LAB: Photometry of the Pleiades Cluster

ASTR 203 - Instructors Olszewski & Leistra

Due IN CLASS on Oct. 18

You will turn in 2 products from this lab:

a) an H-R diagram you made from the data

b) answers to this lab’s posed questions , typed. As always, math can be neatly

hand-written.

Please staple these together. We do not have a stapler available in the classroom.

In this lab, you will create an H-R diagram by measuring the brightnesses and colors of the stars in the Pleiades Cluster. (This is an easily-spotted cluster of stars near the constellation Orion; between six and eight stars are visible to the naked eye, depending on how dark the skies are and how sharp your eyes are.) This will help you understand H-R diagrams, and how astronomers measure the basic properties of stars. The data you'll take make it possible to estimate the age of the cluster (what are the brightest stars on the main sequence?) and the distance (how bright do stars of known luminosity appear to be?)

Introduction

In this lab, we'll give you the apparent brightness of each of 40 stars in the Pleiades (a nearby, young open cluster) in 2 colors (B=blue, R=red). We will assume all of these stars are approximately the same distance away. This is a good assumption, since all these stars are members of the same cluster, and the distance to the cluster is much larger than the size of the cluster. Without this assumption, you couldn't make an H-R diagram without knowing the distance to each star, since the apparent brightness depends not only on the actual luminosity but also on the distance. With the assumption, the only unknown is the distance to the cluster .

From these measurements of apparent brightness, you'll make a Hertzsprung-Russell (H-R) diagram. By now, you're used to the axes being luminosity and temperature. Since we don't know the distance to the Pleiades, and you don't have spectra to get good temperatures, you'll need to use other quantities to stand in. The number of blue photons will stand in for the luminosity, and the RATIO between the number of blue photons and the number of red photons will stand in for the temperature. You know that a blackbody emitting more blue photons than red photons is hotter than one with more red photons than blue photons, even if you can't tell what the actual temperatures are.

In Table 1 we've given you real data for the Pleiades cluster. The first two columns are the positions of the stars (which you don't need to worry about; they're just a way of identifying the stars). Columns 3 and 4 are the apparent brightnesses in a blue filter and a red filter. The numbers given for the apparent brightness are the number of photons measured in a given time, compared to those measured with the same filter in the same time from the bright star Vega. (We don't actually go observe Vega every time, since we know very well how many photons per second it gives us in every filter; it's just chosen as a standard of measurement). For your H-R diagram, you should plot the logarithm of the ratio of brightnesses you measure on the horizontal x axis, and the brightness in the B filter on the vertical y axis. There is a blank graph at the end of this writeup that you should use to plot your data. The horizontal axis is in ordinary linear units; the vertical axis is in logarithmic units. This means the evenly spaced divisions are at 0.1, 0.01, 0.001.... rather than 0.1, 0.2, 0.3, and we can fit all the data on the plot clearly. So if a star has 0.08 and 0.11 in these two columns, it would be 8% as bright as Vega in the blue filter and 11% as bright as Vega in the red filter. The color term is log(RED/BLUE), or log(0.11/0.08) = 0.14. (Your calculator or spreadsheet should have a log button. If you're using a spreadsheet, make sure that its log is base 10; if it is, “log 10” will be 1. If you don't have a calculator that can do this, Google can; just type in, for instance, “log(0.11/0.08)” and it will give you the answer.

In order to plot this in the same way astronomers do (so that temperature increases as you go LEFT on the HR diagram – a historical accident, but one we're stuck with), you want the quantity you plot on the x axis to be the brightness in RED divided by the brightness in BLUE.

If you don't want to type all the numbers into your calculator, there is a computer version of the table you can download to import into a spreadsheet at http://caffeine.as.arizona.edu/~aleistra/a203/lab2_table.dat

We won't help you with the details of Excel (neither one of us uses it). If you choose to do it this way, print out and hand in the spreadsheet you use to do the math along with the rest of your writeup. If you want to turn in a computer-generated diagram, that's OK as long as the axes are correct and the same as on the blank graph we've given you. Again, neither of us knows Excel, so we can't help you make a linear-log plot.

Plotting Your Diagram

1.Create an H-R diagram of your data. Remember that the axes are in logarithmic units.

2.On your H-R diagram, identify the main sequence. Sketch a line through it, and label it clearly.

3.Are all the stars in your diagram on a straight line? If not, what does this tell

you?

4.Notice that there is a star which appears out of place with respect to the main sequence. Circle this star on your H-R diagram. What type of star might this be? Why do you think so?

