Nonlinear Beat Cepheid Models

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Abstract
The numerical hydrodynamic modelling of beat Cepheid behavior has been a longstanding quest in which purely radiative models have failed miserably. We find that beat pulsations occur naturally when turbulent convection is included in our hydrodynamics codes. The development of a relaxation code and of a Floquet stability analysis greatly facilitates the search for and analysis of beat Cepheid models. The conditions for the occurrence of beat behavior can be understood with amplitude equations. Here a discriminant D arises whose sign decides whether single mode or double mode pulsations occur in a model, and this D depends only on the values of the nonlinear coupling coefficients between the fundamental and the first overtone modes. For radiative models D is always found to be negative, but with sufficiently strong turbulent convection its sign reverses, a necessary condition for double mode pulsations

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