Direct non-adiabatic modelling of gravito-inertial and Rossby tidally excited oscillations with the traditional approximation

Context. In recent years, the first detections of tidally excited stellar oscillations (TEOs) have been made in multiple star systems, offering new opportunities to study stellar physics and understand structural properties and stellar evolution. However, from a theoretical standpoint, numerous features in the observed oscillation spectrum cannot be explained, and current models cannot consistently treat the impact of stellar rotation on TEOs without using the Cowling approximation. Aims. We aim to include the effect of the rotation in the modelling of TEOs and to study its consequences on the oscillation spectrum. Methods. We developed a new methodology to include the Coriolis force in the modelling of TEOs through the traditional approximation but consistently treating the potential perturbation by iteratively solving the Poisson equation. Results. By consistently including the Poisson equation, a new kind of mode coupling arises that we call ' gravitational coupling'. Looking at the global oscillation spectrum, we find that the rotation greatly impacts the type of modes excited by the companion. In general, we find that the Rossby modes dominate the oscillation spectrum of TEOs. Conclusions. It is particularly important to account for gravitational coupling at high spin parameters for the ν = 2, m = 2, and m = 0 oscillation modes. By assuming the modes are uncoupled, a simple and consistent treatment of the Poisson equation is possible. Including the effect of rotation in binary oscillation codes is necessary in order to accurately account for the impact of dynamical tides on the orbital evolution of binaries and planetary systems.