Theoretical period ratios for RR Lyrae variables and AQ Leonis

The ratio of the overtone to fundamental periods has been calculated for models of RR Lyrae variables by using the linear nonadiabatic theory. Both homogeneous envelope and helium-enriched surface-layer models have been considered in order to predict the observed period ratio for the only known Population II double-mode RR Lyrae variable AQ Leonis. It is shown that the period ratio for homogeneous models in the radial pulsation instability strip depends only on the fundamental mode period at 0.58 Msun and 0.65 Msun and does not depend on the luminosity or surface effective temperature. The AQ Leo period of 0d.55 and the period ratio of 0.746 can be explained with a homogeneous composition model with a mass of 0.65 Msun. No surface helium enrichment is necessary for this variable even though such enrichment seems to be necessary for the more luminous double- and triple-mode Cepheids. It appears that the double-mode behavior of AQ Leo can be explained by mode switching in its blueward or redward horizontal branch evolution. This mode switching is rapid compared with its lifetime as an RR Lyrae variable.