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There is growing observational evidence that the variability of red giants could be caused by self-excitation of global modes of oscillation. The most recent evidence of such oscillations was reported for α UMa by Buzasi et al. who analysed space photometric data from the WIRE satellite.

Little is understood concerning the oscillation properties in red giants. In this paper we address the question as to whether excited radial and non-radial modes can explain the observed variability in red giants. In particular, we present the results of numerical computations of oscillation properties of a model of α UMa and of several models of a 2-M_☉ star in the red giant phase.

The red giant stars that we have studied have two cavities that can support oscillations: the inner core that supports gravity (g) waves and the outer one that supports acoustic (p) waves. Most of the modes in the p-mode frequency range are g modes confined in the core; those modes with frequencies close to a corresponding characteristic frequency of a p mode in the outer cavity are of mixed character and have substantial amplitudes in the outer cavity. We have shown that such modes of low degree, ℓ=1 and 2, together with the radial (p) modes, can be unstable. The linear growth rates of these non-radial modes are similar to those of corresponding radial modes. In the model of α UMa and in the 2-M_☉ models in the lower regions of the giant branch, high amplitudes in the p-mode cavity arise only for modes with ℓ=2.

We have been unable to explain the observed oscillation properties of α UMa, either in terms of mode instability or in terms of stochastic excitation by turbulent convection. The modes with the lowest frequencies, which exhibit the largest amplitudes and may correspond to the first three radial modes, are computed to be unstable if all of the effects of convection are neglected in the stability analyses. However, if the Lagrangian perturbations of the turbulent fluxes (heat and momentum) are taken into account in the pulsation calculation, only modes with higher frequencies are found to be unstable. The observed frequency dependence of amplitudes reported by Buzasi et al. does not agree with what one expects from stochastic excitation. This mechanism predicts an amplitude of the fundamental mode about two orders of magnitude smaller than the amplitudes of modes with orders n>=5, which is in stark disagreement with the observations.