Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-20T08:01:04.181Z Has data issue: false hasContentIssue false

On the Observed Complexity of Chaotic Stellar Pulsation

Published online by Cambridge University Press:  12 April 2016

Z. Kolláth*
Affiliation:
Konkoly Observatory, P.O. Box 61, H-1525 Budapest, Hungary

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The existence of some variable stars producing very complicated light curves is well known. Theoretical calculations suggest that the irregular behaviour of the pulsation models in the RV Tauri and W Virginis regime is low dimensional is the result of period-doubling or tangent bifurcations (see e.g. Buchler and Kovács 1987, Kovács and Buchler 1988, Tanaka and Takeuti 1988).

The light variation of the RV Tauri star R Scuti covering 150 years was analyzed by Kolláth (1990). A striking similarity was found between the reconstructed attractor of the Rössler model and that of the light variation of R Scuti. This result confirms the theoretical prediction of the existence of chaos, but a discrepancy still exists between the theory and observation. We could not find evidence for low dimension (D = 2– 3). The analyses of other stars also show rather erratic behaviour (e.g. Cannizzo and Goodings 1988, Cannizzo et al. 1990). A possible answer for this discrepancy is the treatment of stochastic perturbations by convection (Perdang 1991).

Type
II. Observational Facts
Copyright
Copyright © Kluwer 1993

References

Buchler, J.R. and Kovács, G.: 1987, Astrophysical Journal, Letters to the Editor 320, L270.CrossRefGoogle Scholar
Canizzo, J.K. and Goodings, D.A.: 1988, Astrophysical Journal 334, L31.CrossRefGoogle Scholar
Canizzo, J.K. Goodings, D.A. and Mattei, J.A.: 1990, Astrophysical Journal 357.Google Scholar
Casdagli, M.: 1989, Physica D35, 335.Google Scholar
Gillet, D., Burki, G. and Duquennoy, A.: 1990, Astronomy and Astrophysics 237, 159.Google Scholar
Grassberger, P. and Procaccia, I.: 1983, Physical Review Letters 50, 346.CrossRefGoogle Scholar
Kolláth, Z.: 1990, Monthly Notices of the RAS 247, 377.Google Scholar
Kovács, G. and Buchler, J.R.: 1988, Astrophysical Journal 334, 971.CrossRefGoogle Scholar
Lorenz, E.N.: 1963, J. Atmos. Sci. 20, 130.2.0.CO;2>CrossRefGoogle Scholar
Mitschke, F., Möller, M. and Lange, W.: 1988, Physical Review A: General Physics 37, 4518.CrossRefGoogle Scholar
Perdang, J.: 1991, in ESO Workshop on Rapid Variability of OB-Stars: Nature and Diagnostic Value, ed. Baade, D. (ESO), p. 349.Google Scholar
Rössler, O.E.: 1976, Phys. Lett. 57A, 397.CrossRefGoogle Scholar
Takens, F.: 1980, Dynamic Systems and Turbulence (Warwick, Lecture Notes Math.) 898, 366.Google Scholar
Tanaka, Y. and Takeuti, M.: 1988, Astrophysics and Space Science 148, 229.Google Scholar
Wolf, A., Swift, J.B., Swinney, L. and Vastano, J.A.: 1985, Physica D 16, 285.Google Scholar