neutron stars, due to nonlinear mode coupling. Emission of gravitational waves drives the f-mode (fundamental mode) unstable in fast-rotating, newborn neutron stars. The initial growth phase of the mode is followed by its saturation, because of energy leaking to other modes of the star. The saturation point determines the strain of the generated gravitational-wave signal, which can then be used to extract information about the neutron star equation of state. The parent (unstable) mode couples via parametric resonances with pairs of daughter modes, with the triplets' evolution exhibiting a rich variety of behaviors. We study both supernova- and merger-derived neutron stars, simply modeled as polytropes in a Newtonian context, and show that the parent may couple to many different daughter pairs during the star's evolution through the instability window, with the saturation amplitude changing by orders of magnitude.

The stochastic background of gravitational waves due to thef-mode instability in neutron stars

This paper presents an estimate for the spectral properties of the stochastic background of gravitational waves emitted by a population of hot, young, rapidly rotating neutron stars throughout the Universe undergoing $f$-mode instabilities, formed through either core-collapse supernova explosions or the merger of binary neutron star systems. Their formation rate, from which the gravitational wave event rate is obtained, is deduced from observation-based determinations of the cosmic star formation rate. The gravitational wave emission occurs during the spin-down phase of the $f$-mode instability. For low magnetized neutron stars and assuming 10\% of supernova events lead to $f$-mode unstable neutron stars, the background from supernova-derived neutron stars peaks at $\Omega_{\text{gw}} \sim 10^{-9}$ for the $l=m=2$ $f$-mode, which should be detectable by cross-correlating a pair of second generation interferometers (e.g. Advanced LIGO/Virgo) with an upper estimate for the signal-to-noise ratio of $\approx$ 9.8. The background from supramassive neutron stars formed from binary mergers peaks at $\Omega_{\text{gw}} \sim 10^{-10}$ and should not be detectable, even with third generation interferometers (e.g. Einstein Telescope).

Constraining the physics of the r-mode instability in neutron stars with X-ray and ultraviolet observations

Rapidly rotating Neutron Stars in Low Mass X-ray Binaries (LMXBs) may be an interesting source of Gravitational Waves (GWs). In particular, several modes of stellar oscillation may be driven unstable by GW emission, and this can lead to a detectable signal. Here we illustrate how current X-ray and ultra-violet (UV) observations can constrain the physics of the r-mode instability. We show that the core temperatures inferred from the data would place many systems well inside the unstable region predicted by standard physical models. However, this is at odds with theoretical expectations. We discuss different mechanisms that could be at work in the stellar interior, and we show how they can modify the instability window and make it consistent with the inferred temperatures.

Non-linear viscous damping and gravitational wave detectability of the f-mode instability in neutron stars

We study the damping of the gravitational radiation-driven f-mode instability in rotating neutron stars by nonlinear bulk viscosity in the so-called supra-thermal regime. In this regime the dissipative action of bulk viscosity is known to be enhanced as a result of nonlinear contributions with respect to the oscillation amplitude. Our analysis of the f-mode instability is based on a time-domain code that evolves linear perturbations of rapidly rotating polytropic neutron star models. The extracted mode frequency and eigenfunctions are subsequently used in standard energy integrals for the gravitational wave growth and viscous damping. We find that nonlinear bulk viscosity has a moderate impact on the size of the f-mode instability window, becoming an important factor and saturating the mode's growth at a relatively large oscillation amplitude. We show similarly that nonlinear bulk viscosity leads to a rather high saturation amplitude even for the r-mode instability. In addition, we show that the action of bulk viscosity can be significantly mitigated by the presence of superfluidity in neutron star matter. Apart from revising the f-mode's instability window we provide results on the mode's gravitational wave detectability. Considering an f-mode-unstable neutron star located in the Virgo cluster and assuming a mode amplitude at the level allowed by bulk viscosity, we find that the emitted gravitational wave signal could be detectable by advanced ground-based detectors such as Advanced LIGO/Virgo and the Einstein Telescope.

An r-mode in a magnetic rotating spherical layer: application to neutron stars

The impact of the combination of rotation and magnetic fields on oscillations of stellar fluids is still not well known theoretically. It mixes Alfv\'en and inertial waves. Neutron stars are a place where both effects may be at work. We wish to decipher the solution of this problem in the context of $r$-modes instability in neutron stars, as it appears when these modes are coupled to gravitational radiation. We consider a rotating spherical shell filled with a viscous fluid but of infinite electrical conductivity and analyze propagation of modal perturbations when a dipolar magnetic field is bathing the fluid layer. We perform an extensive numerical analysis and find that the $m=2$ $r$-mode oscillation is influenced by the magnetic field when the Lehnert number (ratio of Alfv\'en speed to rotation speed) exceeds a value proportional to the one-fourth power of the Ekman number (non-dimensional measure of viscosity). This scaling is interpreted as the coincidence of the width of internal shear layers of inertial modes and the wavelength of the Alfv\'en waves. Applied to the case of rotating magnetic neutron stars, we find that dipolar magnetic fields above $10^{14}$ G are necessary to perturb the $r$-modes instability.

