University of Michigan - Department of Astronomy

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The Structure of the Milky Way Disk

Nothing has shown more fully the prodigious ignorance of human ideas and their littleness, than the discovery of Herschell, that what used to be called the Milky Way is a portion of perhaps an infinite multitude of worlds!

-- Horace Walpole

Overview

Introduction

The Milky Way, like all spiral galaxies, has three basic parts: a central, dense bulge; a very thin roughly spherical halo; and the disk. The bulge is the densest region, though is difficult to view due to the dust in the center of the galaxy. Radio and infrared telescopes were required to fully map its size and shape. In contrast, the halo is difficult to view because it has so little in it. Its structure was recognized in the early twentieth century by Harlo Shapley, who mapped it out using globular clusters. The galactic disk has been recognized since the mid-eighteenth century, when Sir William Herschell (sometimes spelled Hershell) recognized that the band of the Milky Way was not in fact a streak of gas, steam, or anything like that but was in fact the disk of stars of the galaxy we live in. Unfortunately, he didn't know about the interstellar dust, so for over a century and a half, the galaxy was believed to be a slightly flattened disk of about 3 kpc across with the Sun near the center. 20th century astronomers have given us a clearer view of what the galaxy is truly like, from its size and structure to our location nearly 2/3 the way to the edge!

The disk of spiral galaxies is the most obvious (and usually most beautiful) part of the galaxy. The brilliant O and B stars tend to be confined to the spiral arms making it look like the disk is very lumpy. However most of the stars gas and dust follow an exponential law:

where i specifies the type of object you're looking at, R is the distance out from the center, ρi is the density of objects of type i at distance R, ρi,0 is the density of objects of type i in the central region, and H is some scale length. For all stars except the most massive O and B, H is equal to about 3.5 kpc. O and B stars and the gas and dust have different scale lengths that keep them more closely confined within the disk. Other galaxies may have different scale lengths.

In this lab you will create your own galactic disk and look at the distribution of most stars. Each group will have a different scale length so you can see the effect of the different scale lengths on the distribution of stars. You will need a group of 3 - 4 people and a clear table to do this activity.


Part 1: Setting Up the Model

  1. Get a 4-foot by 3-foot piece of paper from your GSI (you may have to cut it yourself). Tape the corners of the paper to the table.
  2. Find and mark the center of the paper. This is to be the center of your galactic disk.
  3. Determine the shortest distance from the center to the edged of the paper or table. Record that distance here: ____________
  4. Your galaxy should have a radius of 18 - 20 kpc. Choose a scale that allows you to take up as much of the paper as possible but is still reasonable convenient for calculations (e.g. if the shortest distance from the center to edge in step 3 was 19 inches, a scale of 1 inch = 1 kpc and a radius of 19 kpc would be very convenient). Record your scale and radius here:

Scale: _____________________________ Radius: ___________________

  1. Draw a circle representing the edge of your galaxy. Label it with the radius in kpc.
  2. Draw 5 more concentric circles inside the first one with roughly equal spacing. Label their radii in kpc.

  3. Get a scale length from your GSI. Record it here: ____________
  4. Enter the outer radius of your central region in table 1.
  5. Calculate the area of the central circle in kpc2. Show your work here and record your answer in table 1.






  6. Count out 100 - 200 kernels of corn for the central circle. Enter this number in table 1.
  7. Determine the central density. Since the disk is equivalant to a plane, the central density will be the surface density, or number of kernels per unit area. Show your work here and record your answer in table 1 (the first row should be complete when you finish this step.)






  8. Write the full exponential law for your model including the scale length and central density here:






  9. Check it with your GSI, then write the equation in the corner of your model as well. Make sure every member of your group understands how you arrived at the equation, including all the numbers in it.

Part 2: Modelling the Galaxy

You are now ready to actually model the galaxy.

  1. Begin by placing the 100 - 200 kernels of corn you counted out in Part 1 in the central circle.
  2. You now need to determine the number of kernels that go in each region. First, you'll need to know the average density for each annulus (the "rings" you drew) determined by your density equation. With the density and the area of he annulus, you can calculate the total number of kernels to spread in each annulus. Come up with a procedure for doing these calculations, write it below, then check it with your GSI.













  3. Once you have the procedure for step 2, fill in the rest of Table 1.
Table 1: Horizontal Plane
outer radius
(kpc)
surface density (kernals/kpc2)
area of annulus
(kpc2)
# of kernels
 
 
 
 
       
       
       
       
       
  1. Count out the correct number of kernels for each annulus and spread them in your model.

Part 3: Vertical Component

  1. Mark a convenient and appropriate place for the Sun. Record the distance from the center to the Sun here:


  2. Get a "tree" and a couple squares of poster board from your GSI and place it in the location of the Sun (move any kernels that are in the way aside for now)
  3. Enter the surface density of this region in table 2.
  4. Measure the base of the tree and calculate its area:



  5. The vertical scale length (or scale height) will be 0.1 of your original scale length. Write your scale height here:

  6. Calculate the number of kernels of corn that should be on the base. Enter this number in table 2 and move that many kernels onto the base from the kernels in that annulus.
  7. Write the exponential law for the vertical direction below. Check it with your GSI and be prepared to explain how you arrived at all the numbers in it!






  8. Calculate the area of the pieces of poster board:



  9. Slide one of the pieces of poster board onto the tree until it is 0.5 - 1 inch above the base. Convert the height in inches to kpc and enter the height into table 2.
  10. Calculate how many kernels you need to place on that level. Enter that value in table 2, then place the correct number of kernels on the piece of poster board.
  11. Slide another piece of poster board onto the tree and figure out how many kernels you need.
  12. Continue in the vertical direction until you have a layer with only 1 kernel. If you run out of tree trunk, see your GSI.
  13. How many levels are needed for you to get to a layer with only 1 kernel?




Table 2: Vertical Plane
Height (kpc)
surface density
# of Kernels
 0    
     
     
     
     
     
     

Part 4: Looking at the models

  1. Observe all the models. How are they different? How are they similar?









  2. Describe how the models change as the scale length increases.









  3. The surface density for all the models decreased exponentially as you moved away from the center. However, in some of the models, the number of kernels actually increased at first before decreasing. Why did this happen?









  4. The dust in the galaxy is more closely confined to the center of the disk. Based on the observations of the models, is this a smaller or larger scale length? Explain your answer.









  5. How will the dust affect observations of the galaxy?










  6. Why are the O and B type stars not only concentraited near the center of the disk, but also to the spiral arms?











Part 5: Observing the Milky Way

Your GSI will give you a set of images. Sort them in order of increasing distance from the center of the galaxy. Describe the features you used to determine the distance and how they relate to the observations of the models.




















Last modified: 6/27/05