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 inclass 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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 Spring '10
 Cline
 White dwarf, white dwarfs, University of Rochester

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