Mode identification in rapidly rotating stars

TL;DR

This paper develops and tests a new method for identifying pulsation modes in rapidly rotating stars using an empirical asymptotic formula, aiming to improve mode classification in complex stellar spectra.

Contribution

The paper introduces a novel mode identification scheme based on fitting an empirical formula to pulsation spectra, validated with artificial and numerical data.

Findings

The scheme successfully identifies modes in artificial spectra.

It can distinguish regular from chaotic mode patterns.

The method is robust against the presence of chaotic modes.

Abstract

Context: Recent calculations of pulsation modes in rapidly rotating polytropic models and models based on the Self-Consistent Field method (MacGregor et al. 2007) have shown that the frequency spectrum of low degree pulsation modes can be described by an empirical formula similar to Tassoul's asymptotic formula (Tassoul 1980), provided that the underlying rotation profile is not too differential (Lignieres & Georgeot 2008, Reese et al. 2009). Aims: Given the simplicity of this asymptotic formula, we investigate whether it can provide a means by which to identify pulsation modes in rapidly rotating stars. Methods: We develop a new mode identification scheme which consists in scanning a multidimensional parameter space for the formula coefficients which yield the best-fitting asymptotic spectra. This mode identification scheme is then tested on artificial spectra based on the asymptotic formula, on random frequencies and on spectra based on full numerical eigenmode calculations for which the mode identification is known beforehand. We also investigate the effects of adding random frequencies to mimic the effects of chaotic modes which are also expected to show up in such stars (Lignieres & Georgeot 2008).