Oscillations and instabilities in neutron stars with poloidal magnetic fields

We study the time evolution of non-axisymmetric linear perturbations of a rotating magnetised neutron star, whose magnetic field is multipolar and purely poloidal. The background stellar configurations are generated self-consistently, allowing for distortions to the density distribution from rotational and magnetic forces. We find that the behaviour of axial-led perturbations is dominated by an instability generic to poloidal fields, which is localised around the `neutral line' where the background field vanishes. Rotation acts to reduce the effect of this instability. Polar-led perturbations do not appear to be unstable and in this case we find global Alfv\'en modes, whose restoring force is the magnetic field. In a rotating magnetised star there are no pure Alfv\'en modes or pure inertial modes, but hybrids of these. We discuss the nature of magnetic instabilities and oscillations in magnetars and pulsars, finding the dominant Alfv\'en mode has a frequency comparable with observed magnetar QPOs.

Instabilities in neutron stars with toroidal magnetic fields

We study m= 1 oscillations and instabilities of magnetized neutron stars, by numerical time evolution of linear perturbations of the system. The background stars are stationary equilibrium configurations with purely toroidal magnetic fields. We find that an m= 1 instability of toroidal magnetic fields, already known from local analyses, may also be found in our relatively low-resolution global study. We present quantitative results for the instability growth rate and its suppression by rotation. The instability is discussed as a possible trigger mechanism for soft gamma repeater flares. Although our primary focus is evolutions of magnetized stars, we also consider perturbations about unmagnetized background stars in order to study m= 1 inertial modes. We track these modes up to break-up frequency ΩK, extending known slow-rotation results.

Hyperon Bulk Viscosity in the Presence of Antikaon Condensate

We investigate the hyperon bulk viscosity due to the non-leptonic process $n + p \rightleftharpoons p + \Lambda $ in $K^-$ condensed matter and its effect on the r-mode instability in neutron stars. We find that the hyperon bulk viscosity coefficient in the presence of antikaon condensate is suppressed compared with the case without the condensate. The suppressed hyperon bulk viscosity in the superconducting phase is still an efficient mechanism to damp the r-mode instability in neutron stars.

Bulk viscosity in kaon condensed matter

We investigate the effect of K{sup -} condensed matter on bulk viscosity and r-mode instability in neutron stars. The bulk viscosity coefficient due to the nonleptonic process n p+K{sup -} is studied here. In this connection, equations of state are constructed within the framework of relativistic field theoretical models where nucleon-nucleon and kaon-nucleon interactions are mediated by the exchange of scalar and vector mesons. We find that the bulk viscosity coefficient due to the nonleptonic weak process in the condensate is suppressed by several orders of magnitude. Consequently, kaon bulk viscosity may not damp the r-mode instability in neutron stars.

Search templates for stochastic gravitational-wave backgrounds

Several earth-based gravitational-wave (GW) detectors are actively pursuing the quest for placing observational constraints on models that predict the behavior of a variety of astrophysical and cosmological sources. These sources span a wide gamut, ranging from hydrodynamic instabilities in neutron stars (such as $\mathrm{r}$-modes) to particle production in the early Universe. Signals from a subset of these sources are expected to appear in these detectors as stochastic GW backgrounds (SGWBs). The detection of these backgrounds will help us in characterizing their sources. Accounting for these backgrounds will also be required by some detectors, such as the proposed space-based detector LISA, so that they can detect other GW signals. Here, we formulate the problem of constructing a bank of search templates that discretely span the parameter space of a generic SGWB. We apply it to the specific case of a class of cosmological SGWBs, known as the broken power-law models. We derive how the template density varies in their three-dimensional parameter space and show that for the LIGO 4 km detector pair, with LIGO-I sensitivities, a few hundred templates will suffice to detect such a background while incurring a loss in signal-to-noise ratio of no more than 3%.

Nonlinear coupling network to simulate the development of thermode instability in neutron stars. II. Dynamics

