Evolutionary Model and Oscillation Frequencies for α Ursae Majoris: A Comparison with Observations

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Abstract
Inspired by the observations of low-amplitude oscillations of α Ursae Majoris A by Buzasi et al. using the WIRE satellite, a grid of stellar evolutionary tracks has been constructed to derive physically consistent interior models for the nearby red giant. The pulsation properties of these models were then calculated and compared with the observations. It is found that, by adopting the correct metallicity and for a normal helium abundance, only models in the mass range of 4.0-4.5 M⊙ fall within the observational error box for α UMa A. This mass range is compatible, within the uncertainties, with the mass derived from the astrometric mass function. Analysis of the pulsation spectra of the models indicates that the observed α UMa oscillations can be most simply interpreted as radial (i.e., l = 0) p-mode oscillations of low radial order n. The lowest frequencies observed by Buzasi et al. are compatible, within the observational errors, with model frequencies of radial orders n = 0, 1, and 2 for models in the mass range of 4.0-4.5 M⊙. The higher frequencies observed can also be tentatively interpreted as higher n-valued radial p-modes, if we allow that some n-values are not presently observed. The theoretical l = 1, 2, and 3 modes in the observed frequency range are g-modes with a mixed mode character, that is, with p-mode-like characteristics near the surface and g-mode-like characteristics in the interior. The calculated radial p-mode frequencies are nearly equally spaced, separated by 2-3 μHz. The nonradial modes are very densely packed throughout the observed frequency range and, even if excited to significant amplitudes at the surface, are unlikely to be resolved by the present observations.