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