Midterm 1 Please use the scratch paper provided. Calculators are OK, but
not necessary. Equations are listed on page 2.
1. State whether the following nuclear reactions are possible. If they are not
valid, state which principle conservation law is violated [9]:
+11 H ⇀
↽21 D + e+ + ν̄
(1)
15
7 N
+11 H ⇀
↽16
8 O+γ
(2)
15
8 O
−
⇀
↽15
7 N+e +ν
(3)
1
1H
2. (a) There are two important relationships for stars: a mass-radius relationship and a mass-luminosity relationship. Assume that M ∝R and that
L ∝M 4 . Take as a given the numbers we derived in class for the characteristic timescales of the Sun: 1000 seconds for the dynamical timescale,
30 million years for the thermal timescale, and 1010 years for the nuclear
timescale. Given the characteristic timescales for a 100 solar mass star.
[10]
(b) Explain which timescale determines the evolution of the star in a few
sentences (i.e. give more detail than just that one is shorter or longer, but
do not write a long essay).[5]
3. Explain why the observed luminosity of a star is normally equal to the
rate of nuclear energy generation in the star, and under what condition it
might not be.[8]
4. What is the Eddington Luminosity of a star? Just explain in words, no
equations necessary. [8]
5. A quark star has a mass equal to 10% that of the sun, and a radius equal
to 1% that of the sun. What is the average density of the quark star, in
units of the average solar density, ρ⊙ . Note: Quark stars do not actually
exist, except in some theorists’ imagination. [8]
1
Some helpful formulae (and some which might be helpful in other situations,
but won’t be for the exam)
U = 32 kb T
P = PI + Pe + Prad = Pgas + Prad , andPgas = βP
(4)
PI = nI kB T
U = − 12 Ω
1
Y
1−X −Y
≈X+ +
,
µI
4
<A>
(5)
1
1
1
+ ,
≡
µ
µI
µe
(6)
ugas = 23 nkB T /ρ
Three characteristic timescales:
τdyn = √1
Gρ
2
τth = GM
RL
2
τnuc = ǫMc
∝
L
Ω = −α GM
R
M
L
2
r̈ = −
∂P
Gm
− 4π
r2
∂m
(7)
˙ = q − ∂F
u̇ + P (1/ρ)
∂m
(8)
Ẋ = f (ρ, T, X)
(9)
2