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Comparing Stability Analyses of Zero-Zero Bipolytropes
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In separate chapters we have discussed the following interrelated aspects of Bipolytropes that have <math>~(n_c,n_e) = (0,0)</math>:
- Using a detailed force-balance analysis to develop an analytic description of their equilibrium structure
- Using a free-energy analysis to analytically identify the properties of equilibrium structures; see also, an explicit, analytic evaluation of the statement of Virial Equilibrium
- Developing the Linear Adiabatic Wave Equation (LAWE) as it applies separately to the core and to the envelope of zero-zero bipolytropic configurations
- Identifying a method to analytically solve the matching LAWEs for a certain subset of configurations
- A summary of this solution technique, along with the first illustrative analytic specification of an eigenvector
- The derivation of analytically specifiable eigenvectors having a variety of mode quantum numbers
- A free-energy analysis of the global stability of zero-zero bipolytropes
Building on these separate discussions, here we examine what might be learned from a comparison of the two traditional approaches to stability analysis, namely: (1) solutions of the LAWE, and (2) a free-energy analysis.
Key Attributes of Equilibrium Configurations
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