University of Michigan - Department of Astronomy

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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 data tables for stars in 4 different galaxies. They have 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. Plot the magnitudes vs the dates for each of the three stars in galaxy 1 (3 graphs).  Be sure to include these plots when you hand in your lab. 
  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. Fill out the period and magnitude for the stars in galaxy 1 in table 1 using the light curves.

    Table 1: Light Curve Results

    Galaxy

    Star

    P (days)

    mave

    1

    1

     

     

    2

     

     

    3

     

     

    2

    1

     

     

    2

     

     

    3

     

     

    3

    1

     

     

    2

     

     

    3

     

     

    4

    1

     

     

    2

     

     

    3

     

     

  7. You should have the light curves for the stars in galaxies 2 – 4.  Use those graphs to complete table 1.

Part 3:The Distance Modulus

  1. There are several copies of 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 galaxy 1 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. repeat the last three steps for the other 3 galaxies, using the appropriate graph.
  7. Calculate the distance to each of your galaxies and record the distances in the spaces below the graphs.

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