Asteroseismology of the multiply periodic delta Scuti star theta Tucanae

We present an asteroseismological analysis of the delta Scuti component of the binary star system theta Tucanae, using the 10 pulsational frequencies obtained photometrically by Paparo et al. and the mode identifications of S terken. We have tested theoretical models with masses between 1.8 and 2.8 M -circle dot that have solar metal abundances, and we find that based upon m ode stability arguments, the photometrically derived mass estimate of 2.1 /- 0.1 M-circle dot, is probably accurate. The models with the best frequen cy match to a Tucanae have masses of 1.9-2.1 M-circle dot, luminosities bet ween 20 and 25 L-circle dot, effective temperatures between 7500 and 7685 K , log g values between 3.82 and 3.92, and rotational velocities between 70 and 90 km s(-1). The luminosities of our models are more than a factor of 2 less than the Hipparcos-derived luminosity of 54 L-circle dot, which sugge sts that the secondary star must be of comparable luminosity. We cannot det ermine whether tidal distortion is causing nonspherical perturbations in th e pulsating component of this system with our current models, but the frequ ency spacing of observed pulsation modes suggests that rotation has a stron g effect on the observed spectrum. Our models are consistent with the obser ved pulsation spectrum if rotational splitting is taken into account. Recen tly, De Mey, Daems, & Sterken determined spectroscopically that the a Tucan ae system is a spectroscopic binary with an anomalous mass ratio of 0.0896. In their model of this system, the delta Scuti component of the system is probably the beneficiary of mass transfer from the secondary, and the syste m was likely once an Algol-type system. The secondary is probably a 0.2 M-c ircle dot, post-red giant branch object at similar to 7000 K (log g similar to 3.0), which has lost most of its mass via mass transfer and winds. This scenario raises the possibility that the interior of the delta Scuti star may be radically different from what single-star evolution models predict, although our results do not show any obvious differences. However, the age and envelope abundances should be different from single-star model predicti ons. We believe that this object provides an excellent opportunity to study the interiors of post-mass transfer objects using asteroseismology, and we suggest future observational and theoretical work that will help us unders tand this system.