Evidence for Low‐dimensional Chaos in Semiregular Variable Stars

An analysis of the photometric observations of the light curves of the fivelarge amplitude, irregularly pulsating stars R UMi, RS Cyg, V CVn, UX Dra andSX Her is presented. First, multi-periodicity is eliminated for thesepulsations, i.e. they are not caused by the excitation of a small number ofpulsation modes with constant amplitudes. Next, on the basis of energetics wealso eliminate stochasticity as a cause, leaving low dimensional chaos as theonly alternative. We then use a global flow reconstruction technique in anattempt to extract quantitative information from the light curves, and touncover common physical features in this class of irregular variable stars thatstraddle the RV Tau to the Mira variables. Evidence is presented that thepulsational behavior of R UMi, RS Cyg, V CVn and UX Dra takes place in a4-dimensional dynamical phase space, suggesting that two vibrational modes areinvolved in the pulsation. A linear stability analysis of the fixed points ofthe maps further indicates the existence of a two-mode resonance, similar tothe one we had uncovered earlier in R Sct: The irregular pulsations are theresult of a continual energy exchange between two strongly nonadiabatic modes,a lower frequency pulsation mode and an overtone that are in a close 2:1resonance. The evidence is particularly convincing for R UMi, RS Cyg and V CVn,but much weaker for UX Dra. In contrast, the pulsations of SX Her appear to bemore complex and may require a 6D space.