Correlations in the chaotic spectrum of pressure modes in rapidly rotating stars

The oscillation spectrum of pressure waves in stars can be determined by monitoring their luminosity. For rapidly rotating stars, the corresponding ray dynamics is mixed, with chaotic and regular zones in phase space. Our numerical simulations show that the chaotic spectra of these systems exhibit strong peaks in the autocorrelation which are at odd with random matrix theory predictions. We explain these peaks through a semiclassical theory based on the peculiar distribution of the actions of classical periodic orbits. Indeed this distribution is strongly bunched around the average action between two consecutive rebounds and its multiples. In stars this phenomenon is a direct consequence of the strong decrease of the sound speed towards the star surface, but it would arise in any other physical system with a similar bunching of orbit actions. The peaks discussed could be observed by space missions and give insight into the star interiors