# Astronomy (and other Space Sciences)

Paper details:Helping Henrietta Leavitt Measure CepheidVariables
Ms. Henrietta Leavitt has invited you to join her at Harvard
College Observatory to look for Cepheid variable stars in the
Magellanic Clouds (nearby galaxies in the southern sky).
Recall these stars can help measure distances to galaxies.
1.) Ms. Leavitt has been shipped a series of photographic
plates taken of the Magellanic Clouds from the Harvard
College Observatory Boyden Station, Arequipa, Peru,(picture
below) and she is now preparing a machine called a blink
comparator to allow her to compare the plates and find any variable stars. She has selected three of
plates where the telescope was pointed to about the same place.
Before comparing the star brightnesses on these plates, she has to align
them so the star images coincide exactly. Help her do this!
Go to
http://astro.unl.edu/naap/vsp/animations/registrationSimulator.html
When you enter the web page, it just has field 1 (photographic plate 1)
in the box.  Ms. Leavitt wants you to place field 2 (plate 2) in the blink
comparator and adjust its position (using precise screw adjusters) so the images of both plates coincide.
To do this, click on the box for starfield 2, and also on the box “make top field transparent” ‐ in general,
the plates would be somewhat transparent, so this is realistic. Use your computer cursor (hold down the
left mouse clicker) to move plate 2 so the star images coincide with those on plate 1. Record the x and y
offsets when field 2 is registered on field 1.
x offset =         y offset =
Go through the same steps for starfield 3 (plate 3) and record the offsets for it.
x offset =       y offset =
The two of you spend the rest of the morning lining up all the other plates and recording the offsets so
you can put them into the machine again and look for variable stars.
2.) You have taken a break for lunch, but now it is time to look for variables. Go to
The “epoch” column identifies the photographic plates by the time when they were taken. The numbers
are days and fractions of days. Therefore, the first number, 1.7215, means the first day of the
observation series, plus 0.7215 times 24 hours past when the day was defined to start, or just over 17
hours, 20 minutes. Ms. Leavitt will show you how to load combinations of pictures into the blink
‐35
2
comparator (it is easiest to start with only two). She tells you to click on the epoch, and then on the add
button. To see all of the epochs, use the slider to the right of the list. Once you have two plates loaded,
click on the blink button, and then click on “show crosshairs” and identify the variable stars you can find.
Enter their positions into the table below, when you center the crosshairs on them with the cursor of
your computer. Because the variable stars change brightness at different rates, you need to compare
plates at a number of epochs to find them all; you may also find it useful to load 3 or 4 plates to be sure.
See how many you can find (there should be 5).
Now find three reasonably bright stars that do not vary and enter them in the table below.
x position y position
113
112
297
Ms. Leavitt and you will use measurements of these stars as a reference in case one of the nights had
thin clouds or something else that made all of the stars appear a little fainter than usual.
However, this has taken all afternoon, so it is time to go home.
3. ) Ms. Leavitt got in early this morning and has set up a photographic plate for you to practice
measuring star brightnesses on (a process astronomers call “photometry”). To find it, go to
http://astro.unl.edu/naap/vsp/animations/photometrySimulator.html
There are two double apertures you can move around to center on stars or put on blank regions. Use
them to measure the stars at the positions in the table below. To make a measurement, center the
apertures on the star (locating the star in the field to the left and then centering using the windows to
the right, arrow keys will move the star). Then record the average counts for the inner disc, and the
average counts for the outer ring. The outer ring gives a measure of the signal from blank sky, so the
difference of averages for inner disc and outer ring gives the signal from the star minus the contribution
from the sky. That number is the measurement of the brightness of the star
Star X position Y position Average inner
disc
Average outer
ring
Difference
example 287 41 4435.62 2310.74 2124.88
1 113 186
2 170 52
3 279 262
4 195 210
5 29 157
Variable # x position y position
1 131 202
2
3
4
5
3
How accurate are these numbers? We can use the dual apertures to find out by putting them on areas
with no stars, measuring the inner disc and outer ring averages, taking their differences, and seeing how
much signal we get. Do this for five positions and enter the results in the table below:
Position # X position Y position Average inner
disc
Average outer
ring
Difference
1
2
3
4
5
From all these measurements, are there any pairs of stars among the five you measured that could be
the same brightness?
Yes__________              or   No___________
If so, which ones?
_____       _____      _____      _____      ______
4.) Well, that took all morning. After lunch, Ms. Leavitt had to go to a meeting with Director Pickering
and left you to look for variable stars on the plates you started with. Go to
http://astro.unl.edu/naap/vsp/animations/variableStarPhotometryAnalyzer.html
First, compare your three non‐varying stars in pairs, to see if they are really constant in comparison with
each other. To do so, move the cursor to center on one of the variable stars and left click, then move the
cursor to another of the stars and left click. The “observations plot” to the upper right shows the
differences in the brightnesses of those two stars for ALL of the epochs when plates were taken.
Compare the three stars in pairs to be sure they are all non‐variable, and if one of them is variable keep
comparing pairs to identify which one and reject it as a reference for brightness.
Good news!!! Ms. Leavitt has compared the reference stars for all the epochs and says that the nights
were good, except for night 6 when it rained. Oh yes, on night 13 the observer was sick, so no plates
were taken on that night either. But for all the other nights, so long as we measure relative to one of our
non‐varying stars we should have full data.
You can now compare selected variable stars with one of the non‐varying ones. The specific stars can be
identified by coordinates again, using the cursor/crosshairs. You will see the differences in brightness of
your stars over the days of the measurements in the upper right. Use the upper right graph to identify
possible Cepheids ‐ you will need to consult the class notes to see what the variations by a true Cepheid
should be like:
http://ircamera.as.arizona.edu/Astr2016/lectures/galaxies.htm      (look for graphs below the photo of
M33)
4
They should vary in brightness smoothly, with periods between about 1.5 and 100 days. For each of the
variable stars you found in Section 2, decide if it looks like a possible Cepheid variable and if it is
estimate the period of its variations. To the lower right, there is a graph that lets you zero in on the best
determined period. There are days along the lower axis, and a graph that should show a dip at the
correct number of days for a periodic star. Slide the triangle until the line below it goes right through the
bottom of the deepest dip. See what is happening to the vertical lines in the upper right graph also; they
mark the periods. To determine accurate periods and get the pattern more exactly, zoom the bottom
plot, and locate a broad low point on the curve which indicates a periodicity. Move the arrow at the top
to put the vertical line right at the low point and read off the period. If you also click on the “phase”
option at the bottom of the “observations plot” and it will fold all the measurements on top of each
other. When you have the arrow at the right place, the observations plot will show all the data in the
variation pattern which can be compared to the pattern in the lecture notes. Enter all this in the table
below:
Remember that the fainter the star, the greater the uncertainty will be in its measurement ‐ the
“observations plot” for faint stars will scatter up and down more than for bright ones, even if they are
not varying.
From the  period‐luminosity relation in the class notes,
http://ircamera.as.arizona.edu/Astr2016/lectures/milkyway.htm   (look for the plot below Ms. Leavitt’s
picture)
what is the rough luminosity of the Cepheids you found, assuming they are of Type I? Just select the
closest to 3 X 102 Lsun, 103 Lsun, 3 X 103 Lsun, or 104 Lsun. (More blanks may have been provided than are
necessary ‐ there may be less than five Cepheid candidates)
____________             ____________         _______________       _______________