Spiral galaxy M81 is outside our Local Group of galaxies, but still near enough so that Cepheid variables can be identified. This was done using the Hubble Space Telescope (HST) by Dr. Wendy Freedman and her group at the Carnegie Institute, published in the Astrophysical Journal, 427(1994)628. You will use some of their data to get your own estimate of the distance to M81.

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. I've already stripped out some of the data, from the first and third blocks of the full data file, but these aren't necessarily the easiest stars to use.

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. The period is not always easy to see, so pick stars that look good and periodic to you! The data points are not equally spaced, so for stars with short periods, you need to look at data points taken close together in time. 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.

Answer the following on the worksheet:

1. Collect and plot the data. For each star, determine the absolute visual magnitude M from the period. You can try using Figure 10.6 from Kutner, but here is a better calibration figure. (You may also use the approximte formula MV=-2.76(logP-1)-4.16 where P is in days.) Then, tabulate the "distance modulus" m-M, where m=V in this case. Make plots of m as a function of log(P) and of m-M as a function of log(P). Does the plot of m-M look more constant as a function of period?
2. Calculate the distance to M81. Get the answer in terms of Megaparsecs (millions of parsecs, Mpc). Show your work in the space provided on the worksheet.
3. Does this answer make sense? How far away do you expect M81 might be, in relation to "nearby" galaxies? Here are a layout and map of the Local Group of galaxies.