R-mode Instability Research Articles

The effect of r-mode instability on the evolution of isolated strange stars

We studied the evolution of isolated strange stars (SSs) synthetically, considering the influence of r-mode instability. Our results show that the cooling of SSs with non-ultrastrong magnetic fields is delayed by heating due to r-mode damping for millions of years, while the spin-down of the stars is dominated by gravitational radiation (GR). Especially for the SSs in a possible existing colour-flavour locked (CFL) phase, the effect of r-mode instability on the evolution of stars becomes extremely important because the viscosity, neutrino emissivity and specific heat involving pairing quarks are blocked. It leads to the cooling of these colour superconducting stars being very slow and the stars can remain at high temperature for millions of years, which differs completely from previous understanding. In this case, an SS in CFL phase can be located at the bottom of its r-mode instability window for a long time, but does not spin-down to a very low frequency for hours.

Cosmological gravitational wave background from phase transitions in neutronstars

It has recently been suggested that collapse of neutron stars induced by a phase transitionto quark matter can be a considerable source of gravitational waves with kHzfrequencies. We demonstrate that if about one per cent of all neutron stars undergo thisprocess, the resulting cosmological gravitational wave background would reach about10−10 times the critical density. The background would peak at kHz frequencies and could havean observationally significant tail down to Hz frequencies. It would be comparable or higherthan other astrophysical backgrounds, for example, from ordinary core collapse supernovae,from r-mode instabilities in rapidly rotating neutron stars, and from magnetars. Thescenario is consistent with cosmological backgrounds in neutrinos and photons.

Gravitational wave bursts induced by r-mode spin-down of hybrid stars

We show that sudden variations in the composition and structure of an hybrid star can be triggered by its rapid spin-down, induced by r-mode instabilities. The discontinuity of this process is due to the surface tension between hadronic and quark matter and in particular to the overpressure needed to nucleate new structures of quark matter in the mixed phase. The consequent mini-collapses in the star can produce highly energetic gravitational wave bursts. The possible connection between the predictions of this model and the burst signal found by EXPLORER and NAUTILUS detectors during the year 2001 is also investigated.

Running coupling constant from lattice data and bulk viscosity of strange quark matter

We study the bulk viscosity of strange quark matter (SQM) in a quasiparticle model at finite chemical potential by extrapolating the previous quasiparticle model of finite temperature lattice QCD. The more proper bulk viscosity coefficient can be given in this model where chemical potential $\mu$ and coupling constant $\emph{g}$ are interdependent. We also apply our result to determine the critical rotation of strange stars by r-mode instability window. Our model is compatible to the millisecond pulsar data for a wide range of mass and radius of the stars.

Bulk viscosity in hybrid stars

We compute the bulk viscosity of a mixed quark-hadron phase. In the first scenario to be discussed, the mixed phase occurs at large densities and we assume that it is composed of a mixing of hyperonic matter and quarks in the Color Flavor Locked phase. In a second scenario, the mixed phase occurs at lower densities and it is composed of a mixing of nucleons and unpaired quark matter. We have also investigated the effect of a nonvanishing surface tension at the interface between hadronic and quark matter. In both scenarios, the bulk viscosity is large when the surface tension is absent, while the value of the viscosity reduces in the second scenario when a finite value for the surface tension is taken into account. In all cases, the r-mode instabilities of the corresponding hybrid star are suppressed.

Nonlinear evolution ofr-modes: The role of differential rotation

Recent work has shown that differential rotation, producing large scale drifts of fluid elements along stellar latitudes, is an unavoidable feature of r-modes in the nonlinear theory. We investigate the role of this differential rotation in the evolution of the l=2 r-mode instability of a newly born, hot, rapidly rotating neutron star. It is shown that the amplitude of the r-mode saturates a few hundred seconds after the mode instability sets in. The saturation amplitude depends on the amount of differential rotation at the time the instability becomes active and can take values much smaller than unity. It is also shown that, independently of the saturation amplitude of the mode, the star spins down to rotation rates that are comparable to the inferred initial rotation rates of the fastest pulsars associated with supernova remnants. Finally, it is shown that, when the drift of fluid elements at the time the instability sets in is significant, most of the initial angular momentum of the star is transferred to the r-mode and, consequently, almost none is carried away by gravitational radiation.

