Long-Term Amplitude and Period Variations of δ Scuti Stars: A Sign of Chaos?

On short time-scales of under a year, the vast majority of δ Scuti stars studied in detail show completely regular multiperiodic pulsation. Nonradial pulsation is characterized by the excitation of a large number of modes with small amplitudes. Reports of short-term irregularity or nonperiodicity in the literature need to be examined carefully, since insufficient observational data can lead to an incorrect impression of irregularity. Some interesting cases of reported irregularities are examined.A few δ Scuti stars, such as 21 Mon, have shown stable variations with sudden mode switching to a new frequency spectrum. This situation might be an indication of deterministic chaos. However, the observational evidence for mode switching is still weak.One the other hand, the case for the existence of long-term amplitude and period changes is becoming quite convincing. Recently found examples of nonradial pulsators with long-term changes are 4 CVn, 44 Tau, τ Peg and HD 2724. (We note that other δ Scuti pulsators such as X Cae and θ2 Tau, have shown no evidence for amplitude variations over the years.) Neither the amplitude nor the period changes are periodic, although irregular cycles with time scales between a few and twenty years can be seen. While the amplitude changes can be very large, the period changes are quite small. This property is common in nonlinear systems which lead to chaotic behavior. There exists observational evidence for relatively sudden period jumps changing the period by about 10−5 and/or slow period changes near dP/dt ≤ 10−9. These period changes are an order of magnitude larger than those expected from stellar evolution.The nonperiodic long-term changes are interpreted in terms of resonances between different nonradial modes. It is shown that a large number of the nonradial acoustic modes can be in resonance with other modes once the mode interaction terms, different radial orders and rotational m-mode splitting are considered. These resonances are illustrated numerically by the use of pulsation model. Observational evidence is presented that these interaction modes exist in the low-frequency domain.