The problem of the gravitational radiation damping of neutron star fundamental ($f$) mode oscillations has received considerable attention. Many studies have looked at the stability of such oscillations in rapidly rotating stars, calculating the grow
th/decay rate of the mode amplitude. In this paper, we look at the relatively neglected problem of the radiation reaction on the spin of the star. We specialise greatly to the so-called Kelvin modes: the modes of oscillation of (initially) non-rotating incompressible stars. We find the unexpected result that the excitation of a mode of angular momentum $delta J$ on an initially non-rotating star ends up radiating an angular momentum $2 delta J$ to infinity, leaving the star itself with a bulk angular momentum of $-delta J$. This result is interesting in itself, and also will have implications for the angular momentum budgets of spinning down neutron stars, should such modes be excited.
As is well known, gravitational wave detections of coalescing binaries are standard sirens, allowing a measurement of source distance by gravitational wave means alone. In this paper we explore the analogue of this for continuous gravitational wave e
mission from individual spinning neutron stars, whose spin-down is driven purely by gravitational wave emission. We show that in this case, the distance measurement is always degenerate with one other parameter, which can be taken to be the moment of inertia of the star. We quantify the accuracy to which such degenerate measurements can be made. We also discuss the practical application of this to scenarios where one or other of distance or moment of inertia is constrained, breaking this degeneracy and allowing a measurement of the remaining parameter. Our results will be of use following the eventual detection of a neutron star spinning down through such gravitational wave emission.
As the era of gravitational-wave astronomy has well and truly begun, gravitational radiation from rotating neutron stars remains elusive. Rapidly spinning neutron stars are the main targets for continuous-wave searches since, according to general rel
ativity, provided they are asymmetrically deformed, they will emit gravitational waves. It is believed that detecting such radiation will unlock the answer to why no pulsars have been observed to spin close to the break-up frequency. We review existing studies on the maximum mountain that a neutron star crust can support, critique the key assumptions and identify issues relating to boundary conditions that need to be resolved. In light of this discussion, we present a new scheme for modelling neutron star mountains. The crucial ingredient for this scheme is a description of the fiducial force which takes the star away from sphericity. We consider three examples: a source potential which is a solution to Laplaces equation, another solution which does not act in the core of the star and a thermal pressure perturbation. For all the cases, we find that the largest quadrupoles are between a factor of a few to two orders of magnitude below previous estimates of the maximum mountain size.
The configuration of the magnetic field in the interior of a neutron star is mostly unknown from observations. Theoretical models of the interior magnetic field geometry tend to be oversimplified to avoid mathematical complexity and tend to be based
on axisymmetric barotropic fluid systems. These static magnetic equilibrium configurations have been shown to be unstable on a short time scale against an infinitesimal perturbation. Given this instability, it is relevant to consider how more realistic neutron star physics affects the outcome. In particular, it makes sense to ask if elasticity, which provides an additional restoring force on the perturbations, may stabilise the system. It is well-known that the matter in the neutron star crust forms an ionic crystal. The interactions between the crystallized nuclei can generate shear stress against any applied strain. To incorporate the effect of the crust on the dynamical evolution of the perturbed equilibrium structure, we study the effect of elasticity on the instability of an axisymmetric magnetic star. In particular we determine the critical shear modulus required to prevent magnetic instability and consider the corresponding astrophysical consequences.
This work explores whether gravitational waves (GWs) from neutron star (NS) mountains can be detected with current 2nd-generation and future 3rd-generation GW detectors. In particular, we focus on a scenario where transient mountains are formed immed
iately after a NS glitch. In a glitch, a NSs spin frequency abruptly increases and then often exponentially recovers back to, but never quite reaches, the spin frequency prior to the glitch. If the recovery is ascribed to an additional torque due to a transient mountain, we find that GWs from that mountain are marginally-detectable with Advanced LIGO at design sensitivity and is very likely to be detectable for 3rd-generation detectors such as the Einstein Telescope. Using this model, we are able to find analytical expressions for the GW amplitude and its duration in terms of observables.
