Resonances between two stellar oscillation modes with nearly equal frequencies

Details Resonances between two stellar oscillation modes with nearly equal frequencies Resonances between two stellar oscillation modes with nearly equal frequencies

Mar 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26a...295..371v&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 295, no. 2, p. 371-392

Astronomy and Astrophysics

Astrophysics

6

Amplitudes, Astronomical Models, Mathematical Models, Modes (Standing Waves), Phase Shift, Resonance, Resonant Frequencies, Stellar Oscillations, Isentropic Processes, Nonlinear Systems, Perturbation Theory, Polytropic Processes, Radial Velocity

Scientific paper

Resonances between two stellar oscillation modes with nearly equal frequencies are studied in a nonlinear, isentropic approach. As governing equations, nonlinear amplitude equations for the time-behavior of the amplitudes and phases of the resonant oscillation modes are derived from coupled-mode equations by means of a perturbation method. Expressions for the nonlinear coupling constants are derived in the approximation that the couplings are not influenced by modes other than the resonant ones. The amplitude equations are extended with two nonadiabatic terms involving the linear growth rates and the nonlinear self-saturations of the resonant modes. As stationary solutions of the amplitude equations, both monomode and double-mode solutions are possible. We studied analytically the existence and stability of the monomode stationary solutions. For a polytropic model, we examined stationary and time-dependent solutions of the amplitude equations for the amplitudes and phases of two chosen resonant modes. We determined radial velocity curves for solutions of the amplitude equations.

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