Astronomy 250 Problem Set No. 5
Due March 23, 2001, 5pm
This problem set is worth 15 points. As usual, you may discuss the problems with others in the class, but
you are expected to turn in your own work. In this homework, you will be using a computer simulation to
take spectra of a group of stars, and because the simulation uses a random number generator, each user
should get data that are unique. You may find reviewing the lectures on stellar spectroscopy and the HR
diagram useful. You should also read through each section before trying to take any data with the
simulation so you understand what you are trying to do. To run the "clea-spec" program, you can either
visit Room 208 in Steward Observatory and use the PCs there or you can download the software from the
class web site. Look under "Problem Sets" and follow the instructions for downloading.
Part 1. (12 points) Constructing an HR Diagram
You will construct an HR diagram for the Pleiades which will allow you to get an estimate of the
distance and age for the cluster. Your work will proceed in two steps. First you will acquire spectra of a
representative sample of stars. Start the program by clicking on the "Start" followed by "Lab Programs"
followed by "Clea Spectroscopy Lab" if working on the machines in Rm 208 or by using the "Run"
command available from the start button in Windows followed by entering the location where you put your
copy of "clea_spe". Click on "Log In", enter your name, and click on OK, and click on yes to indicate that
you have finished logging in. You will get another screen where you should click on "Run" and select
"Take Spectra". A new screen that mimics a telescope control panel will appear. Click on "Dome" to open
the dome to the sky. After the dome opens, click on "Tracking" to start the telescope moving to
compensate for the Earth's rotation (note that the stars appear to be moving slowly when the dome opens
before you turn on the tracking). Click on "Field" and select Pleiades.
The general procedure is to pick a star and move it to the center of the red box using the NSEW buttons
(click on Slew rate if the star moves too slowly). Click on "Monitor" to switch to a magnified view of the
sky. Parallel red lines marking the input slit to the spectrometer will appear. Center the star in the slit. It
needs to be the center both in the left/right sense and in the "up/down" sense. Note the RA and DEC of
this star. Click on "Take Reading".A new control panel for the spectrometer now appears. You should see
a set of axes that will be filled with a spectrum after clicking on "Start/Resume Count". Click on Start and
watch what happens. You should see the spectrum build up as photons are collected. You need to record
the star’s name, and apparent magnitude. Save the spectrum and note the filename.
Plan on measuring at least 10 stars with V<7, 10 with 7<V<9, 5 with 9<V<10, and 5 fainter than 10 th
magnitude. The fainter stars will require the use of a larger telescope than the standard 16-inch used in
the simulation. When you first arrive at the telescope control panel, you may request to use a larger
telescope – the 1.0-meter should suffice. Because this program simulates refusals by a Telescope Time
Allocation Committee, you may need to request a larger telescope more than once. For every star you
measure, you need to
1. Record the star’s name and coordinates.
2. Record the V magnitude of the star. This is the star’s apparent magnitude.
3. Record the final signal/noise ratio.
4. Save the spectrum and keep track of the number under which it was saved.
For good spectral typing, you should aim for at least a signal/noise of 100.
After you collect your data, you need to classify the spectra and assign a spectral type to each
star. The Clea_spec program has a classification utility to help you. Go to the "Classify Spectra" menu.
Initially load the main sequence comparison spectra and use the "Unknown Spectrum" choice followed by
"Saved Spectra" to load the data that you have taken. You can load one of your objects at time into the
classification screen. Your object will appear in the middle between two reference objects. You can judge
pretty well by eye which reference spectra are good matches, but the program provides a nice tool. Click
on "Difference" and the bottom panel will show the top reference spectrum minus the spectrum of your
object. The closer the difference is to a straight line, the closer the reference spectrum is to that of your
object. If you do not get a good match between your object and a main sequence star, you may need to
load one of the other reference sets that include giants and supergiants.
Items to turn in for Part 1
1. List of stars measured including their names, positions, magnitudes, and signal/noise ratios in
their spectra.
2. List of assigned spectral types for the stars.
3. A color-magnitude diagram with both spectral types and temperatures indicated (use Table 1).
Plot apparent magnitudes on the vertical axis with dim at the bottom and bright at the top. Plot
temperature along the horizontal axis with hot to the left and cool to the right. Note that this is
similar to the form of an HR diagram but until we know the distance to the Pleiades, we cannot
convert apparent magnitude to absolute magnitude (or luminosity).
4. Indicate on your diagram where the Pleiades main sequence is located. Do this by plotting the
absolute magnitudes in Table 2 and temperatures from Table 1 on a separate piece of graph
paper. Use the same number of divisions for one magnitude that you have used for your Pleiades
diagram. Overlay your Pleiades plot with this new plot so that the temperatures line up. Move the
new plot up and down until the main sequence on your new plot passes through Pleiades stars. If
you compare the vertical scales, what is the numerical difference between a Pleiades apparent
magnitude and an absolute magnitude at the same position along the main sequence?
5. Compute the distance to the Pleiades using the difference between apparent and absolute
magnitude that you measured in 4). Use the relation between m, M, and d from Lecture 18.
6. Using the data in Table 2, locate the spectral type at the tip of the main sequence. Knowing that
MV=+4.7 for the Sun, compute the luminosity at the tip of the main sequence in solar units.
Compute the mass and approximate lifetime of a star at the tip of the main sequence using the
relations presented in the lecture on binary stars and stellar masses.
Table 1: Calibration of Spectral Type versus Temperature
Spectral Type
T(K)
O5V
38000
B0V
29700
B6V
14100
A1V
9140
A5V
8160
F0V
7020
F5V
6530
G0V
5930
G6V
5620
K0V
5240
K5V
4340
M0V
3800
M5V
3030
Table 2: Main Sequence Absolute Magnitudes
Spectral Type
Absolute Magnitude
O5V
-5.8
B0V
-4.1
B5V
-1.1
A0V
+0.7
A5V
+2.0
F0V
+2.6
F5V
+3.4
G0V
+4.4
G5V
+5.1
K0V
+5.9
K5V
+7.3
M0V
+9.0
M5V
+11.8
M8V
+16.0
Part 2
7.
(worth 2 points): An interstellar cloud has a total mass of 4.5x1035 kgs. This cloud fragments and
forms stars. Assume that 25% of the cloud’s mass goes into stars, a high but not unreasonable
star formation efficiency. You may further assume this cloud only forms relatively high mass stars
– M ≥ 3.0MSun up to a maximum mass of 30MSun . If the newly formed stars are distributed in
mass according to the Initial Mass Function presented in lecture, how many 4.0MSun stars are
formed? How many 5.0MSun stars are formed? How many 15.0MSun stars are formed?
8. (worth 1 point) A star is observed to have V=10.5 and have B-V=0.67. Its spectrum shows that is
an A0 star whose B-V intrinsically is 0.0. If there were no interstellar dust, how much brighter
would this star appear?