Unformatted text preview: With these boundary conditions, you might enjoy deriving the rst terms
in the power series expansion for (), namely
1
n
= 1 6 2 + 120 4 :
Numerical integration of the kind just described can give these socalled LaneEmden functions to any desired accuracy. Here is a graph for n = 0; 1:5; 3:0,
and 3:5. .8
.6
.4 0 0 2 n=
3.5
n=
3 1.5
n= .2 n=0 LaneEmden function φ 1 4
6
scaled radius ξ 8 10 5.2.6 Physical properties of polytropes
For n < 5, the LaneEmden function goes to zero at a nite value of (and
therefore r) which is called 1. This is the surface of the star! The stellar
radius in physical units is therefore
v
u
u (1 + n)c1 nn K
R = a1 = t 4G 1 :
130 ...
View
Full
Document
This note was uploaded on 12/29/2011 for the course AST 350 taught by Professor Dion during the Fall '09 term at SUNY Stony Brook.
 Fall '09
 dion

Click to edit the document details