Spiral Galaxies:
An Analysis Using Digital Imaging
Vivian Hoette and Rich Kron, instructors
Ashley McCann, TA
Judith Lachance-Whitcomb, author

Where do you live? There are many ways that you might respond to that question. You may say any of the following:

At 4310 Ellis
In Chicago
In Cook County
In Illinois
In the United States
In North America
On the planet Earth

All of those answers would be perfectly acceptable. How often, though, do you think of responding to the question by telling people you live in the Milky Way Galaxy? "Well, duhh…", you think. Why would you give your location in such a general manner? After all, if someone wants to know where you live they want you to be quite specific about location. But if you were responding on a universal level to a fictional intergalactic traveler, the galaxy answer would be quite specific. Since we are only one of hundreds of billions of galaxies in our universe, your information would certainly facilitate the traveler’s challenge to find us. Actually though, you’re right. It wouldn’t help that voyager any more than if you told Uncle Radie from Haiti that you live on the North American continent and asked him to come visit. Without additional information, he isn’t going to be locating you in the near future.

This image is of the NGC 2997 galaxy. It is used here to show our position in relation to the nucleus of the Milky Way Galaxy. We believe our Galaxy to be a spiral one, like this one.
Our Galaxy is more than one billion billion kilometers in diameter. That is about 120,000 light years (one light year is the distance that light travels in one year). Our intergalactic friend must locate, out of some 100 billion stars, a single star - our Sun - around which the planets, asteroids, satellites, and comets that make up our solar system revolve. You may suggest to the traveler that her search shouldn’t begin near the center (nucleus) of our Galaxy. Actually, we are about 30,000 light years away from the center. Even with that information, she, like Uncle Radie, won’t be coming for a visit very soon.

what is a galaxy?

If you happen to travel away from the atmospherically and light-challenged areas (due to pollution and lights) of cities and suburbs, you might look up into the night sky and see a wondrous faint band of light arcing high above the horizon. It is the glow from some of the billions of the stars in our universal home, the Milky Way Galaxy. If we travel a great distance into space beyond our Galaxy, we would look back on it and see a shape not unlike what alien spaceships have been depicted to look like. A galactic disc surrounds a bulge. A hundred billion stars form this specter that is approximately 120,000 light years wide but only about 1,000 to 3,000 light years thick. At the center, the nucleus or galactic bulge is made of old stars and extends out a few thousand light years from the galactic center.

A galaxy is a large system of one million to one trillion stars along with dust and gases. However, almost 90% of the material in a galaxy is some totally unknown form called dark matter because it doesn’t shine like stars. These groups are held together by a mutual attraction. This attraction is one of gravitational pull. In a galaxy, each star has its own orbit around the galaxy. Think of our solar system, each planet has an orbital path around the Sun. That orbit is affected by the gravitational pull from the Sun the way that the center of the galaxy attracts the stars and other matter that orbit around it.

How Are Galaxies Classified?

If we could orient ourselves above the Galaxy we would look down upon an enormous pinwheel similar to the one on the left. There seem to be arms swirling about the "dancer" nucleus.

Based upon the work done by many astronomers in the early part of the twentieth century, we now classify galaxies into three basic types, spiral, elliptical, and irregular. The spiral galaxy is the type that has been described above. Two or more arms wind away from the center. We believe that our Milky Way Galaxy is this type.

Another type of galaxy is one that has been called elliptical. These galaxies don’t have spiral arms nor the "spaceship" bulge and disk structure They seem to be groups of stars that form a round or elliptical shape when viewed through a telescope.

Finally, there are galaxies that are called irregular. These are all of the other kinds of galaxies that have been identified. They may be unusually shaped galaxies, galaxies that are colliding, or galaxies that are going through violent energy outbursts.

What Are the Spiral "Arms"?

The mystery of the "arms" of a spiral galaxy has been a question that astronomers have been concerned with for a long time. Assuming that the arms were always made up of the same matter (stars and other material) rotating around the galaxy’s center, they would eventually wind up. To try and understand the astronomer’s dilemma, let’s imagine a poorly planned, rather ridiculous track meet . We will have a bird’s eye view of the track from a helicopter above the track. Now, in this fictional meet, all of the runners run at the same speed. As we observe the runners, we will visualize the alignment of each runner along the track at three points during the race. (Our alignment line will look like this .)

