Hachisu Self-Consistent-Field Technique
In a 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 <math>~K_\mathrm{n}</math> 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 Horedt (1970), by Whitworth (1981), by Kimura (1981a), and by Stahler (1983). Then we will focus in more detail on polytropes of index <math>~n</math> = 1 and <math>~n</math> = 5 because their structures can be described by closed-form analytic expressions.
General Properties
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