Achieving non-linear models for δ Scuti stars

Complete codes describing the oscillations inside a star have always been difficult to attain due to the complex physics related to oscillations, especially for δ Scuti stars, which are known for their rich power spectra. Non-linear models are scarce, far from being complete and have focused on Cepheids and RR Lyrae. In this presentation, we describe the current progress in the development of a complete non-linear code for solving the equations describing the oscillations. The non-linearized equations have been derived from the fundamental equations of hydrodynamics by expanding them up to second order in perturbations in terms of the displacement vector. The scheme presented in Unno et al. (1979) and Aerts et al. (2010) was followed assuming no rotation, no magnetic fields, no viscosity, no adiabaticity and no turbulent convection. Some challenging cross-terms appeared, which prevented us from solving the equations numerically in the classical way of separating the equations into two independent (radial and horizontal) parts. To address this, we adopted the following strategy: solve the classical set of linear adiabatic equations; evaluate the non-linear terms; analyze the results to distinguish those that were essential and which were not; and, finally, the equations were solved with the most significant terms. In summary, this is a remarkable approach to the long sought-after non-linear models that will allow to further investigate the complicated physics of pulsations.