1.) (Problem adapted from textbook:) Which one of the
following is not sensible:
a.) Some of the iron in our blood could have come from
a star that blew up more
than 5 billion years ago.
b.) Someday, humans will need to find another planet because
someday the Sun
will blow up in a supernova explosion.
c.) I'm sure glad that hydrogen, the most common element
in the universe, has
a higher mass per nuclear particle
than many other elements. If it had a lower
mass/(nuclear particle) then the Sun wouldn't burn.
d.) If you could look into the Sun's core today, you
would find that it has a greater
proportion of helium to
hydrogen than it did when the Sun was born.
Answer: "b" is the only nonsense choice.
The Sun will not explode in a supernova
explosion. The sun is
not massive enough for that to happen. Instead, the Sun will
blow off a planetary nebula and will spend the rest of eternity
as a white dwarf.
Nonetheless, there may be other reasons why
humans might want to find another
place to live. For example,
during the Sun's red giant stage, the Earth will be rather hot.
Regarding "a":
This statement makes sense. The iron in our bodies
comes from the
foods we eat, which get it from the Earth. The
iron in the Earth (and in the other
bodies of the solar system)
existed before the solar system was formed. The iron
was created in high-mass stars and dispersed into interstellar space
by supernova
explosions. The production and dispersal of
the iron that is in our bodies must have happened
before the solar system was formed, so more than 4 billion years ago.
Regarding "c":
This statement makes sense. Because hydrogen has higher
mass/(nuclear particle), the fusion of hydrogen yields energy
rather than costing energy.
So, stars are able to burn hydrogen
and create heavier elements. If hydrogen, the
most common element
in the universe, were not able to burn, the sun would have
far less capability to yield energy (thus shortening the time period
in which the Earth
would be kept warm by the sun -- the time
period would be too short for advanced life to evolve).
Regarding "d":
This statement makes sense. The sun is about halfway
through its life
and so has converted about half of the hydrogen
in the core into helium.
2.)
Describe how a low mass star behaves, starting from the time that it
burns off all the
available hydrogen in its core (~20 to 40 words).
Answer: I used many more than 20 to 40 words, but you don't have to.
When the hydrogen fusion rate drops, the core's temperature drops and
so the thermal pressure drops. As a result,
the core becomes less able to hold up the
rest of the star's weight. As the core gets
squeezed; it (and the gas around it) shrinks in size.
As this happens,
the gas in the core and shell around it heats up.
It gets hot enough to burn hydrogen at an even greater
rate than the old core had. So, the star brightens.
Some of the
excess energy is trapped in the star and so causes the star to fluff up.
The bright,
fluffed up star is now called a red giant.
During their giant phases, stars blow winds.
As the shell burns hydrogen into helium, the
helium falls down into
the core. The core, thus, gains mass and so exerts a stronger gravitational
pull. The extra gravitational pull compresses both the core and the
hydrogen-burning shell around it.
As the hydrogen-burning shell becomes denser, it becomes
hotter and burns
hydrogen at a faster rate, making the star even brighter and larger.
(Aside: as
time progresses, the star gets brighter and brighter.
This is a "positive feedback loop",
it is the opposite of a "negative feedback loop",
which is also called a "self correcting process".
An example of a negative feedback loop is the "solar thermostat".)
If the core's
temperature reaches 100 million K, then the helium in the core
will start to burn by nuclear fusion. (If the temperature isn't
large enough, then the core compresses until electron degeneracy
pressure prevents further compression).
Let's follow the case of helium burning. The initial burning
can happen in a flash, called the "helium flash".
After the flash, the core is able to fluff up, which levels off the
burning rate. With
less energy flowing from the core to the surface, the star's radius
decreases somewhat (but is still larger than when the star was on
the main sequence).
When the core runs out of helium to burn, it and the gas around it
contracts. This ignites the helium in the shell around the core.
Thus, there are two burning shells (the helium burning shell, surrounded
by the hydrogen burning shell). The star's luminosity and
size both increase. But, eventually the star runs out of fuel.
It also casts off its outer layers (making a planetary nebula).
The remaining material in the star can no longer fuse. So, it
it has no source of energy. It slowly cools down. If it
isn't already compressed enough to be supported by electron degeneracy
pressure, it will become so. It has evolved into a white dwarf.
3.)
Describe how a high mass star behaves between the time when it
burns off all the
available hydrogen in its core and the time when it
explodes (~20 to 40 words).
Answer: I used many more than 20 to 40 words, but you don't have to.
Like the low mass stars (discussed above), a high mass star
contracts, heating up the core and gas around the core,
then starts to burn hydrogen in the shell around the core.
The net burning rate is higher than in a main sequence star.
As a result, the added thermal and radiation pressure pushes
back the outer parts of the star (i.e. the radius increases).
We now have a huge star (some type of giant) which blows winds.
These winds take material off of the star at a significant rate.
When the core is hot enough, it starts to burn helium
(but, unlike in low mass stars, doesn't make a helium
flash). When it runs out of helium, the core (and shells
around it) shrink and heat up. This enables helium in the shell around
the core to burn.
Unlike in the low mass stars, the core can get hot
enough to burn carbon. At that time, the star would have
a carbon-burning core, surrounded by a helium-burning shell,
surrounded by a hydrogen-burning shell, surrounded by a lot
of non-burning hydrogen. The more massive the star, the
further the sequence goes.
