MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.901: Astrophysics I
Fall Term 2002
PROBLEM SET 7
Due:
Thursday, November 14, 2002
Reading:
Carroll & Ostlie, Chapters 15. You may also fnd it useFul to look at Chapters 2 and 3 oF
Black
Holes, White Dwarfs, and Neutron Stars
by Shapiro and Teukolsky, and Chapter 9 oF Hansen and Kawaler.
1.
Properties of a white dwarf.
Carroll & Ostlie, Problem 15.1
2.
Helium lines in white dwarfs.
Carroll & Ostlie, Problem 15.2
3.
Hydrogen content in white dwarfs.
Carroll & Ostlie, Problem 15.3
4.
White dwarf cooling.
Carroll & Ostlie, Problem 15.8
5.
Massradius relation for polytropic stars.
In this problem, we return to polytropic stars, whose
pressure and density are related as
P
=
Kρ
γ
, where
γ
=1+(1
/n
),
K
and
n
are constants, and
n
is the
polytropic index. Recall that these stars satisFy the LaneEmden equation. In lecture and in Problem
Set 5, we showed that the radius oF the star is
R
=
aξ
1
where
a
=
·
(
n
+1)
K
4
πG
¸
1
/
2
ρ
(1
−
n
)
/
2
n
c
,
and that the mass is
M
=4
πa
3
ρ
c
µ

ξ
2
dθ
dξ
¶
ξ
=
ξ
1
.
(a) Show that the massradius relation For a polytropic star is
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 Spring '10
 Cline
 Neutron, Carroll, Supernova, White dwarf, Neutron star

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