Download Due Date: Thursday, November 16, 2006

Homework, November 9, 2006
AST110-6
Due Date: Thursday, November 16, 2006
1. If nuclear fusion of hydrogen in the core of the Sun were to stop now, what would we
see on the surface of the Sun tomorrow? Why? Will we be able to tell that hydrogen
burning in the core has stopped? How? (20pt)
(Hint: What particles that are generated by the fusion of hydrogen can escape
from the interior of the Sun immediately?)
You won’t be able to see any changes on the surface of the Sun…probably you
won’t see anything from helioseismology data either. This is because photons
generated in the core of the Sun takes about one million years to get to the
surface. This means that the thermal energy generated in the last minute of the
fusion will last for about a million years, and the Sun will just very slowly
contract. So, we will not see changes on the surface until a million years later.
However, we should be able to tell that the hydrogen fusion in the core has
stopped by observing the solar neutrinos. The neutrinos do not interact with the
solar plasma, and can escape the Sun and reach Earth in about 8 minutes. So, we
would find that the neutrino flux is decreased.
2. Chapter 11, Review Question 7. What is the defining characteristic of a main-sequence
star? How is surface temperature related to luminosity for main-sequence stars? (20pt)
3. Is this statement sensible? Why, or why not? (20pt)
If the Sun had been born as a high-mass star some 4.6 billion years ago, rather than as
a low mass star, the planet Jupiter would probably have Earth-like conditions today,
while earth would be hot like Venus.
If the Sun was formed as a high-mass star 4.6 billion years ago, then the Sun would
have exploded as a supernova several billion years ago. Jupiter and Earth probably
would not survive the supernova explosion…
The most significant difference between a high-mass star and the Sun will be their
lifetime! Look at the HR diagram in Figure 11.1. The lifetime of Spica (10 Msun) is
only about 10 million years. The lifetime of Achernar (6 Msun) is only 100 million
years…so when we really should not expect the Sun to still exist today if it was born
as a high-mass star.
4. Chapter 11, Problem 26. Stellar Data. Consider the following data table for several bright stars.
M v is absolute magnitude, and m v is apparent magnitude. (Hint: Remember that the magnitude
scale runs backward, so that brighter stars have smaller (or more negative) magnitudes.) (40pt)
Star
Mv
mv
Spectral Type
Luminosity Class
Aldebaran
-0.2
+0.9
K5
III
Alpha Centauri A
+4.4
0.0
G2
V
Antares
-4.5
+0.9
M1
I
Canopus
-3.1
-0.7
F0
II
Fomalhaut
+2.0
+1.2
A3
V
Regulus
-0.6
+1.4
B7
V
Sirius
+1.4
-1.4
A1
V
Spica
-3.6
+0.9
B1
V
Answer each of the following questions, including a brief explanation with each answer.
a. Which star appears brightest in our sky? Most negative mv --- Sirius
b. Which star appears faintest in our sky? Most positive mv ---Regulus
c. Which star has the greatest luminosity? Most negative Mv --- Antares
d. Which star has the least luminosity? Most positive Mv --- Alpha Centauri A
e. Which star has the highest surface temperature? OBAFGKM --- Spica B1
f. Which star has the lowest surface temperature? Antares M1
g. Which star is most similar to the Sun? Sun is a G2 V star --- Alpha Centauri A
h. Which star is a red supergiant? Antares --- Red (M1), Bright: Luminosity Class I
i. Which star has the largest radius? Antares --- the only supergiant
j. Which stars have finished burning hydrogen in their cores? Albebaran, Antares, and
Canopus
k. Among the main-sequence stars listed, which one is the most massive? Spica --- Hottest
and therefore the most massive.
l. Among the main-sequence stars listed, which one has the longest lifetime? Alpha Centauri
--- G2, lowest temperature and therefore, lowest mass and longest lifetime.