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Pulsational stability of stars in thermal imbalance. IV - Direct solution of differential equation
Aizenman, M. L.; Cox, J. P.
AA(Joint Institute for Laboratory Astrophysics, Boulder, Colo.), AB(Colorado, University, Boulder, Colo.)
Astrophysical Journal, vol. 194, Dec. 15, 1974, pt. 1, p. 663-685. (ApJ Homepage)
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NASA/STI Keywords:
Astronomical Models, Oscillations, Partial Differential Equations, Stellar Structure, Thermal Instability, Variable Stars, Linear Equations, Radial Distribution, Secular Variations, Stellar Motions
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Direct solutions, accurate to the order of (free-fall time)/(secular time), of the exact linearized partial differential equation describing the quasi-adiabatic, radial oscillations of a star in thermal imbalance, have been obtained for a number of simplified stellar models undergoing both homologous and nonhomologous secular motion. Comparison of these solutions with the results obtained by use of the integral expression approach of Cox, Hansen, and Davey and of Cox, Davey, and Aizenman for the same models, yields exact agreement as regards pulsational stability. This agreement provides, we feel, a complete and rigorous justification for the use of the much simpler integral expression approach to compute the pulsational stability of stars in thermal imbalance, at least for quasi-adiabatic oscillations.

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