ps_10 - Astronomy 241 Problem Set#10 Due 12 April 2005 in...

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Astronomy 241 Problem Set #10 Due 12 April 2005, in class Solo problem : 15.8 in Carroll and Ostlie. Team problems : R. The structure of a white dwarf: setup. In the course of Problem Set #10 and the in-class problems, you have shown that the equation of state for degenerate electrons of arbitrary velocity distribution can be expressed parametrically as ( ) ( ) ( ) ( ) ( ) ( ) 4 5 3 3 3 3 3 3 1 2 2 2 , 3 8 , 3 where 1 2 3 3arcsinh , e e H m c P f x af x h m c m A x bx Z h f x x x x x π π ρ = = = + + and . F e x p m c = Use this form for the EOS, define new dimensionless variables, 1 2 3 0 0 2 , , r a r r r M Gb η θ = = = 0 , br and show thereby that the equations of hydrostatic equilibrium and mass conservation can be expressed as ( ) 1 2 2 2 2 3 1 8 4 . x dx d x d x d θ η η θ πη η + = − = Show also that the boundary conditions are split: 0 0 at , 0 at 0 . R x r η θ η = = = = S. The structure of a white dwarf: “exact” numerical solution. Solve the system of equations derived in problem R, to obtain thereby the radius and the run of x
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