Nikolaos Stergioulas

Rotating Stars in Relativity

Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information they might yield about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on the equilibrium properties and on the nonaxisymmetric instabilities in f-modes and r-modes have been updated and several new sections have been added on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity.

Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole

We present a new three-dimensional fully general-relativistic hydrodynamics code using high-resolution shock-capturing techniques and a conformal traceless formulation of the Einstein equations. Besides presenting a thorough set of tests which the code passes with very high accuracy, we discuss its application to the study of the gravitational collapse of uniformly rotating neutron stars to Kerr black holes. The initial stellar models are modeled as relativistic polytropes which are either secularly or dynamically unstable and with angular velocities which range from slow rotation to the mass-shedding limit. We investigate the gravitational collapse by carefully studying not only the dynamics of the matter, but also that of the trapped surfaces, i.e., of both the apparent and event horizons formed during the collapse. The use of these surfaces, together with the dynamical horizon framework, allows for a precise measurement of the black-hole mass and spin. The ability to successfully perform these simulations for sufficiently long times relies on excising a region of the computational domain which includes the singularity and is within the apparent horizon. The dynamics of the collapsing matter is strongly influenced by the initial amount of angular momentum in the progenitor star and, for initial models with sufficiently high angular velocities, the collapse can lead to the formation of an unstable disc in differential rotation. All of the simulations performed with uniformly rotating initial data and a polytropic or ideal-fluid equation of state show no evidence of shocks or of the presence of matter on stable orbits outside the black hole.

Torsional oscillations of relativistic stars with dipole magnetic fields

We investigate torsional Alfven modes of relativistic stars with a global dipole mag- netic field. It has been noted recently (Glampedakis et al. 2006) that such oscillation modes could serve as as an alternative explanation (in contrast to torsional crustal modes) for the SGR phenomenon, if the magnetic field is not confined to the crust. We compute global Alfven modes for a representative sample of equations of state and magnetar masses, in the ideal MHD approximation and ignoring l ± 2 terms in the eigenfunction. We find that the presence of a realistic crust has a negligible effect on Alfven modes for B > 4 × 10 15 G. Furthermore, we find strong avoided crossings between torsional Alfven modes and torsional crust modes. For magnetar-like mag- netic field strengths, the spacing between consecutive Alfvmodes is of the same order as the gap of avoided crossings. As a result, it is not possible to identify modes of predominantly crustal character and all oscillations are predominantly Alfven-like. Interestingly, we find excellent agreement between our computed frequencies and ob- served frequencies in two SGRs, for a maximum magnetic field strength in the range of (0.8-1.2)×10 16 G.

Towards a stable numerical evolution of strongly gravitating systems in general relativity: The conformal treatments

We study the stability of three-dimensional numerical evolutions of the Einstein equations, comparing the standard ADM formulation to variations on a family of formulations that separate out the conformal and traceless parts of the system. We develop an implementation of the conformal-traceless ~CT! approach that has improved stability properties in evolving weak and strong gravitational fields, and for both vacuum and spacetimes with active coupling to matter sources. Cases studied include weak and strong gravitational wave packets, black holes, boson stars and neutron stars. We show under what conditions the CT approach gives better results in 3D numerical evolutions compared to the ADM formulation. In particular, we show that our implementation of the CT approach gives more long term stable evolutions than ADM in all the cases studied, but is less accurate in the short term for the range of resolutions used in our 3D simulations.

NONLINEAR RESONANCE IN THE ACCRETION DISK OF A MILLISECOND PULSAR

Two simultaneous frequencies of quasi-periodic millisecond modulation of the X-ray flux (twin kilohertz quasi-periodic oscillations) have recently been detected in an accreting 2.5 ms X-ray pulsar. Their difference, equal to about of the neutron star spin rate, clearly indicates that resonant oscillations of the accretion disk have been observed. Similar nonlinear resonances may be spontaneously excited in the accretion disk in the absence of a pulsar, e.g., in black holes. We identify modes of disk oscillations whose frequencies are in agreement with the two observed ones when the rotating neutron star is modeled with realistic equations of state.

Three-dimensional numerical general relativistic hydrodynamics. II. Long-term dynamics of single relativistic stars

This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the application of this code to problems in general relativistic astrophysics. In particular, we report on the accuracy of our code in the long-term dynamical evolution of relativistic stars and on some new physics results obtained in the process of code testing. The following aspects of our code have been validated: the generation of initial data representing perturbed general relativistic polytropic models ~both rotating and nonrotating!, the long-term evolution of relativistic stellar models, and the coupling of our evolution code to analysis modules providing, for instance, the detection of apparent horizons or the extraction of gravitational waveforms. The tests involve single nonrotating stars in stable equilibrium, nonrotating stars undergoing radial and quadrupolar oscillations, nonrotating stars on the unstable branch of the equilibrium configurations migrating to the stable branch, nonrotating stars undergoing gravitational collapse to a black hole, and rapidly rotating stars in stable equilibrium and undergoing quasiradial oscillations. We have carried out evolutions in full general relativity and compared the results to those obtained either with perturbation techniques, or with lower dimensional numerical codes, or in the Cowling approximation ~in which all the perturbations of the spacetime are neglected!. In all cases an excellent agreement has been found. The numerical evolutions have been carried out using different types of polytropic equations of state using either the rest-mass density only, or the rest-mass density and the internal energy as independent variables. New variants of the spacetime evolution and new high resolution shock capturing treatments based on Riemann solvers and slope limiters have been implemented and the results compared with those obtained from previous methods. In particular, we have found the ‘‘monotonized central differencing’’ limiter to be particularly effective in evolving the relativistic stellar models considered. Finally, we have obtained the first eigenfrequencies of rotating stars in full general relativity and rapid rotation. A long standing problem, such frequencies have not been obtained by other methods. Overall, and to the best of our knowledge, the results presented in this paper represent the most accurate long-term three-dimensional evolutions of relativistic stars available to date.

