Theoretical model of red variables in globular clusters

The common procedure of using the pulsation constant as a tool for the determination of the dominant mode of pulsation in Mira variables is shown to include a large uncertainty. An alternative way based on theoretical mapping of a luminosity-period relation, which is compared with the well-determined observations of these parameters, is presented. It is shown that the peculiar features of the observed distribution of Miras variables in the period-luminosity plane, for Tue 47, are distinct enough to enable a clear and a definite selection of the dominant mode in these variables - the second overtone for red semiregulars and the first overtone for Miras variables. These results are also confirmed by detailed nonlinear calculations, some of which are presented as well.