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

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.

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"?

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?

Density-Wave Theory of Galactic Spiral Structure

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

1: What Will We Learn?

• How telescopes work;
• How to point the telescope using astronomical coordinates;
• How the magnification can be changed using different eyepieces;
• How the charged-coupled device (CCD) works;
• What stars look like through a telescope;
• What galaxies look like through a telescope;
• The capabilities of the eye versus the digital camera;
• What galaxies are;
• Something about spiral patterns (waves) in galaxies.

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 45^o) with a 10x magnification of the telescope you will have a field of vision of 4.5^o. If you change the magnification to 100x the field of vision would decrease to .45^o.
   

   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 360^o (A). Let’s say that there were two objects that are on opposite sides of the horizon, they would be 180^o apart (B). If one object is now directly overhead and one is on the horizon, they would be 90^o 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

   EVENT		TIME
   Sunset		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

* 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.

1: Our Challenge

Conversion from Apparent Wavelength to Actual Wavelength

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)	is	L
   distance to the galaxy	is	D
   wavelength apparent	is	1
   focal length of telescope	is	d

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,

   D	:	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.
   l	:	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.
   d	:	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

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