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Description
? Scuti stars are variable stars with a complex power spectra in which numerous radial and nonradial modes are excited. Nonlinear contributions to the oscillations have generally not been taken into account, and most studies have remained within the linear regime due to the complexity involved. However, some approximations to nonlinear codes have been developed, mainly focused on RR Lyrae stars and Cepheids. Complete nonlinear codes have been developed for white dwarfs (Brickhill 1991; Wu 2001), but their physics cannot be directly applied to these stars. In this work, we investigate the role of nonlinear contributions by analysing the nonlinear oscillation equations derived from the fundamental hydrodynamic equations expanded to second order in perturbations in terms of the displacement vector. This approach follows the framework presented in Unno et al. (1989) and Aerts et al. (2010), considering no rotation, no magnetic fields, no viscosity, adiabaticity, and no turbulent convection. The expansion introduces numerous cross terms that prevent us from getting a direct numerical solution. To address this problem, we quantify the relative importance of the nonlinear terms. This was done considering the simplest case of radial modes and a snapshot in time at which nonlinear terms have their maximum contribution. We compute the nonlinear terms using stellar models and the eigenfunctions of the linear adiabatic oscillation equations. The results show that some nonlinear terms can locally reach magnitudes comparable to the linear contributions of the continuity, momentum, and energy equations, not only in the outer convective zone but also in deeper regions of the star. These results suggest that nonlinear terms have a non-negligible role in the internal dynamics of ? Scuti oscillations and must be taken into account in the development of nonlinear pulsation codes.
