This exercise is made possible by the data available through the McMaster Cepheid Data Archive. Many variations of this exercise can be arranged, including the use of radial velocity and other measurements, and observations of other galaxies.
The following data tabulate visual apparent magnitudes (V), and their uncertainties, as a function of time for 31 Cepheid variables in M81. The time is listed for each measurement in Julian Days (JD). You can simply subtract the first day listed from the others in the list to get the relative number of days.
Use this worksheet to keep a record of your results. Choose about six stars, with differing periods and average V, on which to base your result. It is best to first plot V versus day, using EXCEL or whatever is handy, for these stars. If you include the uncertainties as error bars in your plot, that might help. Tabulate your estimates for the average V and period P for your chosen stars.
Here are some hints. Consider the groups of stars C1-C5, C6-C10, C11-C16, and C17-C24. Each group represents Cepheids with decreasing periods. You might want to pick one of these groups, especially if you can easily see the average V increase as you go through the list of stars. Also, for stars C1-C24, just stick with the first 50 days of data. The periods range from a maximum of around 50 days to a minimum of around 10 days.
For each star, determine the absolute visual magnitude M from the period using the calibration figure from Karttunen. Then, tabulate the "distance modulus" m-M, where m=V in this case. Can you tell that the vaules of m-M are more consistent with each other than are the values of V?
Calculate the average of the values of m-M. Convert this to a distance d using Zeilik Eq.11-6. This is your calculated distance to M81.
Don't forget to answer the questions on the worksheet.
