Contact binaries. II - Metastable systems and limit cycles

Details Contact binaries. II - Metastable systems and limit cycles Contact binaries. II - Metastable systems and limit cycles

Jun 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986a%26a...161..296k&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 161, no. 2, June 1986, p. 296-302. DFG-supported research.

Mathematics

9

Binary Stars, Stellar Oscillations, Thermal Stability, Branching (Mathematics), Eigenvalues, Metastable State, Stable Oscillations, Stellar Models

Scientific paper

A variety of linear and non-linear thermal phenomena of contact binary models is analyzed in the neighbourhood of the border between thermally stable and unstable systems. The transition between stability and instability proceeds via an intermediate region of metastability (instability only against perturbations of finite amplitude). When sufficiently perturbed, metastable and unstable systems evolve into periodic relaxation oscillations (stable limit cycle). The metastability arises from a subcritical bifurcation in the sequence of steady solutions (equilibrium solutions and limit cycles). It occurs where, in the linear stability analysis, the real part of a conjugate complex pair of eigenvalues vanishes. The imaginary part of these eigenvalues is shown to give the period of the relaxation oscillations.

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