Abstract
Globular clusters, compact groups of about a million stars that move around together in galaxies, are among the oldest objects found in the universe. Since they are found in most galaxies and since they've been around for so long, globular clusters have a lot to tell us about what the universe looks like now and how it got that way. Is our Milky Way Galaxy just like all the other galaxies out there? What are galaxies made of? What can we learn about the universe from looking at galaxies? This project uses statistical analysis of real data to investigate these questions and explore the properties of globular clusters.Summary
Authors: Erica Davis, UCSC and
Jean Brodie, UCO Lick
Edited by Andrew Olson, Ph.D., Science Buddies
Objective
The color of a globular cluster gives clues about the cluster's composition (what kinds of elements and stars are in the cluster) and the cluster's age. Is our galaxy just like any other? Are the globular clusters in our galaxy just one color, and, if not, what's the most common cluster color? Based on the colors of the globular clusters, what might we guess about the ages and compositions of the two galaxies? The goal of this project is to use real globular cluster data and simple statistical analysis to try and answer these questions.
Introduction
Globular clusters are nearly spherical groups of about 10,000 to 1 million stars. A typical galaxy may contain up to a few hundred globular clusters; our galaxy, the Milky Way, has somewhere between 125 and 200 globular clusters orbiting the galactic center.
Most globular clusters are found in the large spherical halo of a galaxy. The average age of globular clusters is somewhere between 10 and 14 billion years, making the clusters some of the oldest objects in the universe.
Since most galaxies contain globular clusters and since globular clusters are so old, the properties of globular clusters can be used to learn about not only the universe today, but also the universe in the past.
Using modern telescopes and computers, astronomers have studied numerous properties of globular clusters. Here are just some of the quantities that we can measure for globular clusters:
- size (radius),
- mass,
- distance from galactic center,
- distance from Earth,
- brightness,
- age,
- color.
Astronomers have used these properties of globular clusters in our Milky Way and in other galaxies to help determine (among other things):
- the approximate age of the universe,
- the location of our sun in the Milky Way,
- the composition of the early universe (what it was made of),
- the ways in which galaxies change and evolve.
This project focuses on the colors of globular clusters in our Milky Way and in the galaxy M87. The color of a globular cluster gives clues about the cluster's composition (what kinds of elements and stars are in the cluster) and the cluster's age. We can compare the colors of Milky Way clusters to the colors of globular clusters in the M87. Is our galaxy just like any other? Are the globular clusters in our galaxy just one color, and, if not, what's the most common cluster color? Based on the colors of the globular clusters, what might we guess about the ages and compositions of the two galaxies? In this project you will use real globular cluster color data and simple statistical analysis to try and answer some of these questions.
The color data you will be using is referred to as V − I. V and I are different filters through which we can look at objects in the sky. Looking through a V filter is like looking through a yellow pair of glasses and looking through an I filter is like looking through infrared glasses (our eyes can't see infrared, but telescopes can). If an object is very yellow, it will be bright through the yellow glasses (the V filter) but not so bright through the infrared glasses (the I filter). If an object is very red, it will be bright in the infrared glasses (the I filter) but not bright through the yellow glasses (the V filter).
To determine the color of an object, we can subtract the brightness in the I filter from the brightness in the V filter. In other words, the color of an object is given by calculating V − I. As you go from red to blue in the spectrum of colors, you go from high to low V − I value. So red objects have higher V-I than orange objects, orange have higher V-I than yellow objects, yellow higher than green, green higher than blue, blue higher than indigo, and indigo higher than violet.
Terms and Concepts
To do this project, you should do research that enables you to understand the following terms and concepts:
- Globular clusters
- Galaxies
- The Milky Way
- Astronomical color index
- Bimodality
- Histograms
- Averages (mean, median, and mode)
Bibliography
- Wikipedia has plenty of information on globular clusters, galaxies, the Milky Way, etc.:
Wikipedia contributors, 2006. Wikipedia Main Page, Wikipedia, The Free Encylopedia. Retrieved February 24, 2006. - This site should help with any astronomical terminology that is unfamiliar:
Madore, B.F., 2002. Astronomical Glossary, from LEVEL 5: A Knowledgebase for Extragalactic Astronomy and Cosmology, Caltech and Carnegie Observatories. Retrieved February 24, 2006. - Google Images is a great place to find pictures of globular clusters, galaxies, etc.
- This webpage explains the how the brightness of stars is measured:
Russell, R and Ward, D. (2008, September 11). Magnitude - A Measure of Brightness. Retrieved April 28, 2009. - This webpage explains the wavelengths of light and their perceived colors:
NASA Science Mission Directorate, 2010. Visible Light. Retrieved March 6, 2018. - This site contains the original compilation of the Milky Way Globular Clusters data.
Harris, W.E., 2003. Catalog of Parameters for Milky Way Globular Clusters: The Database, McMaster University. Retrieved March 6, 2018. - This should help with statistics like mean, median, and mode.
AlgebraLAB. (2009). Finding the Mean, Median, and Mode. Retrieved April 28, 2009. - Here is an Excel tutorial to get you started with using a spreadsheet program:
Excel Easy. (n.d.). Excel Easy: #1 Excel tutorial on the net. Retrieved March 10, 2014.
Materials and Equipment
The only materials required for this project are a computer with Internet access and a spreadsheet program (like Microsoft Excel, WordPerfect QuattroPro, or OpenOffice.org Calc).
Experimental Procedure
- Do your background research so that you are knowledgeable about the terms and concepts.
- Download the Milky Way globular clusters data set.
- The data set is an Excel file. Save it on your computer and then open it with Microsoft Excel or any other spreadsheet program
- Note: This data set was compiled by William E. Harris. See the Bibliography for more details.
- Once you've opened the spreadsheet, find the color column labeled "V − I".
- Copy the entries from the V − I column into new 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: 0.7-0.8, 0.8-0.9, 0.9-1.0, 1.0-1.1, 1.1-1.2, 1.2-1.3, 1.3-1.4, 1.4-1.5, 1.5-1.6, 1.6-1.7, 1.7-1.8, 1.8-1.9, 1.9-2.0, 2.0-2.1, 2.1-2.2, 2.2-2.3, 2.3-2.4, 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 and statistics like mean, mode, and median see the "Finding the Mean, Median, and Mode" 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 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.
Ask an Expert
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 data set 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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