Amplitude Saturation in Beta Cephei Models

Abstract

Although the driving mechanism acting in beta Cephei pulsators is well known (e.g. Dziembowski & Pamyatnykh 1993), problems concerning identification of amplitude limitation mechanism and non-uniform filling of the theoretical instability strip, remain to be solved. In the present analysis, these problems are addressed by non-linear modelling of radial pulsations of these stars. In this approach radial modes are treated as representative for all acoustic oscillations. Several models of different masses and metallicities were converged to limit cycles through Stellingwerf (1974) relaxation technique. Resulting peak-to-peak amplitudes are of order of DeltaV=0.3 mag. Such amplitudes are significantly larger than those observed in beta Cephei pulsators. Assuming that all acoustic modes are similar, we show that collective saturation of the driving mechanism by several acoustic modes can easily lower predicted saturation amplitudes to the observed level. Our calculations predict significant decrease of saturation amplitudes as we go to high mass/high luminosity models. However, this effect is not strong enough to explain scarcity of high mass beta Cephei variables. We also discuss robust double-mode behaviour, encountered in our radiative models. On a single evolutionary track we identify two double-mode domains with two different mechanisms resposible for double-mode behaviour. The non-resonant double-mode domain separates first overtone and fundamental mode pulsation domains. The resonant double-mode domain appears in the middle of the first overtone pulsation domain. Its origin can be traced to the 2omega_1=omega_0+omega_2 parametric resonance, which destabilizes the first overtone limit cycle.