ON THE OSCILLATION SPECTRA OF ULTRA COMPACT STARS

TL;DR

This paper calculates quasinormal modes of ultra compact stars, revealing how their oscillation spectra evolve with compactness and showing the close relationship between polar and axial modes as the stars become more compact.

Contribution

It provides a detailed comparison of polar and axial quasinormal modes in ultra compact stars, highlighting their convergence at high compactness and clarifying their spacetime origin.

Findings

Long-lived polar modes appear when M/R ≥ 1/3.

Polar and axial mode frequencies converge within 1% for M/R > 0.42.

Polar and axial modes are essentially spacetime modes with similar origins.

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.