C © Owned by the authors, published by EDP Sciences, 2013 Red giants rotational splittings

Abstract. The space missions CoRoT and Kepler provide high quality data that allow to test the transport of angular momentum in stars by the seismic determination of the internal rotation profile. Our aim is to test the validity of the 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. We use a non-perturbative approach implemented in the ACOR code [1] that accounts for the effect of rotation on pulsations, and solves the pulsations eigenproblem directly for dipolar oscillation modes. We find that the limit of the perturbation to first order can be expressed in terms of the core rotation and the period separation between consecutive dipolar modes. Above this limit, each family of modes with different azimuthal symmetry m, has to be considered separately. For rapidly rotating red giants, new seismic diagnostics can be found for rotation by exploiting the differences between the period spacings associated with each m-family of modes. 1