Midterm 2 Please use the scratch paper provided. Calculators are OK, but
not necessary. Equations are listed on page 2.
1. (20 points) In one or two paragraphs, tell me about the ‘solar neutrino
problem’ and its resolution.
2. Theory of the main sequence (20 points total)
Draw a ρ − T diagram. Label all the regions. Show the evolution of a
0.2 M⊙ star and of a 1M⊙ star. The diagram may be schematic, but the
slopes of any straight lines should be given, and the general evolutionary
paths for the different masses of stars should end up in the right places.
3. Describe how the distribution of old and young stars are different in the
Andromeda Galaxy, and give a physical reason for why that may be the
case. [10 points]
4. This question has two parts:
a) The main sequence lifetime of the Sun is 10 billion years. Roughly how
long is the main sequence lifetime of a 30 M⊙ star? [10]
b) The mass loss due to solar winds in the sun is 1×10−14 M⊙ yr−1 . If
the mass-loss rate in a 30 M⊙ main sequence star star is a factor of 107
higher, how much mass will the 30 M⊙ star lose in its life time? [10]
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
(1)
PI = nI kB T
U = − 12 Ω
1
Y
1−X −Y
≈X+ +
,
µI
4
<A>
(2)
1
1
1
+ ,
≡
µ
µI
µe
(3)
ugas = 23 nkB T /ρ
Three characteristic timescales:
τdyn = √1
Gρ
2
τth = GM
RL
2
τnuc = ǫMc
∝
L
M
L
Main sequence lifetime timescale:
1
τMS ∝ M
L ∝ M2
Ω = −α GM
R
2
r̈ = −
∂P
Gm
− 4π
r2
∂m
˙ =q−
u̇ + P (1/ρ)
∂F
∂m
Ẋ = f (ρ, T, X)
2
(4)
(5)
(6)