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ay45c5-page18

# ay45c5-page18 - With these boundary conditions you might...

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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 so-called 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 Lane-Emden function φ 1 4 6 scaled radius ξ 8 10 5.2.6 Physical properties of polytropes For n < 5, the Lane-Emden 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 = a1 = t 4G 1 : 130 ...
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