Magnetoelastic oscillations of neutron stars with dipolar magnetic fields

By means of two dimensional, general-relativistic, magneto-hydrodynamical simulations we investigate the oscillations of magnetized neutron star models (magnetars) including the de- scription of an extended solid crust. The aim of this study is to understand the origin of the quasi-periodic oscillations (QPOs) observed in the giant flares of soft gamma-ray repeaters (SGRs). We confirm our previous findings which showed the existence of three different regimes in the evolution depending on the dipolar magnetic field strength: (a) a weak mag- netic field regime B 10 15 G, where magneto-elastic oscillations reach the surface and approach the behavior of purely AlfvQPOs. When the Alfv´ en QPOs are confined to the core of the neutron star, we find qualitatively similar QPOs as in the absence of a crust. The lower QPOs associated with the closed field lines of the dipolar magnetic field configuration are reproduced as in our previous simulations without crust, while the upper QPOs connected to the open field lines are displaced from the polar axis. The position of these upper QPOs strongly depends on the magnetic field strength. Additionally, we observe a family of edge QPOs and one new upper QPO, which was not previously found in the ab- sence of a crust. We extend our semi-analytic model to obtain estimates for the continuum of the Alfvoscillations. Our results do not leave much room for a crustal-mode interpreta- tion of observed QPOs in SGR giant flares, but can accommodate an interpretation of these observations as originating from Alfv´ en-like, global, turning-point QPOs (which can reach the surface of the star) in models with dipolar magnetic field strengths in the narrow range of 5 10 15 G. B. 1:4 10 16 G (for a sample of two stiff EoS and various masses). This range is somewhat larger than estimates for magnetic field strengths in known magnetars. The discrepancy may be resolved in models including a more complicated magnetic field structure or with models taking superfluidity of the neutrons and superconductivity of the protons in the core into account.

Magneto-elastic oscillations and the damping of crustal shear modes in magnetars

In a realistic model of magneto-elastic oscillations in magnetars, we find that crustal shear oscillations, often invoked as an explanation of quasi-periodic oscillations (QPOs) seen after giant flares in soft gamma-ray repeaters (SGRs), are damped by resonant absorption on timescales of at most 0.2s, for a lower limit on the dipole magnetic field strength of 5 10 13 G. At higher magnetic field strengths (typical in magnetars) the damping timescale is even shorter, as anticipated by earlier toy-models. We have investigated a range of equations of state and masses and if magnetars are dominated by a dipole magnetic field, our findings exclude torsional shear oscillations of the crust from explaining the observed low-frequency QPOs. In contrast, we find that the Alfv´ en QPO model is a viable explanation of observed QPOs, if the dipole magnetic field strength exceeds a minimum strength of about several times 10 14 G to

Alfven QPOs in Magnetars

We investigate torsional Alfven oscillations of relativistic stars with a global dipole magnetic field, via two-dimensional numerical simulations. We find that (i) there exist two families of quasi-periodic oscillations (QPOs) with harmonics at integer multiples of the fundamental frequency, (ii) the lower-frequency QPO is related to the region of closed field lines, near the equator, while the higher-frequency QPO is generated near the magnetic axis, (iii) the QPOs are long-lived, (iv) for the chosen form of dipolar magnetic field, the frequency ratio of the lower to upper fundamental QPOs is ∼0.6, independent of the equilibrium model or of the strength of the magnetic field, and (v) within a representative sample of equations of state and of various magnetar masses, the Alfven QPO frequencies are given by accurate empirical relations that depend only on the compactness of the star and on the magnetic field strength. The lower and upper QPOs can be interpreted as corresponding to the edges or turning points of an Alfven continuum, according to the model proposed by Levin (2007). Several of the low-frequency QPOs observed in the X-ray tail of SGR 1806-20 can readily be identified with the Alfven QPOs we compute. In particular, one could identify the 18- and 30-Hz observed frequencies with the fundamental lower and upper QPOs, correspondingly, while the observed frequencies of 92 and 150 Hz are then integer multiples of the fundamental upper QPO frequency (three and five times, correspondingly). With this identification, we obtain an upper limit on the strength of the magnetic field of SGR 1806-20 (if is dominated by a dipolar component) between ∼3 and 7 × 10 15 G. Furthermore, we show that an identification of the observed frequency of 26 Hz with the frequency of the fundamental torsional � = 2 oscillation of the magnetars crust is compatible with a magnetar mass of about from 1.4 to 1.6 Mand an equation of state (EOS) that is very stiff (if the magnetic field strength is near its upper limit) or moderately stiff (for lower values of the magnetic field).

Nonlinear r-Modes in Rapidly Rotating Relativistic Stars

The r-mode instability in rotating relativistic stars has been shown recently to have important astrophysical implications, provided that r-modes are not saturated at low amplitudes by nonlinear effects or by dissipative mechanisms. Here, we present the first study of nonlinear r-modes in isentropic, rapidly rotating relativistic stars, via 3D general-relativistic hydrodynamical evolutions. We find that (1) on dynamical time scales, there is no strong nonlinear coupling of r-modes to other modes at amplitudes of order one-the maximum r-mode amplitude is of order unity. (2) r-modes and inertial modes in isentropic stars are predominantly discrete modes. (3) The kinematical drift associated with r-modes appears to be present in our simulations, but confirmation requires more precise initial data.