R-modes In Neutron Stars Research Articles

Prospects for Detecting Gravitational Waves at 5Hz with Ground-Based Detectors.

We propose an upgrade to Advanced LIGO (aLIGO), named LIGO-LF, that focuses on improving the sensitivity in the 5-30Hz low-frequency band, and we explore the upgrade's astrophysical applications. We present a comprehensive study of the detector's technical noises and show that with technologies currently under development, such as interferometrically sensed seismometers and balanced-homodyne readout, LIGO-LF can reach the fundamental limits set by quantum and thermal noises down to 5Hz. These technologies are also directly applicable to the future generation of detectors. We go on to consider this upgrade's implications for the astrophysical output of an aLIGO-like detector. A single LIGO-LF can detect mergers of stellar-mass black holes (BHs) out to a redshift of z≃6 and would be sensitive to intermediate-mass black holes up to 2000 M_{⊙}. The detection rate of merging BHs will increase by a factor of 18 compared to aLIGO. Additionally, for a given source the chirp mass and total mass can be constrained 2 times better than aLIGO and the effective spin 3-5 times better than aLIGO. Furthermore, LIGO-LF enables the localization of coalescing binary neutron stars with an uncertainty solid angle 10 times smaller than that of aLIGO at 30Hz and 4 times smaller when the entire signal is used. LIGO-LF also significantly enhances the probability of detecting other astrophysical phenomena including the tidal excitation of neutron star r modes and the gravitational memory effects.

R -mode frequencies of rapidly and differentially rotating relativistic neutron stars

R-modes of neutron stars could be a source of gravitational waves for ground based detectors. If the precise frequency $\sigma$ is known, guided gravitational wave searches with enhanced detectability are possible. Because of its physical importance many authors have calculated the r-mode frequency. For the dominant mode, the associated gravitational wave frequency is 4/3 times the angular velocity of the star $\Omega$, subject to various corrections of which relativistic and rotational corrections are the most important. This has led several authors to investigate the dependence of the r-mode frequency on factors such as the relativistic compactness parameter ($M/R$) and the angular velocity of stars with different equations of state. The results found so far, however, are almost independent of the equation of state. Here we investigate the effect of rapid rotation and differential rotation on $\sigma$. We evolve the perturbation equations using the Cowling approximation by applying finite differencing methods to compute the r-mode frequency for a series of rotating neutron stars with polytropic equations of state. We find that rotational effects in the r-mode frequency can be larger than relativistic effects for rapidly spinning stars with low compactness, reducing the observed frequency. Differential rotation also acts to decrease $\sigma$, but its effect inscreases with the compactness. The results presented here are relevant to the design of gravitational wave and electromagnetic r-mode searches.

R-modes in neutron stars: Theory and observations

In this paper, I will review the theory behind the gravitational wave (GW) driven r-mode instability in rapidly rotating neutron stars (NSs) and discuss which constraints can be derived from observations of spins and temperatures in low mass X-ray binaries (LMXBs). I will discuss how a standard, 'minimal' NS model is not consistent with the data, and discuss some of the additional physical mechanisms that could reconcile theory with observations. In particular, I will focus on additional forms of damping due to exotic cores and on strong mutual friction due to superfluid vortices cutting through superconducting flux tubes, and examine the repercussions these effects could have on the saturation amplitude of the mode. Finally I will also discuss the possibility that oscillations due to r-modes may have been recently observed in the X-ray light curves of two LMXBs.

Bulk viscosity and r-modes of neutron stars

The bulk viscosity due to the non-leptonic process involving hyperons in K− condensed matter is discussed here. We find that the bulk viscosity is modified in a superconducting phase. Further, we demonstrate how the exotic bulk viscosity coefficient influences r-modes of neutron stars which might be sources of detectable gravitational waves.

Exotic bulk viscosity and its influence on neutron star r-modes

We investigate the effect of exotic matter in particular, hyperon matter on neutron star properties such as equation of state (EoS), mass-radius relationship and bulk viscosity. Here we construct equations of state within the framework of a relativistic field theoretical model. As hyperons are produced abundantly in dense matter, hyperon–hyperon interaction becomes important and is included in this model. Hyperon–hyperon interaction gives rise to a softer EoS which results in a smaller maximum mass neutron star compared with the case without the interaction. Next we compute the coefficient of bulk viscosity and the corresponding damping time scale due to the non-leptonic weak process including Λ hyperons. Further, we investigate the role of the bulk viscosity on gravitational radiation driven r-mode instability in a neutron star of given mass and temperature and find that the instability is effectively suppressed.

Ekman layer damping of r modes revisited

We investigate the damping of neutron star r-modes due to the presence of a viscous boundary (Ekman) layer at the interface between the crust and the core. Our study is motivated by the possibility that the gravitational-wave driven instability of the inertial r-modes may become active in rapidly spinning neutron stars, eg. in low-mass X-ray binaries, and the fact that a viscous Ekman layer at the core-crust interface provides an efficient damping mechanism for these oscillations. We review various approaches to the problem and carry out an analytic calculation of the effects due to the Ekman layer for a rigid crust. Our analytic estimates support previous numerical results, and provide further insight into the intricacies of the problem. We add to previous work by discussing the effect that compressibility and composition stratification have on the boundary layer damping. We show that, while stratification is unimportant for the r-mode problem, composition suppresses the damping rate by about a factor of two (depending on the detailed equation of state).

