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.
All Science Journal Classification (ASJC) codes
- Astronomy and Astrophysics
- Space and Planetary Science
Iacono, R., & De Felice, M. (2014). Approximate analytic solutions to the isothermal Lane-Emden equation. Celestial Mechanics and Dynamical Astronomy, 118(3), 291 - 298. https://doi.org/10.1007/s10569-014-9539-6