Download HW #9 Answers (Due 10/28)

HW #9 Answers (Due 10/28)
1) Tell what is occurring in a lower mass star as it moves off the main-sequence, to become
a giant, then on to the helium-core burning phase, and finally up the asymptotic giant
branch.
When a lower mass star first moves off the main-sequence, the hydrogen has all been
converted to helium in the core. The core begins to contract under the force of gravity
and this speeds up the helium atoms in the core, which collide allowing them to produce
radiation. This extra radiation from the contracting core causes the star to move up and
to the right on the H-R diagram.
When the core contracts enough, the hydrogen that is present in a shell around the core
becomes hot enough to start fusing hydrogen into helium. When this happens the outside
of the star swells up enormously and the star becomes a giant. During this phase the
core continues to contract.
After the core has contracted for a long time, the temperature in the core becomes large
enough for Helium to begin fusing into Carbon. When this happens the core stops
contracting and produces energy via the triple-alpha process. The hydrogen shell
burning is still occurring as well, and the result is a star that is located to the left of the
giant branch on the H-R diagram, but still at a higher luminosity than the main-sequence
stars.
When the Helium in the core is gone, the core again starts to contract, and along with
hydrogen shell burning, there is now sporadic Helium shell burning. And of course the
star’s core is contracting. This once again sends the star toward the giant branch on the
H-R diagram, and the star is now an asymptotic giant branch star. Because the helium
shell burning is sporadic, it occurs in bursts, which send shocks through the outside of
the star and sends parts of the outer star off into space. This is the beginning of the
formation of a planetary nebula.
A lower mass star cannot convert carbon into anything else because it does not get hot
enough, and so the carbon core is the final stage of evolution. When the rest of the star is
peeled off, the core is exposed and is now referred to as a white dwarf.
2) Why can the position of the coolest white dwarfs on the H-R diagram give us an estimate
of the age of the universe?
The white dwarf star is the exposed Carbon core of a lower mass star. The core
contracts to the point where the free electrons are squeezed in between the nuclei. When
the electrons are confined in this manner they start to act like wave. The wave nature of
the electrons means that they have discrete energies, just like an electron bound to an
atom. The electrons can only exist at unique energies and two electrons can not have
exactly the same energy, there is a repulsive force which is set up in the core that halts
the contraction due to gravity. The core is said to be degenerate and the repulsive force
is supplied by the Pauli exclusion principle.
Once the core is degenerate, it can no longer contract. So from here on out the
radius of the white dwarf is constant. There is nothing left for the white dwarf to do but
to cool off. NOTE: Usually if the core of a star cools off, gravity will cause it to shrink in
size. But this can’t happen with a degenerate white dwarf. So the only think controlling
the changing luminosity of a white dwarf is the temperature. Since cooling of a matter is
very easy to model, it is possible to compute how much time it takes for a white dwarf to
cool to a certain temperature. There are no white dwarf stars cooler than about spectral
type K. This is because there hasn’t been enough time for them to cool any further since
the start of the universe. Knowing the cooling rate, and the cutoff in temperature for the
white dwarfs, gives an age for the universe.
3) What causes a lower mass star to lose its outer envelope as a planetary nebula and thus
expose the core which is a white dwarf?
It is the sporadic helium shell burning which occurs during the asymptotic giant branch
phase. See question #1 for description of this.
4) Why do high mass stars explode when their cores become iron? What is the
characteristic of iron that leads to the explosion.
Iron has the most stable nucleus of all the elements. This means that it is more tightly
bound together than any of the other 91 elements. As a result, when iron is fused into some other
heavier element the fusion process does not release energy. The resulting, new nuleus is more
spread out, which means it has a higher potential energy than iron does. So some of the energy
in the fusion process has to go into expanding the new nucleus, a little bit. This means that the
reaction actually takes more energy than it can produce. Fusing Iron is an endothermic
reaction. Energy does not come out of the reaction. As a result, when the core is completely
iron, there is no mechanism for producing energy to battle against the inward pull of gravity.
The iron core collapses under gravity and the electrons and protons merge to form neutrons.
The core collapses down to an object that has the same density as an atomic nucleus. The
collapse is only stopped by the confined neutrons acting like waves. This is called neutron
degeneracy pressure. When the overlying layers of the star fall into the neutron core, they
rebound off the core and head back out into the other layers which are falling in. This sets up a
shock wave through the star that blows the rest of the star apart.
5) Use angular momentum conservation to explain why a neutron star spins at incredible
rates.
When the core in a high mass star collapses it goes from a very large radius down to a
radius of about 6 miles. Since angular momentum is conserved, the shrinking radius
means that the velocity of spinning must increase. L = mvr. If the radius shrinks by a
factor of 10,000, then the velocity of spinning will increase by 10,000
6) List three things that a supernova explosion does to the regions around it.
A supernova explosion can provide a shock wave that can compress the nearby
molecular cloud and set of a new round of star formation.
A supernova produces many new elements during the explosion which are then sent out
into space. These new elements mix with the molecular clouds causing the new stars that form to
have high levels of heavy elements than the previous generation of stars.
A supernova explosion can destroy life on any planet that is within about 50 to 100 light
years from the explosion