Difference between revisions of "User:Tohline/AxisymmetricConfigurations/HSCF"

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=Hachisu Self-Consistent-Field Technique=
=Hachisu Self-Consistent-Field Technique=


[[Image:LSU_Structure_still.gif|90px|left]] In a [[User:Tohline/SSC/Structure/Polytropes|separate discussion]] we have shown how to determine the structure of isolated polytropic spheres. These are rather idealized stellar structures in which the pressure and density both drop to zero at the surface of the configuration. Here we consider how the equilibrium radius of a polytropic configuration of a given <math>~M</math> and {{User:Tohline/Math/MP_PolytropicConstant}} is modified when it is embedded in an external medium of pressure <math>~P_e</math>.  We will begin by reviewing the general properties of embedded (and truncated) polytropes for a wide range of polytropic indexes, principally summarizing the published descriptions provided by [http://adsabs.harvard.edu/abs/1970MNRAS.151...81H Horedt (1970)], by  [http://adsabs.harvard.edu/abs/1981MNRAS.195..967W Whitworth (1981)], by [http://adsabs.harvard.edu/abs/1981PASJ...33..273K Kimura (1981a)], and by [http://adsabs.harvard.edu/abs/1983ApJ...268..165S Stahler (1983)].  Then we will focus in more detail on polytropes of index {{User:Tohline/Math/MP_PolytropicIndex}} = 1 and {{User:Tohline/Math/MP_PolytropicIndex}} = 5 because their structures can be described by closed-form analytic expressions.
[[Image:LSU_Structure_still.gif|90px|left]] This chapter has been built upon [http://www.phys.lsu.edu/astro/H_Book.current/Applications/Structure/HSCF_Code/HSCF.outline.html an earlier (''circa 1999'') outline of the Hachisu self-consistent-field (HSCF) technique] that appeared in our [http://www.phys.lsu.edu/astro/H_Book.current/H_Book.html original version of this HyperText Book] (H_Book) on the '''Structure, Stability, &amp; Dynamics of Self-Gravitating Systems'''.




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== General Properties==
== General Properties==


=Related Discussions=
=Related Discussions=

Revision as of 19:50, 22 March 2018

Hachisu Self-Consistent-Field Technique

LSU Structure still.gif

This chapter has been built upon an earlier (circa 1999) outline of the Hachisu self-consistent-field (HSCF) technique that appeared in our original version of this HyperText Book (H_Book) on the Structure, Stability, & Dynamics of Self-Gravitating Systems.


Whitworth's (1981) Isothermal Free-Energy Surface
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General Properties

Related Discussions

Whitworth's (1981) Isothermal Free-Energy Surface

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