Evolutionary model and oscillation frequencies for alpha Ursae Majoris: A comparison with observations

Inspired by the observations of low-amplitude oscillations of alpha Ursae M ajoris A by Buzasi et al. using the WIRE satellite, a,grid of stellar evolu tionary tracks has been constructed to derive physically consistent interio r 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, onl y models in the mass range of 4.0-4.5 M. fall within the observational erro r box for alpha UMa A. This mass range is compatible, within the uncertaint ies, with the mass derived from the astrometric mass function. Analysis of the pulsation spectra of the models indicates that the observed alpha UMa o scillations can be most simply interpreted as radial (i.e., l = 0) p-mode o scillations of low radial order n. The lowest frequencies observed by Buzas i et al. are compatible, within the observational errors, with model freque ncies 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 f requency range are g-modes with a mixed mode character, that is, with p-mod e-like characteristics near the surface and g-mode-like characteristics in the interior The calculated radial p-mode frequencies are nearly equally sp aced, separated by 2-3 mu HZ. The nonradial modes are very densely packed t hroughout the observed frequency range and, even if excited to significant amplitudes at the surface, are unlikely to be resolved by the present obser vations.