On the oscillation spectra of ultracompact stars: An extensive survey of gravitational-wave modes

TL;DR

This paper provides a comprehensive survey of gravitational-wave modes in ultracompact uniform density stars, revealing new mode families, their physical origins, and surprising features like avoided crossings, emphasizing the importance of axial modes.

Contribution

It is the first extensive analysis of gravitational-wave modes across a wide range of stellar compactness, highlighting the significance of axial modes and mode interactions in ultracompact stars.

Findings

Polar and axial modes exist for all studied models.

Two distinct families of modes are identified, related to the interior and surface.

Avoided crossings occur between polar modes and the Kelvin f-mode in very compact stars.

Abstract

An extensive survey of gravitational-wave modes for uniform density stars is presented. The study covers stars ranging in compactness from $R/M=100$ to the limit of stability in general relativity: $R/M = 9/4$. We establish that polar and axial gravitational-wave modes exist for all these stellar models. Moreover, there are two distinct families of both axial and polar modes. We discuss the physics of these modes and argue that one family is primarily associated with the interior of the star, while the second family is mainly associated with the stellar surface. We also show that the problem of axial perturbations has all the essential features of the polar problem as far as gravitational waves are concerned. This means that the axial problem is much more important than has previously been assumed. We also find some surprising features, such as avoided crossings between the polar gravitational-wave modes and the Kelvin f-mode as the star becomes very compact. This seems to suggest that the f-mode should be considered on equal footing with the polar w-modes for ultracompact stars. All modes may have the main character of trapped modes inside the curvature potential barrier for $R/M < 3$.