Difference between revisions of "User:Tohline/SSC/Structure/BiPolytropes/Analytic1 5"

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(→‎Key References: Insert reference and link to Buchdahl (1978))
(→‎Key References: Add link to our new discussion of Buchdahl's (1978) work)
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==Key References==
==Key References==
* [http://adsabs.harvard.edu/abs/1962ApJ...136..680S S. Srivastava (1968, ApJ, 136, 680)] ''A New Solution of the Lane-Emden Equation of Index n = 5''
* [http://adsabs.harvard.edu/abs/1962ApJ...136..680S S. Srivastava (1968, ApJ, 136, 680)] ''A New Solution of the Lane-Emden Equation of Index n = 5''
* [http://adsabs.harvard.edu/abs/1978AuJPh..31..115B H. A. Buchdahl (1978, Australian Journal of Physics, 31, 115)]:  ''Remark on the Polytrope of Index 5''
* [http://adsabs.harvard.edu/abs/1978AuJPh..31..115B H. A. Buchdahl (1978, Australian Journal of Physics, 31, 115)]:  ''Remark on the Polytrope of Index 5'' &#8212; the result of this work by Buchdahl has been [[User:Tohline/SSC/Structure/BiPolytropes/Analytic5_1#Buchdahl1978|highlighted inside our discussion of bipolytropes with <math>~(n_c, n_e) = (5, 1)</math>]].
* [http://adsabs.harvard.edu/abs/1980PASAu...4...37M J. O. Murphy (1980a, Proc. Astr. Soc. of Australia, 4, 37)]:  ''A Finite Radius Solution for the Polytrope Index 5''
* [http://adsabs.harvard.edu/abs/1980PASAu...4...37M J. O. Murphy (1980a, Proc. Astr. Soc. of Australia, 4, 37)]:  ''A Finite Radius Solution for the Polytrope Index 5''
* [http://adsabs.harvard.edu/abs/1980PASAu...4...41M J. O. Murphy (1980b, Proc. Astr. Soc. of Australia, 4, 41)]:  ''On the F-Type and M-Type Solutions of the Lane-Emden Equation''
* [http://adsabs.harvard.edu/abs/1980PASAu...4...41M J. O. Murphy (1980b, Proc. Astr. Soc. of Australia, 4, 41)]:  ''On the F-Type and M-Type Solutions of the Lane-Emden Equation''

Revision as of 16:28, 13 April 2015

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

Whitworth's (1981) Isothermal Free-Energy Surface
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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, "mirror image" bipolytropes having <math>~(n_c, n_e) = (5, 1)</math>, 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 especially the work of Murphy & Fiedler (1985) — (see itemization of additional key references, below) in March of 2015 after searching the internet for previous analyses of radial oscillations in polytropes and, then, reading through Horedt's (2004) §2.8.1 discussion of composite polytropes.]

Key References

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:

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Whitworth's (1981) Isothermal Free-Energy Surface

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