Download HW #5 Answers (Due 9/29)

HW #5 Answers (Due 9/29)
1. List the two parameters that nuclear reaction rates depend on in the Sun and explain why
the reaction rate depends on them.
Nuclear reactions rate depend on temperature and density. In order to bring protons together to
make Helium, the protons have to over come the repulsive force between them. This means that
they have to be moving extremely fast or their average kinetic energy has to be very large. That
means a high temperature. Also, collisions have to be head-on collisions. If not the particles
will just scatter off of each other. The more particles in the core, the more likely the chance for
head-on collisions. This is the density.
2. Explain why there is a mass-luminosity relationship for stars on the main-sequence. In
other words, why do high mass stars give off more energy every second than a low mass
star?
High mass stars have more mass, so their gravity is higher. The gravity squeezes the
core more tightly causing the temperature and density to be higher in the core than in a
low mass star. High temperature and density means that the nuclear reaction rates are
more frequent, and more energy is being generated. This leaves the star and the result is
a higher luminosity for high mass stars than low mass stars. This relation only holds on
the main-sequence, where the stars are converting H to He. In other stars, with other
energy sources inside, it is possible for a low mass star to produce a lot of energy and the
relation doesn’t hold.
3. If a star is measured to have a parallax shift of 0.25 arcseconds, then how far away is this
star in parsecs? Show your work.
D = 1/p where p is the parallax angle in arcseconds. So D = 1/.25 = 4 parsecs.
4. Write out the Stefan-Boltzman Law for a radiating source. Explain why it depends on
surface temperature and the radius of a star.
L = σT4(4πR2) As the average kinetic energy (temperature) of the electrons in a
star increases there is more energy available to produce radiation through collisions. So higher
temperature means more energy/second being released as radiation. Higher Luminosity. The
light from a star has to pass out of the surface of the star in order to escape into outer space and
be seen by us. The more surface area that is available for it to pass through, the more of it that
can escape in a given second. So the luminosity depends on the amount of surface area, which
for a spherical star is just the surface area of a sphere, 4πR2
5. In a star cluster it is possible to tell how old the cluster is by looking at the mass of the
stars that are just leaving the main sequence. Explain how this turn-off mass gives us the
age of the cluster.
As we found out in class, the more massive a star is the faster it uses up its fuel supply. For very
massive stars, the fuel is used up in a matter of a couple million years. For less massive stars
like the Sun, the fuel will last 10 billion years. And for really low mass stars, the fuel will last for
hundreds of billions of years. In a star cluster, all the stars form at the same time. The first to
die are the highest mass stars. As time goes by, lower and lower mass stars use up there
hydrogen in the core and leave the main-sequence. If you know the mass of the stars that are
just beginning to leave the main-sequence, then you know the amount of time since they formed.
Thus the age of the cluster.