Homework 1

5 2 and 3 for all cases plot the ratio of the density

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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 second-order Lane-Emden differential equation into two first-order 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.

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