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(→Comparing Stability Analyses of Zero-Zero Bipolytropes: Provide links to various chapters that feed into this overview discussion) |
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=Comparing Stability Analyses of Zero-Zero Bipolytropes= | =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>: | In separate chapters we have discussed the following interrelated aspects of Bipolytropes that have <math>~(n_c,n_e) = (0,0)</math>: | ||
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<li>A [[User:Tohline/SSC/Structure/BiPolytropes/Analytic0_0#Stability_Condition|free-energy analysis of the global stability]] of zero-zero bipolytropes</li> | <li>A [[User:Tohline/SSC/Structure/BiPolytropes/Analytic0_0#Stability_Condition|free-energy analysis of the global stability]] of zero-zero bipolytropes</li> | ||
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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== | |||
=Related Discussions= | =Related Discussions= | ||
Revision as of 20:01, 6 January 2017
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
Related Discussions
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