R-modes of a neutron star with a magnetic dipole field

We study r-modes of a rotating magnetized neutron star, assuming a magnetic dipole field whose axis is aligned with the axis of rotation. We approach the problem by applying a singular perturbation theory to the oscillations of rotating stars. In this treatment, we divide the star into a thin surface magnetic layer and a non-magnetic core. We integrate linearized ideal magnetohydrodynamic (MHD) equations in the surface magnetic layer and non-magnetic oscillation equations in the core, and match the two integrations at the interface to obtain a complete solution. For a polytropic neutron star model of mass M = 1.4 M○. and radius R = 10 6 cm, the magnetic dipole field becomes effective on the modal properties of the r-modes only when the field strength Bs is much greater than 10 14 G. We also find that the damping effects caused by very short magnetic perturbations in the surface layer are not important for the r-mode instability of rapidly rotating neutron stars if the field strength Bs is smaller than 10 12 G.

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.

Nonlinear couplings of R-modes: Energy transfer and saturation amplitudes at realistic timescales

Non-linear interactions among the inertial modes of a rotating fluid can be described by a network of coupled oscillators. We use such a description for an incompressible fluid to study the development of the r-mode instability of rotating neutron stars. A previous hydrodynamical simulation of the r-mode reported the catastrophic decay of large amplitude r-modes. We explain the dynamics and timescale of this decay analytically by means of a single three mode coupling. We argue that at realistic driving and damping rates such large amplitudes will never actually be reached. By numerically integrating a network of nearly 5000 coupled modes, we find that the linear growth of the r-mode ceases before it reaches an amplitude of around 10^(-4). The lowest parametric instability thresholds for the r-mode are calculated and it is found that the r-mode becomes unstable to modes with 13<n<15 if modes up to n=30 are included. Using the network of coupled oscillators, integration times of 10^6 rotational periods are attainable for realistic values of driving and damping rates. Complicated dynamics of the modal amplitudes are observed. The initial development is governed by the three mode coupling with the lowest parametric instability. Subsequently a large number of modes are excited, which greatly decreases the linear growth rate of the r-mode.

Presupernova evolution of accreting white dwarfs with rotation

We discuss the effects of rotation on the evolution of accreting carbon-oxygen white dwarfs, with the emphasis on possible consequences in Type Ia supernova (SN Ia) progenitors. Starting with a slowly rotating white dwarf, we simulate the accretion of matter and angular momentum from a quasi-Keplerian accretion disk. The role of the various rotationally induced hydrodynamic instabilities for the transport of angular momentum inside the white dwarf is investigated. We find that the dynamical shear instability is the most important one in the highly degenerate core. Our results imply that accreting white dwarfs rotate differentially throughout,with a shear rate close to the threshold value for the onset of the dynamical shear instability. As the latter depends on the temperature of the white dwarf, the thermal evolution of the white dwarf core is found to be relevant for the angular momentum redistribution. As found previously, significant rotation is shown to lead to carbon ignition masses well above 1.4 Msun. Our models suggest a wide range of white dwarf explosion masses, which could be responsible for some aspects of the diversity observed in SNe Ia. We analyze the potential role of the bar-mode and the r-mode instability in rapidly rotating white dwarfs, which may impose angular momentum loss by gravitational wave radiation. We discuss the consequences of the resulting spin-down for the fate of the white dwarf, and the possibility to detect the emitted gravitational waves at frequencies of 0.1 >... 1.0 Hz in nearby galaxies with LISA. Possible implications of fast and differentially rotating white dwarf cores for the flame propagation in exploding white dwarfs are also briefly discussed.

Solid Quark Stars?

It is conjectured that cold quark matter with much high baryon density could be in a solid state, and strange stars with low temperatures should thus be solid stars. The speculation could be close to the truth if no peculiar polarization of thermal X-ray emission (in, e.g., RXJ1856), or no gravitational wave in post-glitch phases, is detected in future advanced facilities, or if spin frequencies beyond the critical ones limited by r-mode instability are discovered. The shear modulus of solid quark matter could be ~ 10^{32} erg/cm^3 if the kHz QPOs observed are relevant to the eigenvalues of the center star oscillations.

