Non-linear, non-radial, isentropic oscillations of stars: Third-order coupled-mode equations

Details Non-linear, non-radial, isentropic oscillations of stars: Third-order coupled-mode equations Non-linear, non-radial, isentropic oscillations of stars: Third-order coupled-mode equations

Nov 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...279..417v&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 279, no. 2, p. 417-430

Astronomy and Astrophysics

Astrophysics

8

Coupled Modes, Equations Of Motion, Isentropic Processes, Nonlinear Systems, Stellar Models, Stellar Oscillations, Gravitational Fields, Mathematical Models, Radial Distribution

Scientific paper

The equation of motion governing isentropic, radial and nonradial, oscillations of a static and spherically symmetric star is derived up to the third order in the Lagrangian displacement and is presented in generalized coordinates. The derivation requires expansions for the Lagrangian perturbations of mass density, pressure, and gravitational potential up to the third order in the Lagrangian displacement. From the equation of motion, second-order, ordinary differential equations are established that govern the time-behaviour of the amplitudes of linear, isentropic, radial and nonradial, stellar oscillation modes. The amplitudes of the linear oscillation modes are coupled through the nonlinear terms. Besides the quadratic terms, the third-order terms are included since they are generally necessary for the study of the variations of the amplitudes of linear, isentropic modes of a star on long time scales. The equations, called coupled-mode equations, are derived even for nonradial oscillations since most of the variable stars oscillating in several modes exhibit nonradial oscillations. The nonlinear terms consist of integrals, defined over the star's equilibrium volume, of the eigenfunctions of the coupled modes. Under the assumption of a vanishing pressure at the star's equilibrium surface, these integrals are shown to be invariant with respect to the interchange of the linear, isentropic eigenfunctions involved.

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