Graphing Cepheid Magnitudes: Blog 15, Worksheet 5.2

As we previously learned, Cepheid variables are a special class of stars that radially pulsate in a predictable way. In 1908, Henrietta Swan Leavitt discovered that there is a distinct relationship between a Cepheid’s luminosity and pulsation period by examining many stars in the Magellanic Clouds. Henrietta was a member of “Harvard’s computers,” a group of women hired by Edward Pickering to analyze stellar spectra and light curves. In this worksheet, we will use Henrietta’s original data set to find our own Period-Luminosity relation for Cepheid variables. The data files for this activity will be located on Canvas under the name “Cepheid variables.csv.”

Source

1. The data file, “Cepheid variables.csv,” contains data for 25 Cepheid variables located in the Small Magellanic Cloud (SMC). Each line contains a specific Cepheids: (1) ID number, (2) Maximum apparent magnitude, (3) Minimum apparent magnitude and (4) Period. Calculate the mean apparent magnitude for each Cepheid.

Done! It is pretty easy to do in excel.

2. The distance to the SMC is about 60 kpc, where kpc = 1000 pc. Convert your mean apparent magnitudes into mean absolute magnitudes. Plot the Cepheid mean absolute magnitudes as a function of period. This plot should look exponential.

3. It is often handy to plot exponential (or power-law) functions with one or more logarithmic axes, which “straightens out” the data. Magnitudes are already exponential, so we don’t need to adjust that axis. Plot the Cepheid mean absolute magnitudes as a function of log(Period). Verify that the plot now looks linear.

4. Now that the data look linear, we can estimate the parameters of a linear relation, \(M_V (P) = A log_{10}(Period) + B \). A and B are “free parameters” that allow the function to match the data.

This would make A = -2.033 and B  = -.2782 for a final expression of approximately \[M_V (P) = -2.0 log_{10}(Period) - 2.8 \]