University of Michigan - Department of Astronomy


Cepheids and the Extra-Galactic Distance Scale
Magnitude version worksheets

Part 1: Identifying Variable Stars

Get a pair of images from your GSI. These images are a close up of a small region of a galaxy with six simulated variable stars added.  The image pair corresponds to observations of the galaxy at different times.

  1. After taking a quick look at the images, figure out what to look for to find the variable stars.  Describe what you will look for and you will identify the variables:

  2. There are no fewer than six Cepheid variables in the field.  If you readily find four, look for five. Finding the sixth – quite tricky – earns you the title of ‘Master Variable Star Finder’! This search should give you a taste of what it is like to look for variables in actual data, although you’ve been given “nice” data (fake variables with nice periods were added to an actual image).  Imagine there were 3 variable stars in the field with periods of 5, 10 and 20 days, and the two images were taken 10 days apart.  How many variables would you be able to identify?  Why?

  3. Once you have identified at least four variables, show your GSI where you think they are.  He/she will record how many stars you correctly identified here: __________

Part 2: Light Curves

  1. Your GSI will give you a data table and graph for 3 cepheids in 1 galaxy. The data includes the Date of the observation and the apparent magnitude of 12 Cepheid variables. The date is a simple count of the days for the year the data were taken.
  2. Compare the data to the graph so you see how the graph was made
  3. Why are there gaps in the dates in the plots?

  4. Is the light curve of a Cepheid variable a simple sine curve? 

  5. You will need to determine the period and mean magnitude for the stars.  Explain how to do that from the light curve (a sketch of a Cepheid light curve may be helpful)

  6. Record the number of your galaxy in table 1. Fill out the period and magnitude for the stars in your galaxy using the light curves.

    Table 1: Light Curve Results

    Galaxy number


    P (days)












Part 3:The Distance Modulus

  1. There is a graph with the P-L relation graphed on it.  Why is the logarithm of the period graphed rather than just the period? 

  2. Was the magnitude used for the data points that are already on the graphs the absolute or aparent magnitude?

  3. Plot the mean apparent magnitude vs the logarithm of their periods in days for each of the stars in your galaxy on the first graph.  Draw a best fit line through your data points.
  4. Mark four positions on the two lines and determine the vertical difference between them.  Record the difference on the graph.
  5. Calculate the average difference.  This is the distance modulus for that galaxy.  Record this number in the space at the bottom of the graph.
  6. Calculate the distance to your galaxy and record the distances in the spaces below the graphs.
  7. Record your group number, the distance modulus and distance in the table on the board.
  8. Fill out the table below with the distance modulus and distance to all 4 galaxies. Convert the distances to Mpc for the final column.
    galaxy m-M d (pc) d (Mpc)

Concluding questions

  1. Miss Leavitt had to use photographic plates. How do you think astronomers would find variable stars now?

  2. You were lucky in having to only find the Cepheids and not having to actually measure their brightnesses on numerous images. How do you think astronomers measure the brightness (aka flux or apparent magnitude) of an object?

  3. In this lab, you had to determine the luminosity or absolute magnitude.  Based on what you did and your answer to the previous question, explain why the brightness is generally more accurate than the luminosity/absolute magnitude.

  4. Let’s say we can measure Cepheids out to magnitude 27.5. For reference, the faintest naked-eye stars are about magnitude 6, and each 5 magnitudes is a factor of 100 fainter. Thus, 27.5 is about 200 million times fainter than the faintest naked-eye stars. Using the PL and distance modulus relations, what is the furthest galaxy we could detect Cepheids in if we limit ourselves to a maximum period of 100 days?

  5. Put your galaxies in order from closest to farthest.  Which one(s) is/are part of the local group?  Which is/are in the Virgo cluster?  Which is/are father than the Virgo cluster?

  6. For a Hubble constant of 70 km/s/Mpc, what recessional velocities would you expect to measure for each of the galaxies used in this lab?

Last modified: 9/15/06