Please show all your work, written as neatly as possible.
Hand in your papers to me directly or place them into the
plastic mail folder outside my office door,
anytime up to and including Thurs, Feb 26, at 9:00 AM.
- Plot the following portion of the solar spectrum:
You should see a strong line near 7699 Angstroms.
This is due to a transition in neutral potassium atoms.
The oscillator strength for this transition is f = 0.679.
- Make a graph showing the spectrum, zoomed in on this line.
- Measure the equivalent width of the line.
- Calculate the energy of the transition.
- Figure out the atomic energy levels involved for this atom,
and write them down.
- Following the example in the lecture on "Curve of Growth",
calculate the abundance of potassium atoms in
the solar atmosphere. Show all your work and assumptions
clearly.
- Compare your abundance of potassium in the solar photosphere
to that in some reliable reference source.
- Consider a galaxy as a "gas" of stars. Is it optically thick
or optically thin? Use the following model of a spiral
galaxy: a flat disk
- radius 100 kpc
- thickness 1 kpc
- uniformly sprinkled with 10^(11) stars of 1 solar mass
Ignore all gas and dust in this problem.
Pretend that this spiral galaxy sits directly in between us
and a distant quasar. Light from the quasar must pass through
the galaxy in order to reach us. If the light runs into
a star directly, it will be absorbed.
- Calculate the optical depth of this galaxy if it lies
"face on" to us, so that we see it as a circular
disk of stars.
- Calculate the optical depth of this galaxy if it lies
"edge on" to us, so that we see it as a flat rectangle
of stars.
- Back in "the old days", astronomers sometimes tried to estimate
the distances to some stars via a technique called "secular
parallax." The basic idea was to use the Sun's motion through
space over a period of several decades to establish a baseline.
By measuring the positions of a set of stars scattered
all over the sky at the start
of the interval, and then again at the end of the interval,
astronomers could detect a slight AVERAGE shift of the set.
That would tell them something about the AVERAGE distance
to the stars.
So, consider a set of A0V stars, scattered evenly
over the entire sky. Imagine that these stars are all
fixed exactly in space, so that they don't move at all
relative to each other.
Fred picks a subset of these A0V stars, all of which
have apparent magnitudes of exactly m(V)=11.5.
He measures the positions of them all with
his ground-based telescope.
Fred then waits 40 years, and then measures their
positions again.
- What is the "peculiar velocity" of the Sun relative to the
stars in our neighborhood of the Milky Way?
You can look this up in several places. Please quote
the value in km/sec.
- How far will the Sun move over the 40 year period?
- Using the spectral class of the stars, estimate
their absolute magnitude M(V) and their distance from
the Sun.
- What should be the maximum shift in the apparent
position of these stars over the 40 year period?
- What should be the MINIMUM shift in the apparent
position of these stars over the 40 year period?
Explain why there will be a range of apparent shifts.
- Will Fred be able to detect this shift? Choose a
reasonable precision for measurements of stellar
position from the ground -- justify your choice.
Then compare this precision with the actual size of
the shift.
- Astronomers discover a nice eclipsing binary star.
Its light curve has a period of P = 1.268 days
and looks like this:
The radial velocities of its component stars are measured, too,
and look like this:
Assuming that the orbits are circular and edge-on,
determine as much as you can about the mass and size
and temperature of each star.
If you need to make any additional assumptions,
state them clearly, then use them.
- Look at the data file below, which contains the spectrum
of a star.
Plot the spectrum at least once (but possibly several times
for closeups of different regions). Make your best
guess at a spectral classification of the star.
Describe in detail your reasons, pointing explicitly to
any features of interest.
