Oscillations of rapidly rotating relativistic stars

Non-axisymmetric oscillations of rapidly rotating relativistic stars are studied using the Cowling approximation. The oscillation spectra have been estimated by Fourier transforming the evolution equations describing the perturbations. This is the first study of its kind and provides information on the effect of fast rotation on the oscillation spectra while it offers the possibility in studying the complete problem by including spacetime perturbations. Our study includes both axisymmetric and non-axisymmetric perturbations and provides limits for the onset of the secular bar mode rotational instability. We also present approximate formulae for the dependence of the oscillation spectrum from rotation. The results suggest that it is possible to extract the relativistic star's parameters from the observed gravitational wave spectrum.Comment: this article will be published in Physical Review

A geometric framework for black hole perturbations

Black hole perturbation theory is typically studied on time surfaces that extend between the bifurcation sphere and spatial infinity. From a physical point of view, however, it may be favorable to employ time surfaces that extend between the future event horizon and future null infinity. This framework resolves problems regarding the representation of quasinormal mode eigenfunctions and the construction of short-ranged potentials for the perturbation equations in frequency domain.Comment: 4 pages, 1 figur

Instabilities of Relativistic Stars

Recent developments on the rotational instabilities of relativistic stars are reviewed. The article provides an account of the theory of stellar instabilities with emphasis on the rotational ones. Special attention is being paid to the study of these instabilities in the general relativistic regime. Issues such as the existence relativistic r-modes, the existence of a continuous spectrum and the CFS instability of the w-modes are discussed in the second half of the article.Comment: 41 pages, 12 figures, Proceedings of the 25th John Hopkins Workshop, Florenc

Analytic description of the r-mode instability in uniform density stars

We present an analytic description of the $r$-mode instability in newly-born neutron stars, using the approximation of uniform density. Our computation is consistently accurate to second order in the angular velocity of the star. We obtain formulae for the growth-time of the instability due to gravitational-wave emission, for both current and mass multipole radiation and for the damping timescale, due to viscosity. The $l=m=2$ current-multipole radiation dominates the timescale of the instability. We estimate the deviation of the second order accurate results from the lowest order approximation and show that the uncertainty in the equation of state has only a small effect on the onset of the $r$-mode instability. The viscosity coefficients and the cooling process in newly-born neutron stars are, at present, uncertain and our analytic formaulae enables a quick check of such effects on the development of the instability.Comment: 7 pages, 2 figure

On the r-mode spectrum of relativistic stars in the low-frequency approximation

The axial modes for non-barotropic relativistic rotating neutron stars with uniform angular velocity are studied, using the slow-rotation formalism together with the low-frequency approximation, first investigated by Kojima. The time independent form of the equations leads to a singular eigenvalue problem, which admits a continuous spectrum. We show that for $l=2$, it is nevertheless also possible to find discrete mode solutions (the $r$-modes). However, under certain conditions related to the equation of state and the compactness of the stellar model, the eigenfrequency lies inside the continuous band and the associated velocity perturbation is divergent; hence these solutions have to be discarded as being unphysical. We corroborate our results by explicitly integrating the time dependent equations. For stellar models admitting a physical $r$-mode solution, it can indeed be excited by arbitrary initial data. For models admitting only an unphysical mode solution, the evolutions do not show any tendency to oscillate with the respective frequency. For higher values of $l$, it seems that in certain cases there are no mode solutions at all.Comment: Major revision, corrected results concerning realistic equations of state, now 17 pages, 11 figures, MNRAS typesettin

On the r-mode spectrum of relativistic stars

We present a mathematically rigorous proof that the r-mode spectrum of relativistic stars to the rotational lowest order has a continuous part. A rigorous definition of this spectrum is given in terms of the spectrum of a continuous linear operator. This study verifies earlier results by Kojima (1998) about the nature of the r-mode spectrum.Comment: 6 pages, no figure

Perturbative Analysis of Universality and Individuality in Gravitational Waves from Neutron Stars

The universality observed in gravitational wave spectra of non-rotating neutron stars is analyzed here. We show that the universality in the axial oscillation mode can be reproduced with a simple stellar model, namely the centrifugal barrier approximation (CBA), which captures the essence of the Tolman VII model of compact stars. Through the establishment of scaled co-ordinate logarithmic perturbation theory (SCLPT), we are able to explain and quantitatively predict such universal behavior. In addition, quasi-normal modes of individual neutron stars characterized by different equations of state can be obtained from those of CBA with SCLPT.Comment: 29 pages, 10 figures, submitted to Astrophysical Journa

Workshop on gravitational waves

In this article we summarise the proceedings of the Workshop on Gravitational Waves held during ICGC-95. In the first part we present the discussions on 3PN calculations (L. Blanchet, P. Jaranowski), black hole perturbation theory (M. Sasaki, J. Pullin), numerical relativity (E. Seidel), data analysis (B.S. Sathyaprakash), detection of gravitational waves from pulsars (S. Dhurandhar), and the limit on rotation of relativistic stars (J. Friedman). In the second part we briefly discuss the contributed papers which were mainly on detectors and detection techniques of gravitational waves.Comment: 18 pages, kluwer.sty, no figure

Torsional Oscillations of Relativistic Stars with Dipole Magnetic Fields

We present the formalism and numerical results for torsional oscillations of relativistic stars endowed with a strong dipole magnetic field. We do a systematic search of parameter space by computing torsional mode frequencies for various values of the harmonic index $\ell$ and for various overtones, using an extended sample of models of compact stars, varying in mass, high-density equation of state and crust model. We show that torsional mode frequencies are sensitive to the crust model if the high-density equation of state is very stiff. In addition, torsional mode frequencies are drastically affected by a dipole magnetic field, if the latter has a strength exceeding roughly $10^{15}$G and we find that the magnetic field effects are sensitive to the adopted crust model. Using our extended numerical results we derive empirical relations for the effect of the magnetic field on torsional modes as well as for the crust thickness. We compare our numerical results to observed frequencies in SGRs and find that certain high-density EoS and mass values are favored over others in the non-magnetized limit. On the other hand, if the magnetic field is strong, then its effect has to be taken into account in attempts to formulate a theory of asteroseismology for magnetars.Comment: 17 pages, 5 figure