In the most massive stars, the
sequence ends with iron being made in the core. Iron cannot
burn. The core (and material around it) contracts.
As the core cools, its thermal pressure decreases, making it
unable to hold up the star. The core continues to contract.
Even electron degeneracy pressure isn't strong enough to hold
up the star. The core continues to be compressed.
Electrons and protons get shoved into each other, making
neutrons. Then, the degeneracy pressure of neutrons holds up
the star. There is also an explosion, but that is beyond the
scope of the question.
4.) (Problem adapted from textbook:)
"Summarize some of the observational
evidence supporting
our ideas about how the elements formed and showing that
supernovae really occur".
Answer:
1.) In order to make elements that are heavier than iron from
iron and/or lighter elements, energy must be added. So, we only
expect very heavy elements to be made in places and events that have
lots of excess energy. The best place is a supernova explosion.
Since making these very heavy elements requires extreme circumstances,
we expect there to be fewer atoms of very heavy elements
in the universe than there are atoms of elements between helium
and iron. When we use observations to learn the
the abundances of various elements, we
find that there are fewer atoms of very heavy elements than of
elements between helium and iron, in accord with the theory.
2.) Both living stars and dying stars make elements that had not
existed in the universe before stars existed.
So, all the carbon, nitrogen,
oxygen etc. that exists now was made in stars (or their
explosions) at some time in the universe's history. As time goes
by, more fusion takes place, so the number of heavy elements
(following astronomy convention, heavy element = anything heavier
than helium) floating around the universe increases.
This theoretical
line of thinking is supported by the following observational evidence.
Old stars were made long ago, when there were fewer heavy elements
floating around the galaxy.
Thus, we expect older stars to have lower ratios
of (heavy element)/(hydrogen + helium), and, observationally, we
find that that is true.
3.) It is easier to make some elements than others by nuclear fusion.
Therefore, we expect more atoms of the easier elements than the hard
ones. Easy elements to make are those with even numbers of
protons (except for beryllium), because you can make stable helium
(which has an even number of protons)
from 4 hydrogens, you can make stable carbon (which has an even
number of protons) from 3 heliums, and once
you have carbon, you can add a helium,
then another, then another, etc.. Each helium addition increases
the number of protons by two. When we compare with observations of
stars and gas in the galaxy, we find that the even numbered elements
(except for beryllium) are more prevalent than the odd numbered
elements.
4.) We have seen supernova explosions. SN 1987A was an
explosion in 1987. It was observed -- more specifically, within
a couple of days of the explosions, astronomers discovered a very
bright object (the bubble made from the explosion). They then
looked at older images and realized that there had been a star
in that location previously.
Other explosions have been seen as well. Astronomers see
dozens in other galaxies every year. There are also historical
observations of explosions, such as the
explosion in 1054 that made the Crab nebula.
5.) The bubbles blown by supernova explosions are also a form
of evidence.
5.)
a.) How much mass does a "low mass" star have?
Answer: less than 2 x MSun
b.) How much mass does a "intermediate mass" star have?
Answer: between 2 x MSun and 8 x MSun
c.) How much mass does a "high mass" star have?
Answer: more than 8 x MSun
6.)
a.) What is the heaviest element that a low mass star can burn?
Answer: helium
b.) What elements can high mass stars can burn?
Answer: depending on the mass of the high mass star, it can burn
various elements.
Here are some common reactions:
12C + 4He -> 16O
16O + 4He -> 20Ne (neon)
20Ne (neon) + 4He -> 24Mg (magnesium)
12C + 16O -> 28Si (silicon)
16O + 16O -> 31S (sulfur) + a neutron
28Si (silicon) + 28Si (silicon) -> 56Fe (iron)
The more massive the star, the
heavier the types of elements it can make by nuclear burning. Although it
is possible to fuse iron with other elements, such reactions consume
rather than liberate energy and so I'm not considering them to be
"burning". However, note that
during the supernova explosion, a high mass star does
fuse elements heavier than iron.
7.) By which method (proton-proton chain or CNO cycle)
do the following stars fuse hydrogen into helium?
a.) low mass stars
Answer: proton-proton chain
b.) intermediate mass stars
Answer: CNO cycle
c.) high mass stars
Answer: CNO cycle
8.) Which type of star has a great radiation pressure
(low mass star, intermediate mass star, or high mass star)?
Answer: high mass star
9.) Which type of star can have sunspots
(low mass star or high mass star)?
Answer: low mass star
10.) Which type of star burns its fuel at the fastest rate
(low mass star, intermediate mass star, or high mass star)?
Answer: high mass star
11.) Which type of star runs out of fuel to burn soonest
(low mass star, intermediate mass star, or high mass star)?
Answer: high mass star
12.) After each of these types of
stars burns all of its fuel, what happens to the star?
a.) low mass stars
Answer: it blows a planetary nebula. The remaining stellar core becomes
a white dwarf
b.) intermediate mass stars
Answer: it blows a planetary nebula. The remaining stellar core becomes
a white dwarf
c.) high mass stars
Answer: its center collapses into a neutron star (or black hole) and its
outer layers are blown off into space. We call the explosion a supernova
explosion