1. What is one
way LIGO tries to isolate the mirrors from ground motion, and keep them
from shaking?
2. Compare the force of gravity at the surface of a white dwarf to the force of gravity
at the surface of the Sun, by putting yourself at the surface of both stars and using
Newton’s equation for the force of gravity. The mass of the white dwarf and the Sun
are the same (1 M¤). The radius of the white dwarf is one-thousandth the radius of
the Sun (0.001 R¤), while the radius of the Sun is 1 R¤. What is Fwhite dwarf / FSun?
3. The Sun fuses four ______________________ to create one __________________________ and
along the way releases energy in the form of a photon.
4. Fusion is said to be the source of energy in the Sun. What evidence do we have
that fusion is occurring in the Sun?
5. Sunspots are created when the twisted _______________________________ of the Sun
suppresses ______________________ and cools the region.
On the last page is attached an HR diagram that includes temperature and
luminosity data points for the nearest stars (squares) and brightest stars (x’s). On
the x-axis is the temperature of the star, and on the y-axis is the luminosity of the
star, given as a ratio of the Sun’s luminosity (1 L¤). Some of the stars on this diagram
are Main Sequence (normal) stars, some are red giants (dying stars) and some are
white dwarfs (dead stars). For more information on the HR diagram, you can check
out the following pages:
http://astro.unl.edu/naap/hr/hr_background3.html
http://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolution_hrintro.html
6. There is a general trend in the HR diagram, where the bulk of the stars lie. This is
called the Main Sequence. Circle the Main Sequence.
7. If a star on the Main Sequence has a temperature of 3,000 K, predict what its
luminosity would be, in solar luminosities (L¤).
8. Sirius B is a white dwarf with a temperature of 24,800 K and a luminosity of 0.0026
L¤. Spica is a B star with a temperature of 24,200 K and a luminosity of 2,400 L¤.
Find and label these stars on the HR diagram.
The Stefan-Boltzmann law says that luminosity, temperature, and radius are related
to each other by L = 4πR2σT4, where L is the luminosity, R is the radius of a star, T is
its temperature, and σ is the Stefan-Boltzmann constant. While Spica and Sirius B
have nearly identical temperatures, they have very different luminosities, which
means they should also have very different radii.
9. Find the ratio between the radii of the stars; that is, find RSpica / RSirius B. As with
our other ratio problems, you should find that terms will cancel out. For
simplification, assume the temperatures are equal to one another.
The following table lists properties of several Main Sequence stars, along with the
lifetime of a star with the same spectral type.
12. Find and label the following Main Sequence stars on the HR diagram.
Star
Spectral
type
Temperature
(K)
Luminosity
(L¤) Mass (M¤)
Lifetime
(years)
Sun G 5,800 1 1 10 billion
Sirius A A 10,300 23 2.4
300
million
Spica B 24,200 2,400 10
100
million
61 Cyg A K 4,600 0.088 0.7 30 billion
Barnard’s
star M 3,100 0.00044 0.144 600 billion
Procyon A F 6,500 7.38 1.5 2 billion
11. At some point, these stars will run out of fuel, become red giants, and die. When that
happens, they move off the Main Sequence, to the right, and land on the “red giant
branch.” Let’s focus only on the Main Sequence right now, and ignore the rest of the
diagram.
Let’s assume that all the stars on the Main Sequence in this HR diagram were born at
the same time. After 300 million years, the A stars will begin to die and will leave the
Main Sequence. Any star more massive than an A star will also have died at this
point, because more massive stars die quicker.
Draw a vertical line where the Main Sequence ends, after 300 million years
have passed. There will be no more stars to the left of this line on the Main
Sequence after 300 million years. Do the same for 10 billion years and 100 billion
years.
12. When we see a cluster of stars, we assume they all formed at the same time.
Remember that stars form from a cloud of gas that collapses and fragments – these
fragments are all going to form stars around the same time. If we create an HR
diagram for a cluster, we can look for where the Main Sequence stops and “turns
off,” and get an age for the cluster, like we did above. The HR diagram below has
data for the M3 star cluster. The x-axis here is labeled in units of thousands of
Kelvin, so when it says “5” it means “5,000 K.”
At about what temperature does the Main Sequence stop, and “turn off” to the
right? Look for where the main bulk of stars on the Main Sequence turn off, not just
a few stragglers.
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What spectral type does this temperature correspond to?
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How old (approximately) is the star cluster?