Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983a%26a...125....6b&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 125, no. 1, Aug. 1983, p. 6-12.
Astronomy and Astrophysics
Astrophysics
2
Perturbation Theory, Stellar Evolution, Stellar Oscillations, Stellar Temperature, Relaxation, Stellar Models, Stellar Structure, Systems Stability
Scientific paper
It is demonstrated that a two-zone model for thermal relaxation oscillations (limit cycles) in, for example, thin He burning shells or in X-rays bursters, is vulnerable against an increase in the complication of the model structure, a property termed morphological instability in this paper. The inclusion of a third zone can completely destroy the limit cycle or deform it. As a by-product of the analysis it is found that a slight alteration of the structure of the model is inefficient in transforming the thermal pulses into 'chaotic' fluctuations. The result indicates that the stochastic time behavior, observed for the majority of X-ray bursters, if intrinsic, cannot be accounted for by a mere slight perturbational effect around the energy generating shell source. This general conclusion is reached through a simple analysis of the topology and geometry of the phase-space and -portrait of the non-linear differential equations describing the evolution of the temperatures of the zones considered.
Barranco Manuel
Buchler Jean-Robert
Perdang J.
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