Photoelectric Photometry of the Pleiades

PURPOSE:

Using the Macintosh computer simulation Photoelectric Photometry you will measure the apparent magnitude of 24 stars in the Pleiades star cluster in three colors U, B and V (Ultraviolet, Blue and Visible). From this information you will estimate the distance and age for this young star cluster.

EQUIPMENT:

Scientific pocket calculator, graph paper, ruler, plastic transparency, black marker pen, Macintosh Computer, and Gettysburg College Observatory Computer Program Photoelectric Photometry.

Share the use of the computer and program with your partner to collect data. All calculations and graphing, as well as your narratives, must be your own original work.

INTRODUCTION:

The computer program you will use is a realistic simulation of a UBV photometer attached to a moderate sized research telescope. The telescope is controlled by a computer that allows you to move from star to star and make measurements. Different filters can be selected for each observation, and the integration time (the length of time the photometer samples the starlight) is adjustable. The computer also does much of the busy work needed to convert photon counts into apparent magnitude and provides an estimate of the quality of the collected data.

You will use this instrument to collect data on 24 stars in the region of the Pleiades star cluster. The apparent magnitudes will be measured for each star, in each of three colors. We will assume all of these stars are approximately the same distance away. This is a necessary assumption, and reasonable because all of the stars are members of the same cluster. If we did not make this general assumption, the apparent magnitudes of the stars would also depend on their individual distances, an effect we cannot easily take into account in this lab.

From this information you will plot a Hertzsprung-Russell (H-R) diagram which will display the apparent magnitude of the cluster of stars as a function of their color index. The color index, B-V, is the apparent blue magnitude (B) minus the apparent visual magnitude (V). For your H-R diagram, plot the calculated B-V data on the horizontal x axis, and apparent magnitude on the vertical y axis. Recall that the dimmer a star is, the greater the apparent magnitude number. Bright stars have a small apparent magnitude number; in fact, very bright stars actually have negative apparent magnitudes. Plot your y axis in such a way that zero magnitude is at the top, and 25th magnitude (a very dim star indeed) is at the bottom. The x axis should range from -0.4 on the left to 1.8 at the right:

Lay out your graph like the above example. Expand this miniature example so it occupies most of a sheet of paper. Be sure your graph's y axis runs from 0 at the top to 25 at the bottom as shown above. Creating too small a graph will make it difficult to plot data accurately.

You will then create a second graph like the first on a clear plastic sheet. Alternatively, you can make this second graph on a sheet of paper. The x-axis and y-axis scales must be the same on both graphs and you must be able to "see through" one graph when they are overlayed. On the second graph you will plot a group of main sequence stars with known absolute magnitudes. By overlaying and aligning these main sequence stars on top of your apparent magnitude H-R diagram, you will be able to relate the apparent magnitude (m) of a cluster star to an absolute magnitude (M) from the main sequence plot. Knowing the apparent and absolute magnitude of a star, you can determine its distance d (in parsecs) from the equation:

(1) m - M = 5 log d -5

This equation may be solved for d as

(2) d = 10 ^(m-M+5)/5

where

m = the apparent magnitude

M = the absolute magnitude

d = the distance in parsecs

OPERATING THE COMPUTER PROGRAM:

First, boot up your computer (see your lab instructor if you do not know how to do this). Then, place the diskette titled Photoelectric Photometry into the disk drive slot. [NOTE: The software may already be installed on your computer's hard drive. If so, you will be given information in class as to how to access it.] When the disk icon appears, position the mouse cursor over the icon and double click the mouse button to select the diskette. A menu will appear. Position the mouse cursor over the file name, and double click the mouse button to run the program.

You will use this program in the following order:

Enter student information.

Read the INSTRUCTION screen.

Set the Time Zone

Open the observatory.

Move to a star.

Set the controls.

Take a reading and record your results.

If the program is running properly a copyright screen should appear in a short time. Position the cursor over the OK and click the mouse button ONCE to continue to the INSTRUCTIONS screen. Read the abbreviated instructions carefully before proceeding.

Entering Student Accounting Information

Click the OK button after you have read the instructions to continue to the STUDENT ACCOUNTING screen. Enter your name, and those of your lab partners. Do not use punctuation marks. Press return after each name, or to skip to the next entry. Enter the Workstation Number you are seated at for this experiment. Once you have moved to the next entry, you cannot change your response unless you rerun the program again. When all the information has been entered to your satisfaction, click OK to continue.

Open the Observatory:

Take a moment to study the various controls available to you. Click on OPEN to slide the observatory doors open, which will reveal the night sky and activate the photometer electronics.

Figure 1. The Photometer

Move to a Star

Once the observatory is opened, directional controls appear which can be clicked to move the telescope around in the sky. The small circle in the center of the view is called the photoelectric aperture. See figure 1. The desired star must be carefully positioned within the aperture in order to be measured.

The rotation of the earth will cause the stars to drift through the view. Observe this phenomenon by carefully watching the stars. This is tricky: do the stars drift east or west? Is this toward the left or toward the right on the display screen?

