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Astro 346, Spring Semester 2006
Homework, 4th set, solutions
Problem 10.6
In 100 years one has accreted
N
H
= (10

8
M
¯
yr

1
) (100yrs)
1
m
p
’
10
51
atoms
We know that by fusion we can get
0
.
03
m
p
c
2
in energy per actual Helium nucleus produced,
hence the total nuclear energy released is
E
=
0
.
03
m
p
c
2
4
N
H
’
10
46
erg
If all that was released in a month (
3
·
10
6
seconds), the average luminosity would be
L
’
3
·
10
39
erg s

1
The accretion luminosity was calculate in problem 10.5 (not 10.1!)
and is, neglecting the
initial potential energy,
L
acc
=
˙
M
2
G M
r
i
’
5
·
10
34
erg s

1
The total gravitational energy gain is much higher than the accretion luminosity.
So the
nuclear energy dominates, partly because we accumulate material for some time and partly
because the gravitational well of a white dwarf is not so deep.
Problem 11.1
Take a small path length element
dx
along the photon’s direction of motion. The number of
dust particles per unit area is then
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 Fall '08
 RABE
 Physics, Energy, Work

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