R‐Modes of Neutron Stars with Superfluid Cores

We investigate the modal properties of the r-modes of rotating neutron stars with the core filled with neutron and proton superfluids, taking account of entrainment effects between the superfluids. The stability of the r-modes against gravitational radiation reaction is also examined considering viscous dissipation due to shear and a damping mechanism called between the superfluids in the core. We find that the r-modes in the superfluid core are split into ordinary r-modes and superfluid r-modes, which we call, respectively, ro- and rs-modes. The two superfluids in the core flow together for the ro-modes, while they countermove for the rs-modes. For the ro-modes, the coefficient κ0 ≡ limΩ→0 ω/Ω is equal to 2m/[l'(l' + 1)], almost independent of the parameter η that parameterizes the entrainment effects between the superfluids, where Ω is the angular frequency of rotation, ω is the oscillation frequency observed in the corotating frame of the star, and l' and m are the indices of the spherical harmonic function representing the angular dependence of the r-modes. For the rs-modes, on the other hand, κ0 is equal to 2m/[l'(l' + 1)] at η = 0 (no entrainment), and it almost linearly increases as η is increased from η = 0. The ro-modes, for which w' ≡ v − v ∝ Ω3, correspond to the r-modes discussed by L. Lindblom & G. Mendell, where v and v are the Eulerian velocity perturbations of the neutron and proton superfluids, respectively. The mutual friction in the superfluid core is found ineffective to stabilize the r-mode instability caused by the ro-mode except in a few narrow regions of η. The r-mode instability caused by the rs-modes, on the other hand, is extremely weak and easily damped by dissipative processes in the star.

The Critical Rotation of Strange Stars and Rapidly Rotating Pulsars

We utilize the bulk viscosity of interacting strange quark matter to reevaluate the damping time scale. The presence of medium effect of bulk viscosity leads to a stronger damping of r-modes, which can be over an order of magnitude for realistic parameters. We find that the r-mode instability window is narrowed due to the medium effect, and hence when a pulsar reaches the instability window it will only slow down by gravitational wave emission to a period of 1.78msec instead of 2.5msec given by early estimate. As a theoretical upper rotation limit of pulsars, the period of 1.78msec is very close to the two most rapidly spinning pulsars known, with periods of about 1.6msec.

The pre-supernova evolution of rotating massive stars

Massive stars are born rotating rigidly with a significant fraction of critical rotation at the surface. Consequently, rotationally-induced circulation and instabilities lead to chemical mixing in regions that would otherwise be stable, as well as a redistribution of angular momentum. Differential rotation also winds up magnetic fields, causing instabilities that can power a dynamo and magnetic stresses that lead to additional angular momentum transport. We follow the evolution of typical massive stars, their structure and angular momentum distribution, from the zero-age main sequence until iron core collapse. Without the action of magnetic fields, the resulting angular momentum is sufficiently large to significantly affect the explosion mechanism and neutron star formation. Sub-millisecond pulsars result that could encounter the r-mode instability. In helium cores massive enough, at least at low metalicity, the angular momentum is also sufficiently great to form a centrifugally supported accretion disk around a central black hole, powering the engine of the ‘collapsar’ model for GRBs. Including current estimates of the effect of magnetic fields still allows the formation of rapidly rotating (~ 5-10 ms) pulsars, but might leave too little angular momentum for collapsars.

Strange stars as persistent sources of gravitational waves

We investigate the relevance of the gravitational-wave driven r-mode instability for strange stars. We find that the unstable r-modes affect strange stars in a way that is quite distinct from the neutron star case. For accreting strange stars we show that the onset of r-mode instability does not lead to the thermo-gravitational runaway that is likely to occur in neutron stars. Instead, the strange star evolves towards a quasi-equilibrium state on a timescale of about a year. This mechanism could thus explain the clustering of spin-frequencies inferred from kHz QPO data in Low-mass X-ray binaries. For young strange stars we show that the r-mode driven spin-evolution is also distinct from the neutron star case. In a young strange star the r-mode undergoes short cycles of instability during the first few months. This is followed by a quasi-adiabatic phase where the r-mode remains at a small, roughly constant, amplitude for thousands of years. Another distinguishing feature from the neutron star case is that the r-modes in a strange star never grow to large amplitudes. Our results suggest that the r-modes in strange star emit a persistent gravitational-wave signal that should be detectable with large-scale interferometers given an observation time of a few months. If detected, these signals would provide unique evidence for the existence of strange stars, which would put useful constraints on the parameters of QCD.