At the START, all of the runners are aligned. At alignment point A, the runner on the inside track had gone half way around, while the runner on the outside track has only gone around about 1/6 of the track. It appears that the alignment line is arcing. At alignment point B, the inside track runner has almost reached the starting point once again, while the outside track runner is only about half way around the track. (Can you see why runners in actual races start at staggered points?)

Let’s say that the runners continue running, even when they get back to the starting point. They are all still running, but the runner on the inside is completing the revolutions around the center of the track much sooner than the other runners. From our view in the helicopter, we would see the field continue to rotate, but the arcing alignment arms would wind up more and more.

Stars that are farther from a galaxy’s center take a longer time to go around the center as did the outside track runner. Eventually, after a few galactic rotations* we would no longer see the spiral structure of the galaxy because the arms would have woulund up. That brings us to the question that puzzled astronomers: Why are there so many galaxies that are not wound up? Just what are the spiral arms?

Galaxies take 100 - 200 million years to rotate (depending on galaxy, and the particular part of the galaxy). That is a galactic year. If galaxies are 12 billion years old, how many times have they rotated?

Density-Wave Theory of Galactic Spiral Structure

The explanation came through the Density-Wave Theory of Galactic Spiral Structure. This theory, proposed by the C.C. Lin and Frank Shu, states density waves in the disk of a galaxy cause material to "pile up" temporarily. Remember the discussion, in the introduction of this booklet, about the motion of waves? Vibrations cause particles to "bang" into one another. As they bang, energy is passed from one particle to another.

Have you ever been in line when you were in elementary school and you stopped suddenly because there was a huge glob of bubble gum on the floor? What happened? As you slowed down to step over the gum, classmates behind bumped into you, and the kids in back of them bumped into them, etc. At the point of all this bumping, your line was squished together. When you started walking again, each person going over the gum slowed down to step over it and the process would repeat. Different classmates were "clumping" but until your whole line passed or the gum was picked up, there was always a "squish" pattern. Once everyone was past the gum, your teacher turned around and gave you all "that look" and your line straightened out again. Everyone was still in his or her correct place. You and your classmates formed a density wave.

Astonomers understand the spiral patterns in galaxies to be fixed — not winding up — while the stars and other materials move through a point of clumping. By analyzing data gathered from observations of spiral galaxies, you will begin to understand how the density-wave theory has resolved the puzzle of galactic arms. You will have a chance to use the 10 inch telescope in the Yerkes South Building to obtain digital images of some spiral galaxies. All types exist in nature, and the "10-inch sample" will illustrate some of them (see pitch angle diagram) The telescope, camera, and computer that you will be using are small compared to equipment used by professional astronomers. However, the process that you will be involved in will closely reproduce the work of actual research programs being carried out by astronomers.
"pitch angle" of spiral patterns

SPIRAL GALAXIES: Gathering Data: Observations and Images

Night Lab

1: What Will We Learn?

During this lab you will learn:

2: Interesting Measurement and Number Info...

  1. The CCD camera has a field-of-view that is 9 x 6 arc minutes. The field of vision means the "piece" of area that you or your instrument can see. As magnification increases, the field of view decreases. So, if you are looking through a telescope at approximately 1/4 of the sky from horizon to horizon (apparent field of 45o) with a 10x magnification of the telescope you will have a field of vision of 4.5o. If you change the magnification to 100x the field of vision would decrease to .45o.

    When we are standing on solid ground we can easily measure distances in standard units like meters, kilometers, feet and miles, etc. Objects in the sky can’t be measured the same way. Astronomers use degrees to give the relative placement of objects. Let’s refer to diagrams to help us visualize this. Remember: you’re considering the whole distance around the planet to be 360o (A). Let’s say that there were two objects that are on opposite sides of the horizon, they would be 180o apart (B). If one object is now directly overhead and one is on the horizon, they would be 90o apart. Since many astronomical measurements are smaller than a degree, even smaller units have to be used. If we divide a degree into sixty equal parts, we get an arc minute. If we divide that arc minute into 60 equal parts we get an arc second.

