An Introduction to Modern Astrophysics · Problem 10.17

The Sun — Carroll & Ostlie

Physics — Astrophysics · lane-emden-n0-solution

Problem

Starting with the Lane--Emden equation and imposing the necessary boundary conditions, prove that the

n = 0

polytrope has a solution given by

D_0(\xi) = 1 - \frac{\xi^2}{6}, \quad \text{with } \xi_1 = \sqrt{6}.