Linear and nonlinear models of Mira variable stars

A survey of linear, nonadiabatic models in the Mira instability region of the H-R diagram has been carried out for masses ranging from 0.8 M(,(CIRCLE)) to 2.0 M(,(CIRCLE)), with effective temperatures from 2700 K to 3400 K and luminosities from 1500 L(,(CIRCLE)) to 7000 L(,(CIRCLE)). From this study period-mass-radius relations have been derived for fundamental mode and first overtone pulsation; these relations can then be compared to observations. All models include molecular opacities and an opacity averaging scheme within each zone of rising and falling convective elements. In some models turbulent pressure was also included, and this was found to increase fundamental mode pulsation periods by up to 30 per cent;The nonlinear behavior of several selected models has also been investigated. A time-dependent modulation of the convective velocities was included in all cases. For the 0.8 M(,(CIRCLE)) model without turbulent pressure, pulsation reached a limiting amplitude but was distinctly aperiodic. When turbulent pressure was included in the 0.8 M(,(CIRCLE)) models, pulsation amplitudes increased without limit. For the 1.4 M(,(CIRCLE)) models studied, turbulent pressure was included and steady fundamental mode pulsation was obtained, but with amplitudes much smaller than are observed for Miras. Thus, progress has been made in developing more realistic models, but none has yet been found which fully mimics the observed behavior of Miras