Nonlinear coupling between pulsation and convection in late type stars

A simple idealized nonlinear model applicable to long-period variable stars has been formulated which assumes that the convective envelope of M giants is composed of giant convection cells comparable in size to the stellar radius. The simplicity of this model essentially constitutes a physical analog to the strong dynamic coupling that occurs if the convective envelope of the star undergoes both modes of motion. As shown implicitly in the time scales associated with these motions, the coupling produces asymmetrical fluctuations of the entire star, the mean velocity of which is comparable to the escape velocity of the star at particular values of the ratio of the pulsation and convection time scales. It is suggested that this can account for the mass loss from late-type stars and the circumstellar dust shells that are associated extensively with long-period variables. For critical values of the pulsation and convection time scales, the solutions correspond to the rapid expansion of the entire convective envelope and are the basis of a mechanism that simulates the manner in which pulsating stars ballistically accelerate their convective shells to form planetary nebulae.