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Non-Linear Oscillations and Beats in the Beta Canis Majoris Stars

Published online by Cambridge University Press:  12 April 2016

A. S. Baranov
A. S. Baranov*
Affiliation:
Institute of Theoretical Astronomy of USSR Academy of Sciences, 10, Kutuzov Quay, St. Petersburg, 191187

Extract

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Notwithstanding a great number of hypotheses, suggested for explaining superpositions of the light- and of the velocity variations of the ß Canis Majoris stars, no one of these does it satisfactorily. Possibly it is due to an inadequate elaboration of the non-linearly oscillation theory. Analysis and critical evaluation of the existing hypotheses are given by Mel’nikov and Popov (1970). Our explanation consists in existence of close frequencies corresponding to various oscillation modes which are non-linearly interacting.

Equations of motion of an ideal incompressible fluid under condition of preserving the equilibrium figure symmetry with respect to the equatorial plane (lateral oscillations) have the form (Baranov 1988):

Type
I. Fundamental Theories
Information
International Astronomical Union Colloquium , Volume 134: Nonlinear Phenomena in Stellar Variability , 1993 , pp. 73 - 76
Copyright
Copyright © Kluwer 1993

References

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Chandrasekhar, S.: 1969, Ellipsoidal Figures of Equilibrium (New Haven).Google Scholar
Chandrasekhar, S and Lebovitz, N.R.: 1962, Astrophysical Journalize, 1105.Google Scholar
Mel’nikov, O.A. and Popov, V.S.: 1970, Pulsating Stars (Moscow), p282. (In Russian).Google Scholar
Vilenkin, H.Ja.: 1965, Special Functions and the Group Representation Theory (Moscow). (In Russian).Google Scholar