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Astronomy 120
HOMEWORK - Chapter 21
Stellar Explosions
Use a calculator whenever necessary.
For full credit, always show your work and explain how you got your answer in full, complete
sentences on a separate sheet of paper.
Be careful about units!
Please CIRCLE or put a box around your final answer if it is numerical.
If you wish, you may discuss the questions with friends, but please turn in your own hand-written
solutions, with questions answered in your own way.
1. Chaisson Review and Discussion 21.1
Under what circumstances will a binary star produce a nova? (3 points)
A nova is a binary star system that suddenly brightens and then slowly fades back to normal.
It is caused by an evolving star in a binary that is expanding past its Roche lobe and losing
gas to a companion white dwarf. After a while, the material (primarily hydrogen) builds up
on the white dwarf and reaches a high enough temperature to fuse. In doing so, it causes a
brief explosion of light from the surface of the white dwarf.
2. Chaisson Review and Discussion 21.2
What is an accretion disk, and how does one form? (3 points)
As an object such as a white dwarf, neutron star, or black hole gathers material from an
outside source (such as a binary companion), the material does not fall “straight down,” but
rather forms a flat disk as it spirals inward. This is called an accretion disk.
3. Chaisson Review and Discussion 21.3
What is a light curve? How can it be used to identify a nova or supernova? (4 points)
A light curve is a diagram that plots the changes in the brightness of an object, such as a
star, as a function of time. Time is plotted on the horizontal scale; brightness on the vertical
scale. The light curves of novae and supernovae appear rather different. For example,
supernovae are known to brighten about one million times more than novae. The patterns of
brightening are also different: novae brighten and fade less drastically and more gradually
than supernovae.
4. Chaisson Review and Discussion 21.4
Why does the core of a massive star collapse? (3 points)
If a star is massive enough, it will be able to fuse nuclei into iron, thus building up a core of
iron. But due to the high amount of repulsion iron atoms experience, it requires more energy
to fuse iron with something else than the reaction releases. This actually decreases the
amount of energy available...Nuclear energy generation stops, and as the core collapses
under gravity it cannot produce additional energy to stop the collapse.
5. Chaisson Review and Discussion 21.6
What occurs in a massive star to cause it to explode? (3 points)
Once the core of a massive star becomes neutronized, electron degeneracy pressure cannot
fight gravity any more, and the core goes into free fall. The collapse is only stopped by the
onset of neutron degeneracy pressure, as the resistance of neutrons to being crowded
together opposes gravity. As the core stops collapsing, the rest of the layers of the star rush
inward and rebound from the core. Thus, the explosion begins with an implosion. The shock
waves from these outer layers colliding with the core and each other create the explosion.
6. Chaisson Review and Discussion 21.7
What are the observational differences between Type I and Type II supernovae? (3 points)
Both types of supernovae are explosions, but look different from each other. Type-I
supernovae are observed to have hydrogen-poor spectra and are slightly fainter than the
Type-II. They also fade much more quickly than Type-II supernovae. Type-II supernovae
have strong hydrogen lines in their spectra, get a little brighter at maximum than Type-I, and
their light lingers for much longer.
7. Chaisson Review and Discussion 21.8
What is the Chandrasekhar mass (or limit), and what does it have to do with supernovae? (3
points)
The Chandrasekhar mass is the limiting mass for a white dwarf, 1.4 solar masses. If the mass
exceeds the limit, electron degeneracy pressure can no longer hold up the white dwarf. The
dwarf will collapse, resulting in a supernova explosion as atoms fuse on a massive scale. A
white dwarf can exceed the limit in two ways. First, it could be in a binary system, accreting
matter from its companion. The buildup of matter can push the white dwarf’s mass past the
limit. Alternatively, the white dwarf could begin above the limit, as the core of a
supermassive star.
8. Chaisson Review and Discussion 21.9
How do the mechanisms responsible for Type I and Type II supernovae explain their
observed differences? (4 points)
Type-I supernovae occur when a white dwarf in a binary system (usually a nova)
accumulates enough mass from its companion to exceed 1.4 solar masses. Once the mass
exceeds the Chandrasekhar limit, the white dwarf will collapse. Gravity forces the carbon
atoms in the white dwarf so close together that they must all fuse, creating a huge detonation.