  2. You know, of course, that we observe at night because then we can see astronomical objects that are not apparent in the daylight. The moon and stars don’t "go away" during the day we just can’t see them because of the bright light coming from the sun. As you do your observations, information about the apparent position of the sun on your observation days will be important. Here is an example of some information that may be important:

    AUGUST 8, 1999






    8:06 P.M.

    Sun 12o below horizon


    9:15 P.M.

    Sun 18o below horizon


    10:00 P.M.

    Sidereal Time 18:14


    10:00 P.M.

    In what way might these times be different for August 9? August 10?

3: Suggested Galaxies

The universe is a very big space. Since the time we can spend on this lab is limited, here are some suggestions for locating some galaxies.


Right Ascension (RA)*

Declination (dec)**

Distance (D)

(millions of light years)

NGC 5194 (M 51)

13 29 . 9

47 12

11 x 3.26 = 35.86

NGC 5457 (M 101)

14 03 . 2

54 21

7.6 x 3.26 = 24.776

NGC 5921

15 21 . 9

05 04

30 x 3.26 = 10.6276

NGC 6384

17 32 . 4

07 04

36 x 3.26 = 117.36

NGC 6946

20 34 . 9

60 09

6.7 x 3.26 = 21.842

* Right ascension is a coordinate for measuring the east-west location of astronomical objects. This can be compared to a line of longitude on the earth.

** Declination is the angular distance north or south of the celestial equator. It can be compared to a line of latitude on the earth.

SPIRAL GALAXIES: Gathering Data: Observations and Images

Day Lab

1: Our Challenge

We have a two-dimensional image of a galaxy. Each pixel represents the relative amount of light (that is intensity) from stars and glowing gas coming from that spot in the galaxy. In our investigation, we will plot the intensity versus position in the galaxy of many pixels along a straight line, or slice. Our slice will go through at least two spiral arms. If you recall from the background information and other labs, the wavelength is the distance from one wave crest to the next. In our investigation, the crest to crest measurement is from spiral arm to spiral arm. One question that you will think about during this lab is, "With the information we now have, how would we determine the amplitude of the wave?"

Conversion from Apparent Wavelength to Actual Wavelength

When we complete the challenge above, we will have a measurement of the apparent wavelength (crest to crest separation) based on pixel units of measurement. We must now express the wavelength on a physical basis that will give us the actual wavelength. That means we will be converting our pixel data into thousands of light-years. Here’s how:
  1. Think of the proportional relationship of our image of the galaxy to the real galaxy: (Hint: Think of similar triangles)
  2. Define the variables with symbols:

    wavelength (actual)



    distance to the galaxy



    wavelength apparent



    focal length of telescope



  3. Set up the proportional relationship of these quantities.
    Remember we can do this as long as L and D are measured in the same units and 1 and d are measured in the same units.

  4. Our goal here is to find the actual wavelength (L), it is our unknown. In order to do that with the proportion we set up above, we have to know the values for D, 1, and -. So,



    Depends on the galaxy. Use the table you were given with the night lab, SPIRAL GALAXIES Gathering Data: Observations and Images, # 3. The units are given in millions of light years.



    Number of pixels from one spiral arm to another times the size of each pixel. Each pixel in high resolution mode is 0.009 mm; in medium resolution mode is 0.018 mm; in low resolution mode is 0.027 mm.



    100 inches or 2540 mm

  5. Let’s apply this to an example image. Suppose you have an image obatained in medium-resolution mode, and you count 80 pixels from one wave crest to the next.

    The value for l is: 80 x 0.18 mm which equals 1.44mm.

    Suppose the galaxy is at a distance of 10 x 3.26 which equals 32,600 thousand light years.

    With these numbers, we can now set up our proportion:

    L = D x (1/d)
    L = 32,600 thousand light years x (1.44 mm / 2540 mm)
    L = 18.5 thousand light years

    Let’s check to see if this is sensible. Recall we said that the Milky Way is 120,000 light year in diameter. So, about 120/18.5 equals 7 wavelengths across. Look at an image of a spiral galaxy, does this check out?

3: Using Images to Determine Actual wavelengths

Now we will take data collected during our night lab and calculate the actual wavelengths of the spiral galaxies’ density waves.

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