Pulsation models of delta Scuti variables .1. The high-amplitude double-mode stars

The relations between high-amplitude delta Scuti stars and the much more abundant low-amplitude delta Set variables are not clear. Both groups have similar periods and seem to have almost the same basic physical properties, although their lightcurve characteristics are very different. In the last few years much improved observational data have been published, and improved theoretical physics - in particular the new OPAL/OP opacities - now allows much more accurate calculations of theoretical evolution models including the normal-mode pulsation frequencies. We here use new series of stellar envelope models to give calibrations of the first overtone-to-fundamental mode and the second-to-first overtone period ratios in terms of the primary model parameters: metal content and mass-luminosity relation. Effects of the secondary model parameters: hydrogen content, position within the instability strip and assumed efficiency of convection are also studied in detail, and shown to be small. These results combined with pulsation analysis of new stellar evolution models are applied to discuss the available information for double-mode high-amplitude delta Set stars. We conclude that observed period ratios and positions in the HR-diagram are in agreement with the assumption that these variables are normal stars following standard evolution. Observational data for SX Phoenicis and AI Velorum are compared with theoretical evolution sequences. It is shown that the photometry and the observed two periods of SX Phe constrain the metal content to Z = 0.001, the mass to 1.0 solar masses and the bolometric magnitude to about 2.70 mag. The inferred distance of SX Phe gives a parallax of 0.012 +/- 0.002 arcsec compared with that of the HIPPARCOS Input Catalogue of 0.023 +/- 0.008 arcsec. For AI Vel the available photometry and the two primary observed periods do not provide a unique solution. Models based on OPAL opacities allow Z = 0.01 - 0.02 with corresponding masses 1.6 - 2.0 solar masses. This can be understood by the compensating effects from Z and the mass-luminosity relation in the calibration of the period ratio. It is suggested that the surprisingly narrow interval in the first overtone-to-fundamental mode period ratio observed in the double-mode delta Set stars may be due to these compensating effects. Attempting to fit low-amplitude modes observed in AI Vel in addition to the primary oscillations, it is concluded that the present models cannot explain these oscillations in terms of radial modes. The little understood relations between high- and low-amplitude delta Set stars are briefly discussed, and the problem of mode identification is emphasized.