P-modes in rapidly rotating stars -- looking for regular patterns in synthetic asymptotic spectra

TL;DR

This study investigates the detectability of regular p-mode frequency patterns in synthetic spectra of rapidly rotating stars, revealing dependencies on mode ratios, inclination, and rotational splitting.

Contribution

It demonstrates the conditions under which regular p-mode patterns can be identified in synthetic spectra based on asymptotic theory for rapidly rotating stars.

Findings

Detection depends on the ratio of regular to irregular modes.

Low inclination angles favor pattern detection.

Rotational splitting at 2Ω is easily detectable without differential rotation.

Abstract

According to a recent ray-based asymptotic theory, the high-frequency p-mode spectrum of rapidly rotating stars is a superposition of frequency subsets associated with dynamically independent regions of the ray-dynamics phase space. At high rotation rates corresponding to typical $\delta$ Scuti stars, two frequency subsets are expected to be visible : a regular frequency subset described by a Tassoul like formula and an irregular frequency subset with specific statistical properties. In this paper, we investigate whether the regular patterns can be detected in the resulting spectrum. We compute the autocorrelation function of synthetic spectra where the frequencies follow the asymptotic theory, the relative amplitudes are simply given by the modes' disk-averaging factors, and the frequency resolution is that of a CoRoT long run. Our first results are that (i) the detection of regular patterns strongly depends on the ratio of regular over irregular modes, (ii) low inclination angle configurations are more favorable than near equator-on configurations, (iii) in the absence of differential rotation, the $2 \Omega$ rotational splitting between $m=1$ and $m=-1$ modes is an easy feature to detect.