Asteroseismology of the Multiply Periodic δ Scuti StarθTucanae

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Abstract
We present an asteroseismological analysis of the δ Scuti component of the binary star system θ Tucanae, using the 10 pulsational frequencies obtained photometrically by Paparó et al. and the mode identifications of Sterken. We have tested theoretical models with masses between 1.8 and 2.8 M☉ that have solar metal abundances, and we find that based upon mode stability arguments, the photometrically derived mass estimate of 2.1 ± 0.1 M☉ is probably accurate. The models with the best frequency match to θ Tucanae have masses of 1.9-2.1 M☉, luminosities between 20 and 25 L☉, 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☉, which suggests that the secondary star must be of comparable luminosity. We cannot determine whether tidal distortion is causing nonspherical perturbations in the pulsating component of this system with our current models, but the frequency spacing of observed pulsation modes suggests that rotation has a strong effect on the observed spectrum. Our models are consistent with the observed pulsation spectrum if rotational splitting is taken into account. Recently, De Mey, Daems, & Sterken determined spectroscopically that the θ Tucanae system is a spectroscopic binary with an anomalous mass ratio of 0.0896. In their model of this system, the δ Scuti component of the system is probably the beneficiary of mass transfer from the secondary, and the system was likely once an Algol-type system. The secondary is probably a 0.2 M☉ post-red giant branch object at ~7000 K (log g ~ 3.0), which has lost most of its mass via mass transfer and winds. This scenario raises the possibility that the interior of the δ 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 predictions. 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 understand this system.