Regularities in the spectrum of chaotic

Context. Interpreting the oscillations of massive and intermediate mass stars remains a challenging task. In fast rotators, the oscillation spectrum of p-modes is a superposition of sub-spectra which corresponds to different types of modes, among which island modes and chaotic modes are expected to be the most visible. This paper is focused on chaotic modes, which have not been thoroughly studied before. Aims. We study the properties of high frequency chaotic p-modes in a polytropic model. Unexpected peaks appear in the frequency autocorrelations of the spectra. Our goal is to find a physical interpretation for these peaks and also to provide an overview of the mode properties. Methods. We used the 2D oscillation code “TOP” to produce the modes and acoustic ray simulations to explore the wave properties in the asymptotic regime. Using the tools developed in the field of quantum chaos (or wave chaos), we derived an expression for the frequency autocorrelation involving the travel time of acoustic rays. Results. Chaotic mode spectra were previously thought to be irregular, that is, described only through their statistical properties. Our analysis shows the existence, in chaotic mode spectra, of a pseudo large separation. This means that chaotic modes are organized in series, such that the modes in each series follow a nearly regular frequency spacing. The pseudo large separation of chaotic modes is very close to the large separation of island modes. Its value is related to the sound speed averaged over the meridional plane of the star. In addition to the pseudo large separation, other correlations appear in the numerically calculated spectra. We explain their origin by the trapping of acoustic rays near the stable islands