Two mechanisms for nonlinear mode saturation of the $r$ mode in neutron stars have been suggested: the parametric instability mechanism involving a small number of modes and the formation of a nearly continuous Kolmogorov-type cascade. Using a network of oscillators constructed from the eigenmodes of a perfect fluid incompressible star, we investigate the transition between the two regimes numerically. Our network includes the 4995 inertial modes up to $n\ensuremath{\le}30$ with 146 998 direct couplings to the $r$ mode and 1 306 999 couplings with detuning $<0.002$ (out of a total of approximately ${10}^{9}$ possible couplings). The lowest parametric instability thresholds for a range of temperatures are calculated and it is found that the $r$ mode becomes unstable to modes with $13<n<15$. In the undriven, undamped, Hamiltonian version of the network the rate to achieve equipartition is found to be amplitude dependent, reminiscent of the Fermi-Pasta-Ulam problem. More realistic models driven unstable by gravitational radiation and damped by shear viscosity are explored next. A range of damping rates, corresponding to temperatures ${10}^{6}\text{ }\text{ }\mathrm{K}$ to ${10}^{9}\text{ }\text{ }\mathrm{K}$, is considered. Exponential growth of the $r$ mode is found to cease at small amplitudes $\ensuremath{\approx}{10}^{\ensuremath{-}4}$. For strongly damped, low temperature models, a few modes dominate the dynamics. The behavior of the $r$ mode is complicated, but its amplitude is still no larger than about ${10}^{\ensuremath{-}4}$ on average. For high temperature, weakly damped models the $r$ mode feeds energy into a sea of oscillators that achieve approximate equipartition. In this case the $r$-mode amplitude settles to a value for which the rate to achieve equipartition is approximately the linear instability growth rate.

Nonlinear coupling network to simulate the development of the r-mode instability in neutron stars. I. Construction

R-modes of a rotating neutron star are unstable because of the emission of gravitational radiation. We explore the saturation amplitudes of these modes determined by nonlinear mode-mode coupling. Modelling the star as incompressible allows the analytic computation of the coupling coefficients. All couplings up to n=30 are obtained, and analytic values for the shear damping and mode normalization are presented. In a subsequent paper we perform numerical simulations of a large set of coupled modes.

Differential rotation and hydrodynamic stability of hot neutron stars

Young neutron stars formed in core collapse or originating in the merger of a binary neutron star system may possess significant differential rotation. We consider the stability properties of such hot (non-superfluid) differentially rotating neutron stars. Compared to ordinary stars, the criteria of hydrodynamic instability of neutron stars can be different because generally the thermal diffusivity and viscosity are of the same order of magnitude and are relatively large. For example, the well-known Goldreich-Schubert instability can manifest itself only in rapidly rotating stars and is strongly suppressed if rotation is slow. The rotational instabilities in neutron stars can grow on the thermal or dynamical timescale.

Hall-drift induced magnetic field instability in neutron stars.

In the presence of a strong magnetic field and under conditions as realized in the crust and the superfluid core of neutron stars, the Hall drift dominates the field evolution. We show by a linear analysis that, for a sufficiently strong large-scale background field depending at least quadratically on position in a plane conducting slab, an instability occurs which rapidly generates small-scale fields. Their growth rates depend on the choice of the boundary conditions, increase with the background field strength, and may reach 10(3) times the Ohmic decay rate. The effect of that instability on the rotational and thermal evolution of neutron stars is discussed.

An Instability in Neutron Stars at Birth

Calculations with a two-dimensional hydrodynamic simulation show that a generic Raleigh-Taylor-like instability occurs in the mantles of nascent neutron stars, that it is possibly violent, and that the standard spherically symmetric models of neutron star birth and supemova explosion may be inadequate. Whether this "convective" instability is pivotal to the supemova mechanism, pulsar magnetic fields, or a host of other important issues that attend stellar collapse remains to be seen, but its existence promises to modify all questions concerning this most energetic of astronomical phenomena.

Pulsar timing observations, X-ray transients, and the thermal/timing instability in neutron stars

The formal problem studied in this paper is that of the response of a neutron star to a perturbation in its temperature. It is found that this response is very rich and embraces a wide variety of phenomena. Under certain circumstances the response will be a period jump (a glitch). Detailed numerical integrations are presented which show behavior indistinguishable from the Vela pulsar period jumps. The theory can be made to yield jumps as large as Vela's or as small as the Crab's. It also quite naturally accounts for the observed increase in slowing-down rate, and its subsequent slow decay, after a jump. Finally, there appears to be no reason why these events cannot be arranged to recur every few years. This theory of pulsar glitches makes three predictions which can be observationally tested: that glitches take time to build up, that they are accompanied by a modest heating of the star, and that the time scale for the postglitch decay need not be the same in successive jumps of the same pulsar. Occasional large perturbations to pulsar temperatures yield glitches; more frequent (and random) smaller perturbations, or large perturbations to higher temperatures, yield pulsar timing noise. It is shown that in the limit of high temperatures-i.e., young pulsars-the response to this process will have the statistics of a random walk in the frequency, and in the limit of low temperatures-old pulsars-a random walk in the slowing-down rate. The general case, however, is not described by either of these models. The theory makes a prediction that can be observationally tested: that the pulsar angular velocity can only increaase as a result of a perturbation. The noise process therefore does not have zero mean. The theory also predicts the existence of a phenomenon that has not yet been observed: a giant period jump associated with a giant thermal instability. The X-ray signature of this phenomenon has the characteristics of certain of the X-ray novae. The instability may also have bearing on the absence of long-period pulsars and the uncomfortably large pulsar birthrate derived from pulsar statistics. Subject headings: pulsars - stars: interiors - stars: neutron - X-rays: sources