Nonlinearr-modes in neutron stars: Instability of an unstable mode

We study the dynamical evolution of a large amplitude r-mode by numerical simulations. R-modes in neutron stars are unstable growing modes, driven by gravitational radiation reaction. In these simulations, r-modes of amplitude unity or above are destroyed by a catastrophic decay: A large amplitude r-mode gradually leaks energy into other fluid modes, which in turn act nonlinearly with the r-mode, leading to the onset of the rapid decay. As a result the r-mode suddenly breaks down into a differentially rotating configuration. The catastrophic decay does not appear to be related to shock waves at the star's surface. The limit it imposes on the r-mode amplitude is significantly smaller than that suggested by previous fully nonlinear numerical simulations.

Nonlinear Couplings betweenr‐Modes of Rotating Neutron Stars

The r-modes of neutron stars can be driven to instability by gravitational radiation. While linear perturbation theory predicts the existence of this instability, linear theory cannot provide any information about the nonlinear development of the instability. The subject of this paper is the weakly nonlinear regime of fluid dynamics. In the weakly nonlinear regime, the nonlinear fluid equations are approximated by an infinite set of oscillators that are coupled together so that terms quadratic in the mode amplitudes are kept in the equations of motion. In this paper, the coupling coefficients between the r-modes are computed. The stellar model assumed is a polytropic model in which a source of buoyancy is included so that the Schwarzschild discriminant is nonzero. The properties of these coupling coefficients and the types of resonances possible are discussed in this paper. It is shown that no exact resonance involving the unstable l = m = 2 r-mode occurs and that only a small number of modes have a dimensionless coupling constant larger than unity. However, an infinite number of resonant mode triplets exist that couple indirectly to the unstable r-mode. All couplings in this paper involve the l > |m| r-modes that only exist if the star is slowly rotating. This work is complementary to that of Schenk and coworkers in 2002, who consider rapidly rotating stars that are neutral to convection.

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.

Nonlinear mode coupling in rotating stars and ther-mode instability in neutron stars

We develop the formalism required to study the nonlinear interaction of modes in rotating Newtonian stars in the weakly nonlinear regime. The formalism simplifies and extends previous treatments. At linear order, we elucidate and extend slightly a formalism due to Schutz, show how to decompose a general motion of a rotating star into a sum over modes, and obtain uncoupled equations of motion for the mode amplitudes under the influence of an external force. Nonlinear effects are added perturbatively via three-mode couplings. We describe a new, efficient way to compute the coupling coefficients, to zeroth order in the stellar rotation rate, using spin-weighted spherical harmonics. We apply this formalism to derive some properties of the coupling coefficients relevant to the nonlinear interactions of unstable r-modes in neutron stars, postponing numerical integrations of the coupled equations of motion to a later paper. From an astrophysical viewpoint, the most interesting result of this paper is that many couplings of r-modes to other rotational modes (modes with zero frequencies in the non-rotating limit) are small: either they vanish altogether because of various selection rules, or they vanish to lowest order in the angular velocity. In zero-buoyancy stars, the coupling of three r-modes is forbidden entirely and the coupling of two r-modes to one hybrid rotational mode vanishes to zeroth order in rotation frequency. In incompressible stars, the coupling of any three rotational modes vanishes to zeroth order in rotation frequency.

Crust-core coupling and r-mode damping in neutron stars: a toy model

r-modes in neutron stars with crusts are damped by viscous friction at the crust–core boundary. The magnitude of this damping, evaluated by Bildsten & Ushomirsky (BU) under the assumption of a perfectly rigid crust, sets the maximum spin frequency for neutron stars spun up by accretion in low-mass X-ray binaries (LMXBs). In this paper we explore the mechanical coupling between the core r-modes and the elastic crust, using a toy model of a constant-density neutron star having a crust with a constant shear modulus. We find that, at spin frequencies in excess of ≈50 Hz, the r-modes strongly penetrate the crust. This reduces the relative motion (slippage) between the crust and the core compared with the rigid-crust limit. We therefore revise down, by as much as a factor of 102–103, the damping rate computed by BU, significantly reducing the maximal possible spin frequency of neutron stars with solid crusts. The dependence of the crust–core slippage on the spin frequency is complicated, and is very sensitive to the physical thickness of the crust. If the crust is sufficiently thick, the curve of the critical spin frequency for the onset of the r-mode instability becomes multivalued for some temperatures; this is related to avoided crossings between the r-mode and higher-order torsional modes in the crust. The critical frequencies are comparable to the observed spins of neutron stars in LMXBs and millisecond pulsars.

Nonlinear evolution of the r-modes in neutron stars.

The evolution of a neutron-star r-mode driven unstable by gravitational radiation is studied here using numerical solutions of the full nonlinear fluid equations. The dimensionless amplitude of the mode grows to order unity before strong shocks develop which quickly damp the mode. In this simulation the star loses about 40% of its initial angular momentum and 50% of its rotational kinetic energy before the mode is damped. The nonlinear evolution causes the fluid to develop strong differential rotation which is concentrated near the surface and poles of the star.