We derive accurate analytic approximations to the solution of the isothermal Lane-Emden equation, a basic equation in Astrophysics that describes the Newtonian equilibrium structure of self-gravitating, isothermal fluid spheres. The solutions we obtain, using analytic arguments and rational approximations, have simple forms, and are accurate over a radial extent that is much larger than that covered by conventional series expansions around the origin. Our best approximation has a maximum error on density of 0.04 % at 10 core radii, and is still within 1 % from an accurate numerical solution at a radius three times larger. © 2014 Springer Science+Business Media Dordrecht.

Approximate analytic solutions to the isothermal Lane-Emden equation

De Felice, M.;Iacono, R.
2014

Abstract

We derive accurate analytic approximations to the solution of the isothermal Lane-Emden equation, a basic equation in Astrophysics that describes the Newtonian equilibrium structure of self-gravitating, isothermal fluid spheres. The solutions we obtain, using analytic arguments and rational approximations, have simple forms, and are accurate over a radial extent that is much larger than that covered by conventional series expansions around the origin. Our best approximation has a maximum error on density of 0.04 % at 10 core radii, and is still within 1 % from an accurate numerical solution at a radius three times larger. © 2014 Springer Science+Business Media Dordrecht.
Isothermal Lane-Emden equation;Bonnor-Ebert gas spheres;Padé approximants
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12079/2871
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