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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.

CoRoT and Kepler measurements reveal us that the amplitudes of solar-like oscillations detected in red giant stars scale from stars to stars in a characteristic way. This observed scaling relation is not yet fully understood but constitutes potentially a powerful diagnostic about mode physics. Quasi-adiabatic theoretical scaling relations in terms of mode amplitudes result in systematic and large differences with the measurements performed for red giant stars. The use of a non-adiabatic intensity-velocity relation derived from a non-adiabatic pulsation code significantly reduces the discrepancy with the CoRoT measurements. The origin of the remaining difference is still unknown. Departure from adiabatic eigenfunction is a very likely explanation that is investigated in the present work using a 3D hydrodynamical model of the surface layers of a representative red giant star.

Thanks to the CoRoT and Kepler spacecrafts, scaling relations (linking seismic indices and global stellar parameters) are becoming the cornerstone of ensemble asteroseismology. Among them, the relation between the cut-off frequency and the frequency of the maximum in the power spectrum of solar-like pulsators as well as the relation between mode lifetime and the effective temperature remain poorly understood. However, a solid theoretical background is essential to assess the accuracy of those relations and subsequently of the derived stellar parameters. We will thus present recent advances on the understanding of the underlying mechanisms governing those relations and show that the physics of mode lifetime (thus of mode damping) plays a major role.