Distance to Clusters

You now have enough information to figure out the distance to the cluster. Since color doesn’t change with distance but brightness does, the x-axis stays the same as the cluster gets farther away, while the y-axis changes. Think about this – for a MS star, you’ve measured the apparent brightness, and from the color you know what the true brightness should be. So you can estimate the distance.

The distance to the Pleiades has been measured by this technique, and even better by the technique of stellar parallax. These techniques give a distance of about 420 + 20 light-years.

What fraction of the Milky Way diameter is this? (Milky Way = 100,000 light years across.) Show your work. Is the Pleiades near or far?

In Figure 1 we show you the HR diagram of another cluster, plotted in the same units you've used for the Pleiades. Compare your HR diagram to this one. (If it isn't vaguely similar, you may have done something wrong. Check to make sure you're plotting the BLUE brightness on the y-axis and log(RED/BLUE) on the x-axis.)

1.Is this cluster nearer or farther from the Sun than the Pleiades? How can you tell?

2.Draw a straight line through the main sequence on this HR diagram just like you did for the Pleiades. Measure the value on the y-axis where each of your lines pass through x = 0 (This is just so you can measure the vertical distance between your lines, when theye's 're not on the same plot). How much brighter/fainter is this cluster than the Pleiades?

3.The apparent brightness of an object depends on 1/(distance)2. This means that if you know two stars have the same INTRINSIC brightness (if, for example, they're both on the main sequence and have the same color), and one is 100 times fainter, it must be 10 times farther away. Based on this, about how much nearer/farther is this cluster than the Pleiades? Show your work. How far away is that?

What you've just done is a simplified version of a technique known by astronomers as main-sequence fitting, which is really used to find the distance to clusters of stars.
Data to use for plotting the diagram. “BLUE” and “RED” are the brightnesses of this star in a blue and a red filter, relative to the bright star Vega.

RA DEC BLUE RED

03:47:29.06 +24:06:18.9 0.0810 0.072

03:49:09.74 +24:03:12.3 0.0410 0.035

03:44:52.52 +24:06:48.4 0.0400 0.033

03:45:49.61 +24:22:03.9 0.0330 0.028

03:49:11.22 +24:08:12.2 0.0110 0.0094

03:48:20.82 +23:25:16.5 0.0074 0.0066

03:44:48.21 +24:17:22.1 0.0073 0.0065

03:45:09.74 +24:50:21.3 0.0063 0.0054

03:49:43.53 +23:42:42.7 0.0038 0.0034

03:47:21.04 +24:06:58.6 0.0030 0.0032

03:49:21.75 +24:22:51.4 0.0024 0.0023

03:49:58.05 +23:50:55.3 0.0019 0.0019

03:47:29.45 +24:17:18.0 0.0018 0.0019

03:47:20.97 +23:48:12.0 0.0016 0.0017

03:47:24.42 +23:54:52.9 0.0012 0.0012

03:45:37.79 +24:20:08.2 0.0011 0.0014

03:50:28.06 +24:29:43.8 0.00094 0.0011

03:49:16.80 +24:23:46.1 0.00089 0.001

03:45:51.63 +24:02:20.0 0.00058 0.00079

03:49:25.98 +24:14:51.7 0.00055 0.00072

03:44:00.27 +24:33:25.2 0.00048 0.00065

03:45:26.14 +24:02:06.5 0.00048 0.00065

03:49:12.19 +23:53:12.5 0.00047 0.00064

03:44:25.72 +24:23:41.0 0.00043 0.00066

03:46:16.00 +24:11:23.6 0.00042 0.00067

03:43:43.24 +24:22:28.5 0.00038 0.00055

03:48:13.56 +24:19:06.3 0.00036 0.00062

03:48:43.90 +23:15:35.3 0.00034 0.00051

03:47:04.21 +23:59:42.8 0.00033 0.00049

03:47:26.54 +24:39:30.4 0.00025 0.00035

03:45:20.86 +24:55:19.4 0.00016 0.00033

03:49:32.72 +23:22:49.4 0.00015 0.00028

03:46:16.00 +24:11:23.6 0.00011 0.00025

03:49:12.15 +23:24:30.0 0.0001 0.0002

03:45:59.44 +25:03:05.9 9.3e-05 0.00016

03:48:56.08 +24:01:26.3 9.0e-05 6.4e-05

03:43:58.80 +23:52:57.9 7.8e-05 0.00018

03:46:32.18 +24:52:14.0 7.5e-05 0.00014

03:46:50.53 +23:14:21.1 6.9e-05 0.00014

03:50:34.37 +24:47:29.7 5.7e-05 9.8e-05
Use this blank plot for your HR diagram. Notice how the numbers on the y-axis are spaced.
This is an HR diagram for another cluster at a different distance than the Pleiades. Use this


to answer the questions in the “Distance To Clusters” section.