Astronomy and Astrophysics – Astrophysics
Scientific paper
Mar 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975ap%26ss..33..189d&link_type=abstract
Astrophysics and Space Science, vol. 33, Mar. 1975, p. 189-213.
Astronomy and Astrophysics
Astrophysics
11
Astronomical Models, Dynamic Stability, Stellar Structure, Thermal Instability, Adiabatic Conditions, Asymptotic Series, Kelvin-Helmholtz Instability, Nonisentropicity, Partial Differential Equations, Polytropic Processes, Radial Distribution
Scientific paper
The solution of the partial differential equation describing the `non-isentropic' oscillations of a star in thermal imbalance has been obtained in terms of asymptotic expansions up to the first order in the parameter Hit5, where IT is the adiabatic pulsation period for the fundamental mode and t5, a secular time scale of the order of the Kelvin-Helmholtz time. Use has been made of the zeroth order `isentropic' solution derived in I. The solution obtained allows one to derive unambiguously a general integral expression for the coefficient of vibrational stability for arbitrary stellar models in thermal imbalance. The physical interpretation of this stability coefficient is discussed and its generality and its sim- plicity are stressed. Application to some simple analytic stellar models in homologous and nonhomologous contraction enables one to recover, in a more straightforward manner, results obtained by Cox et a!. (1973), Aizenman and Cox (1974) and Davey (1974). Finally, we emphasize that the inclusion of the effects of thermal imbalance in the stability cal- culations of realistic evolutionary sequences of stellar models, not considered up to now by the other authors, is quite easy and straightforward with the simple formula derived here
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