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 () () () 45 3 33 3 12 22 , 3 8 , 3 where 1 2 3 3arcsinh , e e H mc Pf x a f x h mA xb x Z h fx xx x x π ρ =≡ =+ + and . Fe xpm c = Use this form for the EOS, define new dimensionless variables, 3 00 2 ,, r a rr r M Gb ηθ ⎛⎞ == = ⎜⎟ ⎝⎠ 0 , b r and show thereby that the equations of hydrostatic equilibrium and mass conservation can be expressed as ( ) 2 2 23 1 8 4. x dx dx d x d θ η πη + =− = Show also that the boundary conditions are split: 0 0 at , at 0 . R x r θη 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 (and therefore density and pressure) inside a white dwarf for arbitrary electron velocity distribution, for a range of masses. Do this by employing a
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This note was uploaded on 12/02/2010 for the course PHYS 126 taught by Professor Cline during the Spring '10 term at McGill.

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

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