ON THE OSCILLATION SPECTRA OF ULTRA COMPACT STARS

Abstract

Quasinormal modes of ultra compact stars with uniform energy density have been calculated. For less compact stars, there is only one very slowly damped polar mode (corresponding to the Kelvin f-mode) for each spherical harmonic index $l$. Further long-lived modes become possible for a sufficiently compact star (roughly when $M/R\ge 1/3$). We compare the characteristic frequencies of these resonant polar modes to the axial modes first found by Chandrasekhar and Ferrari [{\em Proc. Roy. Soc. London A} {\bf 434} 449 (1991)]. We find that the two spectra approach each other as the star is made more compact. The oscillation frequencies of the corresponding polar and axial modes agree to within a percent for stars more compact than $M/R=0.42$. At the same time, the damping times are slightly different. The results illustrate that there is no real difference between the origin of these axial and polar modes: They are essentially spacetime modes.

arXiv comment13 pages, LATEX format, 25Kb, 2 postscript figures, Proc. Roy. Soc. London in press

References in corpus (2)

• Spacetime modes of relativistic stars
• A NEW NUMERICAL APPROACH TO THE OSCILLATION MODES OF RELATIVISTIC STARS

Cited by in corpus (14)

• Quasi-Normal Modes of Stars and Black Holes
• Extreme Gravity Tests with Gravitational Waves from Compact Binary Coalescences: (II) Ringdown
• Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects
• Gravitational waves from pulsating stars: Evolving the perturbation equations for a relativistic star
• Parameter estimation of gravitational wave echoes from exotic compact objects
• Ultra Compact Stars: Reconstructing the Perturbation Potential
• Braneworld resonances
• Exotic matter influence on the polar quasi-normal modes of neutron stars with equations of state satisfying the $2M_{\odot }$ constraint
• A Semi-analytic Study of Axial Perturbations of Ultra Compact Stars
• Trapped gravitational wave modes in stars with R>3M
• Trapped and excited w modes of stars with a phase transition and R>=5M
• The ringdown of a black hole surrounded by a thin shell of matter
• Generalised Inverse-Cowling Approximation for Polar $w$-mode Oscillations of Neutron Stars
• Horizonless star based on regular black hole with finite radius and its observational signatures