Kostas D. Kokkotas

Quasi-Normal Modes of Stars and Black Holes

AbstractPerturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.

Testing general relativity with present and future astrophysical observations

One century after its formulation, Einsteins general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einsteins theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

The r-mode instability in rotating neutron stars

In this review we summarize the current understanding of the gravitational-wave driven instability associated with the so-called r-modes in rotating neutron stars. We discuss the nature of the r-modes, the detailed mechanics of the instability and its potential astrophysical significance. In particular we discuss results regarding the spin-evolution of nascent neutron stars, the detectability of r-mode gravitational waves and mechanisms limiting the spin-rate of accreting neutron stars in binary systems.

On the relevance of the r mode instability for accreting neutron stars and white dwarfs

We present a case study for the relevance of the r-mode instability for accreting compact stars. Our estimates are based on approximations that facilitate back of the envelope calculations. We discuss two different cases. (1) For recycled millisecond pulsars, we argue that the r-mode instability may be active at rotation periods longer than the Kepler period (which provides the dynamical limit on rotation) as long as the core temperature is larger than about 2 × 105 K. Our estimates suggest that the instability may have played a role in the evolution of the fastest spinning pulsars and that it may be presently active in the recently discovered 2.49 ms X-ray pulsar, SAX J1808.4-3658, as well as the rapidly spinning neutron stars observed in low-mass X-ray binaries (LMXBs). This provides a new explanation for the remarkably similar rotation periods inferred from kilohertz, quasi-periodic oscillations in the LMXBs. The possibility that the rotation of recycled pulsars may be gravitational-radiation-limited is interesting, because the gravitational waves from a neutron star rotating at the instability limit may well be detectable with the new generation of interferometric detectors. (2) We also consider white dwarfs and find that the r-mode instability may possibly be active in short-period white dwarfs. Our order-of-magnitude estimates (for a white dwarf of M=M☉ and R=0.01 R☉ composed of C12) show that the instability could be operating for rotational periods shorter than P≈27-33 s. This number is in interesting agreement with the observed periods (greater than 28 s) of the rapidly spinning DQ Herculis stars. However, we find that the instability grows too slowly to affect the rotation of these stars significantly.

Deformed oscillator algebras for two-dimensional quantum superintegrable systems

Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum superintegrable systema deformed oscillator algebra, characterized by a structure function specific for each system, is constructed, the generators of the algebra being functions of the quantum integrals of motion. The energy eigenvalues corresponding to a state with finite dimensional degeneracy can then be obtained in an economical way from solving a system of two equations satisfied by the structure function, the results being in agreement to the ones obtained from the solution of the relevant Schrodinger equation. The method shows how quantum algebraic techniques can simplify the study of quantum superintegrable systems, especially in two dimensions.

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.

Gravitational waves from neutron stars: promises and challenges

We discuss different ways that neutron stars can generate gravitational waves, describe recent improvements in modelling the relevant scenarios in the context of improving detector sensitivity, and show how observations are beginning to test our understanding of fundamental physics. The main purpose of the discussion is to establish promising science goals for third-generation ground-based detectors, like the Einstein Telescope, and identify the various challenges that need to be met if we want to use gravitational-wave data to probe neutron star physics.

Gravitational Waves and Pulsating Stars: What Can We Learn from Future Observations?

We present new results for pulsating stars in general relativity. First we show that the so-called gravitational-wave modes of a neutron star can be excited when a gravitational wave impinges on the star. Numerical simulations suggest that the modes may be astrophysically relevant, and we discuss whether they will be observable with future gravitational-wave detectors. We also discuss how such observations could lead to estimates of both the radius and the mass of a neutron star, and thus put constraints on the nuclear equation of state.

Strange stars as persistent sources of gravitational waves

We investigate the relevance of the gravitational-wave driven r-mode instability for strange stars. We find that the unstable r-modes affect strange stars in a way that is quite distinct from the neutron star case. For accreting strange stars, we show that the onset of r-mode instability does not lead to the thermo-gravitational runaway that is likely to occur in neutron stars. Instead, the strange star evolves towards a quasi-equilibrium state on a time-scale of about a year. This mechanism could thus explain the clustering of spin frequencies inferred from kHz quasi-periodic oscillation data in low-mass X-ray binaries. For young strange stars, we show that the r-mode driven spin-evolution is also distinct from the neutron star case. In a young strange star, the r-mode undergoes short cycles of instability during the first few months. This is followed by a quasi-adiabatic phase where the r-mode remains at a small, roughly constant, amplitude for thousands of years. Another distinguishing feature from the neutron star case is that the r-modes in a strange star never grow to amplitudes of the order of unity. Our results suggest that the r-modes in a strange star emit a persistent gravitational-wave signal that should be detectable with large-scale interferometers given an observation time of a few months. If detected, these signals would provide unique evidence for the existence of strange stars, which would put useful constraints on the parameters of quantum chromodynamics.

The inverse problem for pulsating neutron stars: a 'fingerprint analysis' for the supranuclear equation of state

We study the problem of detecting, and inferring astrophysical information from, gravitational waves from a pulsating neutron star. We show that the fluid f and p modes, as well as the gravitational-wave w modes, may be detectable from sources in our own Galaxy, and investigate how accurately the frequencies and damping rates of these modes can be inferred from a noisy gravitational-wave data stream. Based on the conclusions of this discussion we propose a strategy for revealing the supranuclear equation of state using the neutron star fingerprints: the observed frequencies of an f and a p mode. We also discuss how well the source can be located in the sky using observations with several detectors.