# Research 2011

## Hydromagnetic equilibrium in superfluid neutron stars

November 2011

Kostas Glampedakis, Nils Andersson, Sam Lander

Much of the recent theoretical work on neutron star physics has aimed on improving our understanding of the magnetic field equilibrium structure in neutron stars. This is a necessary step if we ever hope to develop truly realistic models of phenomena such as magnetar flares and the quasi-periodic oscillations observed during these events. Our work improves on the existing models of hydromagnetic equilibrium by including a key property of neutron star matter, namely, the combined presence of superfluid and superconducting components.

## The f-mode instability in relativistic neutron stars

July 2011

Erich Gaertig, Kostas Glampedakis, Kostas D. Kokkotas, Burkhard Zink

Rapidly spinning neutron stars are known to harbour pulsation modes that may become unstable and grow in amplitude by emitting gravitational radiation. This is due to the so-called Chandrasekhar-Friedman-Schutz (CFS) mechanism which is based on the general notion of oscillations changing from counter- to co-rotating (with respect to the stellar rotation) as a result of rotational dragging. As soon as a retrograde mode in the comoving frame of the rotating neutron star is dragged forward and moves prograde in the coordinate sytem of an inertial observer, the emission of gravitational waves leads to an instability which removes angular momentum from the neutron star and will spin it down.

Among the various stellar modes, the f-mode is the one typically considered as a promising source of gravitational radiation for ground-based detectors such as LIGO and VIRGO. Improving the existing work on the f-mode instability in Newtonian stellar models, in this work we present the first calculation of the basic properties of the f-mode instability in rapidly rotating relativistic neutron stars, adopting the Cowling approximation. Using a relativistic polytropic stellar model with representative values for mass and radius, we obtain a minimum gravitational growth timescale (for the dominant l=m=4 mode) of the order of 10^{3}-10^{4} seconds near the Kepler spin frequency. This is substantially shorter than the Newtonian value which typically is one or two order of magnitudes larger. By accounting for dissipation in neutron star matter, i.e. shear/bulk viscosity and superfluid mutual friction, we also calculate the associated f-mode instability window.

## Are giant flares in magnetars viable sources of gravitational radiation?

July 2011

Burkhard Zink, Paul D. Lasky, Kostas D. Kokkotas

Few theoretical studies have been concerned with this problem, with the small number using either highly idealized models or assuming a magnetic field orders of magnitude beyond what is supported by observations. We perform nonlinear general-relativistic magnetohydrodynamics simulations of large-scale hydromagnetic instabilities in magnetar models. We utilise these models to find gravitational wave emissions over a wide range of energies, from 10^{40} to 10^{47} erg. This allows us to derive a systematic relationship between the surface field strength and the gravitational wave strain, which we find to be highly nonlinear. In particular, for typical magnetar fields of a few times 10^{15} G, we conclude that a direct observation of f-modes excited by global magnetic field reconfigurations is unlikely with present or near-future gravitational wave observatories, though we also discuss the possibility that modes in a low-frequency band up to 100 Hz could be sufficiently excited to be relevant for observation.

## Magnetic Fields in Relativistic Neutron Stars

June 2011

Paul D. Lasky, Burkhard Zink, Kostas Glampedakis, Kostas D. Kokkotas

Magnetic fields play a pivotal role in multiple aspects of neutron star physics. We are modelling strongly magnetised neutron stars with three-dimensional, non-linear, general relativistic magnetohydrodynamic (GRMHD) simulations to understand the secular and dynamical evolution of these exotic objects. The first of these works studied magnetic field instabilities and the susbequent evolution to new, quasi-equilibria magnetic field configurations. The existence of these stable equilibra may have consequences for neutron star physics, including flare generation mechanisms and interpretations of quasi-periodic oscillations. Read more about this work here.

## Neutron star mass and radius constraints from thermonuclear X-ray burst spectra

May 2011

Stratos Boutloukos

X-ray burst spectra have long been used to estimate neutron star masses and radii. These estimates assumed that burst spectra are accurately described by the model atmosphere spectra developed over the last three decades. We compared RXTE data from a superburst with these spectra and found that the spectra predicted by previously published model atmospheres are strongly inconsistent with these high-precision measurements. This suggests caution in making inferences using these model spectra. In contrast, a simple Bose-Einstein spectrum is fully consistent with the data, as are recently published model atmosphere spectra. Fitting the latter to long stretches of data may yield constraints on the neuron star mass and radius via joint constraints on the surface gravity and redshift.

## Quasi periodic oscillations in magnetars

April 2011

Antonella Colaiuda, Kostas D. Kokkotas

Modelling the so-called quasi periodic oscillations in strongly magnetised neutron stars (magnetars) could help to constrain the equation of state of those compact objects.

According to the magnetar model, energy is fed to the neutron star magnetosphere when local “crustquakes'' occur, giving rise to recurrent bursts with a large range of amplitudes. Giant flares are believed to originate from large-scale rearrangements of the inner field or catastrophic instabilities in the magnetosphere. Both mechanisms are accompanied by quasi-periodic oscillations (QPOs) in the tails of the flares.

In our work, we use a linear general relativistic code in order to find a better model that could fit to the observed frequencies.

## Gravitational wave asteroseismology with fast rotating neutron stars

March 2011

Erich Gaertig, Kostas D. Kokkotas

When a fast rotating neutron star becomes unstable to the CFS-mechanism, the non-axisymmetric instabilities will be a strong emitter of gravitational waves. The detection of these gravitational waves from oscillating neutron stars will allow the study of their interior, in the same way as helioseismology provides information about the interior of the Sun. It is expected that the identification of specific pulsation frequencies in the observational data will reveal the true properties of matter at densities that cannot be probed today by any other experiment.

This is the original suggestion about gravitational wave asteroseismology which was first applied to nonrotating neutron stars. The idea is to compute frequencies and damping times for different neutron star models and a huge variety of equations of state. Based on this data pool, model-independent relationships between oscillation frequencies/damping times and stellar key parametes like mass and radius can be established which will unambiguously pinpoint these parameters once gravitational waves from neutron stars can be detected.

In this study, gravitational wave asteroseismology has been extended to handle rapidly rotating neutron stars as well. The inclusion of rotational effects leads to several complications. First, non-axisymmetric mode frequencies split once the star is spinning and second, depending on the actual model, certain configurations can become secularly unstable. Nevertheless, it was possible to derive again model-independent relationships which in this case also include the angular velocity as fitting parameter.

## HORIZON: Accelerated general relativistic magnetohydrodynamics

February 2011

Burkhard Zink

Massively parallel computations typical of scientific simulations can nowadays make use of GPUs (graphics processing units). HORIZON is a new application code for general relativistic magnetohydrodynamics which is optimized to make full use of these new architectures. Substantial performance improvements over traditional CPU-based computations have been observed in this study.