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Scientific paper
Aug 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990mnras.245..392v&link_type=abstract
Monthly Notices of the Royal Astronomical Society, Vol. Vol. 245, No. 3, p. 392 - 396
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1
Ap Stars: Pulsation Theory
Scientific paper
Some ZZ Ceti and rapidly oscillating Ap stars show some multi-periodic behaviour, including prominent peaks in their power spectra at harmonically spaced frequencies with ratios 1:2:3. The non-linear interaction between three such modes is a combination of the usual three-wave interaction coupled to second-harmonic generation. The amplitude equations for such a combined interaction are fundamentally different, and the Painlevé analysis carried out here shows them to be non-integrable in the Hamiltonian sense, so that for long-term behaviour one expects irregular or chaotic phenomena instead of simple periodic or multi-periodic pulsations, especially when other modes and dissipation are included. Some examples of stars to which this might apply are given. These include VY Hor = BPM 31594 and BG CVn = GD 154 among the ZZ Ceti stars, PG 1351+489 among the DB variable white dwarfs, and HD 60435 and HD 22374 among the rapidly oscillating Ap stars.
Hereman Willy
Serras H.
Verheest Frank
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