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Old 04-02-2009, 06:55 AM
wasabiii69 wasabiii69 is offline
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Exclamation The milky way and Beyond: Globular Clusters

I need to make this experimental procedure and I don't know how to translate the data into a histogram. Can you help me?

Experimental Procedure


Do your background research so that you are knowledgeable about the terms and concepts above.
Go to [url]http://www.physics.mcmaster.ca/Globular.html[/url] and follow the catalog link.
Look at Part II: Photometric Parameters and find the color column labeled "V − I".
Copy the entries from the V − I column into a column in your spreadsheet.
Make a histogram (a bar graph) for the column. This is a plot of color (V − I) vs. number. Your spreadsheet should have a function that helps you make histograms, but you can also make one yourself.
To make a histogram yourself, first figure what range of V − I values you have.
Then split this range up into small, equal sections, called bins. There are several ways to do this, but for our purposes, let's use: 0.70.8, 0.80.9, 0.9-1.0, 1.0-1.1, 1.1-1.2, 1.2-1.3, 1.3-1.4, 1.41.5, 1.5-1.6, 1.61.7, 1.7-1.8, 1.8-1.9, 1.9-2.0, 2.02.1, 2.1-2.2, 2.2-2.3, 2.32.4, 2.4-2.5, 2.5-2.6, and 2.6-2.7. If you want, you can also try splitting up the data into different equal sized sections to see how bin size affects your histogram.
Put these values on your x-axis.
Now count the number of globular clusters with V − I values in each of the small sections.
Draw a bar graph with number of globular clusters on the y-axis.
Make sure to label your axes when you make your histogram. The x-axis should be V − I color ranges, and the y-axis should be the number of globular clusters in each small color range.
For more help with histograms see the "GoMath Mini-Lessons" and "Excel 101" links in the Bibliography.
Now you have a histogram for the colors of Milky Way globular clusters. What do you notice about the histogram? Describe what it looks like.
There should be two peaks in the histogram. (The two peaks look a little like an "M", but with one leg is longer than the other.) This is called color bimodality. Galaxies often show these two peaks in globular cluster color, possibly because there are two different groups of globular clusters in most galaxies (maybe one group formed first or formed from different material).
To make this a bit clearer, let's think about a more familiar example of color bimodality. If you look at a bunch of trees in the fall, they will be bimodal in color: a few trees might be purple or yellow, but most will be either green or reddish. This happens because there are two main groups of trees, evergreens that stay green in the fall and deciduous trees that turn red in the fall. Try to come up with some other examples of bimodality and think about why bimodality happens for each example.
Can you think of other reasons why two groups of globular clusters in the same galaxy might have different colors?
Calculate the mean, median, and mode globular cluster color. Do you get close to the same value for each? Why might the three values be different (hint: think about bimodality)? Are there many globular clusters with color near the mean? Are there many near the median?
Copy the V − I data from the table below into your spreadsheet (put it all in a single column). This is the data for 80 globular clusters in the galaxy M87.
V−I color data for 80 globular clusters in galaxy M87
0.906537 1.23754 1.28654 0.952537
1.22454 1.28254 1.17254 1.16254
1.18654 1.19254 1.28254 1.20954
1.11254 1.04254 0.992537 1.17254
0.902537 0.882537 0.977537 1.10254
1.17254 1.23954 0.952537 0.832537
0.957537 1.00254 0.950537 1.05554
0.922537 0.972537 0.810537 0.945537
1.20254 1.02454 1.08754 1.13654
1.24554 1.12454 0.892537 0.972537
1.08254 1.17354 1.24254 1.14754
1.13354 1.15254 1.09654 0.927537
0.912537 1.00254 1.06254 1.02254
1.26254 0.882537 0.955537 0.954537
0.992537 0.972537 1.12554 1.17154
1.08254 1.11254 1.13754 1.29354
1.28254 0.891537 0.924537 0.912537
0.931537 0.968537 1.23254 1.11254
1.13254 0.946537 1.12954 0.972537
0.767537 0.852537 0.802537 0.804537


Repeat steps 5, 6 and 10 for the column of M87 globular cluster data.
Compare your results from the Milky Way globular cluster data with your results from the M87 globular cluster data. Are the globular clusters in our Milky Way similar in color to those in M87? Are the histograms similar? Are the mean, median, and mode similar in both galaxies?
Why might the globular clusters in our galaxy be different from those in M87? Why might they be similar? To answer these questions, try to think about what might be different in different galaxies. Don't worry about finding a "right" answer. Just try to think of some possibilities. The websites in the Bibliography might help with this.

Variations


Put the data from both galaxies together, repeat the statistics calculations, and make a histogram for the combined data. What is different about the combined data? Does the histogram look similar to the histograms for the individual galaxies? Is the sample still bimodal?
Use the globular cluster catalog to explore more properties of Milky Way globular clusters. Make new tables and repeat the statistics calculations for a few globular cluster properties listed in the catalog (for example, distance from galactic center, distance from sun, or central surface brightness). Think about what we can learn from each of your chosen globular cluster properties.
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