Kostas Glampedakis

Modelling magnetically deformed neutron stars

Rotating deformed neutron stars are important potential sources for ground-based gravitational wave interferometers such as LIGO, GEO600 and VIRGO. One mechanism that may lead to significant non-asymmetries is the internal magnetic field. It is well known that a magnetic star will not be spherical and, if the magnetic axis is not aligned with the spin axis, the deformation will lead to the emission of gravitational waves. The aim of this paper is to develop a formalism that would allow us to model magnetically deformed stars, using both realistic equations of state and field configurations. As a first step, we consider a set of simplified model problems. Focusing on dipolar fields, we determine the internal magnetic field which is consistent with a given neutron star model and calculate the associated deformation. We discuss the relevance of our results for current gravitational wave detectors and future prospects.

Magnetohydrodynamics of superfluid and superconducting neutron star cores

Mature neutron stars are cold enough to contain a number of superfluid and superconducting components. These systems are distinguished by the presence of additional dynamical degrees of freedom associated with superfluidity. In order to consider models with mixtures of condensates, we need to develop a multifluid description that accounts for the presence of rotational neutron vortices and magnetic proton fluxtubes. We also need to model the forces that impede the motion of vortices and fluxtubes, and understand how these forces act on the condensates. This paper concerns the development of such a model for the outer core of a neutron star, where superfluid neutrons co-exist with a type II proton superconductor and an electron gas. We discuss the hydrodynamics of this system, focusing on the role of the entrainment effect, the magnetic field, the vortex/fluxtube tension and the dissipative mutual friction forces. Our final results can be directly applied to a number of interesting astrophysical scenarios, e.g. associated with neutron star oscillations or the evolution of the large-scale magnetic field.

Pulsar glitches: the crust is not enough.

Pulsar glitches are traditionally viewed as a manifestation of vortex dynamics associated with a neutron superfluid reservoir confined to the inner crust of the star. In this Letter we show that the nondissipative entrainment coupling between the neutron superfluid and the nuclear lattice leads to a less mobile crust superfluid, effectively reducing the moment of inertia associated with the angular momentum reservoir. Combining the latest observational data for prolific glitching pulsars with theoretical results for the crust entrainment, we find that the required superfluid reservoir exceeds that available in the crust. This challenges our understanding of the glitch phenomenon, and we discuss possible resolutions to the problem.

Elastic or magnetic? A toy model for global magnetar oscillations with implications for quasi-periodic oscillations during flares

We use a simple toy-model to discuss global magnetohydrodynamic modes of a neutron star, taking into account the magnetic coupling between the elastic crust and the fluid core. Our results suggest that the notion of pure torsional crust modes is not useful for the coupled system. All modes excite Alfven waves in the core. However, we also show that the modes that are most likely to be excited by a fractured crust, e.g. during a magnetar flare, are such that the crust and the core oscillate in concert. For our simple model, the frequencies of these modes are similar to the ‘pure crustal’ frequencies. In addition, our model provides a natural explanation for the presence of lower frequency (<30 Hz) quasi-periodic oscillations seen in the 2004 December giant flare of SGR 1806−20.

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, for example, 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 2 (depending on the detailed equation of state).

Hydrodynamical trigger mechanism for pulsar glitches.

We describe a new instability that may trigger the global unpinning of vortices in a spinning neutron star, leading to the transfer of angular momentum from the superfluid component to the stars crust. The instability, which is associated with the inertial r modes of a superfluid neutron star, sets in once the rotational lag in the system reaches a critical level. We demonstrate that our simple model agrees well with the observed glitch data. This new idea should stimulate work on more detailed neutron star models, which would account for the crustal shear stresses and magnetic field effects we have ignored.

