Asymptotic analysis of high-frequency acoustic modes in rapidly rotating stars

TL;DR

This paper develops an asymptotic analysis of high-frequency acoustic modes in rapidly rotating stars, revealing complex phase space structures and their impact on the acoustic spectrum, with implications for asteroseismology.

Contribution

It introduces a novel asymptotic framework combining Hamiltonian ray dynamics and quantum physics tools to analyze acoustic modes in rotating stars.

Findings

Phase space has mixed chaotic and stable regions.

High-frequency spectrum decomposes into independent sub-spectra.

Stable regions' modes are regular and quantized, chaotic regions' modes are irregular.

Abstract

The asteroseismology of rapidly rotating pulsating stars is hindered by our poor knowledge of the effect of the rotation on the oscillation properties. Here we present an asymptotic analysis of high-frequency acoustic modes in rapidly rotating stars. We study the Hamiltonian dynamics of acoustic rays in uniformly rotating polytropic stars and show that the phase space structure has a mixed character, regions of chaotic trajectories coexisting with stable structures like island chains or invariant tori. In order to interpret the ray dynamics in terms of acoustic mode properties, we then use tools and concepts developed in the context of quantum physics. Accordingly, the high-frequency acoustic spectrum is a superposition of frequency subsets associated with dynamically independent phase space regions. The sub-spectra associated with stable structures are regular and can be modelled through EBK quantization methods while those associated with chaotic regions are irregular but with generic statistical properties. The results of this asymptotic analysis are successfully confronted with the properties of numerically computed high-frequency acoustic modes. The implications for the asteroseismology of rapidly rotating stars are discussed.