Amplitude Saturation in β Cephei Models - Preliminary Results

We present preliminary results concerning amplitude saturation in β Cephei models. Using nonlinear approach we have investigated amplitude limitation mechanism in β Cephei stars. In our approach radial modes have been treated as representative for all acoustic oscillations. We have studied pulsation properties of several models (7–20 M ⊙ , Z = 0.02, 0.015) using radiative Lagrangean hydrocodes (essentially those of Stellingwerf 1974, 1975). Nonlinear limit cycles (monoperiodic full-amplitude oscillations) have been calculated through Stel-lingwerf's (1974) relaxation technique, which also provides information about limit cycle stability. In our main survey (Z = 0.02) only the fundamental and the first overtone modes are linearly excited. Nonlinear growth rates have been used to determine the modal selection (see e.g. Stellingwerf 1975). We found that fundamental mode pulsation is dominant. First overtone pulsation is restricted to intermediate masses and to the vicinity of the blue edge. The first overtone and the fundamental mode pulsation domains are separated by either-or or narrow double-mode domains. Predicted, single mode saturation amplitudes have been compared to amplitudes observed for monoperiodic β Cephei variables (Fig. 1, left). Predicted amplitudes are significantly higher. The amplitudes may be lowered by decreasing the metal abundance of the models, Z. We have found that for Z = 0.015, decrease of model amplitudes is not sufficient. At the same time instability strip shrinks and leaves a lot of stars beyond the blue edge. By lowering Z we are not able to match simultaneously the observed amplitudes and the instability strip. Predicted amplitudes may be easily lowered to the observed level if one assumes collective saturation of the pulsation instability, by n similar acoustic modes. In this hypothetical multimode solution, amplitudes of individual modes are a factor of ∼ √ n lower than in single mode solution. Using linear code of Dziembowski (1977) we have determined the number of linearly unstable acoustic modes for models of different masses, located in the center of the