Telescopes are equipped with a motor drive which moves the telescope in a direction opposite to the drift and at the same rate. The motor (often called the clock drive) cancels the effect of the earth's rotation and the star seems to stand still permitting extended study. Turn on TRACKING and note how the stars cease to drift.

The directional controls move the telescope, not the sky! Moving the telescope to the west appears to make the stars move in the opposite direction. Try it. The SLEW control adjusts in steps, and changes how much the telescope is moved each time the directional controls are clicked.

Set the Controls

Make sure the tracking is on, and move the telescope to center a star in the aperture. The right ascension and declination of the aperture center are displayed in the upper right of the screen. Select a filter (U, B or V - they cycle when clicked). Select an integration time. Use short integration

times for bright stars, and long integrations for faint stars. Integration times are in seconds. Bright stars generate many photons, and cause high counts.

Take a Reading and Record the Results

Take a reading. Watch the message box for important information. The computer will take a series of four integrations, and display the individual and average photon counts in the count box on the left. After the integrations are completed, the apparent magnitude of the object under study is displayed in the message box.

Also displayed in the message box is the signal-to-noise ratio of the reading. A high SNR means you have a lot of desired photons, and only a little noise. You should strive for SNR figures of 100 or more. You can increase the SNR by increasing the integration time because SNR is directly proportional to the square root of the average counts. Integrations that are too long (particularly on a bright star) cause the counting electronics to overflow. Should this happen, repeat the reading with a shorter integration time.

The Pleiades Photometry Laboratory Project

For each star in the field (24 in all), record the right ascension, declination, and U, B and V apparent magnitudes in a table. Record all magnitudes to the nearest 0.001 magnitude. (Close the observatory when you are done.)

Calculate the color index B-V for each star to the nearest 0.01 magnitude and record it in your data table. Hot blue stars have low, and even negative B-V. Cooler red stars have B-V values somewhat greater than 1.

Create an H-R diagram of your data, as explained in the introduction section. Use regular graph paper. On the basis of this graph identify and answer the following:

1. Identify the main sequence, and label it clearly.

2. Identify, by RA and Dec, three possible red giant stars

3. Consider the star near RA 3h 44m and Dec 24° 35'. It seems curiously out of place with respect to the main sequence. What type of star might this be? Upon what did you base your decision?

Distance to the Cluster

Place the clear plastic over your graph, and using the ruler trace both x and y axes. Label and scale the x axis the same as the graph paper, but re-number the scale of the y axis of the plastic overlay to range from -8 (at the top) to +17 (at the bottom). Label this new y axis V ABSOLUTE MAGNITUDE. Leave the plastic laying on the graph paper so you can use the grid lines.

Plot the following calibration stars on the plastic overlay. They are main sequence stars for which absolute visual magnitudes have been determined (adapted from Allen, Astrophysical Quantities):

Spectral Type

B-V

Absolute V Magnitude

O5	-0.35	-5.8
B0	-0.31	-4.1
B5	-0.16	-1.1
A0	0.00	+0.7
A5	+0.13	+2.0
F0	+0.27	+2.6
F5	+0.42	+3.4
G0	+0.58	+4.4
G5	+0.70	+5.1
K0	+0.89	+5.9
K5	+1.18	+7.3
M0	+1.45	+9.0
M5	+1.63	+11.8
M8	+1.80	+16.0

Table 1: Main Sequence Stars

Slide the plastic overlay up and down until the main sequence on the overlay best aligns with the main sequence on your paper graph. Keep the y axes precisely parallel. Seek a best fit for the central portion of the combined patterns. The cool red stars in the lower right of your paper graph are quite scattered and may not fit very well.

Consider what you are doing: You have graphs of two groups of main sequence stars. One graph is in terms of visual apparent magnitude (m) and the other one in visual absolute magnitude (M). When the patterns are matched, it is clear that each star on the combined main sequence can be described either in terms of m or M. It just depends on which scale you read.

Notice that once the two main sequences are aligned, a fixed relationship is established between the apparent and absolute magnitude scales, no matter where you read the y axis or which star you pick. So, pick any convenient magnitude on the absolute magnitude scale and read its corresponding apparent magnitude on the paper scale. Read each scale to the nearest 10th of a magnitude.

Use equation (1) or (2) in the introduction to calculate the distance to the cluster in parsecs and light-years. Show all work.

In 1958, H. L. Johnson and R. I. Mitchell calculated the distance to this cluster to be about 410 light-years. As a percentage, how does your calculated value compare? Is your value higher or lower than the Johnson and Mitchell value?

Using only your graphs and results, calculate the apparent magnitude of the Sun if it were located in the Pleiades cluster. Explain your procedure in a narrative, and show all your math!!

(HINT: You'll need the absolute magnitude of the Sun. The Sun is a type G2 star with a B-V of about +0.62. Now, you can use the clear plastic graph to estimate its absolute magnitude.)

Include your answers to all these questions in your report for this project.