Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977ap%26ss..52..313p&link_type=abstract
Astrophysics and Space Science, vol. 52, no. 2, Dec. 1977, p. 313-350. Research supported by the Fonds National de la Recherche
Astronomy and Astrophysics
Astrophysics
2
Dynamic Stability, Stellar Structure, Structural Stability, Boundary Value Problems, Function Space, Matrix Methods, Nuclear Fusion
Scientific paper
A proof of the existence of continuous spectra of eigenvalues developed in the framework of the function space of q-regularizations is extended by relaxing the severe restrictions previously imposed on the mathematical structure of the stellar stability equations. It is stressed that these local modes depend on the variable system in terms of which the linearized stellar-structure equations are set up. A systematic procedure to select the most satisfactory system to analyze local stability is illustrated in great detail in the case of nonradial adiabatic stability. When applied to nonadiabatic perturbations, it reveals the existence of two types of local instability which seem to prevail in the majority of stars in a thermonuclear burning phase: a nonradial local secular instability and a radial local nuclear instability. Numerical test calculations show that the latter enables certain evolutionary features of stars to be understood; in particular, it provides an interpretation of Hayashi et al.'s (1962) rule.
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