User:Tohline/SSC/Structure/BiPolytropes/Analytic1 5

BiPolytrope with <math>n_c = 1</math> and <math>n_e=5</math>

Here we construct a bipolytrope in which the core has an <math>~n_c=1</math> polytropic index and the envelope has an <math>~n_e=5</math> polytropic index. As in the case of our separately discussed, <math>~(n_c, n_e) = (5, 1)</math> bipolytropes, this system is particularly interesting because the entire structure can be described by closed-form, analytic expressions. [On 12 April 2015, J. E. Tohline wrote: I became aware of the published discussions of this system by Murphy and others (see itemization of key references, below) in March of 2015 after reading through Horedt's (2004) §2.8.1 discussion of composite polytropes.

Steps 2 & 3

Based on the discussion presented elsewhere of the structure of an isolated <math>n=5</math> polytrope, the core of this bipolytrope will have the following properties:

Related Discussions

• Polytropes emdeded in an external medium
• Constructing BiPolytropes

© 2014 - 2021 by Joel E. Tohline |   H_Book Home   |   YouTube   | Appendices: | Equations | Variables | References | Ramblings | Images | myphys.lsu | ADS | Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation