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Paper: Nonradial Mode Instability in Static and Radially Pulsating Models of RR Lyrae Stars
Volume: 135, A Half Century of Stellar Pulsation Interpretations: a Tribute to Arthur N. Cox
Page: 232
Authors: Van Hoolst, T.; Dziembowski, W. A.; Kawaler, S. D.
Abstract: Anomalous behaviours such as amplitude modulation or two mode excitation among classical pulsating stars remains unexplained. The possible role of nonradial mode excitation has already been suggested (Kovacs 1993, Van Hoolst & Waelkens 1995) but no calculations for realistic models have been done. As a first step toward clarifying the problem, we investigate linear nonadiabatic properties of nonradial modes in centrally condensed stars. We begin with an outline of the method of calculation of the nonadiabatic oscillations in full and realistic models of such stars. The method is then applied to a static model which corresponds to a RR Lyrae star in the mid of the instability strip. We find a large number of unstable low degree modes in the vicinity of unstable radial modes. The growth rates of such modes, however, are considerably lower than those of the radial. We also recover an old result (Dziembowski 1977, Osaki 1977) that at higher degrees there are modes trapped in the envelope with growth rates similar to that of radial modes. Subsequently, we consider monomode radial pulsation of this model. We assume that the excited mode saturates the linear instability of all modes and we study the destabilizing effect of the 1:1 resonance between the radial mode and nearby nonradial modes of low degrees. The instability depends on the radial mode amplitude, the frequency difference, and the damping rate of the nonradial mode. We find that at the pulsation amplitudes typical for RR Lyrae stars the resonant excitation of some nonradial oscillation is almost certain and that the excitation of the l=1 mode is most likely. References: Dziembowski, W.D., 1977, Acta Astron. 27, 95 Kovacs, G., 1993, in: Annals of the New York Academy of Sciences, eds.: J.R. Buchler and H.E. Kanrup, p.70 Osaki, Y., 1977, Publ. Astron. Soc. Japan 29, 235 Van Hoolst, T, Waelkens, C, 1995, Astron. Astrophys. 295, 361
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