Astronomy and Astrophysics – Astrophysics
Scientific paper
Jul 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983a%26a...123..331b&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 123, no. 2, July 1983, p. 331-342. Research supported by the Centre National d
Astronomy and Astrophysics
Astrophysics
8
Entropy, Magnetohydrodynamic Stability, Nonlinear Equations, Stellar Oscillations, Stellar Structure, Adiabatic Conditions, Asymptotic Methods, Hydrostatics, Nonstabilized Oscillation, Resonance, Vibration Mode
Scientific paper
The two-time formalism is applied to the problem of nonlinearities in both radial and nonradial stellar oscillations. In the case of a vibrationally unstable nonradial mode it is shown that an initially spherically symmetric entropy profile loses this symmetry in second order in the amplitude, so that the hydrostatic equilibrium reference state, about which the oscillation is described, ceases to exist. Beyond the linear regime a single nonradial mode causes thus a dynamic instability of other modes. In contrast, in the case of the low order resonances (2ωi ≅ ωj or ωi ≅ ωj+ωk) between radial or nonradial modes attractors may already occur in lowest order, where there is no feedback on the evolution (s(m) = constant).
Buchler Jean-Robert
Regev Oded
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