Since white dwarfs have little hydrogen, they spectrum of a Type-I supernova will have weak
hydrogen lines. A Type-II supernova results from the collapse of the iron core of a single
supermassive star. The star first collapses inward, and then “rebounds” outward. Since
most of the star is hydrogen and helium, the spectrum of a Type-II supernova will have
strong lines from these elements. Type-II supernovae fuse more mass than Type-I
supernovae, and thus get brighter and linger longer.
9. Chaisson Review and Discussion 21.11
What evidence is there that many supernovae have occurred in our Galaxy? (3 points)
When the supernova explosion occurs, it rapidly ejects a vast cloud of gas. This is called a
supernova remnant. Supernova remnants can last for thousands of years and provide
evidence of an earlier supernova. We see many of these structures around the Galaxy, such
as the Crab Nebula. We also see all around us the very complex elements that are typically
created in supernova explosions.
10. Chaisson Review and Discussion 21.13
What proof do astronomers have that heavy elements are formed in stars? (3 points)
There are two lines of proof that heavy elements are formed in stars. First, the abundance of
the elements in the Universe varies greatly with atomic number, in a manner that can be
predicted by models of supernova nucleosynthesis. Second, the decline of a supernova’s light
curve after the explosion is consistent with the “afterglow” that comes from the decay of
complex radioactive elements created in the explosion.
11. Chaisson Review and Discussion 21.16
How are nuclei heavier than iron formed? (3 points)
Nuclei heavier than iron are formed by neutron capture. The nucleus of an element captures
one or more neutrons, which have no charge and thus no electromagnetic repulsion. Once
attached, the neutron can decay into a proton, forming a new, heavier element. This process
can proceed slowly inside of massive stars (the “s-process”) or very rapidly (the “rprocess”) during a supernova explosion.
12. Chaisson Review and Discussion 21.18
Why was supernova 1987A so important? (4 points)
Supernova 1987A is the closest supernova to Earth in the telescope era. While it was not in
our Galaxy, it occurred in one of our satellite galaxies, the Large Magellanic Cloud. This
made Supernova 1987A very accessible and easy to see. The distance to the LMC is very
well determined, so astronomers could immediately determine its brightness and total energy
output. There is very little dust between us and the LMC to obscure our vision. Lastly, since
we could track down exactly where the explosion came from, we could locate the star that
exploded from archived photos. For the first time astronomers had observed a star and knew
its basic properties before it exploded. Supernova 1987A was and will continue to be a very
important supernova for a long time because astronomers have been able to follow it, from
its progenitor stage completely through its development as a Type-II supernova.
13. Chaisson Problem 21.7
A supernova’s energy is often compared to the total energy output of the sun over its lifetime.
Using the sun’s current energy output, calculate its total energy output, assuming that the sun
has a 1010 year main-sequence lifetime. How does this compare with the energy released by a
supernova? (4 points)
We can find the total energy output of the Sun over its lifetime by multiplying the Sun’s
luminosity (energy output per second) by the number of seconds in the Sun’s 10 billion year
lifetime:
 4 10    3 10  10
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7
10
 1.2 1044 J.
This is about 10 times as much energy as a supernova gives off in the form of visible light,
but about one-tenth of the energy it gives off in the form of neutrinos.
14. Chaisson Problem 21.9
The Crab Nebula is now about 1 pc in radius. If it was observed to explode in C.E. 1054,
roughly how fast is it expanding? (Assume a constant expansion rate. Is that a reasonable
assumption?) (5 points)
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Speed is distance divided by time. The distance is 1 7pc or 3.1 ×10 m, and the time is10958
years from 1054 to 2012. Since
one year is 3.2 ×10 s, the time is equal to 3.05 × 10 s. The
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speed is then about 1 ×10 m/s or 1,000 km/s. The assumption of a constant rate of
expansion is probably not a very good one, since the initial explosion likely resulted in a very
rapid expansion at first. It would then slow down as it collides with the interstellar medium,
with gravity playing almost no role.