During their most recent observing run, LIGO/Virgo reported the gravitational wave (GW) transient S191110af, a burst signal at a frequency of 1.78 kHz that lasted for 0.104 s. While this signal was later deemed non-astrophysical, genuine detections o
f uncertain origin will occur in the future. Here we study the potential for detecting GWs from neutron star fluid oscillations, which have mode frequency and duration matching those of S191110af and which can be used to constrain the equation of state of nuclear matter. Assuming that such transient oscillations can be excited to energies typical of a pulsar glitch, we use measured properties of known glitching pulsars to estimate the amplitude of GWs produced by such events. We find that current GW detectors may observe nearby pulsars undergoing large events with energy similar to Vela pulsar glitch energies, while next generation detectors could observe a significant number of events. Finally, we show that it is possible to distinguish between GWs produced by rapidly rotating and slowly rotating pulsars from the imprint of rotation on the f-mode frequency.
Many low-mass X-ray binary (LMXB) systems are observed to contain rapidly spinning neutron stars. The spin frequencies of these systems may be limited by the emission of gravitational waves. This can happen if their mass distribution is sufficiently
non-axisymmetric. It has been suggested that such `mountains may be created via temperature non-axisymmetries, but estimates of the likely level of temperature asymmetry have been lacking. To remedy this, we examine a simple symmetry breaking mechanism, where an internal magnetic field perturbs the thermal conductivity tensor, making it direction-dependent. We find that the internal magnetic field strengths required to build mountains of the necessary size are very large, several orders of magnitude larger than the inferred external field strengths, pushing into the regime where our assumption of the magnetic field having a perturbative effect on the thermal conductivity breaks down. We also examine how non-axisymmetric surface temperature profiles, as might be caused by magnetic funnelling of the accretion flow, lead to internal temperature asymmetries, but find that for realistic parameters the induced non-axisymmetries are very small. We conclude that, in the context of this work at least, very large internal magnetic fields are required to generate mountains of the necessary size.
Quasi-periodic oscillations have been seen in the light curves following several magnetar giant flares. These oscillations are of great interest as they probably provide our first ever view of the normal modes of oscillation of neutron stars. The sta
te-of-the-art lies in the study of the oscillations of elastic-magnetic stellar models, mainly with a view to relating the observed frequencies to the structure and composition of the star itself. We advance this programme by considering several new physical mechanisms that are likely to be important for magnetar oscillations. These relate to the superfluid/superconducting nature of the stellar interior, and the damping of the modes, both through internal dissipation mechanisms and the launching of waves into the magnetosphere. We make simple order-of-magnitude estimates to show that both the frequencies and the damping time of magnetar oscillations can evolve in time, identifying three distinct `pathways that can be followed, depending upon the initial magnitude of the mode excitation. These results are interesting as they show that the information buried in magnetar QPOs may be even richer than previously thought, and motivate more careful examination of magnetar light curves, to search for signatures of the different types of evolution that we have identified.
Neutron stars may harbour the true ground state of matter in the form of strange quark matter. If present, this type of matter is expected to be a color superconductor, a consequence of quark pairing with respect to the color/flavor degrees of freedo
m. The stellar magnetic field threading the quark core becomes a color-magnetic admixture and, in the event that superconductivity is of type II, leads to the formation of color-magnetic vortices. In this Letter we show that the volume-averaged color-magnetic vortex tension force should naturally lead to a significant degree of non-axisymmetry in systems like radio pulsars. We show that gravitational radiation from such color-magnetic `mountains in young pulsars like the Crab and Vela could be observable by the future Einstein Telescope, thus becoming a probe of paired quark matter in neutron stars. The detectability threshold can be pushed up toward the sensitivity level of Advanced LIGO if we invoke an interior magnetic field about a factor ten stronger than the surface polar field.
