Non-perturbative effect of rotation on dipolar mixed modes in red giant stars

¹ Institut d’Astrophysique et de Géophysique de l’Université de Liège, Allée du 6 Août 17, 4000 Liège, Belgium
² Observatoire de Paris, LESIA, CNRS UMR 8109, 92195 Meudon, France
e-mail: rhita-maria.ouazzani@obspm.fr
³ Georg-August-Universität Göttingen, Institut für Astrophysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany

Received: 12 October 2012
Accepted: 13 March 2013

Abstract

Context. The space missions CoRoT and Kepler provide high-quality data that allow us to test the transport of angular momentum in stars by the seismic determination of the internal rotation profile.

Aims. Our aim is to test the validity of seismic diagnostics for red giant rotation that are based on a perturbative method and to investigate the oscillation spectra when the validity does not hold.

Methods. We use a non-perturbative approach implemented in the ACOR code that accounts for the effect of rotation on pulsations and solves the pulsation eigenproblem directly for dipolar oscillation modes.

Results. We find that the limit of the perturbation to first order can be expressed in terms of the rotational splitting compared to the frequency separation between consecutive dipolar modes. Above this limit, non-perturbative computations are necessary, but only one term in the spectral expansion of modes is sufficient as long as the core rotation rate remains significantly smaller than the pulsation frequencies. Each family of modes with different azimuthal symmetry, m, has to be considered separately. In particular, in case of rapid core rotation, the density of the spectrum differs significantly from one m-family of modes to another, so that the differences between the period spacings associated with each m-family can constitute a promising guideline toward a proper seismic diagnostic for rotation.