Forward modelling and the quest for mode identification in rapidly-rotating stars

TL;DR

This paper reviews the challenges and recent advances in mode identification in rapidly rotating stars, emphasizing the role of forward modelling, pattern analysis, and machine learning to interpret complex oscillation spectra.

Contribution

It provides a comprehensive overview of mode geometries, frequency patterns, and new techniques like machine learning to improve seismic modelling of rapid rotators.

Findings

Progress in deciphering gravity-mode spectra

Development of machine-learning classification methods

Enhanced forward seismic modelling for rapid rotators

Abstract

Asteroseismology has opened a window on the internal physics of thousands of stars, by relating oscillation spectra properties to the internal physics of stars. Mode identification, namely the process of associating a measured oscillation frequency to the corresponding mode geometry and properties, is the cornerstone of this analysis of seismic spectra. In rapidly rotating stars this identification is a challenging task that remains incomplete, as modes assume complex geometries and regular patterns in frequencies get scrambled under the influence of the Coriolis force and centrifugal flattening. In this article, I will first discuss the various classes of mode geometries that emerge in rapidly-rotating stars and the related frequency and period patterns, as predicted by ray dynamics, complete (non-)adiabatic calculations, or using the traditional approximation of rotation. These patterns scale with structural quantities and help us derive crucial constraints on the structure and evolution of these stars. I will summarize the amazing progress accomplished over the last few years for the deciphering of gravity-mode pulsator oscillation spectra, and recent developments based on machine-learning classification techniques to distinguish oscillation modes and pattern analysis strategies that let us access the underlying physics of pressure-mode pulsators. These approaches pave the way to ensemble asteroseismology of classical pulsators. Finally, I will highlight how these recent progress can be combined to improve forward seismic modelling. I will focus on the example of Rasalhague, a well-known rapid rotator, to illustrate the process and the needed advances to obtain \`a-la-carte modelling of such stars.