Non-adiabatic modelling of gravito-inertial and Rossby tidally excited oscillations

The last few years have seen the first detection of tidally excited stellar oscillations (TEO) in multi- ple star systems opening new opportunities to study the physics of stars, understand their struc- tural properties and their evolution. The BRITE constellation extensively contributed to the study of TEOs through the discovery, the observations and the characterisation of many Heartbeat stars (Shultz et al, 2015, Pablo et al.,2017, 2019, Richardson et al, 2018). However, from a theoretical standpoint, numerous features in the observed oscillations spectrum cannot be explained, and cur- rent models cannot consistently treat impact of stellar rotation on TEOs. When modelling rotation stars, in the case of free oscillations, the inclusion of the impact of the Coriolis force is made using the so-called traditional approximation. In this approximation, the ef- fect of the radial component of the Coriolis force on the horizontal component is neglected along with the radial motion induced by Coriolis (Unno et al. 1989) which is valid in the domain of low fre- quency non-radial oscillations dominated by the horizontal motion. This approximation is usually used coupled to the Cowling approximation (Cowling, 1941) which neglect the potential perturba- tion as the Poisson equation becomes non-separable in this framework. In the case of TEOs, having a consistent treatment of the potential perturbation is essential as the orbital migration, eccentricity variation and all the orbital effects caused by the TEOs (called dy- namical tides in this context) are proportional to the imaginary part of the potential perturbation. In this talk, we present a new methodology to include the Coriolis force in the modelling of TEOs though the traditional approximation but consistently treating the potential perturbation by itera- tively solving the Poisson equation. We will show how the coupling between oscillations modes in fast rotators can affect the amplitudes of the dynamical tides and the orbital evolution of binary stars. We will also discuss the case of tidally excited Rossby modes, for which a few observed tar- gets are already in a good range of rotation and orbital period. Authors: L. Fellay & M.-A. Dupret