Regular Oscillation Sub-spectrum of Rapidly Rotating Stars

TL;DR

This paper develops an asymptotic theory for pressure mode frequency spacings in rapidly rotating stars, providing semi-analytical formulas that align well with numerical models and reveal how these spacings evolve with stellar rotation.

Contribution

It introduces a novel asymptotic approach based on the ray limit to analytically describe regular frequency spacings in rapidly rotating stars.

Findings

Semi-analytical formulas match numerical data well.

Frequency spacings depend explicitly on star's internal properties.

Mode frequencies evolve predictably with rotation rate.

Abstract

We present an asymptotic theory that describes regular frequency spacings of pressure modes in rapidly rotating stars. We use an asymptotic method based on an approximate solution of the pressure wave equation constructed from a stable periodic solution of the ray limit. The approximate solution has a Gaussian envelope around the stable ray, and its quantization yields the frequency spectrum. We construct semi-analytical formulas for regular frequency spacings and mode spatial distributions of a subclass of pressure modes in rapidly rotating stars. The results of these formulas are in good agreement with numerical data for oscillations in polytropic stellar models. The regular frequency spacings depend explicitly on internal properties of the star, and their computation for different rotation rates gives new insights on the evolution of mode frequencies with rotation.