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Unformatted text preview: numerical integrator, compute and compare the
density profiles for polytropes n = 1, 1.5, 2, and 3. For all cases, plot the
ratio of the density to the central density (ρ/ρc) as a function of r = ξrn. Also
compute the values of ξ1 and dθn/dξ at ξ1, where the density goes to zero
(i.e., the surface). It is helpful to split the secondorder LaneEmden
differential equation into two firstorder differential equations: f (ξ ) = dθ n
dξ df
2f
n
=−
− θn
dξ
ξ
Show both your plot(s) and the code (e.g., C, Mathematica, IDL, etc.) used
to calculate these profiles.
(g) [10 pts] For the polytropes computed above, create a table with values
for the following:
•
•
•
• ξ1
dθn/dξ evaluated at ξ1
ratio of the average density <ρ> = 3M/4πR3 to central density ρc
ratio of central pressure Pc to GM2/R4. Verify that the first three values agree with Table 7.1 in HKT (don’t cheat!)
(h) [10 pt] The interior pressure in main sequence stars arises primarily from
a combination of ideal gas and radiat...
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This document was uploaded on 02/28/2014 for the course PHYS 223 at UCSD.
 Winter '08
 Fuller,G
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