Abstract
Context.Interpreting the oscillations of massive and intermediate mass stars remains a challenging task. In fast rotators, the oscillation spectrum ofp-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 chaoticp-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.
Highlights
Despite the many successful advancements made in stellar seismology, we are still unable to unlock most of the information contained in the acoustic oscillations of typical massive and intermediate mass stars
Using the semiclassical periodic orbit theory, which relates the mode properties to the acoustic ray dynamics, we show in Sect. 4.1 that the ∆c regularity is caused by the strong decrease of the sound speed at the surface, and present a theory which predicts the occurrence of the peak and its characteristics from the ray dynamics
We found that the chaotic spectrum can be described as a set of series of modes, where a series corresponds to modes separated by approximately ∆c and having similar amplitude distribution
Summary
Despite the many successful advancements made in stellar seismology, we are still unable to unlock most of the information contained in the acoustic oscillations of typical massive and intermediate mass stars. The first family was studied in detail through numerical computations (Lignières et al 2006; Reese et al 2008, 2009; Ouazzani et al 2015) and semi-analytical models (Pasek et al 2011, 2012) These modes show regular frequency spacings and should be the most visible in the observed spectra. We construct a large set of high-frequency chaotic modes, computed at various rotation rates and azimuthal numbers m, analyze the mode properties, and interpret them using semiclassical methods Among these properties, the presence of peaks in the autocorrelation of the chaotic mode spectrum had not been reported in the experimental or modeled wave systems considered in the fields of quantum chaos.
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