# Frequency regularities of acoustic modes and multi-colour mode identification in rapidly rotating stars

## TL;DR

This study explores methods for identifying pulsation modes in rapidly rotating stars by analyzing frequency regularities and amplitude ratios, improving seismic diagnostics despite uncertainties in mode amplitudes.

## Contribution

It demonstrates that auto-correlation and Fourier analysis of theoretical spectra can reveal key stellar parameters, even with uncertain mode amplitudes, advancing mode identification techniques.

## Key findings

- Auto-correlation can extract large frequency separation or half its value.
- Fourier transforms are sensitive to the large frequency separation.
- Amplitude ratios help group modes and constrain stellar parameters.

## Abstract

Context: Mode identification has remained a major obstacle in the interpretation of pulsation spectra in rapidly rotating stars. Aims: We would like to test mode identification methods and seismic diagnostics in rapidly rotating stars, using oscillation spectra based on new theoretical predictions. Methods: We investigate the auto-correlation function and Fourier transform of theoretically calculated frequency spectra, in which modes are selected according to their visibilities. Given the difficulties in predicting intrinsic mode amplitudes, we experimented with various ad-hoc prescriptions for setting these, including using random values. Furthermore, we analyse the ratios between mode amplitudes observed in different photometric bands. Results: When non-random intrinsic mode amplitudes are used, our results show that it is possible to extract the large frequency separation or half its value, and sometimes twice the rotation rate, from the auto-correlation function. The Fourier transforms are mostly sensitive to the large frequency separation or half its value. When the intrinsic mode amplitudes include random factors, the results are far less favourable. We also find that amplitude ratios provide a good way of grouping together modes with similar characteristics. By analysing the frequencies of these groups, it is possible to constrain mode identification as well as determine the large frequency separation and the rotation rate.