Polytropic gas spheres: an approximate analytic solution of the Lane-Emden equation

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Abstract
Polytropic models play a very important role in galactic dynamics and in the theory of stellar structure and evolution. However, the solution of the Lane—Emden equation cannot in general be given analytically, only numerically. In this paper we give a good approximate analytic solution of the Lane-Emden equation. This approximation is very good, and is simple for any finite polytropic index n and for the isothermal case at a level < 1 per cent. We also give analytic expressions of the mass, pressure, temperature and potential energy as a function of radius.
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