A NEW NUMERICAL APPROACH TO THE OSCILLATION MODES OF RELATIVISTIC STARS

TL;DR

This paper introduces a new complex-coordinate numerical method to analyze oscillation modes of relativistic stars, successfully computing highly damped and slowly damped modes, revealing non-monotonic damping behavior, and correcting previous spectral artefacts.

Contribution

The authors develop and validate a novel numerical approach based on complex coordinates, enabling accurate computation of stellar oscillation modes, including those previously inaccessible or misrepresented.

Findings

Agreement with recent eigenfrequency results

Identification of numerical artefacts in previous spectra

Discovery of non-monotonic damping behavior in high-frequency modes

Abstract

The oscillation modes of a simple polytropic stellar model are studied. Using a new numerical approach (based on integration for complex coordinates) to the problem for the stellar exterior we have computed the eigenfrequencies of the highly damped w-modes. The results obtained agree well with recent ones of Leins, Nollert and Soffel (1993) Specifically, we are able to explain why several modes in this regime of the complex frequency plane could not be identified within the WKB approach of Kokkotas and Schutz (1992). Furthermore, we have established that the ``kink'' that was a prominent feature of the spectra of Kokkotas and Schutz, but did not appear in the results of Leins {\em et al.}, was a numerical artefact. Using our new numerical code we are also able to compute, for the first time, several of the slowly damped (p) modes for the considered stellar models. For very compact stars we find, somewhat surprisingly, that the damping of these modes does not decrease monotonically as one proceeds to higher oscillation frequencies. The existence of low-order modes that damp away much faster than anticipated may have implications for questions regarding stellar stability and the lifetime of gravitational-wave sources. The present results illustrate the accuracy and reliability of the complex-coordinate method and indicate that the method could prove to be of great use also in problems involving rotating stars. There is no apparent reason why the complex-coordinate approach should not extend to rotating stars, whereas it is accepted that all previous methods will fail to do so.