An attempt to pin down the instability domain of long-period variables

The period-luminosity relation of Miras and semiregular variables in the Large Magellanic Cloud and in the Galaxy are used to locate their instability domain in the Hertzsprung-Russell diagram. We take advantage of the considerable width in luminosity of the relation at given period to assign masses to the observed long-period variables using stellar models on the the asymptotic giant branch and nonadiabatic pulsation computations. We study the sensitivity to chemical abundance of the position of the instability region on the Hertzsprung-Russell diagram. The mass function of the longperiod variables along the AGB is discussed for Galactic and LMC variables. Finally, we contribute to the dispute on the pulsation mode of Miras and lend support to the view that, for most of the Mira variables, the pulsation in the fundamental mode is more likely.