Cepheid Distance Scale Lab


Most of the material for this lab can be found on a web page created by Northwestern University: Determining the Extragalactic Distance Scale, http://www.astro.northwestern.edu/labs/m100/m100.html
These instructions are available on the web at: http://www.astro.psu.eduhttp://homepages.umflint.edu/~mistark/outreach/cepheid/


Page Directory and Lab Summary:

  1. Introduction to Cepheid Hunting
  2. Cepheid Data Sheet
  3. Distance Determination
  4. Distances to Other Galaxies
  5. Summary

I. Introduction to Cepheid Hunting:

  1. You may want to briefly go through these pages for general background information on this lab (this will display in a second web browser window):
  2. Go through these pages for instructions on how to identify Cepheids for this lab (this will display in a second web browser window):
  3. A Demonstration of the Cepheid Hunt:
  4. On to the hunt!!!




II. Cepheid Data Sheet:


Cepheid Name
Grid Number
P
(Period)
mV
(Apparent Magnitude)
MV
(Absolute Magnitude)
       mV-MV      
(Distance Modulus)
           
           
           
           
           




III. Distance Determination:

Use the graph titled Period-Luminosity Relation to find the Absolute Magnitude (basicly the luminosity) for each Cepheid you found and enter it on your Cepheid Data Sheet, or you could use this equation to calculate it: . Then compute the value of mV-MV - this number is called the "Distance Modulus" (Note: MV will be a negative number! so when you calculate mV-MV, you will be subtracting a negative number, which is the same as just adding it as a positive number: i.e. 10-(-4)=10+4=14 -- ask me if you are confused!). Once you have calculated mV-MV find the average value for the five Cepheids (first find the sum of the five measurements, then divide the sum by 5 to get the average).






IV. Distances to Other Galaxies

As galaxies get further away, precise measurements of their distance become impossible (they are just too far away to make out individual stars with our current level of technology so finding Cepheids is impossible). So alternative methods are needed to ESTIMATE the distances to galaxies that are too far away to look for Cepheids in. The simplest method assumes that all galaxies of the same type are the same size (i.e. all spiral galaxies are the same size, or all elliptical galaxies are the same size). In this case, the size a galaxy appears to us (its apparent diameter) would decrease with increasing distance (you experience this all the time on earth - things that are further away look smaller than things that are nearby).

  1. Test this hypothesis:

    1. READ THROUGH ALL OF THESE DIRECTIONS (#a-g) BEFORE STARTING THIS PART OF THE EXERCISE!!!
    2. Roll up a piece of paper to about the diameter of a paper towel roll.
    3. Use this roll of paper like a telescope and look at your computer monitor through it from about 2 feet away
    4. Carefully sketch as much of the image on your computer monitor as you can see through your "telescope" - be careful to draw it to the correct scale!!! (Hint: concentrate on the scale and appearence of general sizes and shapes in the picture, rather than on getting all of the little details of the picture.)
    5. Next move back away from the computer 4-5 feet
    6. Again, carefully to scale, draw as much of the image on the monitor as you can see this time
    7. When you are ready to begin your sketches, click here to display an image on the screen - keep it up for BOTH of your sketches. The image will display in this web browser window, so when you are done with your two sketches click on the "back" button on your browser to return to this page.

    Near drawing:                                                               Far Drawing:












  2. In a sentence or two compare the apparent sizes of the images in your two drawings. How did the size of some part of the image change as you moved away from it? Write a statement describing the relationship between the apparent size of an object and your distance from the object.








    3. This same phenomena can be seen in images taken by HST.

    Here are the dimensions of WFPC2 measured in arcseconds observed on the sky:


  3. Now based on the following image of M100 and the dimensions of WFPC2, estimate the apparent diameter of M100 in arcseconds:
    (Note: the entire diameter of M100 does not fit in a single WFPC2 image)


    The apparent diameter of M100 is: ________________________ in units of: __________




    4. Now we are going to estimate the distance to another group of galaxies called the Coma Cluster - all of the galaxies in the following image are members of the Coma Cluster.

  4. First, estimate the apparent diameter (in arcseconds - don't forget to include the units with your number!) of the "large", white-colored, spiral galaxy in the upper right corner of this image from WFPC2:


    The apparent diameter of the Coma Spiral is: ________________________

  5. Next, using your estimates of the apparent diameter of the Coma Spiral Galaxy, and your estimate of the distance and apparent diameter of M100, estimate the distance to the Coma Cluster using proportions.

    Be careful! This is an inverse proportion, smaller diameter corresponds to a larger distance! So watch out!

    (DiameterM100)/(DiameterComa) = (DistanceComa)/(DistanceM100)
          (Remember: " / " means "divide")


    The distance to the Coma Cluster is: ________________________





V. Summary

Write at least one well structured paragraph on a separate sheet of paper summarizing the major points covered in this lab. Be sure to at least mention what a Cepheid is, how you found them, and how you used them to find the distance to M100, then describe one other method used to estimated the distances to galaxies that we can't see Cepheids in and the basic ideas and assumptions behind this method.