Lars Samuelsson

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.

Neutron star asteroseismology. Axial crust oscillations in the Cowling approximation

Recent observations of quasi-periodic oscillations in the aftermath of giant flares in soft gamma-ray repeaters suggest a close coupling between the seismic motion of the crust after a major quake and the modes of oscillations in a magnetar. In this paper, we consider the purely elastic modes of oscillation in the crust of a neutron star in the relativistic Cowling approximation (disregarding any magnetic field). We determine the axial crust modes for a large set of stellar models, using a state-of-the-art crust equation of state and a wide range of core masses and radii. We also devise useful approximate formulae for the mode-frequencies. We show that the relative crust thickness is well described by a function of the compactness of the star and a parameter describing the compressibility of the crust only. Considering the observational data for SGR 1900+14 and SGR 1806?20, we demonstrate how our results can be used to constrain the mass and radius of an oscillating neutron star.

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.

Are neutron stars with crystalline color-superconducting cores relevant for the LIGO experiment?

We estimate the maximal deformation that can be sustained by a rotating neutron star with a crystalline color-superconducting quark core. Our results suggest that current gravitational-wave data from the Laser Interferometer Gravitational-Wave Observatory have already reached the level where a detection would have been possible over a wide range of the poorly constrained QCD parameters. This leads to the nontrivial conclusion that compact objects do not contain maximally strained color crystalline cores drawn from this range of parameter space. We discuss the uncertainties associated with our simple model and how it can be improved in the future.

Relativistic mechanics of neutron superfluid in (magneto)elastic star crust

At densities below the neutron drip threshold, a purely elastic solid model (including, if necessary, a frozen-in magnetic field) can provide an adequate description of a neutron star crust, but at higher densities it will be necessary to allow for the penetration of the solid lattice by an independently moving current of superfluid neutrons. In order to do this, the previously available category of relativistic elasticity models is combined here with a separately developed category of relativistic superfluidity models in a unified treatment based on the use of an appropriate Lagrangian master function. As well as models of the purely variational kind, in which the vortices flow freely with the fluid, such a master function also provides a corresponding category of non-dissipative models in which the vortices are pinned to the solid structure.

Axial quasi-normal modes of neutron stars: accounting for the superfluid in the crust

We present the results of the first study of global oscillations of relativistic stars with both elastic crusts and interpenetrating superfluid components. For simplicity, we focus on the axial quasi-normal modes. Our results demonstrate that the torsional crust modes are essentially unaffected by the coupling to the gravitational field. This is as expected since these oscillations are known to be weak gravitational-wave sources. In contrast, the presence of a loosely coupled superfluid neutron component in the crust can have a significant effect on the oscillation spectrum. We show that the entrainment between the superfluid and the crust nuclei is a key parameter in the problem. Our analysis highlights the need for a more detailed understanding of the coupled crust-superfluid at the microphysical level. Our numerical results have, even though we have not considered magnetized stars, some relevance for efforts to carry out seismology based on quasi-periodic oscillations observed in the tails of magnetar flares. In particular, we argue that the sensitive dependence on the entrainment may have to be accounted for in attempts to match theoretical models to observational data.

CARTER'S CONSTANT REVEALED

A new formulation of Carters constant for geodesic motion in Kerr black holes is given. It is shown that Carters constant corresponds to the total angular momentum plus a precisely defined part which is quadratic in the linear momenta. The characterization is exact in the weak field limit obtained by letting the gravitational constant go to zero. It is suggested that the new form can be useful in current studies of the dynamics of extreme mass ratio inspiral (EMRI) systems emitting gravitational radiation.

A characteristic approach to the quasi-normal mode problem

In this paper we discuss a new approach to the quasi-normal mode problem in general relativity. By combining a characteristic formulation of the perturbation equations with the integration of a suitable phase-function for a complex-valued radial coordinate, we reformulate the standard outgoing-wave boundary condition as a zero Dirichlet condition. This has a number of important advantages over previous strategies. The characteristic formulation permits coordinate compactification, which means that we can impose the boundary condition at future null infinity. The phase function avoids oscillatory behaviour in the solution, and the use of a complex radial variable allows a clean distinction between out- and ingoing waves. We demonstrate that the method is easy to implement, and that it leads to high precision numerical results. Finally, we argue that the method should generalize to the important problem of rapidly rotating neutron star spacetimes.

CONSTRAINTS OF INITIAL DATA FOR A DISCRETE UNIVERSE

The matter distribution of the universe is observed to be discrete in the form of stars, galaxies and clusters of galaxies. Due to the non-linearities of the Einstein field equations, the discrete nature of the matter implies modifications of the standard Friedmann cosmology paradigm. The modifications affect both the dynamics and the possible cosmological initial data. We discuss properties and restrictions for the intial data of a universe with a discrete matter distribution, in particular possible implications for the curvature and topology.

HOW MATTER GENERATES SPATIAL CURVATURE

We estimate the cosmological spatial curvature as generated by the actual matter content of the universe. The result is that the present day universe appears to be very nearly spatially flat due to the low density and the nonrelativistic peculiar velocities. The sign of the spatial curvature comes out as positive.