Amplitude modulation due to internal resonances as a possible explanation of the Blazhko effect in RR Lyrae stars

Simultaneous effects of the resonant mode coupling and the nonlinear saturation of driving mechanism on the finite amplitude development of pulsation instability are studied. Simple amplitude equations including only lowest order nonlinear terms are used. It is shown that under certain conditions the only stable solution is a limit cycle in the form of a slow periodic modulation of the amplitudes. In the case of RR Lyrae stars the 2:1 resonance between fundamental mode and the 3rd overtone is the most likely cause of such a behaviour. It is argued that upon a reasonable choice of parameters entering the theory one can reproduce observed periods of the Blazhko effect. Possible connection between double mode pulsations and the Blazhko-type modulation is discussed. 24 refs., 6 figs., 2 tabs. (author)