Chaotic Pulsations in Variable Stars With Harmonic Mode Coupling

Abstract

Some ZZ Ceti and rapidly oscillating Ap stars show a kind of multiperiodic behaviour, with among others prominent peaks in their power spectra at harmonically spaced frequencies with ratios 1:2:4. The nonlinear interaction between three such modes is a combination of two coupled second{harmonic interactions. The amplitude equations are shown by a Painleve analysis to be nonintegrable in the hamiltonian sense, so that one expects for the longterm behaviour irregular or chaotic phenomena instead of simple periodic or multiperiodic pulsations, especially when other modes and dissipation are included. An example of stars to which this might apply is G 191-16 among the variable white dwarfs. 1 1 Introduction In some variable stars amplitudes of individual pulsation modes vary with time, indicative of some kind of nonlinear mode coupling. Power spectra of e.g. nonradial oscillations in certain ZZ Ceti and rapidly oscillating Ap stars contain, among others, prominent peaks at harmonically..

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