Numerical evolutions of nonlinearr-modes in neutron stars

Nonlinear evolution of the gravitational radiation ~GR! driven instability in the r-modes of neutron stars is studied by full numerical 3D hydrodynamical simulations. The growth of the r-mode instability is found to be limited by the formation of shocks and breaking waves when the dimensionless amplitude of the mode grows to about three in value. This maximum mode amplitude is shown by numerical tests to be rather insensitive to the strength of the GR driving force. Upper limits on the strengths of possible nonlinear mode-mode coupling are inferred. Previously unpublished details of the numerical techniques used are presented, and the results of numerous calibration runs are discussed.

Gravitational radiation from the r-mode instability

The instability in the r-modes of rotating neutron stars can (in principle) emit substantial amounts of gravitational radiation (GR) which might be detectable by LIGO and similar detectors. Estimates are given here of the detectability of this GR based on the non-linear simulations of the r-mode instability by Lindblom, Tohline and Vallisneri. The burst of GR produced by the instability in the rapidly rotating 1.4M⊙ neutron star in this simulation is fairly monochromatic with frequency near 960 Hz and duration about 100 s. A simple analytical expression is derived here for the optimal signal-to-noise ratio S/N for detecting the GR from this type of source. For an object located at a distance of 20 Mpc we estimate the optimal S/N to be in the range 1.2–12.0 depending on the LIGO II configuration.

Effect of hyperon bulk viscosity on neutron-starr-modes

Neutron stars are expected to contain a significant number of hyperons in addition to protons and neutrons in the highest density portions of their cores. Following the work of Jones, we calculate the coefficient of bulk viscosity due to nonleptonic weak interactions involving hyperons in neutron-star cores, including new relativistic and superfluid effects. We evaluate the influence of this new bulk viscosity on the gravitational radiation driven instability in the r-modes. We find that the instability is completely suppressed in stars with cores cooler than a few times 10 9 K, but that stars rotating more rapidly than 10‐30% of maximum are unstable for temperatures around 10 10 K. Since neutron-star cores are expected to cool to a few times 10 9 K within seconds ~much shorter than the r-mode instability growth time! due to direct Urca processes, we conclude that the gravitational radiation instability will be suppressed in young neutron stars before it can significantly change the angular momentum of the star.

The spin evolution of nascent neutron stars

The loss of angular momentum owing to unstable r-modes in hot young neutron stars has been proposed as a mechanism for achieving the spin rates inferred for young pulsars. One factor that could have a significant effect on the action of the r-mode instability is fallback of supernova remnant material. The associated accretion torque could potentially counteract any gravitational-wave-induced spin-down, and accretion heating could affect the viscous damping rates and hence the instability. We discuss the effects of various external agents on the r-mode instability scenario within a simple model of supernova fallback on to a hot young magnetized neutron star. We find that the outcome depends strongly on the strength of the magnetic field of the star. Our model is capable of generating spin rates for young neutron stars that accord well with initial spin rates inferred from pulsar observations. The combined action of r-mode instability and fallback appears to cause the spin rates of neutron stars born with very different spin rates to converge, on a time-scale of approximately 1 year. The results suggest that stars with magnetic fields ≤1013 G could emit a detectable gravitational wave signal for perhaps several years after the supernova event. Stars with higher fields (magnetars) are unlikely to emit a detectable gravitational wave signal via the r-mode instability. The model also suggests that the r-mode instability could be extremely effective in preventing young neutron stars from going dynamically unstable to the bar-mode.

Properties ofrmodes in rotating magnetic neutron stars. II. Evolution of thermodes and stellar magnetic field

The evolution of the r-mode instability is likely to be accompanied by secular kinematic effects which will produce differential rotation with large scale drifts of fluid elements, mostly in the azimuthal direction. As first discussed by Rezzolla, Lamb and Shapiro 2000, the interaction of these secular velocity fields with a pre-existing neutron star magnetic field could result in the generation of intense and large scale toroidal fields. Following their derivation in the companion paper, we here discuss the numerical solution of the evolution equations for the magnetic field. The values of the magnetic fields obtained in this way are used to estimate the conditions under which the r-mode instability might be prevented or suppressed. We also assess the impact of the generation of large magnetic fields on the gravitational wave detectability of r-mode unstable neutron stars. Our results indicate that the signal to noise ratio in the detection of gravitational waves from the r-mode instability might be considerably decreased if the latter develops in neutron stars with initial magnetic fields larger than 10^10 G.