Laboratoire de Physique Théorique
Toulouse - UMR 5152

In a recent letter published in Physical Review Letters, Bertrand Georgeot and Mickael Pasek from LPT and Francois Lignieres and Daniel Reese from the Institut de Recherche en Astrophysique et Planétologie have built an asymptotic formula describing a subset of acoustic modes of rapidly rotating stars.

The short-wavelength limit enables to obtain geometrical optic from electromagnetic waves or classical mechanics from quantum mechanics. In this limit, the system is described by trajectories of a Hamiltonian system and notions of chaos and regularity are well-defined. The field of quantum chaos has studied wave systems whose short-wavelength limit is chaotic. A number of results enabled to define precise properties shared by such systems, which have been checked on many examples.

A new domain of application of these concepts has been recently developed. Indeed, acoustic waves also admit a short-wavelength limit, where the system is described by acoustic rays. Such acoustic waves can be observed in stars, using methods of stellar seismology. With the launching of the space missions COROT (December 2006) and KEPLER (2009), stellar seismology, which already revolutionarized our knowledge of internal structure of the sun, is bound to do the same for other stars. In order to interpret the observed frequencies in term of constraints on stellar interiors, the physics of oscillation eigenmodes associated to these frequencies should be well understood. This is actually the case for acoustic modes of slowly rotating stars like the sun, which can be considered to be spherically symmetric. For such stars, acoustic rays cannot be chaotic. In contrast, current theories do not allow to understand the effects of centrifugal distorsions, thus making the interpretation of the frequency spectrum of rapidly rotating stars a major challenge in present-day stellar seismology.

A collaboration on this subject has developed in the past few years between researchers from the LPT and the Observatoire Midi-Pyrénées. They have developed a mathematical formalism and numerical tools which allow to take into account for the first time the centrifugal distorsions in the computation of acoustic modes. These studies allowed to show that the dynamics of acoustic rays offers an adequate theoretical framework to understand the structure of the frequency spectrum. This dynamics can become chaotic as soon as the rotation becomes important. This explains why the methods developed in astrophysics for the case of slowly rotating stars cannot apply to rapidly rotating ones. The interpretation of observational spectra for such stars should thus make use of the concepts of quantum chaos and semiclassical theory. In the paper recently published in Physical Review Letters, the acoustic ray dynamics is used to build an asymptotic theory for the subset of regular modes which are the easiest to observe and identify. Comparisons with 2D numerical simulations of oscillations in polytropic stars show that both the frequency and amplitude distributions of these modes can accurately be described by an asymptotic theory for almost all rotation rates. The spectra are mainly characterized by two quantum numbers ; their extraction from observed spectra should enable one to obtain information about stellar interiors.

A more detailed exposition (in French) can be seen at the CNRS website.