How viscous is a superfluid neutron star core

We discuss the effects of superfluidity on the shear viscosity in a neutron star core. Our study combines existing theoretical results for the viscosity coefficients with data for the various superfluid energy gaps into a consistent description. In particular, we provide a simple model for the electron viscosity which is relevant both when the protons form a normal fluid and when they become superconducting. This model explains in a clear way why proton superconductivity leads to a significant strengthening of the shear viscosity. We present our results in a form which permits the use of data for any given modern equation of state (our final formulas are explicitly dependent on the proton fraction). We discuss a simple description of the relevant superfluid pairing gaps, and construct a number of models (spanning the range of current uncertainty) which are then used to discuss the superfluid suppression of shear viscosity. We conclude by a discussion of a number of challenges that must be met if we are to make further progress in this area of research.

Approximating the inspiral of test bodies into Kerr black holes

We present a new approximate method for constructing gravitational radiation driven inspirals of test bodies orbiting Kerr black holes. Such orbits can be fully described by a semilatus rectum p, an eccentricity e, and an inclination angle iota, or, by an energy E, an angular momentum component L-z, and a third constant Q. Our scheme uses expressions that are exact (within an adiabatic approximation) for the rates of change ((p)over dot, (e)over dot, (iota)over dot) as linear combinations of the fluxes ((E)over dot, (L)over dot(z),(Q)over dot), but uses quadrupole-order formulas for these fluxes. This scheme thus encodes the exact orbital dynamics, augmenting it with an approximate radiation reaction. Comparing inspiral trajectories, we find that this approximation agrees well with numerical results for the special cases of eccentric equatorial and circular inclined orbits, far more accurate than corresponding weak-field formulas for ((p)over dot, (e)over dot, (iota)over dot). We use this technique to study the inspiral of a test body in inclined, eccentric Kerr orbits. Our results should be useful tools for constructing approximate waveforms that can be used to study data analysis problems for the future Laser Interferometer Space Antenna gravitational-wave observatory, in lieu of waveforms from more rigorous techniques that are currently under development.

Modelling the spin equilibrium of neutron stars in low-mass X-ray binaries without gravitational radiation

In this paper we discuss the spin equilibrium of accreting neutron stars in low-mass X-ray binaries (LMXBs). We demonstrate that, when combined with a naive spin-up torque, the observed data lead to inferred magnetic fields which are at variance with those of Galactic millisecond radio pulsars. This indicates the need for either additional spin-down torques (e.g. gravitational radiation) or an improved accretion model. We show that a simple consistent accretion model can be arrived at by accounting for radiation pressure in rapidly accreting systems (above a few per cent of the Eddington accretion rate). In our model the inner disc region is thick and significantly sub-Keplerian and the estimated equilibrium periods are such that the LMXB neutron stars have properties that accord well with the Galactic millisecond radio pulsar sample. The implications for future gravitational-wave observations are also discussed briefly.

Ambipolar diffusion in superfluid neutron stars

In this paper, we reconsider the problem of magnetic field diffusion in neutron star cores. We model the star as consisting of a mixture of neutrons, protons and electrons, and allow for particle reactions and binary collisions between species. Our analysis is in much the same spirit as that of Goldreich & Reisenegger, and we content ourselves with rough estimates of magnetic diffusion time-scales rather than solving accurately for some particular field geometry. However, our work improves upon previous treatments in one crucial respect: we allow for superfluidity in the neutron star matter. We find that the consequent mutual friction force, coupling the neutrons and charged particles, together with the suppression of particle collisions and reactions, drastically affects the ambipolar magnetic field diffusion time-scale. In particular, the addition of superfluidity means that it is unlikely that there is ambipolar diffusion in magnetar cores on the time-scale of the lifetimes of these objects, contradicting an assumption often made in the modelling of the flaring activity commonly observed in magnetars. Our work suggests that if a decaying magnetic field is indeed the cause of magnetar activity, the field evolution is likely to take place outside of the core and might represent Hall/Ohmic diffusion in the stellar crust, or else that a mechanism other than standard ambipolar diffusion is active, e.g. flux expulsion due to the interaction between neutron vortices and magnetic fluxtubes.