Astronomy and Astrophysics – Astrophysics
Scientific paper
Sep 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976ap%26ss..43..459s&link_type=abstract
Astrophysics and Space Science, vol. 43, Sept. 1976, p. 459-468.
Astronomy and Astrophysics
Astrophysics
6
Polytropic Processes, Stellar Models, Variable Stars, Weighting Functions, Cepheid Variables, Stellar Envelopes, Variational Principles
Scientific paper
Weight functions for determining the periods of linear adiabatic nonradial oscillations of polytropes are calculated for the f mode and low-order p and g modes of quadrupole oscillations. The variational principle associated with the linear adiabatic radial wave equation is employed in the calculations. One group of static models considered consists of polytropes with an index in the range from 1.0 to 4.0 and in which the adiabatic exponent is fixed at 5/3; these models include those that are convectively stable, unstable, and of neutral stability. Another group consists of polytropes with an index of 3.0, convective shells or cores, and an adiabatic exponent set at different values in each region in order to produce stability or instability. The results show that: (1) g and p modes are generated in the core and envelope, respectively, for models of intermediate central condensation; (2) the low-order modes behave like g modes in the core and p modes in the envelope for high central condensation; and (3) the insertion of a convective region drastically reduces the weight function of that region with regard to production of positive g modes.
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