Mass loss, long-period variables, and the formation of circumnebular shells

We have found that the rate of mass loss M increases with an increase in the period of pulsation for Mira-type variables. This result suggests that the rate of mass loss is accelerated with time until a maximum value is reached before the ejection of the outer envelope. The matter from the continuous mass loss during the evolution of the star produces supersonic shock waves that sweep up the interstellar gas upon encountering the interstellar medium, so that a shell is formed. This phenomenon may account for the observations of extended regions of emission that surround planetary nebulae.